Patent Application
20220196981
This invention relates generally to lens systems using free form lenses, and more particularly relates to lens systems configured to provide matching of the object space to the image space according to the application for which the lens system is used. An aspect of this invention relates generally to lens systems using double plane symmetry freeform lenses, and more particularly relates to lens systems using double plane symmetry lens elements for time of flight and machine vision applications where the surface or Z-sag of the double plane symmetry surface is defined by an X-Y polynomial
The general task of an optical design is to make a perfect conjugation between the object space or plane and the image space or sensor plane, with no aberrations, distortions or other errors. Although many lenses are very good, such perfection is elusive. Even small increments can provide significant benefit.
Rotational symmetry is widely used in conventional lenses, with the field of view and the aperture stop both being rotationally symmetric. With only rare exception, this results in the final design comprising rotationally symmetric elements. An example of such a conventional design is shown in
However, most sensors—the photosensitive structures that record the image—are rectangular in shape. Thus, as shown in
Lens designs using only rotationally symmetric lenses attempt to achieve as good as possible image quality (IQ) inside the circular image space field of view. The objective includes minimizing optical aberrations such as spherical errors, coma, astigmatism, field curvature, distortion, axial and lateral aberration, color, and others. An inherent characteristic of rotationally symmetric designs is that the optical errors in the lenses are the same at all points equidistant from the center of the lens, even though points outside the area of the sensor are of no consequence to the stored image. Thus, optimal lens performance cannot be matched to the sensor's field of view, and the result is similar to that shown in
Conventional optical systems introduce perspective aberrations for wide angle, low distortion lenses. The larger the field of view and the lower the distortion, the more pronounced such perspective aberrations become. As an example, it is common for objects at the edge of a wide angle image to appear stretched. This can be seen whether the undistorted wide angle image is the result of the optics, or is digitally dewarped from a distorted image. This perspective aberration is less apparent in images that have significant distortion, and becomes more apparent as distortion is reduced.
For lenses capturing fields of view larger than 180 degrees, the image which actually reaches the typical rectangular sensor is a circle that does not fill up the whole rectangular sensor. This results in a lower resolution image than the sensor is capable of detecting. However, traditional rotationally symmetrical lenses typically are unable to create a non-circular image plane without introducing unacceptable image degradation due to aberrations.
Depending upon the application of the lens system, numerous other considerations must be taken into account, including total track length of the lens system, f-number, aspect ratio, color rendering index (CRI), chief ray angle (CRA), chief ray height (CRH), uniformity over relative illumination, and so on. Frequently, trade-offs must be made among these various considerations to provide a lens system well suited to a particular application. Rotationally symmetric lenses frequently do not offer the desired flexibility
As a result, there is a need for lens system designs that take into account the particular application when matching the object space to the image space, for example the field of view of a sensor.
The present invention provides a plurality of optical designs using free form lenses which overcome the limitations of conventional rotationally symmetric designs while also taking into consideration the particular application and the considerations associated with that application. At a fundamental level, the optical designs of the present invention permit—depending upon the application—different optical power, field of view, aberration correction, and so on to be made along the X axis than along the Y axis. To achieve this improvement, one or more optical elements having double plane symmetry or other free form characteristics is introduced into the optical system.
Depending upon the embodiment, a freeform optical element as contemplated by the present invention can have one optical surface with double plane symmetry, while the other surface is rotationally symmetrical. Alternatively, both surfaces can have double plane symmetry, or one surface may have another form of asymmetry, such as a surface defined by a Zernike or Chebyshev polynomial, or a hybrid Zernike lens element, or a lens element with a diffractive surface. Multiple such freeform optical elements are also possible in the optical system. In the case of multiple elements having double plane symmetry, the orientation of the freeform elements in the assembly has to be aligned.
Through the use of one or more such freeform optical elements, the image projected onto the sensor is better matched to the field of view of the sensor, resulting in enhanced resolution of the captured imaged and, effectively, higher resolution. This better matching offers significant benefits in many optical applications, including lens modules for smartphone cameras, virtual reality and augmented reality optics, time of flight systems, machine vision systems, security cameras, and so on. One example of the benefits of such better matching is in the virtual reality context, where dewarping an image taken with conventional rotational optics can take two days or more, while dewarping of that same image when captured with an appropriately designed free form lens system may take only a few hours.
