Patent Publication Number: US-2022229342-A1

Title: Polarization-insensitive phase modulator

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims the benefit of U.S. Provisional Patent Application 62/308,903, filed Mar. 16, 2016, which is incorporated herein by reference. This application is a Continuation in Part of U.S. patent application Ser. No. 14/428,426, filed in the national phase of PCT Patent Application PCT/1132013/058989, filed Sep. 30, 2013, which claims the benefit of U.S. Provisional Patent Application 61/707,962, filed Sep. 30, 2012, which is incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to electro-optical devices, and particularly to optical phase modulators. 
     BACKGROUND 
     A dynamic phase modulator is an optical device that allows phase modulation of transmitted light, wherein the phase modulation is electronically controllable. Among its various applications are optical modulators for communication and wave front shaping for optical uses such as microscopy, astrophysics and optometry. One sought-after application is an electrically-controlled dynamic lens. 
     U.S. Pat. No. 9,335,562 describes methods and apparatus for providing a variable optic insert into an ophthalmic lens. A liquid crystal layer may be used to provide a variable optic function, and in some embodiments the liquid crystal layer may comprise polymer networked regions of interstitially located liquid crystal material. 
     SUMMARY 
     Embodiments of the present invention that are described hereinbelow provide phase modulators that are independent of the polarization of incident light. 
     There is therefore provided, in accordance with an embodiment of the invention, an optical device, which includes an electro-optical layer, including a liquid crystal material with a heliconical structure having a pitch that is less than 250 nm and is modifiable by an electric field. An array of excitation electrodes extends over the electro-optical layer. Control circuitry is coupled to apply control voltage waveforms to the excitation electrodes and is configured to modify the control voltage waveforms so as to locally modify a molecule director angle of the heliconical structure and thus to generate a specified phase modulation profile in the electro-optical layer. 
     In a disclosed embodiment, the liquid crystal material includes a combination of one or more liquid crystals and a chiral additive. Alternatively, the liquid crystal material comprises a chiral liquid crystal. 
     Typically, the phase modulation profile is independent of a polarization of the incident light. 
     In some embodiments, the control circuitry is configured to apply the control voltage waveforms to the excitation electrodes so that the device functions as a lens, having focal properties determined by the phase modulation profile, for example an ophthalmic lens with an electrically controllable focal length. 
     There is also provided, in accordance with an embodiment of the invention, an optical device, including a first polarization-dependent lens, which include a first electro-optical layer, which is configured to refract a first polarization component of light propagating along an optical path, with an effective first local index of refraction at any given location that is determined by first control voltage waveforms applied across the first electro-optical layer, and a first array of excitation electrodes extending across the first electro-optical layer. A second polarization-dependent lens is arranged in series with the first polarization-dependent lens along the optical path and includes a second electro-optical layer, which is configured to refract a second polarization component of the light, orthogonal to the first polarization component, with an effective second local index of refraction at any given location that is determined by second control voltage waveforms applied across the second electro-optical layer, and a second array of excitation electrodes extending across the second electro-optical layer. Control circuitry is coupled to apply the first and second control voltage waveforms respectively to the first and second arrays of the excitation electrodes and is configured to modify the first and second control voltage waveforms so as to generate a specified phase modulation profile in the first and second electro-optical layers. 
     In some embodiments, the specified phase modulation profile includes a first phase modulation profile that is generated in the first electro-optical layer by the first control voltage waveforms and defines a first focal length of the first lens and a second phase modulation profile that is generated in the second electro-optical layer by the second control voltage waveforms and defines a second focal length of the second lens. Typically, the first and second polarization-dependent lenses are positioned at respective locations that are separated by a predefined distance along the optical path, and the first and second control voltage waveforms are selected to determine the first and second focal lengths so that a difference between the first and second focal lengths compensates for the predefined distance in forming respective first and second images at a focal plane. In a disclosed embodiment, the first and second polarization-dependent lenses are configured to serve as an ophthalmic lens with an electrically-controllable focal length, and the first and second focal lengths are chosen so that both the first and second polarization components are imaged on a retina of a user of the ophthalmic lens with equal magnifications. 
     There is additionally provided, in accordance with an embodiment of the invention, a method for producing an optical device. The method includes providing an electro-optical layer, including a liquid crystal material with a heliconical structure having a pitch that is less than 250 nm and is modifiable by an electric field. An array of excitation electrodes is positioned to extend over the electro-optical layer. Control circuitry is coupled to apply control voltage waveforms to the excitation electrodes and to modify the control voltage waveforms so as to locally modify a molecule director angle of the heliconical structure and thus to generate a specified phase modulation profile in the electro-optical layer. 
