Patent Grant
7413306
The present invention is generally related to optical devices, systems, and methods, and in one embodiment provides a fluid lens capable of being adjusted in spherical and/or cylindrical power so as to allow, for example, correction of refractive errors of the human eye.
Refractive errors of the human eye are measured in a variety of ways, including both subjective and objective approaches. Subjective measurements of the eye may be made by placing corrective lenses or a corrective optical system before the eye and conducting a controlled test of the resulting corrected vision. These eye tests are commonly used to identify a sphero-cylindrical correction that provides improved vision to a subject while that subject is reviewing a suitable target image.
When conducting subjective refraction measurements, a series of individual trial lenses may be positioned before the eye of the test subject. In many subjective refraction tests, the subject looks through a phoropter, an instrument having a bank of lenses. The lenses of the phoropter can be positioned sequentially in front of the eye, with the subject often choosing between two or more alternative lens arrangements so as to provide the most improved visual acuity. Although some modern phoropters have motorized mechanisms that move or select the lenses, most remain manual devices.
In addition to the subjective measurements of human refractive errors, there are a variety of structures intended to produce objective measurements of the human eye. Objective measurements may be made by a variety of automatic refractors, for example. These instruments often have variable correcting optical trains that can correct either spherical errors alone, or that can correct sphero-cylindrical errors of the eye throughout an adjustment range. Automatic refractors alter the spherical (and often the cylindrical) power of an optical train using motors, gears, slides, bearings, pulleys, and/or the like. These moving components tend to make automatic refractors complex, bulky, susceptible to wear and damage, and quite expensive.
In light of the above, it would be advantageous to provide improved optical devices, systems, and methods. It would be particularly beneficial if these improvements allowed adjustment, correction, and/or measurement of spherical, cylindrical, toroidal, and possibly other errors, particularly for measurement of errors of the human eye. It would be particularly advantageous if these improvements could be realized without relying on a large number of alternative lenses and without the motors, gears, slides, bearings, pulleys, and other moving parts of known eye measurement systems.
The present invention generally provides improved optical devices, systems, and methods. Embodiments of the present invention can produce sphero-cylindrical, cylindrical spherical, and other lens shapes throughout a range of powers and cylindrical axes. The invention often makes use of fluid focus lenses employing electrical potentials to vary the shape of a fluid/fluid interface. The fluid/fluid interface between two immiscible fluids having differing indices of refractions can be altered by varying a position and/or angle of the interface relative to a surrounding container wall. In some embodiments, the container may have the form of a rectangular prism, with a cylindrical lens being formed by applying a potential to opposed side walls of the prism, optionally with a different potential applied to end walls of the prism. Alternative embodiments may make use of a substantially cylindrical container with a series of electrodes distributed circumferentially about an optical path, so as to allow both spherical, cylindrical, and other powers to be varied. Advantageously, no moving parts (other than the fluids) may be employed, even when providing independently variable spherical power, cylindrical power, and cylindrical orientation throughout the full range of human eye vision adjustment.
In a first aspect, the invention provides an optical apparatus comprising at least one housing defining at least one opening having an optical path therethrough. A plurality of fluids are disposed in the at least one opening so as to define one or more fluid/fluid interfaces. An electrical potential source is coupled to the at least one opening. The source is configured to vary at least one electrowetting potential so as to change a cylindrical orientation of the one or more fluid/fluid interfaces in response to a first input.
The source may be configured to alter the at least one electrowetting potential so as to change a cylindrical power in response to a second input, and/or to alter the at least one electrowetting potential so that the one or more fluid/fluid interfaces vary in spherical power in response to a third input. Preferably, the spherical power may be varied throughout a range from at least about minus 20.0 diopters to at least about plus 20.0 diopters so as to accommodate substantially the full range of human eye spherical aberrations. Similarly, the apparatus will preferably have cylindrical powers which can be varied throughout a range from at least minus 6.0 diopters to at least plus 6.0 diopters, with the cylindrical orientation variable throughout a range of ate least about 90°; optionally being at least about 180°, so that the optical apparatus can compensate for substantially the full range of cylindrical aberrations in the human eye.