In an embodiment of the invention, the lens design of the present invention is particularly well suited to wide angle lenses, but in some implementations is also advantageous for normal and telephoto or zoom lenses. In addition, the lens design can be implemented as a fixed focal length lens attachment to an existing lens, such as might be integrated into a smart phone. In other applications, for example non-imaging applications such as time-of-flight sensing, lens characteristics are optimized around narrow wavelength bands such as infrared or near infrared. More broadly, the present invention makes possible numerous machine vision solutions not available with conventional rotationally symmetric lenses. Such solutions can be implemented across a wide range of wavelengths, for example from 350 nanometers to 2500 nanometers. The materials used for the optical elements will typically be optimized for the relevant wavelength to ensure proper transmittance,
While double plane symmetric lenses and their associated lens systems offer excellent solutions for many optical applications, as noted above other free form lens designs offer options not available with either rotationally symmetric or double plane symmetric lens systems.
Perspective aberration can be corrected with these types of free form optical elements. As noted above, perspective aberration results in an elongation, or stretching, of the object on the image plane of the sensor. The larger the field of view and the lower the optical distortion, the more apparent such perspective aberration becomes. Traditional optical system typically results in a constant effective focal length of the optical system throughout the field of view. The use of such freeform lens elements in accordance with the present invention implements a varying effective focal length of the optical system with respect to the field of the view. The changing effective focal length can be implemented for lenses that are rotationally symmetric, as discussed below in connection with
For rotationally symmetric optical systems having a field of view larger than 180 degrees, the image plane on the sensor is a circle that does not completely fill the sensor. The freeform optical elements of the present invention allow a different effective focal length in the X-axis than in the Y-axis. This results in an image plane that is not a circle and instead may be an oval which fills up more of the rectangle sensor. This increases the effective resolution of the image. Those skilled in the art will recognize that the design characteristics of a double-plane symmetry lens in accordance with one aspect of the present invention can be described by an XY polynomial, for example. In addition, certain forms of a Zernike polynomial can also be used to describe a double-plane symmetry lens in accordance with the present invention. Further, some forms of a Chebyshev polynomial can be used to describe a double-plane symmetry lens according to an aspect of the present invention.
Using polynomial expressions such as Zernike and Chebyshev in addition to X-Y polynomials also permits the design of more complicated lens systems utilizing the benefits of free-form lenses. Such lens designs can include, but are by no means limited to: panoramic free form lens systems with a low f-number and short total track length; super-wide angle lens systems; lens systems for mobile phone applications with very short track length and very high on-axis performance; hybrid free form lens designs having an f-number in the range of 1.6 while also capable of mating to a large sensor and a short total track length; diffractive free-form lens designs for mobile phone applications; and lens designs for non-imaging applications such as 3D cameras or time of flight systems for applications in, for example, mobile, autonomous and semi-autonomous vehicles, or other machine vision applications.
The elements of these lens systems, and the lenses themselves, can be fabricated using existing techniques and can be scaled in size. Thus, in addition to the above examples, lens system designs in accordance with the present invention are suitable for a variety of applications, including security cameras, smart phone attachments, dash cams, action cams, web cams, drone cameras, front facing “selfie” cameras, and a broad variety of machine vision systems including time of flight systems. Broadly stated, aspects of the present invention can be implemented to provide significant improvement in many imaging and non-imaging sensing applications.
Additional aspects of the invention are set forth in the attached Appendix, the disclosure of which is incorporated herein for all purposes.
These and other benefits of the design of the present invention can be appreciated from the following detailed description of the invention, taken together with the appended figures.
Referring first to
Next with reference to
Thus, as can be seen from
The lens design of
The optical performance of the lens of
Similarly,
A Galileo type afocal telescopic system in accordance with an aspect of the present invention, together with its performance characteristics, are shown in
Referring particularly to
While the afocal lenses of
Traditional optical systems have a constant effective focal length throughout the whole field of view of the sensor as in
Another way that the effective focal length can change to reduce the perspective aberration using double symmetry freeform lenses is to have the same or different rates of change parallel to the X-axis and Y-axis. In this manner, lines parallel to the X-axis or Y-axis in the object plane remains straight in the image plane when captured by the sensor as show in
Free form lenses in accordance with different aspects of the invention can also provide significant benefits when compared with conventional, rotationally symmetric lens systems. As discussed in greater detail below, embodiments reflecting different aspects of the present invention can achieve ultra-wide, or panoramic, fields of view, or can provide a lens system with high MTF as well as high Strehl while at the same time achieving small track length, or can provide a lens system utilizing a hybrid free form lens and suitable for mobile applications with a very low f-number and short track length configured to be mated to a large sensor, or can provide a lens system suitable for mobile applications with fewer lens elements and utilizing a free form lens with a diffractive surface defined by a Zernike polynomial, or can provide a non-imaging lens system suitable for time-of-flight applications and having a wide field of view with relatively uniform illumination, low stray light and low f-number at a chosen frequency such as the infrared or near-infrared range.