     There is further provided, in accordance with an embodiment of the invention, a method for producing an optical device. The method includes providing a first polarization-dependent lens, which includes a first electro-optical layer, which is configured to refract a first polarization component of light propagating along an optical path, with an effective first local index of refraction at any given location that is determined by first control voltage waveforms applied across the first electro-optical layer, and a first array of excitation electrodes extending across the first electro-optical layer. A second polarization-dependent lens is arranged in series with the first polarization-dependent lens along the optical path. The second polarization-dependent lens includes a second electro-optical layer, which is configured to refract a second polarization component of the light, orthogonal to the first polarization component, with an effective second local index of refraction at any given location that is determined by second control voltage waveforms applied across the second electro-optical layer, and a second array of excitation electrodes extending across the second electro-optical layer. Control circuitry is coupled to apply the first and second control voltage waveforms respectively to the first and second arrays of the excitation electrodes and to modify the first and second control voltage waveforms so as to generate a specified phase modulation profile in the first and second electro-optical layers. 
     The present invention will be more fully understood from the following detailed description of the embodiments thereof, taken together with the drawings in which: 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic perspective view of an optical device, in accordance with an embodiment of the present invention; 
         FIG. 2  is a schematic perspective view of the structure of a heliconical liquid crystal material used in a polarization-independent optical phase modulator, in accordance with an embodiment of the present invention; 
         FIG. 3  is a schematic perspective view of a polarization-independent optical device, in accordance with an embodiment of the present invention; and 
         FIGS. 4A-B  are schematic side views of a polarization-independent ophthalmic lens, in accordance with an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Overview 
     When dynamic lenses, for example the dynamic lens described in the above-mentioned PCT Patent Application PCT/IB2013/058989, are based on birefringent materials, such as nematic liquid crystals, they typically operate only on polarized light. In order to modulate the phases of both polarizations, two such devices can be stacked with their directions of polarization crossed. In this case, however, the necessary spacing between the two devices affects the relative magnifications of the imaging system in the two polarizations. 
     As another possible solution to the problem of polarization-dependence, a dynamic lens could be based on cholesteric liquid crystals (CLC), which have an axially symmetrical helical structure when no voltage is applied across the layer of liquid crystal. In this state the optical path length across the CLC, and therefore the optical phase change, is independent of the polarization of the incident light. However, when a voltage is applied across a traditional CLC material, the liquid crystal material switches to an intermediate state, such as a focal conic state or a fingerprint state. These states are disordered and therefore scatter the incident light. Further increasing the voltage results in a homeotropic state, in which all the molecules are mutually parallel, with the common direction of the molecules perpendicular to the walls of the liquid crystal cell. As a result, continuous electronic control of the focal properties of a dynamic lens based on a traditional CLC material is generally not feasible. 
     The embodiments of the present invention that are described herein address these problems by providing electronically controllable optics that are polarization-independent. 
     In some embodiments of the present invention, polarization-independence is achieved using a novel liquid crystal material with a heliconical structure having a pitch that is less than 250 nm. The pitch and director angle of the liquid crystal molecules are modifiable by an electric field. An array of excitation electrodes extends over the layer of liquid crystal. Control circuitry is coupled to apply control voltage waveforms to the excitation electrodes and is configured to modify these waveforms so as to modify the director angle and and/or pitch of the liquid crystal material and thus generate a specified phase modulation profile in the liquid crystal layer. 
     In other embodiments of the present invention, the polarization-independence is achieved by stacking two polarization-dependent lenses in series along the optical path, with orthogonal polarization axes. Each lens comprises an electro-optical layer with an array of excitation electrodes extending over the layer. Control circuitry is coupled to apply control voltage waveforms to the arrays of excitation electrodes and is configured to modify the control voltage waveforms so as to generate a specified phase modulation profile in each of the electro-optical layers. In some of these embodiments, the control voltage waveforms are chosen so that the two lenses have different focal powers, so that both polarizations are imaged with the same magnification to avoid a doubling of the image. 
     Polarization-Independence Using Heliconical Liquid Crystals 
       FIG. 1  is a schematic perspective view of an optical device  20 , in accordance with an embodiment of the present invention. Optical device  20  comprises an optical phase modulator  22  and control circuitry  23 . Optical phase modulator  22  comprises a layer of a heliconical liquid crystal material  24  sandwiched between an upper substrate  26  and a lower substrate  27 , wherein the substrates comprise a transparent material, for example, glass. Substrates  26  and  27  can be coated on their insides with a polyimide alignment layer, for example PI-1211, produced by Nissan Chemical Industries Ltd., Japan (not shown). Liquid crystal material  24  is typically contained by suitable encapsulation, as is known in the art. 
