Patent Grant
10838208
Display systems may include a beam splitter, a quarter wave retarder and a reflective polarizer.
U.S. Pat. No. 7,242,525 (Dike) describes an optical system that projects a real image into space and includes one or more features located along the optical path that enhance the viewability of the real image. The optical system includes a converging element for converging a portion of source light so as to form the real image.
U.S. Pat. No. 6,271,969 (Mertz) describes an optical collimating assembly for imaging light from a display. The optical assembly includes first and second linear polarization filters having polarization directions that are orthogonal to one another. A folded imaging assembly that includes a first beam splitter, a first ΒΌ wave plate, and a second beam splitter is located between the polarization filters.
U.S. Pat. No. 8,780,039 (Gay et al) describes an optical system for varying the shape of a surface in which an image displayed by the display device is perceived. The optical system comprises first and second spaced-apart partial reflectors, at least one of which is switchable between a first non-flat shape and a second different shape, which may be flat or non-flat. The reflectors, together with polarization optics, provide a light path such that light from the display is at least partially transmitted by the first reflector, partially reflected by the second reflector, partially reflected by the first reflector and partially transmitted by the second reflector.
Reflective polarizers may be multilayer optical films. U.S. Pat. No. 6,916,440 (Jackson et al.) describes a process for stretching multilayer optical films in a uniaxial fashion. U.S. Pat. No. 6,788,463 (Merrill et al.) describes post-formed multilayer optical films.
In some aspects of the present description, an optical system including an image surface, a stop surface, a first optical stack disposed between the image surface and the stop surface, and a second optical stack disposed between the first optical stack and the stop surface is provided. The first optical stack is convex toward the image surface along orthogonal first and second axes, and includes a first optical lens and a partial reflector having an average optical reflectance of at least 30% in a desired plurality of wavelengths. The second optical stack is convex toward the image surface along the first and second axes, and includes a second optical lens, a multilayer reflective polarizer substantially transmitting light having a first polarization state and substantially reflecting light having an orthogonal second polarization state, and a first quarter wave retarder disposed between the reflective polarizer and the first optical stack.
In some aspects of the present description, an optical system including an image surface, a stop surface, a first optical stack disposed between the image surface and the stop surface, and a second optical stack disposed between the first optical stack and the stop surface is provided. The first optical stack includes a first optical lens, and a partial reflector having an average optical reflectance of at least 30% in a desired plurality of wavelengths. The second optical stack includes a second optical lens, a multilayer reflective polarizer including at least one layer substantially optically biaxial at at least one first location on the at least one layer away from an optical axis of the second optical stack and substantially optically uniaxial at at least one second location away from the optical axis, and a first quarter wave retarder disposed between the reflective polarizer and the first optical stack. Substantially any chief light ray that passes through the image surface and the stop surface is incident on each of the first optical stack and the second optical stack with an angle of incidence less than about 30 degrees.
In some aspects of the present description, an optical system including an image source emitting an undistorted image, an exit pupil, a partial reflector and a reflective polarizer is provided. The partial reflector has a first shape convex toward the image source along orthogonal first and second axes and has an average optical reflectance of at least 30% in a pre-determined plurality of wavelengths. The reflective polarizer has a different second shape convex toward the image source along the first and second axes, such that a distortion of the emitted undistorted image transmitted by the exit pupil is less than about 10%.
In some aspects of the present description, an optical system including an image source, an exit pupil, a first optical stack disposed between the image source and the exit pupil, and a second optical stack disposed between the first optical stack and the exit pupil is provided. The first optical stack includes a first optical lens, and a partial reflector having an average optical reflectance of at least 30% in a desired plurality of wavelengths. The second optical stack includes a second optical lens, a multilayer reflective polarizer, and a first quarter wave retarder disposed between the reflective polarizer and the first optical stack. Substantially any chief light ray having at least first and second wavelengths at least 150 nm apart in the desired plurality of wavelengths and emitted by the image source and transmitted by the exit pupil has a color separation distance at the exit pupil of less than 1.5 percent of a field of view at the exit pupil.
In some aspects of the present description, an optical system including an image source, an exit pupil, a first optical stack disposed between the image source and the exit pupil, and a second optical stack disposed between the first optical stack and the exit pupil is provided. The first optical stack includes a first optical lens, and a partial reflector having an average optical reflectance of at least 30% in a desired plurality of wavelengths. The second optical stack includes a second optical lens, a multilayer reflective polarizer, and a first quarter wave retarder disposed between the reflective polarizer and the first optical stack. Substantially any chief light ray having at least first and second wavelengths at least 150 nm apart in the desired plurality of wavelengths and emitted by the image source and transmitted by the exit pupil has a color separation distance at the exit pupil of less than 20 arc minutes.
In some aspects of the present description, an optical system including an image surface having a maximum lateral dimension A, a stop surface having a maximum lateral dimension B, and an integral optical stack disposed between the image surface and the stop surface is provided. A/B is at least 3. The integral optical stack includes a first optical lens, a partial reflector having an average optical reflectance of at least 30% in a pre-determined plurality of wavelengths, a multilayer reflective polarizer substantially transmitting light having a first polarization state and substantially reflecting light having an orthogonal second polarization state, and a first quarter wave retarder at at least one wavelength in the pre-determined plurality of wavelengths. At least one chief light ray transmitted through the stop surface and the image surface passes through the stop surface at an incident angle of at least 40 degrees. An integral optical stack may be described as an optical stack with the various components and layers in the optical stack formed together or adhered together, for example.
In some aspects of the present description, an optical system including an image surface, a substantially planar stop surface, and, disposed between the image surface and the stop surface, first, second and third optical lenses, a partial reflector having an average optical reflectance of at least 30% in a pre-determined plurality of wavelengths, a multilayer reflective polarizer substantially transmitting light having a first polarization state and substantially reflecting light having an orthogonal second polarization state, and a first quarter wave retarder at at least one wavelength in the pre-determined plurality of wavelengths is provided. The optical system includes a plurality of major surfaces disposed between the image surface and the stop surface, each major surface convex toward the image surface along orthogonal first and second axes, and at least six different major surfaces have six different convexities.
In some aspects of the present description, a thermoformed multilayer reflective polarizer substantially rotationally symmetric about an optical axis passing thorough an apex of the thermoformed multilayer reflective polarizer and convex along orthogonal first and second axes orthogonal to the optical axis is provided. The thermoformed multilayer reflective polarizer has at least one inner layer substantially optically uniaxial at at least one first location away from the apex, and at least one first location on the reflective polarizer having a radial distance, r1, from the optical axis and a displacement, s1, from a plane perpendicular to the optical axis at the apex, where s1/r1 is at least 0.2.
In some aspects of the present description, a thermoformed multilayer reflective polarizer substantially rotationally symmetric about an optical axis passing thorough an apex of the thermoformed multilayer reflective polarizer and convex along orthogonal first and second axes orthogonal to the optical axis is provided. The thermoformed multilayer reflective polarizer has at least one first location on the reflective polarizer having a radial distance, r1, from the optical axis and a displacement, s1, from a plane perpendicular to the optical axis at the apex, where s1/r1 is at least 0.2. For an area of the reflective polarizer defined by s1 and r1, a maximum variation of a transmission axis of the reflective polarizer is less than about 2 degrees.
In some aspects of the present description, a method of making an optical stack is provided. The method includes the steps of providing a thermoform tool centered on a tool axis and having an external surface rotationally asymmetric about the tool axis; heating an optical film resulting in a softened optical film; conforming the softened optical film to the external surface while stretching the softened film along at least orthogonal first and second directions away from the tool axis resulting in a conformed optical film rotationally asymmetric about an optical axis of the conformed film, where the optical axis coincident with the tool axis; cooling the conformed optical film resulting in a symmetric optical film rotationally symmetric about the optical axis; and molding an optical lens on the symmetric optical film resulting in the optical stack.
In some aspects of the present description, a method of making a desired optical film having a desired shape is provided. The method includes the steps of providing a thermoform tool having an external surface having a first shape different than the desired shape; heating an optical film resulting in a softened optical film; conforming the softened optical film to the external surface having the first shape while stretching the softened film along at least orthogonal first and second directions resulting in a conformed optical film having the first shape; and cooling the conformed optical film resulting in the desired optical film having the desired shape.
In some aspects of the present description, an optical system including an image surface, a stop surface, a first optical stack disposed between the image surface and the stop surface, and a second optical stack disposed between the first optical stack and the exit pupil is provided. The first optical stack includes a first optical lens, and a partial reflector having an average optical reflectance of at least 30% in a desired plurality of wavelengths. The second optical stack includes a second optical lens, a thermoformed multilayer reflective polarizer rotationally symmetric about an optical axis of the second optical stack and convex toward the image source along orthogonal first and second axes orthogonal to the optical axis, and a first quarter wave retarder disposed between the reflective polarizer and the first optical stack. The thermoformed multilayer reflective polarizer has at least one first location having a radial distance, r1, from an optical axis passing through an apex of the thermoformed multilayer reflective polarizer, and a displacement, s1, from a plane perpendicular to the optical axis at the apex, where s1/r1 is at least 0.1.
In some aspects of the present description, an optical stack is provided. The optical stack includes a first lens, a second lens adjacent the first lens, a quarter wave retarder disposed between the first and second lenses, a reflective polarizer disposed on the second lens opposite the first lens, and a partial reflector disposed on the first lens opposite the second lens. The reflective polarizer is curved about two orthogonal axes, and the optical stack is an integral optical stack.
In some aspects of the present description, an optical system including a partial reflector, a multilayer reflective polarizer, and a first quarter wave retarder disposed between the partial reflector and the multilayer reflective polarizer is provided. The partial reflector has an average optical reflectance of at least 30% in a desired plurality of wavelengths. The multilayer reflective polarizer substantially transmits light having a first polarization state and substantially reflects light having an orthogonal second polarization state. The multilayer reflective polarizer is convex along orthogonal first and second axes, and has at least one first location on the multilayer reflective polarizer having a radial distance r1 from an optical axis of the multilayer reflective polarizer and a displacement s1 from a plane perpendicular to the optical axis at an apex of the multilayer reflective polarizer, where s1/r1 is at least 0.1. The multilayer reflective polarizer comprises at least one layer substantially optically biaxial at at least one first location on the at least one layer away from the optical axis and substantially optically uniaxial at at least one second location away from the optical axis.
In some aspects of the present description, an optical system including a first optical stack, a second optical stack disposed adjacent to the first optical stack and convex along orthogonal first and second axes, and a first quarter wave retarder disposed between the second optical stack and the first optical stack is provided. The first optical stack includes a first optical lens and a partial reflector having an average optical reflectance of at least 30% in a desired plurality of wavelengths. The second optical stack includes a second optical lens, and a multilayer reflective polarizer substantially transmitting light having a first polarization state and substantially reflecting light having an orthogonal second polarization state. The reflective polarizer includes at least one first location on the multilayer reflective polarizer having a radial distance r1 from an optical axis of the second optical stack and a displacement s1 from a plane perpendicular to the optical axis at an apex of the multilayer reflective polarizer, where s1/r1 is at least 0.1. The multilayer reflective polarizer includes at least one layer substantially optically biaxial at at least one first location on the at least one layer away from the optical axis and substantially optically uniaxial at at least one second location away from the optical axis.
In some aspects of the present description, an optical system including a first optical stack, a second optical stack disposed adjacent to the first optical stack and convex along orthogonal first and second axes, and a first quarter wave retarder disposed between the second optical stack and the first optical stack is provided. The first optical stack includes a first optical lens and a partial reflector having an average optical reflectance of at least 30% in a desired plurality of wavelengths. The second optical stack includes a second optical lens, a reflective polarizer substantially transmitting light having a first polarization state and substantially reflecting light having an orthogonal second polarization state. The reflective polarizer has at least one first location on the multilayer reflective polarizer having a radial distance r1 from an optical axis of the second optical stack and a displacement s1 from a plane perpendicular to the optical axis at an apex of the reflective polarizer, where s1/r1 is at least 0.1. The optical system has a contrast ratio of at least 50 over a field of view of the optical system.
In some aspects of the present description, an optical system including a first optical stack, a second optical stack disposed adjacent to the first optical stack and convex along orthogonal first and second axes, and a first quarter wave retarder disposed between the second optical stack and the first optical stack is provided. The first optical stack includes a first optical lens and a partial reflector having an average optical reflectance of at least 30% in a desired plurality of wavelengths. The second optical stack includes a second optical lens and a reflective polarizer substantially transmitting light having a first polarization state and substantially reflecting light having an orthogonal second polarization state. At least one first location on the reflective polarizer has a radial distance r1 from an optical axis of the second optical stack and a displacement s1 from a plane perpendicular to the optical axis at an apex of the reflective polarizer, where s1/r1 is at least 0.1. The optical system is adapted to provide an adjustable dioptric correction.