Optionally, the at least one housing may define a first opening with a first fluid/fluid interface therein and a second opening with a second fluid/fluid interface therein. The first and second openings may each comprise a rectangular cross section relative to the optical path. Varying of a first electrowetting potential may effect changes in a first variable cylindrical power of the first fluid/fluid interface, the first variable cylindrical power having a first cylindrical orientation extending laterally across the optical path. Varying a second electrowetting potential may effect changes in a second variable cylindrical power of the second fluid/fluid interface, the second variable cylindrical power having a second cylindrical orientation extending laterally across the optical path. The first cylindrical orientation may be angularly offset from the second cylindrical orientation about the optical path.
The at least one housing may define a third opening with a third fluid/fluid interface therein, the third opening comprising a rectangular cross section. Varying of a third electrowetting potential may effect changes in a third variable cylindrical power of the third fluid/fluid interface disposed within the third opening. The third variable cylindrical power has a third cylindrical orientation extending laterally across the optical path, the third cylindrical orientation being angularly offset from the first and second cylindrical axes about the optical path. For example, the first cylindrical orientation may be substantially perpendicular to the second cylindrical orientation, while the third cylindrical orientation is angularly offset from the first cylindrical orientation by about 45°.
In many embodiments, first and second electrodes may be disposed along opposing sides of the first opening. Similarly, third and fourth electrodes may be disposed along opposing sides of the second opening, while fifth and sixth electrodes are disposed along opposing sides of the third opening. The electrodes along opposing sides of each opening may be coupled electrically so that a common electrowetting potential can be easily applied to both sides of each opening. Varying the electrowetting potential along both sides of the opening can controllably vary angles defined between the sides of the rectangular opening and the fluid/fluid interface within that opening, and/or vary positions of the fluid/fluid interface along the container wall adjacent the potential. This can be used to variably control the cylindrical power of the fluid/fluid interface, particularly where ends of the rectangular opening (connecting the opposed sides) are configured to maintain a 90° angle between the fluid/fluid interface and the end surface, such as by providing an end electrode at an appropriate electrowetting potential for each end of each rectangular opening.
In some embodiments, the housing may comprise a wall disposed around the optical path, and may further include a plurality of conductors distributed circumferentially about the wall. The conductors may define an electrode array, with each electrode of the array disposed circumferentially between (and electrically separated from) two adjacent electrodes of the array. There will often be five or more electrodes in this circumferential array, optionally being eight or more electrodes, and in some embodiments being ten or more electrodes. The power source may apply a circumferential series of potentials about the optical path. The series of potentials may comprise a substantially sinusoidal pattern of DC voltages. The power source may be configured to vary an amplitude of the sinusoidal pattern in response to the second input. The power source may also be configured to rotate the sinusoidal voltage pattern about the optical path in response to the first input. Preferably, the power source is configured to vary an average voltage of the pattern in response to a third input so as to alter a spherical power along the optical path.
In many embodiments, the optical apparatus may vary the cylindrical power and the cylindrical orientation by affecting movement of the fluids within the at least one housing and without affecting other movement of the apparatus. The power source may comprise a processor, with the processor determining a plurality of electrowetting potentials in response to the first and second inputs. The processor may further determine the electrowetting potentials in response to a third input so as to vary a spherical optical power along the optical path. The at least one fluid/fluid interface may optionally be capable of acting as a pure cylindrical lens without significant spherical power along the optical path.
In another aspect, the invention provides a fluid cylindrical lens apparatus comprising a first housing having a first prismatic opening with an optical path therethrough. The first opening has a first surface and a second surface, the second surface being offset from the first surface with an optical path therebetween. A plurality of fluids are disposed in the opening so as to define a first fluid/fluid interface traversing the first and second surfaces. An electrical potential source is coupled to the first and second surfaces to apply a first variable potential thereto so as to change a first variable cylindrical power of the fluid/fluid interface along the optical path.