Turning next to
Thus, the embodiment shown in
where the coefficient CV is the curvature, CC is the conic constant, r is the radial coordinate, Zi is the Zernike polynomial and the coefficients asi are the corresponding Zernike coefficients. Those skilled in the art will recognize that there are several types of Zernike polynomials in the literature, including Standard Zernike, Fringe Zernike, Extended Fringe Zernike, etc. For the sake of clarity of communication, and to best conform with currently available experimental measurement and machines, the form of Zernike polynomial used herein is the fringe Zernike polynomial which has a total of 37 terms, the same as the Zernike polynomial implemented in Code V software. These 37 terms are defaulted in the simulation package, OSLO [Optics Software for Layout and Optimization, from Lambda Research.] The polynomial contains essentially two variables, radial coordinate ρ and the angle θ
Mathematically, the Zernike polynomials Z follow the equations
Z
n
m(r,θ) =Rnm(r)sin(mθ)
and
Z
n
−m(r,θ)=Rnm(r)cos(mθ)
where the radial polynomial R follows the equation
and n=0,1,2, . . . is the degree of the Zernike polynomials and m=−n ton is the order.
The table, below, provides an illustration of the implementation of the Zernike polynomials used in various embodiments of the present invention.
The main lens characteristics of the lens system of
The Zernike surface on the sixth element 2530 is characterized by the coefficients in the following table, where the higher numbered coefficients 15-37 are all 0.
A panoramic lens system designed to create a camera-quality image will preferably have a high MTF, high Strehl, low stray light and low f-number. For the embodiment shown in
In addition, for implementations such as mobile, where available volume is limited, low track length is highly desirable. By the use of a free form lens a tilted optical axis, as provided by the Zernike surface detailed above, enables such lens characteristics to be achieved. Those same characteristics cannot be achieved by conventional rotationally symmetric lenses, even when aspheric elements are incorporated into the lens system.
Some, though not all, of the desirable characteristics of the above-described panoramic lens system can be achieved with the use of a free form lens having double plane symmetry. Two types of double plane symmetry can be used, either non-rotated or rotated, each of which uses only four Zernike terms. The below table illustrates one example, where the Zernike items not listed all have a coefficient value of 0.
If non-rotated, the Zernike polynomial can be generalized to f(ρ)*cos(2*θ)+g(ρ), while the rotated version can be generalized to f(ρ)*sin(2*θ)+g(ρ) where the additional g(ρ) term is used to provide correction for distortion, piston, defocus/field curvature, and/or first, second, third, fourth order spherical aberration. In the foregoing generalized equations, f(ρ)=sqrt(x2+y2). For embodiments not using double plane symmetry, the Zernike equations are similar but the (2*θ) terms will typically be replaced with (3*θ), (4*θ), or (n*θ).
Referring next to
The free form element 2700, and particularly its rear free form surface 2700B, can be better appreciated from
From the above coefficients it can be appreciated that the free form surface on element 2700 is only slightly asymmetrical. The major characteristics of the lens system of
Notable among the above characteristics is the extremely short track length together with a high Strehl ratio, close to the diffraction limit, as well as a high MTF. It will also be appreciated that a high Strehl ratio implies that the lens system is relatively tolerant of alignment error during assembly. Shown in
Referring next to
Exemplary Zernike coefficients for the surface of the portion 2915B can be seen in the below table. On-axis wavefront error for the embodiment of
Referring next to
The first element 3100 can be better appreciated from
The corresponding coefficients of the exemplary Zernike surface can be seen in the table below.
The diffractive surface on the free form surface follows a phase distribution in even power of the radial coordinate, r, according to the following equation.
where the corresponding coefficients are:
Turning next to
Turning next to
The machine vision lens illustrated in
Turning next to
Unlike most imaging applications, TOF applications typically include a light source. In such TOF applications, and many machine vision applications, providing a light source that enables good relative illumination across the field of view becomes important. While a lens system for the camera in a mobile phone operates acceptably with relative illumination at the edge of only 20% or 30% of the on-axis illumination, TOF applications require better off axis performance, and relative illumination is preferably at least 50% of axial illumination.