In some aspects of the present description, a head-mounted display including first and second optical systems is provided. The first optical system includes a first image surface, a first exit pupil, a first reflective polarizer disposed between the first exit pupil and the first image surface, and a first quarter wave retarder disposed between the first reflective polarizer and the first partial reflector. The first reflective polarizer is convex about two orthogonal axes. The first partial reflector is disposed between the first reflective polarizer and the first image surface, and the first partial reflector has an average optical reflectance of at least 30% in a pre-determined plurality of wavelengths. The second optical system includes a second image surface, a second exit pupil, a second reflective polarizer disposed between the second exit pupil and the second image surface, a second partial reflector disposed between the second reflective polarizer and the second image surface, and a second quarter wave retarder disposed between the second reflective polarizer and the second partial reflector. The second reflective polarizer is convex about two orthogonal axes. The second partial reflector has an average optical reflectance of at least 30% in the pre-determined plurality of wavelengths.
In some aspects of the present description, a camera including an aperture and an image recording device is provided. The camera includes a reflective polarizer disposed between the aperture and the image recording device. The reflective polarizer is curved about two orthogonal axes. A partial reflector having a having an average optical reflectance of at least 30% in a pre-determined plurality of wavelengths is disposed between the reflective polarizer and the image recording device. A quarter wave retarder disposed between the reflective polarizer and the partial reflector.
In some aspects of the present description, a beam expander is provided. The beam expander includes a partial reflector having a having an average optical reflectance of at least 30% in a pre-determined plurality of wavelengths, a reflective polarizer disposed adjacent to and spaced apart from the partial reflector, and a quarter wave retarder disposed between the reflective polarizer and the partial reflector. The reflective polarizer curved about two orthogonal axes.
In some aspects of the present description, a projection system including a light source, an image forming device disposed to receive light from the light source and emit a converging patterned light, and a beam expander is provided. The beam expander includes a partial reflector having a having an average optical reflectance of at least 30% in a pre-determined plurality of wavelengths, a reflective polarizer disposed adjacent to and spaced apart from the partial reflector, and a quarter wave retarder disposed between the reflective polarizer and the partial reflector. The reflective polarizer curved about two orthogonal axes. The beam expander is disposed such that the converging patterned light from the image forming device is incident on the partial reflector and the beam expander transmits a diverging patterned light.
In some aspects of the present description an illuminator including a beam expander, a polarizing beam splitter, a light source and a reflective component is provided. The beam expander includes a reflective polarizer curved about two orthogonal directions. The polarizing beam splitter includes a first prism having an input face, an output face and a first hypotenuse; a second prism having a first face and a second hypotenuse with the second hypotenuse disposed adjacent the first hypotenuse; and a second reflective polarizer disposed between the first hypotenuse and the second hypotenuse. The light source is disposed adjacent the input face and defines an input active area on the input face. The reflective component is disposed adjacent the first face for receiving light emitted from the light source and emitting a converging light. The reflective component has a largest active area which defines an output active area on the output face. The beam expander is disposed to receive the converging light and transmit a diverging light. One or both of the input active area and the output active area are less than about half the largest active area of the reflective component.
In some aspects of the present description, a magnifying device including an optical system is provided. The optical system includes an exit pupil, a reflective polarizer proximate the exit pupil and curved about two orthogonal axes, a partial reflector disposed adjacent the reflective polarizer opposite the exit pupil and spaced apart from the reflective polarizer. The partial reflector has a having an average optical reflectance of at least 30% in a pre-determined plurality of wavelengths. A quarter wave retarder is disposed between the reflective polarizer and the partial reflector.
In the following description, reference is made to the accompanying drawings that forms a part hereof and in which various embodiments are shown by way of illustration. The drawings are not necessarily to scale. It is to be understood that other embodiments are contemplated and may be made without departing from the scope or spirit of the present disclosure. The following detailed description, therefore, is not to be taken in a limiting sense.
According to the present description, it has been found that optical systems including a reflective polarizer that is convex about two orthogonal axes and disposed between a stop surface (e.g., an exit pupil or an entrance pupil) and an image surface (e.g., a surface of a display panel or a surface of an image recorder) can provide a system having a high field of view, a high contrast, a low chromatic aberration, a low distortion, and/or a high efficiency in a compact configuration that is useful in various devices including head-mounted displays, such as virtual reality displays, and cameras, such as cameras included in a cell phone, for example.
The optical system may include a partial reflector disposed between the reflective polarizer and the image surface and may include at least one quarter wave retarder. For example, a first quarter wave retarder may be disposed between the reflective polarizer and the partial reflector and in some cases a second quarter wave retarder may be disposed between the partial reflector and the image surface. The optical systems may be adapted to utilize wavelengths in a desired or pre-determined plurality of wavelengths and the partial reflector may have an average optical reflectance of at least 30% in the desired or pre-determined plurality of wavelengths and may have an average optical transmittance of at least 30% in the desired or pre-determined plurality of wavelengths. The quarter wave retarder(s) may be quarter wave retarder(s) at at least one wavelength in the desired or pre-determined plurality of wavelengths. In some embodiments, the desired or pre-determined plurality of wavelengths may be a single continuous range of wavelengths (e.g., a visible range of 400 nm to 700 nm) or it may be a plurality of continuous ranges of wavelengths. The partial reflector may be a notch reflector and the desired or pre-determined plurality of wavelengths may include one or more wavelength ranges at least some of which having a full width at half maximum reflection band of no more than 100 nm or no more than 50 nm. The reflective polarizer may be a notch reflective polarizer and may have reflection bands that match or substantially match reflection the bands of the partial reflector. In some cases, the optical system may be adapted for use with one or more lasers and the plurality of desired or predetermined wavelengths may include narrow band(s) (e.g., 10 nm in width) about the laser(s) wavelength(s).
The reflective polarizer, the partial reflector and/or the quarter wave retarder(s) may also be curved about two orthogonal axes. In some embodiments, each of the reflective polarizer, the first quarter wave retarder and partial reflector are curved about two orthogonal axes, and in some embodiments each of these layers or components are convex toward the image surface. In some embodiments, a plurality of surfaces are provided between the stop surface and the image surface, and each of the reflective polarizer, the first quarter wave retarder and partial reflector are disposed on one of the surfaces. These layers or components may be each disposed on different surfaces, or two or more of the layers components may be disposed on a single surface. In some embodiments, one, two, three, or more lenses are disposed between the stop surface and the image surface and the plurality of surfaces may include the major surfaces of the one or more lenses. One or more of the lenses may be positioned between the reflective polarizer and the partial reflector, one or more of the lenses may be positioned between the stop surface and reflective polarizer, and one or more of the lenses may be position between the partial reflector and the image surface.
The reflective polarizer may be a thermoformed reflective polarizer and may be a thermoformed polymeric multilayer optical film reflective polarizer or may be a thermoformed wire grid polarizer, for example. Thermoforming refers to a forming process carried out above ambient temperature. Conventional display designs incorporating a reflective polarizer either use a flat reflective polarizer or use a reflective polarizer disposed in a cylindrically curved shape which is curved about a single axis. Curving a reflective polarizer into a cylindrical shape does not stretch the reflective polarizer and so does not substantially alter its performance as a reflective polarizer. The reflective polarizers of the present description may be curved about two orthogonal axes and may be stretched as a result of forming the reflective polarizer into the curved shape. According to the present description, it has been found that such compound curved reflective polarizers can be used in optical systems for display and camera applications, for example, while contributing to various improved optical properties (e.g., reduced color separation, reduced distortion, improved field of view, improved contrast ratio, etc.) even though the reflective polarizer is stretched into the compound curved shape. As discussed further elsewhere herein, it has been found that convex reflective polarizers made by thermoforming polymeric multilayer optical film that was uniaxially oriented prior to thermoforming are particularly advantageous when used in the optical systems of the present description. In some embodiments, the uniaxially oriented multilayer reflective polarizers is APF (Advanced Polarizing Film, available from 3M Company, St. Paul, Minn.). In some embodiments, optical systems include a thermoformed APF and any or substantially any chief ray in the optical system that is incident on the thermoformed APF has a low angle of incidence (e.g., less than about 30 degrees, less than about 25 degrees, or less than about 20 degrees).
The first optical stack 110 includes a first optical lens 112 having opposing first and second major surfaces 114 and 116 respectively. The first and/or second major surfaces 114 and 116 may have one or more layers or coatings disposed thereon. The first optical stack 110 also includes a partial reflector disposed on one of the first or second major surfaces 114 and 116, as described further elsewhere herein (see, e.g.,
The second optical stack includes a second optical lens 122 having first and second major surfaces 124 and 126. The first and/or second major surfaces 124 and 126 may have one or more layers or coatings disposed thereon. As described further elsewhere herein (see, e.g.,
In some embodiments, the second optical stack 120 includes a reflective polarizer on one of the first and second major surfaces 124 and 126. The optical system 100 includes a first quarter wave retarder disposed between the first and second lenses 112 and 122. The first quarter wave retarder may be disposed on the second surface 126 of the second optical stack 122 (in which case, it may be considered to be part of second optical stack 120 or it may be considered to be disposed between the first and second optical stacks 110 and 120), or may be included as a separate component with spacings between the first and second optical stacks 110 and 120, or may be disposed on first surface 114 of the first optical stack 110 (in which case, it may be considered to be part of first optical stack 110 or it may be considered to be disposed between the first and second optical stacks 110 and 120).
The multilayer reflective polarizer substantially transmits light having a first polarization state and substantially reflects light having an orthogonal second polarization state. The first and second polarization states may be linear polarization states. The first quarter wave retarder is disposed between the reflective polarizer and the first optical stack 110.
The optical stacks of the present description can be made by thermoforming any films included in the optical stack and then injection molding a lens onto the films using a film insert molding process, for example. As described further elsewhere herein, the reflective polarizer film may have anisotropic mechanical properties which may make the film rotationally asymmetric after cooling if it is thermoformed on a rotationally symmetric mold. It may be difficult to injection mold a rotationally asymmetric film onto a rotationally symmetric lens without causing wrinkling or other defects in the film. It has been found that using a rotationally asymmetric thermoform mold can result in a rotationally symmetric film after cooling if the film has anisotropic mechanical properties. A rotationally symmetric lens can be insert molded onto the resulting rotationally symmetric film without wrinkling or otherwise damaging the thermoformed film.
Image surface 130 may be any surface where an image is formed. In some embodiments, an image source comprises the image surface 130 and the stop surface 135 is an exit pupil. For example, image surface 130 may be an output surface of an image forming device such as a display panel. Stop surface 135 may be an exit pupil of optical system 100 and may be adapted to overlap an entrance pupil of a second optical system, which may be a viewer's eye or a camera, for example. The entrance pupil of the second optical system may be an entrance pupil of a viewer's eye, for example. The image source may emit polarized or unpolarized light. In some embodiments, image surface 130 is an aperture adapted to receive light reflected from objects external to optical system 100.
The optical system 100 may include one or more additional retarders. For example, a second quarter wave retarder may be included in first optical stack 110 and may be disposed on one of the first and second major surfaces 114 and 116 or may be disposed on the partial reflector. It may be desirable to include the second quarter wave retarder, for example, when the image surface 130 is a surface of a display panel producing polarized light. The display panel may emit linearly, circularly or elliptically polarized light. For example, the display panel may be a liquid crystal display (LCD) panel or a Liquid Crystal on Silicon (LCoS) display panel and may emit linearly polarized light. In some embodiments, a second quarter wave retarder is disposed between the partial reflector and the image surface, and in some embodiments a linear polarizer (e.g., a linear absorbing polarizer or a second reflective polarizer) is disposed between the second quarter wave retarder and the image surface 130. In some embodiments, the display panel is substantially flat. In other embodiments a curved display panel is used. For example, a curved OLED (organic light emitting diode) display may be used. In some embodiments, a transparent or semi-transparent display (e.g., transparent OLED, LCD, or electrophoretic displays) may be used. In some embodiments, an image source comprises the image surface where the image source may include a display panel and may optionally include a shutter. In some embodiments, a shutter (e.g., a liquid crystal shutter or a PDLC (polymer dispersed liquid crystal) shutter, or a photochromic shutter, or a physically removable shield that can function as a shutter) may be used with a transparent or semi-transparent display panel to selectively allow or disallow ambient light to pass through the transparent or semi-transparent display panel. A semi-transparent display panel may have a transmission in at least one state of the display panel of at least 25 percent, or at least 50 percent for at least one visible wavelength. In some embodiments, the image source may comprise a florescent material that can be irradiated with non-visible light to produce visible images.