The first variable cylindrical power will often have a first orientation that traverses end surfaces of the first opening. The potential source may apply another potential to the end surfaces, with the other potential being different than the first potential, particularly when the first cylindrical power is different than zero. The fluid cylindrical lens apparatus may also include a second housing having a second opening with a third surface and a fourth surface with the optical path therebetween. A plurality of fluids may be disposed in the second opening so as to define a second fluid/fluid interface. The power source may be coupled to the third and fourth surfaces so as to apply a second variable potential thereto that changes the second variable cylindrical power. The second variable cylindrical power may have a second orientation which is angularly offset about the optical path relative to the first orientation. A third housing may have a third opening. The third opening may have fifth and sixth surfaces with the optical path again therebetween. Once again, a plurality of fluids may be disposed in the third opening so as to define a third fluid/fluid interface. The potential source may be coupled to the fifth and sixth surfaces to apply a third variable potential so as to change a third cylindrical power having a third orientation. The third orientation may be angularly offset from the first and second axes, thereby allowing the apparatus to vary spherical power along the optical path, cylindrical power along the optical path, and cylindrical orientation about the optical path.
In yet another embodiments, the invention provides an optical apparatus comprising at least one housing defining at least one opening having an optical path extending axially therethrough. A plurality of fluids are disposed in the at least one opening so as to define at least one fluid/fluid interface. A plurality of electrical conductors are distributed circumferentially about the optical path. An electrical potential source is coupled to the electrical conductors so as to simultaneously apply a plurality of differing electrowetting potentials thereto. The source is configured to alter the at least one fluid/fluid interface so as to controllably vary at least a sphero-cylindrical power along the optical path.
Optionally, the housing may comprise a substantially cylindrical wall, prismatic, or other shaped wall extending around the optical path. The electrical conductors may be distributed circumferentially about the wall. There will often be four or more electrical conductors, often being five or more electrical conductors, and in many cases, eight or more electrical conductors distributed circumferentially about the wall. The source may be configured to alter the fluid/fluid interface so as to vary a spherical power along the optical path, and optionally, a cylindrical orientation of the cylindrical power. Each electrical conductor may extend along the optical path, and a spherical power along the optical path may be varied by varying the average potential applied to the electrical conductors. In addition to providing cylindrical and spherical powers, such a structure may also provide other anamorphic lens shapes. The potentials may differ circumferentially, and some embodiments may employ a plurality of openings, each having a fluid/fluid interface, so that not all of the differing potentials need be applied about the same opening.
In yet another aspect, the invention provides a phoropter or automatic refractor comprising at least one housing defining at least one opening having an optical path therethrough. A plurality of fluids are disposed in the at least one opening so as to define one or more fluid/fluid interfaces. A plurality of electrical conductors are disposed near the at least one opening, and an electrical potential source is coupled to the electrical conductors so as to apply at least one electrowetting potential. The source is configured to alter the one or more fluid/fluid interfaces so as to controllably vary one or more characteristics selected from among: a spherical power along the optical path; a cylindrical power along the optical path; and a cylindrical orientation along the optical path. In many embodiments, the electrical potential source will be configured to alter two or more of the characteristics, in many cases all three of the characteristics.
In yet another aspect, the invention provides a fluid lens optical method comprising configuring one or more fluid/fluid interfaces by applying at least one electrowetting potential so as to change a cylindrical orientation along an optical path.
In many embodiments, the one or more fluid/fluid interfaces is reconfigured by changing the at least one potential so that a cylindrical power can also be changed. A spherical power along the optical axis may also be provided by changing the at least one potential. The cylindrical power, cylindrical orientation, and spherical power may be controllably varied by moving fluids in response to the at least one potential, and without other movement along the optical path.
In yet another aspect, the invention may provide a fluid lens optical method comprising configuring at least one fluid/fluid interface traversed by an optical path by simultaneously applying a plurality of circumferentially differing electrowetting potentials about the optical path. The potentials may be applied so as to simultaneously provide a first curvature of the at least one fluid/fluid interface and a second curvature of the at least one fluid/fluid interface. This may optionally provide a variable sphero-cylinder lens using a single fluid/fluid interface, or using a plurality of fluid/fluid interfaces.