Stray light is another characteristic where TOF applications impose tighter requirements. While a mobile phone camera operates acceptably with a reduction ratio of 1.0×10{circumflex over ( )}−6, stray light for machine vision and TOF applications preferably is at least 1×10{circumflex over ( )}−7. Likewise, while the f-number for a mobile phone camera can be 1.8, or 2.0, 2.2, or even higher, the f-number for TOF applications is generally smaller, in the range of 1.0 to 1.6. The f-number for other types of machine vision applications can vary from the low f-number s desired for TOF applications to the higher f-numbers suitable for phone cameras, or even higher.
Still further, maintaining good optical performance for off-axis objects (or field points) is desirable for machine vision and TOF applications. It will also be appreciated by those skilled in the art that many, even all, of the foregoing desirable optical characteristics are equally desirable for other types of lenses, not just machine vision and TOF lenses.
Referring again to
It will be appreciated by those skilled in the art that the various lens designs disclosed herein can be scaled up to match sensor size. Thus, while the sensors in some embodiments are shown as, approximately, one-fourth inch, one-third inch, or one-half inch, the invention can be equally well adapted to smaller or larger sensors, such as one-sixth inch sensors, one inch sensors, full frame sensors, or even larger. In terms of pixel count, such sensors can range from less than the eight megapixels typical of some cell phone cameras, all the way to fifty-five or more megapixels typical of some high end DSLR cameras.
Further, while fringe Zernicke polynomials have been described for ease of illustration of the invention, numerous other approaches using Zernike polynomials offer usable alternatives, as do Chebyshev and Extended X-Y polynomials.
Turning next to
where z, x, y are cartesian coordinates of the surface, c is surface curvature, r is the surface radial coordinate, k is the conical constant, Ai are polynomial coefficients, Σ(x,y) are polynomials.
Examples of Σ(x,y) are: X2Y2, X4Y6, X8Y4, etc. Conical constant k in the illustrated embodiment is 0, but can be of any value as long as the term under the square root is greater than or equal to zero.
The above equation gives the freedom to separate x and y coordinates, and to define different coefficients for different XOZ and YOZ planes of the system.
In this case the lens system of
As noted above, lens systems for mobile phone cameras typically operate with different constraints than lens systems for time of flight applications. More specifically, key characteristics of such camera lens systems are low distortion, reasonable field of view but not necessarily wide angle, acceptable f-number where lower is desirable but not always critical, and, perhaps most important, total track length. Typically, the total track length must be less than the Z-height of the phone so that the lens module does not stick out above the phone casing. Thus, shown in the Table, below, are key parameters for the lens system illustrated in
Still referring to
The double plane symmetry front and rear surfaces 3530A-B of element 3525 are defined by the Extended X-Y polynomial shown hereinabove, where the constants have the same meaning. The coefficients Ai thus characterize the double plane symmetry surfaces 3530A-B of element 3525, and can be appreciated from
In general, the following specifications will permit the design of alternative embodiments to the illustrated lens system, but will still define a similar type of lens suitable for use in a visible light mobile phone camera: F-number range is in the range of 1.4 -2.0 (current value is 1.4); the diagonal FOV typically ranges between 45-100 degrees (current value is 75 degrees); optical distortion is preferably low, in the range of 0.5-10% (current value is 2%), but can be allowed to increase as a trade-off against a lower f-number; the ratio of the largest diameter element to optical total track length is in the range of 0.5-1 (Current value ˜0.95); and the ratio of Lens Focal Length to 1st element focal length is in the range of 0.3-2 (Current value ˜0.78).
Those skilled in the art can, given the teachings herein, appreciate that a new and novel design for a wide range of improved lens systems utilizing free form lens elements, including a low distortion lens having at least one element with double plane symmetry usable in a Kepler type telescopic lens, a Galileo type telescopic lens, a wide angle lens, various lenses suitable for mobile use, and lens systems particularly suited for use in machine vision applications, including some for time-of-flight systems. While various embodiments of the invention have been disclosed in detail, it will be appreciated that the features of the exemplary embodiments discussed herein are not to be limiting, and that numerous alternatives and equivalents exist which do not depart from the scope of the invention. As such, the present invention is to be limited only by the appended claims.
This invention relates generally to lens systems using double plane symmetry freeform lenses, and more particularly relates to lens systems using double plane symmetry lens elements for time of flight and machine vision applications where the surface or Z-sag of the double plane symmetry surface is defined by an X-Y polynomial.