In some embodiments, an image recorder comprises the image surface 130 and the stop surface 135 is an entrance pupil. For example, in camera applications, the aperture stop of the camera may be an entrance pupil for optical system 100 and the image surface 130 may be a surface of the camera's image sensor, which may, for example, be a charge-coupled device (CCD) sensor or a complementary metal-oxide-semiconductor (CMOS) sensor.
Optical system 100 may be centered on folded optical axis 140 which may be defined by an optical path of a central light ray transmitted through the image surface 130. The optical axis 140 is folded because the optical path of the central light ray propagates in the minus z-direction in one segment of the optical path between the first and second optical stacks 110 and 120 and propagates in the plus z-direction on another segment of the optical path between the first and second optical stacks 110 and 120.
The first and second optical stacks 110 and 120 may have a substantially same shape or may have different shapes. Similarly, the first and second optical lenses 112 and 122 may have a substantially same shape or may have different shapes. Any one or more of the reflective polarizer, the first quarter wave retarder, the partial reflector, the first and second major surfaces 114 and 116 of the first optical lens 112, and the first and second major surfaces 124 and 126 of the second optical lens 120 may have a shape described by an aspheric polynomial sag equation. The various surfaces or layers may have a same shape or may have different shapes and may be described by the same or different aspheric polynomial sag equations. An aspheric polynomial sag equation may take the form
where c, k, D, E, F, G, H, and I are constants, z is the distance from a vertex (e.g., distance s1 in
First optical stack 110 is disposed at a distance d1 from the image surface 130, second optical stack 120 is disposed at a distance d2 from the first optical stack 110 and at a distance d3 from the stop surface 135. In some embodiments, the distances d1, d2 and/or d3 are adjustable. In some embodiments, the distance between image surface 130 and stop surface 135 (d1+d2+d3) is fixed and d1 and/or d3 are adjustable. The distances d1, d2 and/or d3 may be user-adjustable by mounting one or both of the first and second optical stacks 110 and 120 on a rail providing mechanical adjustment of the positions, for example.
The ability to adjust the positions of the first and second optical stacks 110 and/or 120 relative to themselves or relative to the image and/or stop surfaces 130 and 135 allows a dioptric correction provided by the optical system 100 to be adjustable. For example, moving the second optical stack 120 while keeping the remaining components fixed allows light rays emitted by the image surface 130 and transmitted through the stop surface to be adjustable from parallel at the stop surface 135 to converging or diverging at the stop surface 135. In some embodiments, diopter values may be indicated on a mechanical adjustment device, selectable physically through the use of a hard stop, detent or similar device, or electronically adjusted such as with a stepper motor, or motor or linear actuator used in conjunction with an electronic scale. In some embodiments, the image size on the display panel comprising the image surface 130 may be changed based on the diopter adjustment. This can be done manually by the user or done automatically through the adjustment mechanism. In other embodiments, one, two, three or more optical lenses may be provided. In any embodiments in which a partial reflector is disposed on a surface of a first lens and a reflective polarizer is disposed on a surface of a different second lens, a changeable dioptric power may be provided, at least in part, by providing an adjustable position of the first and/or second lens, and/or providing an adjustable distance between the first and second lenses.
In some embodiments, one or both of the first and second optical lenses 112 and 122 may be shaped to provide a diopter value and/or a cylinder power (e.g., by molding the lenses with a toroidal surface, which may be described as a surface having differing radii of curvature in two orthogonal directions) so that the optical system 100 may provide a desired prescription correction for the user. An example of a toric lens having spherical and cylinder power in reflection and that can be utilized in the optical systems of the present description is illustrated in
Another use for moveable optical lenses is to minimize vergence-accommodation mismatch in stereoscopic viewers. In many stereoscopic head-mounted displays, sense of depth is created by moving the left eye and right eye images of certain objects closer together. The left and right eye converge in order to see the virtual image of the object clearly and this is a cue that gives a perception of depth. However when the eyes view a real object that is near they not only converge, but the lens of each eye focuses (also called accommodation) to bring the near object into focus on the retina. Because of disparity between the vergence cues present in stereoscopic viewers and the lack of accommodation in the eye to view the virtual image of near objects, many users of stereoscopic head-mounted displays can suffer from visual discomfort, eye-strain and/or nausea. By adjusting the positions of the first and second lenses, the virtual image distance can be adjusted to near points so that the eyes focus to see the virtual image of objects. By combining vergence cues with accommodation cues, the positions of one or more lenses in the optical system can be adjusted so that vergence-accommodation mismatch can be reduced or substantially removed.
In some embodiments, a head-mounted display includes any of the optical systems of the present description and also may include an eye-tracking system. The eye-tracking system may be configured to detect where in the virtual image that the user is looking and the optical system may be adapted to adjust the virtual image distance to match the depth of the object as presented stereoscopically by adjusting the positions of one or more lenses in the optical system.
In some embodiments, the first and/or second optical lenses 112 and 122 may be shaped to have spherical and/or cylinder power in reflection or refraction or both. This can be done, for example, by using thermoforming molds and film insert molds having the desired shape. Cylinder power may be created by applying a stress to a rotationally symmetric lens as it cools after an injection molding process, for example. Alternatively, the lens may be curved (spherically or cylindrically or a combination) by post processing, diamond turning, grinding or polishing.
In some embodiments, one or both of the first and second optical lenses 112 and 122 can be flexed in the optical system dynamically or statically. An example of a static flexure is a set screw or set screws or similar mechanism statically applying a compressive or tensile force to the lens or lenses. In some embodiments, set screws could be provided in an annular manner to provide for astigmatism correction along multiple axes to account for all three types of astigmatism: with the rule, against the rule and oblique astigmatism. This would provide for accurate correction such as with eyeglass lenses which are typically made to address astigmatism in increments of 30 degrees or 15 degrees or 10 degrees of obliquity. The pitch of the set screw can be related to cylinder power to provide a measure of correction based on turns or partial turns of the screw. In some embodiments, piezo-electric, voice-coil, or stepper-motor actuators or other types of actuators can be used to flex the lens or lenses (e.g., based on user input to the device such as entering a prescription).
In prescription lens terminology, a plano lens is a lens with no refractive optical power. In some embodiments, the first optical lens 112 and/or the second optical lens 122 may be plano lenses having little or no optical power in transmission, but may have optical power in reflection (for example, due to the overall curvature of the lenses). The curvature of the first and second major surfaces 114 and 116 of the first optical lens 112 may be the same or substantially the same, and the curvature of the first and second major surfaces 124 and 126 of the second optical lens 122 may be the same or substantially the same. The first and second optical lenses 112 and 122 may have the substantially same shape. In some embodiments, the first optical lens 112 and/or the second optical lens 122 may have optical power in transmission and may also have optical power in reflection.
Optical system 100 includes a reflective polarizer and a quarter wave retarder in second optical stack 120 and includes a partial reflector in first optical stack 110. There are various possibilities of how the reflective polarizer, the quarter wave retarder and the partial reflector can be arranged in the optical stacks.
The first optical stack 210 includes a first optical lens 212 having opposing first and second major surfaces 214 and 216 respectively. The first optical stack 210 includes a partial reflector 217 disposed on the first major surface 214. The partial reflector 217 has an average optical reflectance of at least 30% in a desired or pre-determined plurality of wavelengths and may have an average optical transmission of at least 30% in the desired or pre-determined plurality of wavelengths, which may be any of the wavelength ranges described elsewhere herein.
The second optical stack includes a second optical lens 222 having first and second major surfaces 224 and 226. The second optical stack 220 includes a reflective polarizer 227 disposed on the second major surface 226 and includes a quarter wave retarder 225 disposed on the reflective polarizer 227. Quarter wave retarder 225 may be a film laminated on the reflective polarizer 227 or may be a coating applied to the reflective polarizer 227. The optical system 200 may include one or more additional retarders. For example, a second quarter wave retarder may be included in first optical stack 210 and may be disposed on the second major surface 216. The first quarter wave retarder 225 and any additional quarter wave retarders included in optical system 200 may be quarter wave retarders at at least one wavelength in the pre-determined or desired plurality of wavelengths. The second optical stack 220 may alternatively be described as including the second lens 222 and the reflective polarizer 227 disposed on the second lens 222 and the first quarter wave retarder 225 may be regarded as a separate layer or coating that is disposed on the second optical stack 220 rather than being included in the second optical stack 220. In this case, the first quarter wave retarder 225 may be described as being disposed between the first optical stack 210 and the second optical stack 220. In some embodiments, the first quarter wave retarder 225 may not be attached to the second optical stack 220, and in some embodiments, the first quarter wave retarder 225 is disposed between and spaced apart from the first and second optical stacks 210 and 220. In still other embodiments, the first quarter wave retarder 225 may be disposed on the partial reflector 217 and may be described as being included in the first optical stack 210 or may be described as being disposed between the first and second optical stacks 210 and 220.
Light rays 237 and 238 are each transmitted through the image surface 230 and the stop surface 235. Light rays 237 and 238 may each be transmitted from the image surface 230 to the stop surface 235 (in head-mounted display applications, for example), or light rays 237 and 238 may be transmitted from the stop surface 235, to the image surface 230 (in camera applications, for example). Light ray 238 may be a central light ray whose optical path defines a folded optical axis 240 for optical system 200, which may be centered on the folded optical axis 240. Folded optical axis 240 may correspond to folded optical axis 140.
In embodiments in which light ray 237 is transmitted from the image surface 230 to the stop surface 235, light ray 237 (and similarly for light ray 238) is, in sequence, transmitted through image surface 230, transmitted through second major surface 216 (and any coatings or layers thereon), transmitted through first optical lens 212, transmitted through partial reflector 217, transmitted through the quarter wave retarder 225 disposed on the reflective polarizer 227, reflected from reflective polarizer 227, transmitted back through quarter wave retarder 225, reflected from partial reflector 217, transmitted through quarter wave retarder 225, transmitted through reflective polarizer 227, transmitted through second lens 222, and transmitted through stop surface 235. Light ray 237 may be emitted from the image surface 230 with a polarization state which is rotated to a first polarization state upon passing through quarter wave retarder 225. This first polarization state may be a block state for the reflective polarizer 227. After light ray 237 passes through first quarter wave retarder 225, reflects from partial reflector 217 and passes back through quarter wave retarder 225, its polarization state is a second polarization state substantially orthogonal to the first polarization state. Light ray 237 can therefore reflect from the reflective polarizer 227 the first time that it is incident on the reflective polarizer 227 and can be transmitted through the reflective polarizer 227 the second time that it is incident on the reflective polarizer 227.
Other light rays (not illustrated) reflect from the partial reflector 217 when incident on the partial reflector 217 in the minus z-direction or are transmitted by the partial reflector 217 when incident on the partial reflector 217 in the plus z-direction. These rays may exit optical system 200.
In some embodiments, substantially any chief light ray that passes through the image surface 230 and the stop surface 235 is incident on each of the first optical stack 210 and the second optical stack 220 with an angle of incidence less than about 30 degrees, less than about 25 degrees, or less than about 20 degrees, the first time or each time that the chief light ray is incident on the first or second optical stacks 210 or 220. In any of the optical systems of the present description, substantially any chief light ray that passes through the image and stop surfaces is incident on each of the reflective polarizer and the partial reflector with an angle of incidence less than about 30 degrees, less than about 25 degrees, or less than about 20 degrees, the first time or each time that the chief light ray is incident on the reflective polarizer or the partial reflector. If a large majority (e.g., about 90 percent or more, or about 95 percent or more, or about 98 percent or more) of all chief rays transmitted through the stop and image surfaces satisfy a condition, it may be said that substantially any chief ray satisfies that condition.
Various factors can cause light to be partially transmitted through the reflective polarizer 227 the first time that light emitted by the image surface 230 is incident on the reflective polarizer 227. This can cause unwanted ghosting or image blurriness at the stop surface 235. These factors can include performance degradation of the various polarizing components during forming and unwanted birefringence in the optical system 200. The effects of these factors can combine to degrade the contrast ratio and efficiency of the optical system 200. The effects of these factors on the contrast ratio can be seen, for example, in
It has been found that suitably choosing the shapes of the various major surfaces (e.g., second major surface 226 and first major surface 214) that the optical system can provide distortion sufficiently low that the image does not need to be pre-distorted. In some embodiments, an image source, which is adapted to emit an undistorted image, comprises the image surface 230. The partial reflector 217 and the reflective polarize 227 may have different shapes selected such that a distortion of the emitted undistorted image transmitted by the stop surface 235 is less than about 10%, or less than about 5%, or less than about 3%, of a field of view at the stop surface 235. The field of view at the stop surface may be greater than 80 degrees, greater than 90 degrees, or greater than 100 degrees, for example.