In yet another aspect, the invention provides an optical apparatus comprising at least one housing defining at least one opening having an optical path therethrough. A plurality of fluids are disposed in the at least one opening so as to define at least one fluid/fluid interface. An electrical potential source coupled to the at least one opening is configured to simultaneously apply a plurality of electrowetting potentials so that the at least one fluid/fluid interface controllably varies in spherical and cylindrical power.
The present invention generally provides improved optical devices, systems, and methods. The invention often makes use of fluid lenses, particularly for varying a cylindrical axis or orientation, cylindrical power, spherical power, sphero-cylindrical characteristics, and/or other optical properties of a fluid/fluid interface. The relatively low cost, small size, light weight, and ease of manufacture of the fluid lenses described herein may allow common optical devices (such as binoculars, telescopes, cameras, microscopes, endoscopes, and even eye glasses) to compensate for cylindrical and/or spherical error of a user's eye by including these fluid lenses therein. While the devices and methods of the present invention are particularly well suited for measuring and/or compensating for standard aberrations of the human eye, they may also find applications in optical recording techniques, optical communications, optical signal processing and telecommunications, digital cameras, camera phones, endoscopes, light and image projection, and the like.
Fluid lenses may comprise two immiscible fluids of differing refractive index. One fluid, for example, may be an electrically conducting aqueous solution, while the other may comprise an electrically non-conducting oil. The fluid lenses may be contained in one or more housings, with internal surfaces of the housing being coated with a hydrophobic coating. In general terms, the molecules of a liquid attract each other. An equal attractive force in all directions balances the interactions of a molecule in the bulk of each liquid, while the molecules on the surfaces of the liquid experience an imbalance of forces, resulting in the presence of energy at the interfaces. This energy generates an interface tension. Hydrophobic coatings may increase the interface tension of at least one of the fluids, for example, changing a contact angle between the fluid/fluid boundary and the hydrophobic coating. This interface tension can also limit contact between the hydrophobic coating and the aqueous solution, causing the aqueous solution to form itself into a mass along one end of the container and the fluid/fluid interface to curve in a controllable manner. Hence, this curving fluid/fluid interface may act as a lens along an optical path traversing the interface.
The shape of the fluid/fluid interface of a fluid lens may be adjusted by applying one or more electrical fields across the hydrophobic coating such that it becomes less hydrophobic. This process is sometimes referred to as “electrowetting” and may electrically induce changes in the static contact angle between the fluid/fluid interface and the adjacent surface of the container wall. By altering the boundary conditions of the fluid/fluid interface along the wall, the electrical potential can drive the interface to a different boundary configuration, and also to a new overall shape with desired refractive properties throughout the fluid/fluid interface. These changes in the interface shape may be induced by changing the static contact angle between a solid container wall and the fluid/fluid boundary, which may in turn be induced by altering the relative interface tensions. Once the boundary conditions are set by appropriate electrowetting potential(s) along the container walls, the rest of the surface may assume a shape to minimize the surface energy associated with the interface tension, or to minimize surface area of the interface.
Embodiments of the invention may control the refractive properties of fluid lenses by locally varying the boundary conditions of the fluid/fluid interface about a perimeter of the fluid/fluid interface. The boundary conditions, and specifically the static contact angle of the fluid/fluid interface against the container wall, may optionally be determined using a wetting coefficient K, where K=cos α (α being the static contact angle between the fluid/fluid boundary and the container wall) as follows:
in which σff is the interface tension between the two fluids, σsfp is the interface tension between the more polar of the two fluids and the solid container wall, and σsfn is the interface tension between the non-polar fluid and the solid container wall. Liquids (such as water) having relatively strong intermolecular interactions (and thus high interface tensions) are referred to as polar liquids, while liquids having lower surface tensions are referred to as non-polar. The immiscible liquids A and B in the fluid lenses described herein will often include one relatively polar fluid and one relatively non-polar fluid, which is less polar than the polar fluid.