     Light impinges on optical phase modulator  22  as an incident light  30 , and exits the phase modulator as a transmitted light  32 . The optical phase of transmitted light  32  is locally modified, with respect to the optical phase of incident light  30 , by the local optical path through liquid crystal material  24 . The local optical path is modified in response to applied control voltage waveforms, as will be detailed below. 
     Excitation electrodes  28  and  29  are disposed respectively over substrates  26  and  27 . Excitation electrodes  28  and  29  comprise a transparent, conductive material, such as indium tin oxide (ITO), as is known in the art. Alternatively, non-transparent excitation electrodes may be used, as long as they are thin enough so that they do not cause disturbing optical effects. 
     Excitation electrodes  28  in this embodiment are arranged as an array of parallel stripes. (“Parallel” in this context may include, as well, excitation electrodes that deviate in angle by several degrees.) For example, the electrode pattern shown in  FIG. 1  may be formed by lithography on substrate  26 . Although excitation electrodes  28  are shown in  FIG. 1  as having uniform shape and spacing, the stripes may alternatively have varying sizes and/or pitch. Alternatively, any other suitable electrode arrangements may be used (for example, concentric ring-shaped electrodes). In an embodiment of the present invention, excitation electrode  29  (not visible in  FIG. 1 ) is disposed and formed as a uniform layer on substrate  27 , functioning as an electrical ground plane. Alternatively, the excitation electrodes on substrate  27  may comprise stripes, which are typically oriented perpendicularly to electrodes  28 , or may be formed in any other suitable pattern. 
     After forming excitation electrodes  28  and  29 , substrates  26  and  27  are cemented together at a predefined distance, typically a few microns, by using cements and/or etched spacers as are known in the art. Liquid crystal material  24  is then inserted and sealed in the gap between the substrates. Although for the sake of visual clarity, only a few excitation electrodes  28  are shown in  FIG. 1 , in practice, for good optical quality, optical phase modulator  22  will typically comprise at least 100 stripe electrodes for excitation, and possibly even 400 or more. 
     Control circuitry  23  is coupled to each of excitation electrodes  28  and  29 , and is configured to apply control voltage waveforms to the excitation electrodes for modifying the local optical phase modulation through liquid crystal material  24  in response to the local control voltage waveform. 
     The pictured embodiment combining striped excitation electrodes  28  and uniform electrode  29  enables optical device  20  to function as a one-dimensional optical phase modulator. In an embodiment of the present invention, optical device  20 , as a one-dimensional phase modulator, emulates a cylindrical lens. The focal length of the cylindrical lens and the position of the focal line in a direction orthogonal to the line are determined by the phase modulation profile, which is induced in liquid crystal material  24  by the control voltage waveforms that control circuitry  23  applies to excitation electrodes  28 . Alternatively, other control voltage waveforms may be applied to emulate lenses yielding other one-dimensional wavefronts, including free-form one-dimensional lenses. 
     In some embodiments of the present invention, a two-dimensional optical phase modulator (not shown) is assembled from two identical or similar one-dimensional phase modulators  22  by stacking them in series, with the directions of their striped excitation electrodes  28  orthogonal to each other. Control circuitry  23  is in this embodiment coupled to both optical phase modulators  22 . The control voltage waveforms applied by control circuitry  23  across excitation electrodes  28  and  29  of the two optical phase modulators  22  may be chosen so as to yield a phase modulation profile that is circularly symmetrical, thus emulating a spherical lens. The focal length, as well as the position of the focal spot in the focal plane, may be adjusted by the control voltage waveforms applied by control circuitry  23  across each of a set of excitation electrodes  28  and  29  of the two optical phase modulators  22 . Alternatively, different, symmetrical or non-symmetrical, patterns of control voltage waveforms may be applied so that the combination of two orthogonal optical phase modulators  22  emulates, for example, an astigmatic lens, an aspheric lens, a toric lens, a lenslet array, or a free-form lens. 
     In an alternative embodiment of the present invention, as mentioned above, excitation electrodes  29  are formed as parallel stripes, similar to excitation electrodes  28 , but running in a direction orthogonal to excitation electrodes  28 . This embodiment enables a single optical phase modulator  22  to function as a two-dimensional phase modulator. When suitable control voltage waveforms are applied by controller  23  across excitation electrodes  28  and  29 , optical phase modulator  22  may emulate, for example, a spherical lens, an astigmatic lens, an aspheric lens, a toric lens, a lenslet array, or a free-form lens. By applying a constant control voltage waveform by controller  23  to all of excitation electrodes  28  or to all of excitation electrodes  29 , optical phase modulator  22  reverts to functioning as a one-dimensional phase modulator, whose functions were described above. 