An alternate embodiment is shown in
The image surface 530 has a first maximum lateral dimension and the stop surface 535 has a second maximum lateral dimension. In some embodiments, the first maximum lateral dimension divided by the second maximum lateral dimension may be at least 2, at least 3, at least 4, or at least 5. The image surface 530 and/or the stop surface 635 may be substantially planar or may be curved about one or more axes.
The partial reflector has an average optical reflectance of at least 30% in a desired or pre-determined plurality of wavelengths and may have an average optical transmission of at least 30% in the desired or pre-determined plurality of wavelengths, which may be any of the wavelength ranges described elsewhere herein. The quarter wave retarder(s) included in optical system 500 may be quarter wave retarders at at least one wavelength in the pre-determined or desired plurality of wavelengths. The multilayer reflective polarizer substantially transmits light having a first polarization state (e.g., linearly polarized in a first direction) and substantially reflects light having an orthogonal second polarization state (e.g., linear polarized in a second direction orthogonal to the first direction). As described further elsewhere herein, the multilayer reflective polarizer may be a polymeric multilayer reflective polarizer (e.g., APF) or may be a wire grid polarizer, for example.
Optical system 500 may be centered on folded optical axis 540 which may be defined by the optical path of a central light ray transmitted through image surface 530.
It has been found that using a single integrated optical stack, such as integrated optical stack 510, can provide a high field of view in a compact system. Light ray 537, which is transmitted through an outer edge of image surface 530, is a chief ray that intersects stop surface 535 at the folded optical axis 540 with a view angle of ΞΈ, which may be at least 40 degrees, at least 45 degrees, or at least 50 degrees, for example. The field of view at the stop surface 535 is 2ΞΈ, which may be at least 80 degrees, at least 90 degrees, or at least 100 degrees, for example.
Integral optical stack 610 can be made by first forming reflective polarizer 627 with first quarter wave retarder 625 coated or laminated to reflective polarizer 627 and then thermoforming the resulting film into a desired shape. As described further elsewhere herein, the thermoforming tool may have a shape different than the desired shape so that the film obtains the desired shape after cooling. Partial reflector 617 and second quarter wave retarder 615 may be prepared by coating a quarter wave retarder onto a partial reflector film, by coating a partial reflector coating onto a quarter wave retarder film, by laminating a partial reflector film and a quarter wave retarder film together, or by first forming lens 612 (which may be formed on a film that includes reflective polarizer 627 and first quarter wave retarder 625) in a film insert molding process and then coating the partial reflector 617 on the second major surface 616 and coating the quarter wave retarder 615 on the partial reflector 617. In some embodiments, a first film including reflective polarizer 627 and first quarter wave retarder 625 is provided an a second film including partial reflector 617 and second quarter wave retarder 615 is provided and then integral optical stack 610 is formed by injection molding lens 612 between the first and second thermoformed films in a film insert molding process. The first and second films may be thermoformed prior to the injection molding step. Other optical stacks of the present description may be made similarly by thermoforming an optical film, which may be a coated film or a laminate, and using a film insert molding process to make the optical stack. A second film may be included in the film insert molding process so that the lens formed in the molding process is disposed between the films.
Image source 631 includes the image surface 630 and stop surface 635 is an exit pupil for optical system 600. Image source 631 may be a display panel, for example. In other embodiments, a display panel is not present and, instead, image surface 630 is an aperture adapted to receive light reflected from objects external to optical system 600. A second optical system 633 having an entrance pupil 634 is disposed proximate optical system 600 with stop surface 635 overlapping entrance pupil 634. The second optical system 633 may be a camera, for example, adapted to record images transmitted through image surface 637. In some embodiments, the second optical system is a viewer's eye and entrance pupil 634 is the pupil of the viewer's eye. In such embodiments, the optical system 600 may be adapted for use in a head-mounted display.
The partial reflector 617 has an average optical reflectance of at least 30% in a desired or pre-determined plurality of wavelengths and may have an average optical transmission of at least 30% in the desired or pre-determined plurality of wavelengths, which may be any of the wavelength ranges described elsewhere herein. The first quarter wave retarder 625 and any additional quarter wave retarders included in optical system 600 may be quarter wave retarders at at least one wavelength in the pre-determined or desired plurality of wavelengths. The multilayer reflective polarizer 627 substantially transmits light having a first polarization state (e.g., linearly polarized in a first direction) and substantially reflects light having an orthogonal second polarization state (e.g., linear polarized in a second direction orthogonal to the first direction). As described further elsewhere herein, the multilayer reflective polarizer 627 may be a polymeric multilayer reflective polarizer (e.g., APF) or may be a wire grid polarizer, for example.
Light ray 637 is emitted from the image source 631 and transmitted through the image surface 630 and the stop surface 635. Light ray 637 is transmitted through second quarter wave retarder 615 and partial reflector 617 into and through lens 612. Other light rays (not illustrated) reflect from partial reflector 617 after passing through second quarter wave retarder 615 and are lost from the optical system 600. After making a first pass through lens 612, the light ray passes through first quarter wave retarder 625 and reflects from reflective polarizer 627. Image source 631 may be adapted to emit light having a polarization along the pass axis for reflective polarizer 627 so that after passing through both second quarter wave retarder 615 and first quarter wave retarder 625 it is polarized along the block axis for the reflective polarizer 627 and therefore reflects from the reflective polarizer 627 when it is first incident on it. In some embodiments, a linear polarizer is included between the display panel 631 and the second quarter wave retarder 617 so that light incident on second quarter wave retarder 615 has the desired polarization. After light ray 637 reflects from reflective polarizer 627, it passes back through first quarter wave retarder 625 and lens 612 and is then reflected from partial reflector 617 (other light rays not illustrated are transmitted through partial reflector 617) back through lens 612 and is then again incident on the reflective polarizer 627. After passing through first quarter wave retarder 625, reflecting from partial reflector 617 and passing back through first quarter wave retarder 625, light ray 637 has a polarization along the pass axis for reflective polarizer 627. Light ray 637 is therefore transmitted through reflective polarizer 627 and is then transmitted through stop surface 635 into second optical system 633.
In alternate embodiments, the integrated optical stack 610 is replaced with first and second optical stacks as in
Image recorder 732 includes the image surface 730, and stop surface 735 is an entrance pupil for optical system 700. The stop surface may be an aperture stop of a camera, for example. Image recorder 732 may be a CCD or a CMOS device, for example. Optical system 700 may be a camera or a component of a camera and may be disposed in a cell phone, for example.
The partial reflector 717 has an average optical reflectance of at least 30% in a desired or pre-determined plurality of wavelengths and may have an average optical transmission of at least 30% in the desired or pre-determined plurality of wavelengths, which may be any of the wavelength ranges described elsewhere herein. The first quarter wave retarder 725 and any additional quarter wave retarders included in optical system 700 may be quarter wave retarders at at least one wavelength in the pre-determined or desired plurality of wavelengths. The multilayer reflective polarizer 727 substantially transmits light having a first polarization state (e.g., linearly polarized in a first direction) and substantially reflects light having an orthogonal second polarization state (e.g., linear polarized in a second direction orthogonal to the first direction). As described further elsewhere herein, the multilayer reflective polarizer 727 may be a polymeric multilayer reflective polarizer (e.g., APF) or may be a wire grid polarizer, for example.
Light ray 737 is transmitted through the stop surface 735 and transmitted through the image surface 730 into image recorder 732. Light ray 737 is, in sequence, transmitted through reflective polarizer 727 (other light rays not illustrated may be reflected by reflective polarizer 727), transmitted through quarter wave retarder 725 and optical lens 712, reflected from partial reflector 717 and transmitted back through lens 712 and quarter wave retarder, reflected from reflective polarizer 727 and transmitted through the quarter wave retarder 725, the lens 712 and the partial reflector 717. The light ray 737 is then transmitted through image surface 730 into image recorder 732.
Any of the integral optical stacks 510, 610, and 710 may optionally include a second lens adjacent the first lens with one or more of the reflective polarizer, the quarter wave retarder and the partial reflector disposed between the two lenses. The two lenses may be laminated together using optically clear adhesive.
The first and second lenses 2612 and 2622 may be formed from first and second materials, respectively, that may be the same or different. For example, the material of the lenses 26122622 may be a same glass, may be different glasses, may be the same polymer, may be different polymers, or one may be a glass and the other may be a polymer. The material chosen for the lenses will typically exhibit some degree of dispersion (dependence of the refractive index on wavelength). In some cases, the effects of dispersion can be reduced by choosing different materials for the different lenses such that the dispersion in one lens compensates or partially compensates for the dispersion in the other lens. The Abbe number of a material is can be used to quantify the dispersion of a material. The Abbe number is given as (nDβ1)/(nFβnC) where nD is the refractive index at 589.3 nm, nF is the refractive index of 486.1 nm and nC is the refractive index at 656.3 nm. In some embodiments, the first and second lenses 2612 and 2622 have differing Abbe numbers. In some embodiments, a difference in the Abbe numbers of the first and second lenses 2612 and 2622 is in a range of 5 to 50. In some embodiments, one of the first and second lenses 2612 and 2622 has an Abbe number greater than 45, or greater than 50, and the other of the first and second lenses 2612 and 2622 has an Abbe number less than 45, or less than 40. This can be achieve, for example, by using a glass for one of the lenses, and using a polymer for the other of the lenses.
Optical system of the present description may include one, two, three or more lenses disposed between an image surface and a stop surface. In some embodiments a plurality of major surfaces is disposed between the image surface and the stop surface with each major surface convex toward the image surface along the first and second axes. In some embodiments, at least six such major surfaces are included. In some embodiments, at least six different major surfaces have at least six different convexities. Including three or more lenses in an optical system may be useful when a small panel having a high resolution is utilized, for example, since having three or more lenses provides six or more major surfaces whose shape can be selected to give desired optical properties (e.g., large field of view) at the stop surface of the optical system.
The image surface 830 has a first maximum lateral dimension and the stop surface 835 has a second maximum lateral dimension. In some embodiments, the first maximum lateral dimension divided by the second maximum lateral dimension may be at least 2, at least 3, at least 4, or at least 5.
Optical system 800 may be centered on folded optical axis 840 which may be defined by an optical path of a central light ray transmitted through the image surface 830.
The partial reflector may have an average optical reflectance of at least 30% in a pre-determined or desired plurality of wavelengths and may have an average optical transmittance of a least 30% in the pre-determined or desired plurality of wavelengths, which may be any of the wavelength ranges described elsewhere herein. The first quarter wave retarder and any additional quarter wave retarders included in optical system 800 may be quarter wave retarders at at least one wavelength in the pre-determined or desired plurality of wavelengths. The multilayer reflective polarizer may substantially transmit light having a first polarization state, which may be a linear polarization state, and substantially reflect light having an orthogonal second polarization state, which may be an orthogonal linear polarization state. As described further elsewhere herein, the multilayer reflective polarizer may be a polymeric multilayer reflective polarizer (e.g., APF) or may be a wire grid polarizer, for example.
In some embodiments, each of the major surfaces major surfaces 864, 866, 824, 826, 814 and 816 have a convexity different from the convexity of each of the remaining major surfaces. In other words, the major surfaces major surfaces 864, 866, 824, 826, 814 and 816 may have six different convexities.
An image source may comprise the image surface 830 and the stop surface 835 may be an exit pupil, which may be adapted to overlap an entrance pupil of a second optical system. The entrance pupil of the second optical system may be an entrance pupil of a viewer's eye, for example. Alternatively, an image recorder may comprises the image surface 830 and the stop surface 835 may be an entrance pupil.
Chief light ray 937 and envelope rays 939a and 939b are transmitted through image surface 930 and through stop surface 935. Chief light ray 937 and envelope rays 939a and 939b propagate from image surface 930 and through stop surface 935. In other embodiments, the directions of the light paths are reversed and image surface 930 may be a surface of an image recorder. Envelope rays 939a and 939b intersect the stop surface 935 at boundaries of the stop surface 935 while chief ray 937 intersect the stop surface 935 at optical axis 940, which may be defined by an optical path of a central light ray transmitted through the image surface 930.
Chief light ray 937 is incident on the stop surface 935 at optical axis 940 at an incidence angle ΞΈ. Twice the maximum incidence angle on the stop surface 935 of a chief ray incident on the stop surface 935 along the optical axis 940 is the field of view of optical system 900. In some embodiments, optical system 900 has a low chromatic aberration. For example, in some embodiments, substantially any chief light ray having at least first and second wavelengths at least 150 nm apart in a visible wavelength range (e.g., first and second wavelengths of 486 nm and 656 nm, respectively) and that is transmitted through the image surface 930 and the stop surface 935 has a color separation distance at the stop surface 935 of less than 1.5 percent, or less than 1.2 percent, of a field of view at the stop surface 935. In some embodiments, substantially any chief light ray having at least first and second wavelengths at least 150 nm apart in a visible wavelength range and that is transmitted through the image surface 930 and the stop surface 935 has a color separation distance at the stop surface 935 of less than 20 arc minutes, or less than 10 arc minutes.