When the electrical field between the surface of the container and the immiscible fluids changes, the interface tension between the solid container wall and the polar fluid may change significantly. The same change in electrical field may induce less change (or even no change or a change in the opposite direction) in the interface tension between the solid container wall and the non-polar fluid. This difference may, at least in part, be related to the imbalance of force on the surface molecules. The polar liquid interface molecules generally induce greater forces when surrounded by similar molecules on one side and something different on the other side. By changing the electrostatic field, the relatively strong attraction of these surface molecules to the polar fluid can be changed, thereby changing the magnitude of the interface tension. The non-polar molecules along the container wall will be effected less by the same change in electrostatic field, so that the interface tension of the non-polar fluid doesn't change as much. As can be seen in the above equation, the numerator of the equation (and hence the wetting coefficient) can undergo a change in magnitude or even sign if one interface tension changes while the other does not (or changes less, or even in an opposite direction). It should be noted, however, that embodiments of the invention need not be tied to a particular theory of operation, and that alternate methodologies may be used to determine the relationship between the applied electrical potential, the fluid characteristics, and the optical properties of the lens, including empirical approaches.
As a result of the change in electrical potential (and hence in static contact angle) and the constrained quantities of fluids and space in the container, the aqueous solution may (for example) increasingly wet the walls of the fluid lens container, altering the location of the fluid/fluid boundary along the container walls as well as the radius of curvature of the fluid/fluid interface (and hence the power of the lens). By increasing an applied electrical field the fluid/fluid interface of the fluid lens can be controllably varied from convex, through completely flat or plano, to concave. The fluid lenses described herein typically will (though they need not necessarily) change from positive to negative power as the interface curvature varies from concave to convex. However, by adding a biasing spherical lens of fixed power, the center of the refracting range may be set at will to any chosen value.
As more fully described in PCT publication WO 03/069380, the full disclosure of which is incorporated herein by reference, one of the two non-immiscible liquids in a fluid lens may comprise an electrically insulating liquid such as silicone oil or an alkane. The electrically conducting liquid may comprise water containing a salt solution. The two liquids preferably have a sufficiently equal density so that the lens functions independently of orientation and without significant gravitational effects between the two liquids. Typical refractive indices of the insulating fluid may be between about 1.25 and 1.60. Typical indices of refraction of the conductive solution may vary from about 1.33 to about 1.48. In many embodiments, an electrical conductor or electrode will be in fluid contact with the conductive fluid within the container of the fluid lens.
The fluid lenses will often be disposed in containers having cross-sectional dimensions (relative to the optical path) of less than about 1 cm, often being less than about 5 mm. Lengths along the optical path for each container may also be less than about 1 cm, often being less than about 5 mm.
Referring now to
Apparatus 12 generally has an optical path 14 providing optical coupling between eye E and test image 10. In addition to ocular optics 16, objective optics 18, and other optional optical components such as apertures and the like, apparatus 12 includes a fluid lens assembly 20 that provides variable spherical and/or cylindrical focus capabilities so as to compensate for the regular astigmatism aberrations of eye E. An eye refractor or other device having such a variable focus sphero cylindrical correction system is often used with a relaying lens system where the action of the sphero cylindrical corrector is relayed into the plane of the pupil of the eye of the subject.
The configuration of at least one fluid/fluid interface is varied by altering an electrowetting potential applied to the fluid lens assembly 20 from a potential source 22. More specifically, source 22 is configured to provide a plurality of electrical potentials which vary in response to a spherical power input 24, a cylindrical power input 26, and a cylindrical orientation input 28. In response to these inputs the processor 30 of source 22 configures the electrowetting potentials so as to generate an overall desired spherical power, cylindrical power, and cylindrical orientation within fluid lens assembly 20 and/or apparatus 12 so as to compensate for the refractive errors.
In some embodiments, the only movable elements along optical path 14 of apparatus 12 are the fluids within the fluid lenses of fluid lens assembly 20. In other embodiments, at least a portion of the defocus and/or astigmatism of eye E may be compensated for using one or more selectable lenses, movement of one or more lenses, and the like. For example, a relatively simply spherical fluid lens such as the FluidFocus™ fluid lens developed by Royal Philips Electronics of the Netherlands might be combined with a Stokes cross cylinder lens assembly so as to provide a full variable focus sphero-cylindrical corrector. While relying on the fluid lens to provide adjustability for spherical power may provide some advantages over prior phoropters and/or automatic refractors, the complexity, cost, and bulkiness of the mechanical Stokes cross-cylinder lens assembly (or another mechanically adjustable lens system) may remain.