The general task of an optical design is to make a perfect conjugation between the object space or plane and the image space or sensor plane, with no aberrations, distortions or other errors. Although many lenses are very good, such perfection is elusive. Even small increments can provide significant benefit.
Rotational symmetry is widely used in conventional lenses, with the field view and the aperture stop both being rotationally symmetric. With only rare exception, this results in the final design comprising rotationally symmetric elements. However, most sensors—the photosensitive structures that record the image—are rectangular in shape. Thus, the image space created by a rotationally symmetric lens creates a circular field of view, while the sensor that records the image is a rectangle.
An inherent characteristic of rotationally symmetric designs is that the optical errors in the lenses are the same at all points equidistant from the center of the lens, even though points outside the area of the sensor are of no consequence to the stored image. Thus, optimal lens performance cannot be matched to the sensor's field of view.
Optics for machine vision applications span a wide range of optical solutions. One subset of machine vision is time of flight (TOF). TOF applications calls for optics that have low f-number, wide field of view, good rejection of stray light, narrow wavelength band, relative uniformity upon illumination, among other considerations, but can tolerate optical distortion. Machine vision applications, viewed more broadly, often are best served by lens systems suitable for creating a planar image, such as those found in smartphone cameras.
Rotationally symmetric lens systems typically cannot meet the requirements for matching object space to the image space defined by a rectangular sensor. This is particularly true when taking into account the above considerations. As a result, there is a need for lens system designs that take into account the particular application when matching the object space to the image space, for example the field of view of a sensor.
The present invention provides designs for optical lens systems using at least one double plane symmetry lens element to overcome the limitations of conventional rotationally symmetric designs while also taking into consideration the particular application and the considerations associated with that application. The surface or Z-sag of the double plane symmetry lens elements are defined by X-Y polynomials. More particularly, embodiments of the present invention provide an improved time of flight [TOF] lens system, and an improved visible light machine vision lens system.
Depending upon the embodiment, a freeform optical element as contemplated by the present invention can have one optical surface with double plane symmetry, while the other surface is rotationally symmetrical. Alternatively, both surfaces can have double plane symmetry. Multiple such freeform optical elements are also possible in the optical system. In the case of multiple elements having double plane symmetry, the orientation of the freeform elements in the assembly can be aligned.
Through the use of one or more such double plane symmetry optical elements, the image projected onto the sensor is better matched to the field of view of the sensor, resulting in enhanced resolution of the captured imaged and, effectively, higher resolution.
The elements of these lens systems, and the lenses themselves, can be fabricated using existing techniques and can be scaled in size. These and other benefits of the design of the present invention can be appreciated from the following detailed description of the invention, taken together with the appended figures.
APPENDIX
APPENDIX
APPENDIX
APPENDIX
APPENDIX
APPENDIX
Hereinafter, within following Detailed Description of the Invention that forms part of this APPENDIX, the foregoing APPENDIX
Turning first to
Unlike most imaging applications, TOF applications typically include a light source. In such TOF applications, and many machine vision applications, providing a light source that enables good relative illumination across the field of view becomes important. While a lens system for the camera in a mobile phone operates acceptably with relative illumination at the edge of only 20% or 30% of the on-axis illumination, TOF applications require better off-axis performance, and relative illumination can be at least 50% of axial illumination.
Stray light is another characteristic where TOF applications impose tighter requirements. While a mobile phone camera operates acceptably with a reduction ratio of 1.0×10−6, stray light for machine vision and TOF applications can be at least 110 −7. Likewise, while the f-number for a mobile phone camera can be 1.8, or 2.0, 2.2, or even higher, the f-number for TOF applications is generally smaller, in the range of 1.0 to 1.6. The f-number for other types of machine vision applications can vary from the low f-number s desired for TOF applications to the higher f-numbers suitable for phone cameras, or even higher. Still further, maintaining good optical performance for off-axis objects (or field points) is desirable for machine vision and TOF applications.
For most time of flight applications, and also for many machine vision applications, low stray light is very important as well as low f-number. In addition, while some machine vision applications do not require a wide field of view (FOV), a wide FOV can be used in many machine vision and TOF applications. For implementations using a wide field of view, very good relative illumination is also desirable. While “normal” cameras such as those in mobile phones are intended to create a planar image, TOF applications have a different objective. In TOF applications, the objective is to obtain spatially correlated data representative of every object in the field of view, or what can be referred to as a depth map. To do so, TOF systems create synchronized signals over every pixel such that the time difference of light illuminating objects in the field of view and being reflected back to the sensor can be accurately determined, thus yielding the desired spatial information about those objects in the field of view.