Additional optical systems of the present description are illustrated in
In some embodiments, the reflective polarizer is rotationally symmetric or substantially rotationally symmetric about optical axis 1040. A film or component may be said to be substantially rotationally symmetric if the azimuthal variation in the shape of the film or component is no greater than about 10 percent. In the embodiments in
A polymeric multilayer optical film may be thermoformed to provide reflective polarizer 1127. The optical film may initially have at least one layer uniaxially oriented with a block axis along the y-direction. During thermoforming the optical film is stretched to conform to the shape of a thermoform tool. The optical film is stretched since the desired shape is curved about two orthogonal axes. In contrast to this, an optical film would not need to be stretched to conform to a shape curved about only one axis. The process of thermoforming can leave the optical film substantially uniaxially oriented at second location 1152 (since the film is stretched along the orientation direction at this location during thermoforming), but result in biaxial orientation at first location 1153 due to the stretching of the optical film as it is thermoformed. The block axes at first and second locations 1153 and 1152 are indicated by the arrows at those locations. The block axis is shifted by Ξ± degrees at the first location 1153. The transmission axis may orthogonal to the block axis and may also be shifted by Ξ± degrees at the first location 1153. In some embodiments, a maximum variation of a transmission axis (or of a block axis) of the reflective polarizer 1127 is less than about 5 degrees, or less than about 3 degrees, or less than about 2 degrees, or less than about 1.5 degrees, or less than about 1 degree over the entire area of the reflective polarizer or over an area of the reflective polarizer defined by s1 and r1, or over a reflection aperture of the reflective polarizer, where s1 and s2 are as described for reflective polarizer 1027. The reflection aperture refers to the portion of the reflective polarizer that is utilized by the optical system in reflection. The reflection aperture may be substantially the entire area of the reflective polarizer or may exclude a portion of the reflective polarizer near a boundary of the reflective polarizer. The maximum variation of the transmission axis may be determined as the maximum angular difference between the transmission axis and a fixed direction (e.g., the x-direction in
Any of the reflective polarizers used in any of the optical systems described herein may be linear reflective polarizers which may be adapted to reflect light having a first linear polarization state and transmit light having a second linear polarization state orthogonal to the first linear polarization state.
Any of the reflective polarizers used in any of the optical systems of the present description may be a thermoformed reflective polarizer which may be a thermoformed polymeric multilayer optical film. The polymeric multilayer optical film may include a plurality of alternating first and second polymeric layers. This is illustrated in
In some embodiments, at least one layer of the first and second polymeric layers 1272 and 1274 may be substantially uniaxially oriented at some locations in the layer. In some embodiments, the multilayer optical film, prior to thermoforming, has at least one layer having indices of refraction in a length direction (e.g., x-direction) and a thickness direction (e.g., z-direction) that are substantially the same, but substantially different from an index of refraction in a width direction (e.g., y-direction). In some embodiments, the multilayer optical film, prior to thermoforming, is a substantially uniaxially drawn film and has a degree of uniaxial character U of at least 0.7, or at least 0.8, or at least 0.85, where U=(1/MDDRβ1)/(TDDR1/2β1) with MDDR defined as the machine direction draw ratio and TDDR defined as the transverse direction draw ratio. Such uniaxially oriented multilayer optical films are described in U.S. Pat. No. 2010/0254002 (Merrill et al.), which is hereby incorporate herein by reference to the extent that it does not contradict the present description. In other embodiments, the multilayer optical film, prior to thermoforming, is not substantially uniaxially drawn.
Uniaxially oriented multilayer reflective polarizers include APF (Advanced Polarizing Film, available from 3M Company). APF includes a plurality of alternating first and second polymeric layers with the first polymeric layers having indices of refraction in a length direction (e.g., x-direction) and a thickness direction (e.g., z-direction) that are substantially the same, but substantially different from an index of refraction in a width direction (e.g., y-direction). For example, the absolute value of the difference in the refractive indices in the x- and z-directions may be less than 0.02 or less than 0.01, and the absolute value of the difference in the refractive indices in the x- and y-directions may be greater than 0.05, or greater than 0.10. APF is a linear reflective polarizer with a block axis along the width direction and a pass axis along the length direction. Any of the reflective polarizers used in any of the optical systems of the present description may be a thermoformed APF. Unless specified differently, refractive index refers to the refractive index at a wavelength of 550 nm.
A reflective polarizer which is not uniaxially oriented is DBEF (Dual Brightness Enhancement Film available from 3M Company, St. Paul, Minn.). DBEF may have first layers with refractive indices in the width, length and thickness directions of about 1.80, 1.62 and 1.50, respectively, while APF may have first layers with refractive indices in the width, length and thickness directions of about 1.80, 1.56 and 1.56, respectively. Both APF and DBEF may have substantially isotropic second layers. In some embodiments, the optical system may use DBEF as the reflective polarizer, and in some embodiments, the optical system may use APF as the reflective polarizer. In still other embodiments, multilayer polymeric reflective polarizer films other than DBEF or APF may be used. APF has unexpectedly been found to offer improvements over DBEF when thermoformed into a shape convex about two orthogonal axes. Such improvements include a higher contrast ratio and reduced off-axis color when used in a display system. Other improvements include a reduced variation in the orientation of the transmission and block axes.
Both DBEF and APF are polymeric multilayer reflective polarizers that include alternating polymeric layers. Other reflective polarizers may be used in the optical systems of the present description. In some embodiments, the reflective polarizer is a wire grid polarizer. This is illustrated in
In some embodiments, instead of using a wire grid polarizer that includes a wire grid layer on a substrate layer, a wire grid polarizer is formed on a lens surface by depositing metallic traces on the surface of the lens.
In some embodiments, an optical system includes a partial reflector, a reflective polarizer, and a first quarter wave retarder disposed between the reflective polarizer and the partial reflector. The partial reflector and the reflective polarizer may be adjacent to and spaced apart from one another. The optical system may include an image surface and a stop surface with the partial reflector disposed between the image surface and the stop surface, and the reflective polarizer disposed between the stop surface and the partial reflector. An image source may comprise the image surface and the stop surface may be an exit pupil, or an image recorder may comprise the image surface and the stop surface may be an entrance pupil. The image source may include a display panel which may be transparent or semi-transparent and the image source may further include a shutter. In some embodiments, the image surface may be adapted to receive light reflected from objects external to optical system. The partial reflector has an average optical reflectance of at least 30% in a desired or pre-determined plurality of wavelengths and may also have an average optical transmittance of at least 30% in the desired or pre-determined plurality of wavelengths. The desired or pre-determined plurality of wavelengths may include one or more continuous wavelength ranges. In some cases, the desired or pre-determined plurality of wavelengths may be the visible wavelength range (e.g., 400 nm to 700 nm). Both the average optical reflectance and the average optical transmittance in the desired or pre-determined plurality of wavelengths may be between 30% and 70%, or between 40% and 60%, for example. The first quarter wave retarder, and any optional additional quarter wave retarders, may be a quarter wave retarder at at least one wavelength in the desired or pre-determined plurality of wavelengths. The quarter wave retarder(s) may be oriented so that the fast axis of the retarder is oriented at 45 degrees relative the transmission or block axis of the reflective polarizer. The reflective polarizer is curved about orthogonal first and second axes. The optical system may include a plurality of surfaces (e.g., the major surfaces of one, two, three, or more optical lensesβsee, e.g.,
Any of the partial reflectors used in any of the optical systems of the present description may have an average optical reflectance of at least 30% in a desired or pre-determined plurality of wavelengths, and/or may have an average optical transmittance of at least 30% in a desired or pre-determined plurality of wavelengths. The desired or pre-determined plurality of wavelengths may be a desired or pre-determined wavelength range or may be a plurality of desired or pre-determined wavelength ranges. Any of the optical systems of the present description may include one or more retarders which are quarter wave retarders at at least one wavelength in the desired or pre-determined plurality of wavelengths. The desired or pre-determined plurality of wavelengths may, for example, be any wavelength range in which the optical system is designed to operate. The pre-determined or desired plurality of wavelengths may be a visible range, and may for example, be the range of wavelengths from 400 nm to 700 nm. In some embodiments, the desired or pre-determined plurality of wavelengths may be an infrared range or may include one or more of infrared, visible and ultraviolet wavelengths. In some embodiments, the desired or pre-determined plurality of wavelengths may be a narrow wavelength band, or a plurality of narrow wavelength bands, and the partial reflector may be a notch reflector. In some embodiments, the desired or pre-determined plurality of wavelengths include at least one continuous wavelength range that has a full width at half maximum of no more than 100 nm, or no more than 50 nm.
In any of the optical systems described herein, unless the context clearly indicates differently, an image source may comprise the image surface and the stop surface may be an exit pupil, which may be adapted to overlap an entrance pupil of a second optical system. The entrance pupil of the second optical system may be an entrance pupil of a viewer's eye, for example. In any of the optical systems described herein, unless the context clearly indicates differently, an image recorder may comprises the image surface and the stop surface may be an entrance pupil.
Any of the optical systems of the present description may have a substantially planar image surface and/or a substantially planar stop surface, or one or both of these surfaces may be curved. The image surface may have a maximum lateral dimension A, and a stop surface may have a maximum lateral dimension B, where A/B is at least 2, or at least 3, or at least 4, or at least 5. In some embodiments, A/B may be in a range of 2 to 20, or 3 to 10, for example.
Any of the optical systems of the present description may have a field of view of at least 80 degrees, of at least 90 degrees, or of at least 100 degrees. Any of the optical systems of the present description may be adapted such that at least one chief light ray transmitted through the stop surface and the image surface may pass through the stop surface at an incident angle of at least 40 degrees, or at least 45 degrees, or at least 50 degrees.
In some aspects of the present description a device is provide that includes any one or more of the optical systems of the present description. The device may be or may include, for example, a display device, such as a head-mounted display or a projection system, an illuminator, which may also be a projector, a beam expander, a camera, or a magnifying device. The magnifying device may be a telescope, binoculars, or a microscope, for example.
In some embodiments, the reflective polarizer is thermoformed. Optical films, such as reflective polarizers, may have anisotropic mechanical properties which make obtaining a desired shape of the thermoformed optical film difficult due to anisotropic contraction of the optical film after removing the film from the thermoform mold. The anisotropic mechanical properties can arise in a multilayer polymeric reflective polarizer due to the anisotropic orientation of the polymeric molecules in at least some layers of the reflective polarizer. Anisotropic mechanical properties in a wire grid polarizer comprising wires on a surface of a polymeric film can arise due to the anisotropy of the wires which may extend in one direction. According to the present description, methods have been found for providing an optical film having a desired shape when the optical film has anisotropic mechanical properties.
In some embodiments, the desired optical film is any optical film having anisotropic mechanical properties and may be any of the reflective polarizers described herein. In some embodiments, the desired optical film is a reflective polarizer with a quarter wave coating or a laminated reflective polarizer film and quarter wave retarder film. The desired shape may be a shape that is rotationally symmetric about an optical axis (e.g., parallel to the z-axis of
Any of the reflective polarizers of the present description, which may be included in any of the optical systems of the present description, may be thermoformed according to the process 1580 and/or using the thermoform tool 1681. The reflective polarizer, and other optical films, may be integrated into an optical stack including an optical lens by injection molding a suitable lens material (e.g., polycarbonate) onto the film(s) in a film insert molding process, for example.
Any of the optical systems of the present description may be used in a device such as a head-mounted display (e.g., a virtual reality display) or a camera (e.g., a camera disposed in a cell phone).
The camera 1796, which may optionally be omitted, may include any optical system of the present description with the stop surface an entrance pupil of the optical system and with an image recorder comprising the image surface. For example, camera 1796 may include the first and second optical stacks 110 and 120 of optical system 100. Image surface 130 may be a surface of an image recorder disposed adjacent inner surface 1788 and the stop surface 135 may be disposed adjacent outer surface 1786 or may lie outside of the camera away from the viewer (in the plus z-direction from outer surface 1786).
Head-mounted display 1790 may include three of the optical systems of the present description. In other embodiments, only one or two optical systems of the present description is included in a head-mounted display. For example, in some embodiments a head-mounted display may include a single optical system of the present description to provide images to one eye of a user while the other eye has an unobstructed view of the user's environment. In still other embodiments, more than three optical systems of the present description may be included. For example, two camera units each including an optical system of the present description may be included to provide stereoscopic views or to provide multiple views (e.g., picture in picture) to the user while two display units are utilized as in
The head-mounted display 1790 may include an eye-tracking system comprising eye-tracking unit 1798, which may optionally be omitted. The system may monitor the diameter and position of a user's pupil utilizing an imaging sensor and processor. Light from a display panel included in first portion 1798 may reflect from the user's pupil and reflect from the reflective polarizer of an optical system disposed in first portion 1798 into eye-tracking unit 1798. Alternatively eye-tracking unit 1798 may include a light source (e.g., an infrared light source) which emits light toward a reflective component in first portion 1794a which is reflected towards the viewer's eye. This light then reflects from the eye and reflects from the reflective component in first portion 1794a back towards eye-tracking unit 1798.