Fluid lens assembly 20 may have a total length along optical axis 14 of 2 cm or less, in some cases having a length of 1 cm or less. The cross sectional dimensions of fluid lens assembly may be 2 cm or less, in many cases being 1 cm or less. Fluid lens assembly 20 may provide spherical powers from +20.0 D to −20.0 D. Spherical and cylindrical powers may be adjustable in increments (for example, in 0.25 D steps) or may alternatively be smoothly and continuously adjustable throughout at least a portion of the overall power range. The cylindrical power input 26 may allow cylindrical powers to be adjusted throughout at least a range from about −6.0 D to +6.0 D, while the cylindrical orientation input 28 allows rotation of the cylindrical axis or orientation about optical path 14 throughout a range of at least about 90°, optionally throughout the range of at least about 180°. Focal ranges provided by fluid lens assembly 20 may extend, for example, throughout a range from about 5 cm to infinity and may be quite fast, with switching of the fluid lenses over the full focal range being complete in less than 100 ms, optionally be complete in less than 10 ms.
Advantageously, fluid lens electrowetting potentials may be provided by a DC voltage source, and may represent primarily a capacitive load, so that the lens assembly lens consumes very little power. Hence, electrical power may optionally be provided by a battery 32 of power source 22. Optical apparatus 12 may thus comprise a portable structure which can be hand moved and/or hand held during use. The durability of fluid lenses can also be quite high, optionally providing over one million focusing operations without loss of optical performance. Fluid lens assembly 20 and apparatus 12 can be both shock resistant and capable of operating over a wide temperature range, making them particularly suitable for mobile applications. Advantageously, high volume manufacturing techniques can be applied for some or all of the components of the fluid lens assembly 20 and apparatus 12.
A first fluid lens component capable of generating a variable power cylindrical lens for use in fluid lens assembly 20 can be understood with reference to
First and second opposed parallel surfaces 50, 52 of container 42 are offset from optical path 44 with the optical path extending along and between these surfaces. Parallel surfaces 50, 52 are sometimes referred to as “sides” of container 42. End surfaces 54, 56 extend between the side surfaces 50, 52, with the exemplary ends being normal to the sides. While the sides will often be longer than the ends, the ends may also be the same length as the sides or longer than the sides.
Four electrodes 58a, 58b, 58c, and 58d (collectively referred to as “electrodes 58”) surround optical path 44, with each of the electrodes extending along an associated side 50, 52, or end 54, 56. Each electrode 58 maintains a substantially uniform electrical field throughout much of, preferably most of, the associated side or end, and is electrically isolated from the circumferentially adjacent electrodes relative to optical path 44. Preferably, side electrodes 58a, 58b are electrically coupled to each other by a conductive structure so that the electrodes are at substantially the same electrical potential. Similarly, end electrodes 58c, 58d may also be coupled so as to be at the same potential. One of surfaces 46, 48 may be coupled to side electrodes 58a, 58b. Hence, the two parallel sides of the container and the “top” (which may be at any orientation) of the container may have an electrical potential field which is applied and/or varied as desired. In some embodiments, the field on the end electrodes 58c, 58d may be kept at a constant strength.
As can be understood by reference to
While imposing voltage V1 along sides 50, 52 via electrodes 58a and 58b, a different voltage V2 is also applied to end electrodes 58c, 58d. Under the influence of V2, fluid/fluid interface 66 forms a right angle at ends 54, 56, forcing the cross section between these surfaces to a flat configuration so that the fluid/fluid interface 66 forms a cylindrical lens of variable power, as can be seen in the perspective view of
Referring now to
The shape of the fluid/fluid interface within the lens will generally be driven by the position and/or angle of the lens along the sides and end of the container. Some distortion of an ideal lens shape may occur at the corners between the sides and end, where the electrical fields along the container/fluid interface are defined by some combination of the side and end electrodes. Adjustment to the end electrode voltage can also be made as desired to provide the desired lens properties.