Referring again to
The Double Plane Symmetry surface is described through an Extended Polynomial equation:
where z, x, y are cartesian coordinates of the surface, c is surface curvature, r is the surface radial coordinate, k is the conical constant, Ai are polynomial coefficients, Σ(x,y) are polynomials.
Examples of Σ(x,y) are: X2Y2, X4Y6, X8Y4, etc. Conical constant k in the illustrated embodiment is 0, but can be of any value as long as the term under the square root is greater than or equal to zero.
The above equation gives the freedom to separate x and y coordinates, and to define different coefficients for different XOZ and YOZ planes of the system.
Exemplary values for coefficients Ai for the lens system of
Values for coefficients Ai for other embodiments can vary significantly from design to design. In general, the following specifications will permit the design of alternative embodiments to the illustrated lens system, but will still define a similar type of lens suitable for infrared time of flight applications: F-number in the range of 1.0-2.0 (current value is 1.3); diagonal FOV in the range of 130-180 degrees (current value is 160 degrees); optical distortion is less important in this application, can be corrected generally; ratio of largest diameter element to optical Total Track Length is in the range of 0.25-0.8 (Current value ˜0.58); ratio of Lens Focal Length to third element focal length is in the range of 0.3-1 (Current value ˜0.4). As for the freeform coefficients: second order coefficients (e.g. X2Y0) define paraxial (close to optical axis) properties of the optical lens—focal length and etc., while all the other higher orders are used for different aberration correction. Those skilled in the art will recognize that the freeform coefficients Ai presented in the table of
Turning next to
As with the embodiments shown in
In general, the following specifications will permit the design of alternative embodiments to the illustrated lens system, but will still define a similar type of lens suitable for use in a visible light machine vision camera: f-number range is in the range of 1.5-1.9 (current value is 1.8); the diagonal FOV typically ranges between 75-120 degrees (current value is 120 degrees); optical distortion is preferably low, in the range of 0.5-10% (Current value is 5%), but can be allowed to increase as a trade-off against a lower f-number; the ratio of the largest diameter element to optical Total Track Length is in the range of 0.5-1 (Current value ˜0.66); and the ratio of Lens Focal Length to 4th element focal length is in the range of 0.3-2 (Current value ˜0.38).
Those skilled in the art can, given the teachings herein, appreciate that multiple embodiments of the invention have been disclosed herein, specifically an infrared time of flight lens system, and a low f-number lens system for use in visible light machine vision applications. Each embodiment takes advantage of the benefits of a lens element with at least one surface having double plane symmetry as defined by an X-Y Polynomial. It will be appreciated that numerous alternatives and equivalents exist which do not depart from the scope of the invention. As such, the present invention is to be limited only by the appended claims.
Lens systems for use in infrared time of flight applications, and visible light machine vision application, each with at least one surface of a lens element having double plane symmetry as defined by an X-Y Polynomial. The lens elements of the invention can be implemented using existing manufacturing techniques.
This application is a conversion of U.S. Patent Application Ser. No. 62/748,961, filed Oct. 22, 2018, having the same title as the present application, and further is a conversion of U.S. Patent Application Ser. No. 62/748,976, also filed Oct. 22, 2018, entitled Low F-Number Optical System Utilizing Double Plane Symmetry Defined by X-Y Polynomial. Further, this application is a continuation-in-part of U.S. patent application Ser. No. 15/958,804 filed on Apr. 20, 2018, entitled Low Distortion Lens Using Double Plane Symmetric Element, which in turn is a continuation-in-part of PCT Application PCT/IB2016/001630 having International Filing Date 20 Oct. 2016, which in turn claims the benefit of U.S. Patent Application 62/244,171, filed 20 Oct. 2015. The present application claims the benefit of priority of each of the foregoing applications, all of which are incorporated herein for all purposes.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/US19/57467 | 10/22/2019 | WO | 00 |
| Number | Date | Country | |
|---|---|---|---|
| 62748961 | Oct 2018 | US | |
| 62748976 | Oct 2018 | US | |
| 62244171 | Oct 2015 | US |
| Number | Date | Country | |
|---|---|---|---|
| Parent | 15958804 | Apr 2018 | US |
| Child | 17236871 | US | |
| Parent | PCT/IB2016/001630 | Oct 2016 | US |
| Child | 15958804 | US |