The attributes of the eye that the eye monitoring system can detect may include one or more of the following: the viewing direction of the eye, diameter and changes in the diameter of the pupil, blinking of the eyelids, the eye tracking objects, and saccade movement. Eye tracking parameters may include velocity of the eye rotation and lag or phase between movement of an object and movement of the eye. Saccade movement may include duration, velocity, and pattern of the movement. The system may quantify fatigue and cognitive processing load of the user of the system based on pupillary response with considerations of ambient light conditions and may be personalized to the user based on historical data.
In some embodiments, the eye-tracking unit includes a camera (e.g., a red-green-blue (RGB) camera or an infrared (IR) camera) which may or may not include an optical system of the present description and that can capture an image of the eye. An IR camera can be used to determined ambient light conditions since the average IR luminance of the eye image is indicative of the ambient light levels.
In some embodiments, the head-mounted display 1790 includes an eye tracking system adapted to detect changes in pupil size and use that information to quantify user fatigue and cognitive processing load. In some embodiments, the head-mounted display 1790 is adapted (e.g., using an algorithm running on an embedded processor) to implement one or more or all of the following steps:
Step 1: Capture a grayscale image of the eye.
Step 2: Filter out noise (e.g. using a Gaussian filter).
Step 3: Calculate gradient magnitude and direction for each pixel in the image of the eye.
Step 4: Identify pixels with higher gradient magnitudes (these are likely to be an edge of an object).
Step 5: Identify edges by, for example, connecting the pixels identified in the previous step according to the Helmholtz Principle of human visual perception.
Step 6: Compare edge line segments to the equation of an ellipse or other shape defined by a polynomial equation. The smallest ellipse-like shape can be identified as the pupil. The area of the iris can also be determined and may be used to improve accuracy. Other elliptical shapes that may be in the image, such as glint, can be eliminated.
Step 7: Calculate the pupil size (e.g., diameter or area) based on the line fitting done previously and the distance between the eye and the camera.
Step 8: Determine and apply an adjustment factor to the calculated pupil size to account for ambient light conditions. Ambient light conditions can be determined using an additional sensor included in the head-mounted system or via luminance analysis of the image captured.
Step 9: Optionally save the adjusted pupil size in a database. The pupil size may be recorded as a function of time and may be stored as a time-series (a sequence of data points made over time).
The head-mounted display 1790 may be adapted to change the light intensity generated by the display panels in first and second portions 1794a and 1794b based on pupil size and/or pupil direction information determined using eye-tracking unit 1798. The eye-tracking system may be configured to detect where in the virtual image that the user is looking and the optical system may be adapted to adjust the virtual image distance to match the depth of the object as presented stereoscopically by adjusting the positions of one or more lenses in the optical system as described elsewhere herein.
In some embodiments, head-mounted display 1790 is configured so that prescription lenses may be attached adjacent inner surfaces 1784a and/or 1784b.
In some aspects of the present description, a device is provided that includes an optical system of the present description. An example of such a device is a head-mounted display such as head-mounted display 1790 that include one or more of the optical systems of the present description.
Device 2490 can be, for example, a display device, a beam expander, a camera, or a magnifying device such as a telescope, a microscope, binoculars or the like. In the case of binoculars or head-mounted displays, more than one optical system 2400 may be included. For example, two of optical systems 2400 (one for each eye) may be included; an example of a device including two optical systems is illustrated in
Device 2490c includes an objective portion 2499-1 and an objective portion 2499-2. The objective portions 2499-1 and 2499-2 are adapted to face an object being viewed and the eyepiece portions are adapted to face a viewer's eyes. An image surface of optical system 2400-1 (and similarly for optical system 2400-2) may be between the partial reflector 2417-1 and the objective portion 2499-1, may be within the objective portion 2499-1 or may be between the eyepiece portion 2497-1 and the objective portion 2499-1. A stop surface of the optical system 2400-1 (and similarly for optical system 2400-2) may be an exit pupil adapted to overlap a pupil of a user.
The objective portion 2499-1 may contain one or more optical lenses 2491-1 and the objective portions 2499-2 may contain one or more optical lenses 2491-2. In alternate embodiments, the eyepiece portion 2497-1 and the objective portion 2499-1 are provided without the eyepiece portion 2497-2 and the objective portion 2499-2 for use as a telescope or microscope.
In some embodiments, the first prism 2510a has a first volume, the second prism 2520a has a second volume, and the first volume is no greater than about half (or no greater than about 60 percent, or no greater than about 40 percent) of the second volume. Device 2590 may be a beam expander and may correspond to device 2490. Device 2590 may include a reflective polarizer, a partial reflector and a first quarter wave retarder disposed between the reflective polarizer and the partial reflector. When used as a beam expander, device 2590 may be adapted to receive an input light beam incident on the partial reflector and transmit an expanded output light beam. For example, the input light beam may be converging or collimated and the output light beam may be diverging, or the input light beam may have a first divergence angle and the output light beam may have a greater second divergence angle. The device 2590 may be oriented such that the partial reflector faces the illuminator 2502a. An additional polarizer (e.g., an additional reflective polarizer or an absorbing polarizer) may be disposed between device 2590 and output face 2514a, or may be included in device 2590 proximate the partial reflector opposite the reflective polarizer. Illuminator 2502a may provide a compact illumination system and device 2590 may be used as a beam expander to provide a wider field of view. Other illuminators that can be used with device 2590 are described in U.S. Provisional App. No. 62/186,944 entitled βIlluminatorβ, filed on Jun. 30, 2015, and hereby incorporated herein by reference to the extent that it does not contradict the present description. Device 2590 may be a beam expander including a partial reflector and a reflective polarizer adjacent to and spaced apart from one another, and the beam expander may be adapted to receive converging light incident on the partial reflector and transmit diverging light through the reflective polarizer.
The second reflective component 2534a has a largest active area 2536a. The second reflective component 2534a may be an image forming device and the largest active area 2536a may be a largest image area of the image forming device. Light is emitted (by being reflected, for example) from second reflective component 2534a in envelope 2554a. One or both of the first and second reflective components 2532a and 2534a may have a specular reflectance of greater than 70 percent, or greater than 80 percent, or greater than 90 percent. The first and/or second reflective components 2532a and 2534a may be flat or may be curved in one or more axes.
In some embodiments, second reflective component 2534a is adapted to modulate light incident thereon. For example, second reflective component 2534a may be an image forming device that reflects light having a spatially modulated polarization state. Second reflective component 2534a may be pixelated and may produce a patterned light. Light reflected from second reflective component 2534a in envelope 2554a may be converging patterned light. Suitable image forming devices that can be utilized as second reflective component 2534a include Liquid Crystal on Silicon (LCoS) devices. The LCoS device may be flat or may be curved in one or more axes.
The various components in
Folded optical axis 2557a includes first segment 2557a-1 extending in a first direction (positive x-direction) from the light source 2550a to the first reflective component 2532a, second segment 2557a-2 extending in a second direction (negative x-direction) opposite the first direction, third segment 2557a-3 extending in a third direction (negative y-direction), and fourth segment 2557a-4 extending in a fourth direction (positive y-direction) opposite the third direction. First and second segments 2557a-1 and 2557a-2 are overlapping though they are shown with a small separation in
Light source 2550a produces a light beam having envelope 2552a and this defines the input active area 2513a as the area of input face 2512a that is illumined with light from the light source 2550a that is used by the illuminator 2502a. Light source 2550a may either substantially not produce light outside of the envelope 2552a or any light that is produced outside this envelope is at an angle that it escapes from the illuminator without entering device 2590.
At least a portion of the light from light source 2550a is, in sequence, transmitted through the first prism 2510a, transmitted through the reflective polarizer 2530a, transmitted through the second prism 2520a, reflected from the first reflective component 2532a, transmitted back through the second prism 2520a, reflected from the reflective polarizer 2530a, transmitted through the second prism 2520a and is incident on second reflective component 2534a, reflected from second reflective component 2534a, transmitted through second prism 2520a and reflective polarizer 2530a and first prism 2510a, and finally exits the illuminator through device 2590. This is illustrated in
The illuminator 2502a allows an image to be projected by directing a light beam (in envelope 2552a) through a folded light path illuminator 2502a onto an imaging forming device (second reflective component 2534a), and reflecting a converging patterned light (in envelope 2554a) from the image forming device. The step of directing a light beam through the folded light path illuminator 2502a includes directing light to the first reflective component 2532a through the polarizing beam splitter 2500a, reflecting at least some of the light back towards the polarizing beam splitter 2500a, and reflecting at least some of the light from the polarizing beam splitter 2500a towards the image forming device. At least a portion of the converging patterned light is transmitted through the polarizing beam splitter 2500a and through device 2590.
Light from light source 2550a illuminates a maximum area of second reflective component 2534a after the light is reflected from the first reflective component 2532a and the reflective polarizer 2530a. This maximum area may be equal to the largest active area 2536a. Alternatively, the largest active area 2536a may be a largest area of second reflective component 2534a that is reflective. For example, second reflective component 2534a may be an image forming device that has a largest image area. Any light incident on the image forming device outside the largest image area may not be reflected towards device 2590. In this case, the largest active area 2536a would be the largest image area of the image forming device. The largest active area 2536a defines the output active area 2515a on output face 2514a and largest acceptance area 2543a of device 2590 since light is reflected from the largest active area 2536a towards device 2590 in envelope 2554a which illuminates the output face 2514a substantially only in the output active area 2515a and illuminates the device 2590 substantially only in the largest acceptance area 2543a. Illuminator 2502a is configured such that light in envelope 2554a that is reflected from the second reflective component 2534a and that passes through the device 2590 is convergent between the second reflective component 2534a and the device 2590. This results in a largest active area 2536a that is smaller than the output active area 2515a which is smaller than the largest active area 2536a.
In some embodiments, the input active area 2513a and/or the output active area 2515a are less than about 60 percent, or less than about 50 percent (i.e., less than about half), or less than about 40 percent, or less than about 35 percent of the largest active area 2536a, which may be a largest image area. In some embodiments, the largest surface area of input face 2512a (the total area of input face 2512a) is less than about half the largest image area. In some embodiments, the largest surface area of the output face 2514a (the total area of output face 2514a) is less than about half the largest image area.
Light source 2550a, or any of the light sources of the present description, may include one or more substantially monochromatic light emitting elements. For example, light source 2550a may include red, green and blue light emitting diodes (LEDs). Other colors, such as cyan and yellow may also be included. Alternatively, or in addition, broad spectrum (e.g., white or substantially white) light sources may be utilized. In some embodiments, the light source 2550a includes a blue emitter and a phosphor. In some embodiments, the light source 2550a includes an integrator that may be utilized to combine light from discrete light sources (e.g., the integrator may combine light from red, green and blue LEDs). The light source 2550a may include a polarizing element such that light having substantially a single polarization state is directed into first prism 2510a towards reflective polarizer 2530a. In some embodiments, light source 2550a may be or may include one or more of an LED, an organic light emitting diode (OLED), a laser, a laser diode, an incandescent lighting element, and an arc lamp. Light source 2550a may also include a lens, such as a condenser lens, in addition to lighting emitting element(s) such as LED(s). In some embodiments, the first or second prisms may have one or more curved faces to provide a desired optical power.
The optical systems of the present description may include one or more lenses having a non-uniform edge profile, which may be designed to conform to a face when used as a component of a head-mounted display. The lens(es) may have an edge profile to conform to an average face, to categories of face shapes, or may be designed for individual faces.
The reliefs of the lens assembly may be created in the molding of the lenses making up the lens assembly. Alternatively, the lenses may be custom ground for individuals using appropriate measurements of the face. Relief provided for the lens can restrict the area of the display visible to the user. In some embodiments, the relief data is provided to a computer controlling display panel 2731 and the computer may limit the display area to the regions visible to the user in order to reduce power consumption and/or in order to reduce visible artifacts from ghost images, for example.
An advantage of providing a consistent amount of relief of the lens from the face is that ambient light can be effectively blocked with the image while still providing adequate air circulation near the eye. Utilizing extended surfaces of the lens(es) of the optical systems can improve both the field of view and comfort to the user.