Materials for fabricating container 42 may be similar to those used for spherical fluid lens structures. For example, electrodes 58 and 60 will often comprise a metallic material, while insulating layer 62 may comprise a polymer such as parylene. Fluid contact layer 64 may comprise a fluorocarbon such as a PTFE including Teflon™ produced by DuPont. The transparent surfaces 46, 48 traversed by the optical path may comprise clear polymers, glass, or the like.
Referring now to
To understand how three variable power cylinder lenses may be used to create any sphero cylindrical power, the power of a single cylinder lens will first be expressed in terms of the cross-cylinder lens and a sphere lens. A pure cylinder lens of power equal to C has one principal meridional power equal to C and the other equal to O. Its orientation is expressed in terms of its axis, a direction aligned along the meridian of 0 power. But such a lens may also be described in terms of the combination of the pure spherical lens of power C/2 and a cross-cylinder lens of power C/2. A cross-cylinder is defined as the combination of two pure cylinder lenses of equal but opposite power C/2 oriented with respect to one another such that their axes are at right angles. The orientation of this cross cylinder is defined as the orientation of the axis of one of the pure cylinder lenses that make the cross-cylinder.
This decomposition method for describing a pure cylindrical power in terms of a sphere and cross-cylinder is now extended to any sphero cylindrical combination which is typically expressed in terms of a sphere power, a cylinder power and an orientation. The concept of the sphere equivalent can then be introduced. Sphere equivalent is the sphere power of the sphero cylindrical combination plus one half the cylinder power. Sphere equivalent can thus take the place of the sphere component described above for the pure cylinder lens. The cross-cylinder component power is again one half the cylinder power. Indeed, the pure cylinder is just a sphero cylindrical combination with the sphere equal to zero.
When expressed in this fashion, sphero cylindrical powers form a 3 dimensional vector space with one axis the sphere equivalent value and the other two axes forming a cross-cylinder double angle vector space.
Now considering a desired sphero cylindrical power with values sphere=S, cylinder=C and axis or orientation=A, in this type of representation of sphero cylindrical power the sphere may take a positive or negative value but the cylinder always has the same sign. Let us use a positive cylinder value for easy of exposition. This may be expressed in terms of the three refractive space components
Sphere equivalent (SE)=S/2
Cross-cylinder at 0-90° (C+)=C/2 cos(2A)
Cross-cylinder at 45-135° (Cx)=C/2 sin(2A)
In the double angle cross-cylinder space, the C+ axis is at right angles to the Cx axis so in this space, the two cross-cylinder components form a true vector. If cross-cylinder components, unlike the cylinder value, can take positive or negative values and if the sign of a component is changed, it flips through 180° in the double angle cross-cylinder space. Let us orient that fluid focus cylinders so that one has its axis at 0°, one has its axis at 90° and the other has its axis at 45°. If then the same power is created in the cylinder at 0° and the one at 90°, their sphere equivalent components will be equal. Their cross-cylinder components will both be only of the C+ variety and will have equal magnitudes but they will have opposite signs because they are oriented at 90° from one another. This means when they are added as vectors in the double angle cross-cylinder space, they will cancel one another and the result will be only the addition of the two sphere equivalent components giving a net result of a spherical lens effect. The effect of creating a spherical effect with two pure cylinders show how this theory gives expected results.
The other variable cylinder can only create a Cx component, i.e. one oriented at 45 or 135° depending on whether the variable cylinder is given a positive or negative power. This is the only variable power lens that can create Cx, it will be treated first. Knowing the desired value of Cx from the decomposition of the desired sphero cylindrical combination, the power of the variable cylinder is increased until it creates with cross cylinder power. If the power of this variable cylinder lens be designated C45, then
C45=2Cx (1)
At the same time it creates a sphere equivalent power SEcx=C45/2=Cx. This value mayor may not have the right sign to partially supply the needed SE but it is now subtracted from that value to see how much more SE value is needed. This will be called SE′=SE−Cx. This value should now be supplied by the other two variable cylinder lenses in addition to supplying the needed C+ component.