An optical system similar to optical system 200 was modeled. A second quarter wave retarder was disposed on second major surface 216. Each of the surfaces corresponding to surfaces 224, 226, 214 and 216 were taken to be aspheric surfaces described by Equation 1 with each of the polynomial coefficients D, E, F, G, H, I . . . equal to zero. The conic constant k was 0.042435 and the surface radius, r=1/c, was β36.82391 mm. Table 1 lists the parameters describing each of these surfaces.
The surface numbers in this table count the times that a ray starting from stop surface 235 (Surf. 1) and ending at the image surface 230 (Surf. 8 or IMA) is incident on a surface. Surf. 2 corresponds to first surface 224, Surf. 3 and Surf. 5 correspond to second surface 226, Surf. 4 and Surf. 6 correspond to first surface 214, and Surf. 7 corresponds to surface 216. The diameter refers to the clear aperture of the surface, EVANASPH refers to even asphere (only even powers of r appear in the expansion in Equation 1), the radius is the inverse of the parameter c in Equation 1, conic is the parameter k in Equation 1, and IMA refers to the image surface 230.
The first optical lens 212 was modeled as Zenon E48R having a refractive index of 1.53 and the second optical lens 222 was modeled as polycarbonate having a refractive index of 1.585. The focal length was 32.26271 mm, the field of view was 90 degrees, the image height was 27.14 mm (the diameter of the image surface 230 was 54.28 mm), the F# was 2.13, the eye relief (distance from stop surface to first lens surface) was 23.8 mm, and the eye box (diameter of the stop surface 235) was 15 mm.
Each chief light ray that was emitted by the image surface and that was transmitted through the stop surface was incident on each of the first optical stack and the second optical stack at an angle of incidence less than about 20 degrees each time the chief light ray was incident on the first or second optical stack.
The optical system had a field of view of 90 degrees at the stop surface. Chief light rays having wavelengths of 486 nm and 656 nm which were transmitted through the image surface and the stop surface had a maximum color separation distance at the stop surface of 3.4 arc minutes which was about 0.12 percent of the field of view at the stop surface.
An optical system similar to optical system 200 was modeled. A second quarter wave retarder was disposed on second major surface 216. Each of the surfaces corresponding to surfaces 224, 226, 214 and 216 were taken to be aspheric surfaces described by Equation 1. Tables 2 and 3 list the parameters describing each of these surfaces. The nomenclature in the tables is similar to that in Example 1. The units for the aspheric polynomial coefficients in Table 3 are mm to 1 minus the power of the polynomial.
The surface numbers in these tables count the times that a ray starting from stop surface 235 (Surf. 1) and ending at the image surface 230 (Surf. 12 or IMA) is incident on a surface. Surf. 2 corresponds to first surface 224, Surf. 3 and Surf. 5 correspond to second surface 226, Surf. 4 and Surf. 6 correspond to first surface 214, and Surf. 7 corresponds to surface 216. Surfs. 8-11 refer to surface layers disposed on the image surface 230.
The first optical lens 212 was modeled as Zenon E48R having a refractive index of 1.53 and the second optical lens 222 was modeled as polycarbonate having a refractive index of 1.585. The focal length was 17.560 mm, the field of view was 90 degrees, the image height was 14.36 mm (the diameter of the image surface 230 was 28.72 mm), the F# was 2.55, the eye relief was 15 mm, and the eye box (diameter of stop surface 235) was 10.0 mm.
Each chief light ray that was emitted by the image surface and that was transmitted through the stop surface was incident on each of the first optical stack and the second optical stack at an angle of incidence less than about 20 degrees each time the chief light ray was incident on the first or second optical stack.
The optical system had a field of view of 90 degrees at the stop surface. Chief light rays having wavelengths of 486 nm and 656 nm which were transmitted through the image surface and the stop surface had a maximum color separation distance at the stop surface of 10.8 arc minutes which was about 0.38 percent of the field of view at the stop surface.
An optical system similar to optical system 600 was modeled. Each of the surfaces corresponding to surfaces 614 and 616 were taken to be aspheric surfaces described by Equation 1. Tables 4 and 5 list the parameters describing each of these surfaces. The nomenclature in the table are similar to that in Examples 1 and 2.
The surface numbers in these tables count the times that a ray starting from stop surface 635 (Surf. 1) and ending at the image surface 630 (Surf. 6 or IMA) is incident on a surface. Surf. 2 and Surf. 4 correspond to first surface 614, and Surf. 3 and Surf. 5 correspond to second surface 616,
The focal length was 35.0 mm, the field of view was 90 degrees, the image height was 33.3 mm (the diameter of the image surface 630 was 66.6 mm), the F# was 2.3, the eye relief was 19.4 mm, and the eye box (diameter of stop surface 635) was 15 mm.
Each chief light ray that was emitted by the image surface and that was transmitted through the stop surface was incident on each of the first optical stack and the second optical stack at an angle of incidence less than about 20 degrees each time the chief light ray was incident on the first or second optical stack.
The optical system had a field of view of 90 degrees at the stop surface. Chief light rays having wavelengths of 486 nm and 656 nm which were transmitted through the image surface and the stop surface had a maximum color separation distance at the stop surface of 29.5 arc minutes which was about 0.9 percent of the field of view at the stop surface.
An optical system similar to optical system 800 was modeled. A reflective polarizer was disposed on second major surface 866 of third optical lens 862 and a first quarter wave retarder was disposed on the reflective polarizer. A partial reflector was disposed on first major surface 824 of second optical lens 822 and a second quarter wave retarder was disposed on second major surface 826 of second optical lens 822. Each of the surfaces corresponding to surfaces 864, 866, 824, 826, 814, and 816 were taken to be aspheric surfaces described by Equation 1. Tables 6 and 7 list the parameters describing each of these surfaces. The nomenclature in the tables is similar to that in the previous Examples.
The surface numbers in these tables count the times that a ray starting from stop surface 835 (Surf. 1) and ending at the image surface 830 (Surf. 10 or IMA) is incident on a surface. Surf. 2 corresponds to first surface 864, Surf. 3 and Surf. 5 correspond to second surface 866, Surf. 4 and Surf. 6 correspond to first surface 824, Surf. 7 corresponds to surface 266, Surf. 8 corresponds to surface 814, and Surf. 9 corresponds to surface 816.
The focal length was 19.180 mm, the field of view was 82 degrees, the image height was 15.89 mm (the diameter of the image surface 830 was 31.87 mm), the F# was 2.12, the eye relief was 11 mm, and the eye box (diameter of stop surface 835) was 9 mm.
Each chief light ray that was emitted by the image surface and that was transmitted through the stop surface was incident on each of the first optical stack and the second optical stack at an angle of incidence less than about 20 degrees each time the chief light ray was incident on the first or second optical stack.
The optical system had a field of view of 80 degrees at the stop surface. Chief light rays having wavelengths of 486 nm and 656 nm which were transmitted through the image surface and the stop surface had a maximum color separation distance at the stop surface of 14.9 arc minutes which was about 0.52 percent of the field of view at the stop surface.
An optical system similar to optical system 200 was modeled. A second quarter wave retarder was disposed on second major surface 216. Each of the surfaces corresponding to surfaces 224, 226, 214 and 216 were taken to be aspheric surfaces described by Equation 1 with each of the polynomial coefficients D, E, F, G, H, I . . . equal to zero. Table 8 lists the parameters describing each of these surfaces with the nomenclature similar to that in previous Examples.
The surface numbers in this table count the times that a ray starting from stop surface 235 (Surf. 1) and ending at the image surface 230 (Surf. 8 or IMA) is incident on a surface. Surf. 2 corresponds to first surface 224, Surf. 3 and Surf. 5 correspond to second surface 226, Surf. 4 and Surf. 6 correspond to first surface 214, and Surf. 7 corresponds to surface 216. The diameter refers to the clear aperature of the surface, EVANASPH refers to even asphere (only even powers of r appear in the expansion in Equation 1), the radius is the inverse of the parameter c in Equation 1, conic is the parameter k in Equation 1, and IMA refers to the image surface 230.
The first optical lens 212 was modeled as Zenon E48R having a refractive index of 1.53 and the second optical lens 222 was modeled as polycarbonate having a refractive index of 1.585. The focal length was 42.7 mm, the field of view was 100 degrees, the image height was 50.94 mm (the diameter of the image surface 230 was 101.88 mm), the F# was 3.25, the eye relief was 25 mm, and the eye box (diameter of the stop surface 235) was 15 mm.
Each chief light ray that was emitted by the image surface and that was transmitted through the stop surface was incident on each of the first optical stack and the second optical stack at an angle of incidence less than about 20 degrees each time the chief light ray was incident on the first or second optical stack.
The optical system had a field of view of 100 degrees at the stop surface. Chief light rays having wavelengths of 486 nm and 656 nm which were transmitted through the image surface and the stop surface had a maximum color separation distance at the stop surface of 11.9 arc minutes which was about 0.29 percent of the field of view at the stop surface.
An undistorted image produced at image surface 230 was simulated and the distortion of the image at the stop surface 235 was determined to be less than 1 percent.
DBEF (Example 6), APF (Example 7) and APF with a quarter wave retarder coating (Example 8) were thermoformed to give the films a geometry matching to the geometry of an outer surface of a lens. The films were trimmed to fit in an injection molding tool lens cavity and placed on a surface of the lens cavity. The trimmed films had a diameter of 63 mm and a radius of curvature of 87 mm. An injection mold polycarbonate resin was used to form the lens on the film. The films were formed on the side of the lens that would face the stop surface when used in an optical system of the present description. In Example 7, the film was formed on the lens so that when used in an optical system of the present description, the APF would face the stop surface and the quarter wave retarder faced away from the stop surface.
The thermoforming of the films were done in a MAAC sheet feed thermoforming system using vacuum to pull the heated film onto an external surface of a thermoform tool similar to thermoform tool 1681. The external surface was approximately ellipsoidal shaped with the major axis about 1.02 times the minor axis so that the resulting thermoformed film would be rotationally symmetric after cooling and relaxing. The thermoforming process parameters were: Sheet Oven Temperature=320Β° F.-380Β° F. (160Β° C.-193Β° C.); Forming Time=18 seconds; and Sheet Forming Temperature=330Β° F.-365Β° F. (156Β° C.-185Β° C.).
Images of the thermoformed DBEF (Example 6) and APF (Example 7) reflective polarizer samples were taken using a non-polarized near-Lambertian light source to emit light through the samples to a camera that included an analyzing polarizer aligned with the block axis of the analyzing polarizer at varying angles from the block axis of the reflective polarizer. At zero degrees both films were substantially transparent and at higher angles, the DBEF showed optical artifacts that were not present in the APF sample. For example, at an angle of 70 degrees, the APF sample was substantially uniformly dark while the DBEF sample showed colored rings. The film insert injection molding process was done in a reciprocating screw horizontal clamp injection molding system built by Krauss-Maffei (Germany). The injection molding tooling used was for a 6 base lens part and a Bayer MAKROLON 3107-550115 polycarbonate resin (available from Bayer MaterialScience LLC, Pittsburgh, Pa.) was used to form the lens. The injection molding process parameters were: Mold Temperature=180Β° F. (82Β° C.); Melt Temperature=560Β° F. (293Β° C.); Fill Time=1.56 seconds; Hold Time=5.5 seconds; Hold Pressure=11,000 psi (75.8 MPa); Cool Time=15 seconds.
Reflective polarizers were thermoformed as generally described in Examples 6-8 into a convex rotationally symmetric shape having a diameter of 50.8 mm and a radius of curvature of 38.6 mm. The reflective polarizers were DBEF (Example 9), APF (Example 10) and a wire grid polarizer (Example 11). The polarizance orientation was measured for each sample using an Axometrics AXOSCAN polarimeter (available from Axometrics, Inc., Huntsville, Ala.). For each sample, an area of the sample centered on the apex of the film and having a 20 mm diameter circular aperture was identified and the maximum variation of a transmission axis of the sample (maximum angular deviation of the transmission axis from a fixed direction minus minimum angular deviation of the transmission axis from the fixed direction) in the aperture was determined. For DBEF, the maximum variation was 1.707 degrees, for APF the maximum variation was 0.751 degrees, and for the wire grid polarizer, the maximum variation was 0.931 degrees. The boundary of the area had a sag of 1.32 mm at a radial distance of 10 mm from a rotational symmetry axis of the samples.
The following is a list of exemplary embodiments.
Embodiment 1 is an optical system, comprising:
an image surface;
a stop surface;
a first optical stack disposed between the image surface and the stop surface and convex toward the image surface along orthogonal first and second axes, the first optical stack comprising:
at least one inner layer substantially optically uniaxial at at least one first location away from the apex; and
at least one first location on the reflective polarizer having a radial distance, r1, from the optical axis and a displacement, s1, from a plane perpendicular to the optical axis at the apex, s1/r1 being at least 0.2.