Let us define the cylinder power of the variable cylinder with axis 0 degrees as Co, and the cylinder power of variable cylinder with axis 90 degrees as C90. Both these power may be positive or negative. The sphere equivalent power of the Co is Co/2 and the sphere equivalent power of the C90 is C90/2. Their sum should equal SE′ so:
SE−Cx=Co/2+C90/2
Likewise the sum of the cross-cylinders created by these two variable focus lenses equals the value C+. However the sign of the cross-cylinder created by the C90 variable power lens can have its sign changed for the reasons explained above so:
C+=Co/2−C9012
These two equations may now be solved for the values Co and C90 by adding them to find Co and then subtracting them to find C90. This results in the expressions of:
SE−Cx+C+=Co
SE−Cx−C+=C90
By independently driving the fluid/fluid interfaces of the three containers 42, 42a, 42b to appropriate positive or negative configurations using an electropotential source, the combination of these three fluid lenses can reproduce any desired spherical power, cylindrical power, and cylindrical orientation. Hence, processor 30 of source 22 (see
The above includes descriptions of fluid lenses having prismatic containers, and in which electrowetting potentials applied to opposing surfaces of the containers can by varied so as to provide varying cylindrical powers of a fluid/fluid interface bordered by the opposing surfaces. More generally, by varying an electrowetting potential circumferentially about the periphery of a fluid/fluid interface, a desired shape can be generated throughout the fluid/fluid interface. The control over the shape of the fluid/fluid interface from its periphery is (in some ways) analogous to controlling the shape of a bubble.
In the case of a bubble, the shape of the boundary can force the fluid film to take a very specific shape. The boundary of a bubble can be described as having an elevation above some base plane. In the case of the fluid/fluid boundary it may be the first derivative or surface slope that is set at the boundary, not the elevation. Regardless, once the boundary (elevation or slope) is set (for example, by setting a circumferentially local electrowetting potential), the overall surface can be forced to take a very definite shape, particularly once the additional constraint of the interface tension is introduced. The fluid/fluid interface tension will generally cause the interface surface to change shape until the mean curvature is equal everywhere. Until this occurs, the interface tension will create a pressure gradient and fluid will flow.
Spherical surfaces have the property that curvature is equal throughout the surface. Sphero cylindrical or toroidal surfaces have the property that mean curvature can be equal throughout the surface. This can occur because the astigmatic portion can be considered to have zero mean curvature and the spherical equivalent portion has the same curvature—non-zero usually—everywhere. Therefore, sphero cylindrical surfaces will have the advantageous property that they can exist in equilibrium within a fluid/fluid interface. As these shapes can be determined from their boundary conditions, a peripheral electrowetting potential may be used to set the specific sphero-cylinder that will form.
In addition to spheres, toroids, and sphero-cylinders, the structures, methods, and systems described herein may also provide other surfaces that can be described as the combination of a sphere (having constant curvature) and any other shape with a zero mean curvature (in other words, in which the Laplacian is equal to zero). Along with combinations of spheres and cylinders, other shapes such as a trefoil or quadrafoil (which have a zero Laplacian) may also be combined with spheres and/or cylinders, or with each other.
Referring now to
The potentials may be varied across the array so that a potential at a given electrode of the array may be different than the potentials of both circumferentially adjacent electrodes. The electrodes may be coated with insulating and/or hydrophobic materials as described above, so that electrowetting potentials applied at each electrode 86 of the array, relative to a cap electrode 90 help determine a contact angle of fluid/fluid interface 66 along that electrode, as well as a position of the fluid/fluid interface along the electrode (once the interface has assumed its stable, low energy configuration).
Referring now to
Referring now to
Referring now to
A driver 88′ coupled to stepper motor 100 may be modified for use in the flexible fluid lens 80 of
While the exemplary embodiments have been described in detail for clarity of understanding and by way of example, a variety of adaptations, changes, and modifications will be obvious to those of skill in the art. For example, while the inputs into the optical assembly of
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