Embodiment 335 is the thermoformed multilayer reflective polarizer of embodiment 334, wherein for an area of the reflective polarizer defined by s1 and r1, a maximum variation of a transmission axis of the reflective polarizer is less than about 2 degrees.
Embodiment 336 is the optical system of embodiment 335, wherein the maximum variation of the transmission axis of the reflective polarizer is less than about 1.5 degrees.
Embodiment 337 is the optical system of any of embodiments 334 to 336, wherein a maximum variation of a transmission axis of the reflective polarizer in a reflection aperture of the reflective polarizer is less than about 1.5 degrees.
Embodiment 338 is the optical system of any of embodiments 334 to 336, wherein a maximum variation of a transmission axis of the reflective polarizer in a reflection aperture of the reflective polarizer is less than about 1 degree.
Embodiment 339 is the thermoformed multilayer reflective polarizer of any of embodiments 334 to 338, wherein the at least one inner layer is substantially optically biaxial at at least one second location on the at least one layer away from the apex.
Embodiment 340 is a thermoformed multilayer reflective polarizer substantially rotationally symmetric about an optical axis passing thorough an apex of the thermoformed multilayer reflective polarizer and convex along orthogonal first and second axes orthogonal to the optical axis, the thermoformed multilayer reflective polarizer having:
at least one first location on the reflective polarizer having a radial distance, r1, from the optical axis and a displacement, s1, from a plane perpendicular to the optical axis at the apex, s1/r1 being at least 0.2,
wherein for an area of the reflective polarizer defined by s1 and r1, a maximum variation of a transmission axis of the reflective polarizer is less than about 2 degrees.
Embodiment 341 is the thermoformed multilayer reflective polarizer of embodiment 340, wherein the maximum variation of the transmission axis of the reflective polarizer is less than about 1.5 degrees.
Embodiment 342 is the thermoformed multilayer reflective polarizer of embodiment 340 or 341 comprising at least one layer that is substantially optically biaxial at at least one first location on the at least one layer away from an optical axis of the reflective polarizer and substantially optically uniaxial at at least one second location away from the optical axis.
Embodiment 343 is the thermoformed multilayer reflective polarizer of any of embodiments 334 to 342, wherein s1/r1 is less than about 0.8.
Embodiment 344 is the thermoformed multilayer reflective polarizer of any of embodiments 334 to 343, wherein the reflective polarizer has a second location having a radial distance, r2, from the optical axis and a displacement, s2, from the plane, s2/r2 being at least 0.3.
Embodiment 345 is the thermoformed multilayer reflective polarizer of any of embodiments 334 to 344, wherein an azimuthal variation in s1/r1 is less than 10 percent.
Embodiment 346 is the thermoformed multilayer reflective polarizer of any of embodiments 334 to 344, wherein an azimuthal variation in s1/r1 is less than 8 percent.
Embodiment 347 is the thermoformed multilayer reflective polarizer of any of embodiments 334 to 344, wherein an azimuthal variation in s1/r1 is less than 6 percent.
Embodiment 348 is the thermoformed multilayer reflective polarizer of any of embodiments 334 to 344, wherein an azimuthal variation in s1/r1 is less than 4 percent.
Embodiment 349 is the thermoformed multilayer reflective polarizer of any of embodiments 334 to 344, wherein an azimuthal variation in s1/r1 is less than 2 percent.
Embodiment 350 is the thermoformed multilayer reflective polarizer of any of embodiments 334 to 344, wherein an azimuthal variation in s1/r1 is less than 1 percent.
Embodiment 351 is the thermoformed multilayer reflective polarizer of any of embodiments 334 to 350 comprising alternating polymeric layers.
Embodiment 352 is the thermoformed multilayer reflective polarizer of any of embodiments 334 to 351 being thermoformed APF.
Embodiment 353 is the thermoformed multilayer reflective polarizer of any of embodiments 334 to 351 comprising a wire grid polarizer.
Embodiment 354 is a lens having a surface curved about two orthogonal directions, and comprising the thermoformed multilayer reflective polarizer of any of embodiments 334 to 353 disposed on the surface.
Embodiment 355 is an optical stack comprising:
a first lens;
a second lens adjacent the first lens;
a quarter wave retarder disposed between the first and second lenses;
a reflective polarizer disposed on the second lens opposite the first lens; and
a partial reflector disposed on the first lens opposite the second lens,
wherein the reflective polarizer is curved about two orthogonal axes, and wherein the optical stack is an integral optical stack.
Embodiment 356 is the optical sack of embodiment 355, wherein the first lens comprises a first material and the second lens comprises a second material.
Embodiment 357 is the optical stack of embodiment 356, wherein the first and second materials are the same.
Embodiment 358 is the optical stack of embodiment 356, wherein the first and second materials are different.
Embodiment 359 is the optical stack of embodiment 355, wherein at least one of the first and second materials is a polymer.
Embodiment 360 is the optical stack of embodiment 359, wherein the first material is a first polymer and the second material is a second polymer.
Embodiment 361 is the optical stack of embodiment 360, wherein the first and second polymers are different.
Embodiment 362 is the optical stack of any one of embodiments 355, or 356, or 358 to 361, wherein the first and second lenses have different Abbe numbers.
Embodiment 363 is the optical stack of embodiment 362, wherein a difference in the Abbe numbers of the first and second lenses is in a range of 5 to 50.
Embodiment 364 is the optical stack of any of embodiments 355 to 363, wherein one of the first and second lenses has an Abbe number greater than 45 and the other of the first and second lenses has an Abbe number less than 45.
Embodiment 365 is the optical stack of any of embodiments 355 to 364, wherein one of the first and second lenses has an Abbe number greater than 50 and the other of the first and second lenses has an Abbe number less than 40.
Embodiment 366 is the optical stack of any of embodiments 355 to 365, wherein the reflective polarizer is the thermoformed multilayer reflective polarizer of any of embodiments 334 to 353.
Embodiment 367 is the optical stack of any of embodiments 355 to 366, wherein the partial reflector has an average an average optical reflectance of at least 30% in a desired plurality of wavelengths.
Embodiment 368 is the optical stack of any of embodiments 355 to 367, wherein the partial reflector has an average an average optical transmittance of at least 30% in a desired plurality of wavelengths.
Embodiment 369 is the optical stack of any of embodiments 355 to 368, wherein the partial reflector is a reflective polarizer.
Embodiment 370 is the optical stack of any of embodiments 355 to 369, wherein the desired plurality of wavelengths comprise at least one continuous wavelength range.
Embodiment 371 is the optical stack of any of embodiments 355 to 370, wherein the desired plurality of wavelengths comprises a visible range of wavelengths.
Embodiment 372 is the optical stack of embodiment 371, wherein the visible range is from 400 nm to 700 nm.
Embodiment 373 is the optical stack of any of embodiments 355 to 372, wherein the desired plurality of wavelengths comprises an infrared range of wavelengths.
Embodiment 374 is the optical stack of any of embodiments 355 to 373, wherein the desired plurality of wavelengths comprises one or more of infrared, visible and ultraviolet wavelengths.
Embodiment 375 is the optical stack of any of embodiments 355 to 374, wherein the partial reflector is a notch reflector.
Embodiment 376 is the optical stack of any of embodiments 355 to 375, wherein the desired plurality of wavelengths comprises one or more continuous wavelength ranges, and wherein at least one of the continuous wavelength ranges has a full width at half maximum of no more than 100 nm.
Embodiment 377 is the optical stack of any of embodiments 355 to 376, wherein the full width at half maximum is no more than 50 nm.
Embodiment 378 is an optical system comprising an image surface, a stop surface, and the optical stack of any of embodiments 355 to 376 disposed between the image surface and the stop surface.
Embodiment 379 is an optical system comprising an image surface, a stop surface, and the thermoformed multilayer reflective polarizer of any of embodiments 334 to 353 disposed between the image surface and the stop surface.
Embodiment 380 is the optical system of embodiment 379 further comprising:
a quarter wave retarder disposed between the image surface and the reflective polarizer; and a partial reflector disposed between the image surface and the quarter wave retarder.
Embodiment 381 is the optical system of any of embodiments 1 to 333, wherein the reflective polarizer is a thermoformed multilayer reflective polarizer according to any of embodiments 334 to 353.
Embodiment 382 is a method of making an optical stack, comprising:
providing a thermoform tool centered on a tool axis and having an external surface rotationally asymmetric about the tool axis;
heating an optical film resulting in a softened optical film;
conforming the softened optical film to the external surface while stretching the softened film along at least orthogonal first and second directions away from the tool axis resulting in a conformed optical film rotationally asymmetric about an optical axis of the conformed film, the optical axis coincident with the tool axis;
cooling the conformed optical film resulting in a symmetric optical film rotationally symmetric about the optical axis; and molding an optical lens on the symmetric optical film resulting in the optical stack.
Embodiment 383 is the method of embodiment 382, wherein the cooling step further comprises releasing the optical film from the tool.
Embodiment 384 is the method of embodiment 382 or 383, wherein the molding an optical lens step includes molding a second film onto the optical lens opposite the optical film.
Embodiment 385 is the method of embodiment 384, wherein the second film comprises a partial reflector.
Embodiment 386 is the method of any of embodiments 382 to 385, wherein the optical film comprises a reflective polarizer.
Embodiment 387 is the method of embodiment 386, wherein the optical film further comprises a quarter wave retarder.
Embodiment 388 is the method of embodiment 386 or 387, wherein the reflective polarizer is a multilayer polymeric reflective polarizer.
Embodiment 389 is the method of embodiment 388, wherein the reflective polarizer is APF.
Embodiment 390 is the method of embodiment 386 or 387, wherein the reflective polarizer is a wire grid polarizer.
Embodiment 391 is a method of making a desired optical film having a desired shape, comprising:
providing a thermoform tool having an external surface having a first shape different than the desired shape;
heating an optical film resulting in a softened optical film;
conforming the softened optical film to the external surface having the first shape while stretching the softened film along at least orthogonal first and second directions resulting in a conformed optical film having the first shape; and
cooling the conformed optical film resulting in the desired optical film having the desired shape.
Embodiment 392 is the method of embodiment 391, wherein the cooling step further comprises releasing the conformed optical film from the tool.
Embodiment 393 is the method of any of embodiments 391 or 392, wherein the desired shape is rotationally symmetric about an optical axis of the desired optical film.
Embodiment 394 is the method of any of embodiments 391 to 393, wherein the thermoform tool is centered on a tool axis and the external surface is rotationally asymmetric about the tool axis.
Embodiment 395 is the method of any of embodiments 391 to 393, further comprising molding an optical lens on the desired optical film resulting in an optical stack.
Embodiment 396 is the method of embodiment 395, wherein the molding an optical lens step includes molding a second film on the optical lens opposite the desired optical film.
Embodiment 397 is the method of embodiment 396, wherein the second film comprises a partial reflector.
Embodiment 398 is the method of any of embodiments 391 to 397, wherein the desired optical film comprises a reflective polarizer.
Embodiment 399 is the method of embodiment 398, wherein the desired optical film further comprises a quarter wave retarder.
Embodiment 400 is the method of embodiment 398 or 399, wherein the reflective polarizer is a multilayer polymeric reflective polarizer.
Embodiment 401 is the method of embodiment 400, wherein the reflective polarizer is APF.
Embodiment 402 is the method of embodiment 398 or 399, wherein the reflective polarizer is a wire grid polarizer.
Embodiment 403 is an optical system, comprising:
an image surface;
a stop surface;
a first optical stack disposed between the image surface and the stop surface and comprising:
Unless otherwise indicated, all numbers expressing quantities, measurement of properties, and so forth used in the specification and claims are to be understood as being modified by the term βaboutβ. Accordingly, unless indicated to the contrary, the numerical parameters set forth in the specification and claims are approximations that can vary depending on the desired properties sought to be obtained by those skilled in the art utilizing the teachings of the present application. Not as an attempt to limit the application of the doctrine of equivalents to the scope of the claims, each numerical parameter should at least be construed in light of the number of reported significant digits and by applying ordinary rounding techniques. Notwithstanding that the numerical ranges and parameters setting forth the broad scope of the invention are approximations, to the extent any numerical values are set forth in specific examples described herein, they are reported as precisely as reasonably possible. Any numerical value, however, may well contain errors associated with testing or measurement limitations.
Descriptions for elements in figures should be understood to apply equally to corresponding elements in other figures, unless indicated otherwise or unless the context clearly indicates otherwise. Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that a variety of alternate and/or equivalent implementations can be substituted for the specific embodiments shown and described without departing from the scope of the present disclosure. This application is intended to cover any adaptations or variations of the specific embodiments discussed herein. Therefore, it is intended that this disclosure be limited only by the claims and the equivalents thereof.
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