     Similarly to excitation electrodes  28 , the stripes of excitation electrodes  29  may alternatively have varying sizes and/or pitch, or any other suitable electrode arrangements may be used. 
     Control circuitry  23  typically comprises amplifiers and/or switches, as are known in the art, which control either the amplitude or the duty cycle, or both, of the voltage that is applied to each of electrodes  28  and  29 . The pattern of amplitudes and/or duty cycles applied to the excitation electrodes determines the phase modulation profile of liquid crystal material  24 . The circuit components in control circuitry  23  are typically fabricated as a silicon chip. Control circuitry  23  may be located separately from optical phase modulator  22 , and connected to each of excitation electrodes  28  and  29  by suitable bonding wires or other connections, as is shown in  FIG. 1 . Alternatively, control circuitry  23  may be cemented onto one of substrates  26  or  27 , and connected to each of excitation electrodes  28  and  29  by suitable bonding wires or other connections (not shown). Control circuitry  23  can be located at the side of the array of excitation electrodes  28  or  29 , and there is no need for any parts of the control circuitry to be located over the active area of layer  24 . 
     Control circuitry  23  is configured to modify the control voltage waveforms applied to each of excitation electrodes  28  and  29  concurrently and independently. This concurrent driving may apply to all of the electrodes as a group (in which case the control voltage waveforms of all the electrodes are updated together) or to sub-groups of the electrodes. For example, control circuitry  23  may update the control voltage waveforms applied to all the odd excitation electrodes in the array alternately with all the even excitation electrodes. This sort of approach scales readily to large electrode counts, and can thus be used to create electrically-tunable optical systems with high pixel counts and fine resolution. 
       FIG. 2  is a schematic perspective view of the structure of heliconical liquid crystal material  24 , in accordance with an embodiment of the present invention. Heliconical (also known as “oblique helicoidal”) liquid crystal material  24  has recently been reported by Xiang et al. in “Electrically tunable selective reflection of light from ultraviolet to visible and infrared by heliconical cholesterics”,  Advanced Materials  27, pp. 3014-3018 (2015). 
     A chain  34  of molecules  36  of heliconical liquid crystal material  24  is shown schematically between substrates  26  and  27 . A director {circumflex over (n)}, which is a unit vector  37  along the local orientation of the molecules of liquid crystal material  24 , rotates around a helicoidal axis  38  as it follows chain  34  of molecules  36 , defining a tilt angle θ with the axis, also referred to as the molecule director angle. For heliconical liquid crystal material  24 , tilt angle θ is less than 90° (as opposed to CLC, where θ=90°). A pitch P, denoted by a double-arrow  39 , of heliconical liquid crystal material  24  can be very short, for example less than 250 nm. A break  40  in chain  34  indicates that in reality there are many more periods of heliconical liquid crystal material  24  (from tens to hundreds of periods between substrates  26  and  27  than the 1-2 periods that are drawn in  FIG. 2 . Due to the short helical pitch P, heliconical liquid crystal material  24  is polarization-independent for light that enters device  20  along helicoidal axis  38 . 
     Another advantage of using a pitch P that is less than 250 nm relates to Bragg-reflections from the periodic structure of heliconical liquid crystal material  24 . Bragg-reflections take place for light incident on the liquid crystal along helicoidal axis  38  in a spectral band centered at a so-called Bragg-wavelength λ Bragg =n ave ×P, wherein n ave  is the average refractive index of the heliconical liquid crystal material. Using a typical value of n ave =1.65 and a pitch P=200 nm, the Bragg-wavelength is λ Bragg =330 nm. The reflected light is well in the ultra-violet (UV) region of the spectrum, ensuring that incident light in the visible spectrum will pass through optical phase modulator  22  without significant losses from Bragg-reflections. 
     Heliconical liquid crystal material  24 , as suggested by Xiang et al., for example, comprises a mixture of two dimeric liquid crystals: (1′,7′-bis(4-cyanobiphenyl-4′-yl)heptane (CB7CB) and 1-(4-cyanobiphenyl-4′-yl)-6-(4cyanobiphenyl-4′-yloxy)hexane (CB6OCB)), and a standard liquid crystal, pentylcyanobiphenyle (5CB). The mixture is doped with a left-handed chiral additive S811, which determines the pitch. All of the above components of heliconical liquid crystal material  24  are manufactured by Merck &amp; Co., Inc., Kenilworth, N.J., USA. A possible mixture composition CB7CB:CB6OCB:5CB:S811 (in weight units) is 30:20:45:5 (cholesteric phase in the range 20.0° C.-66.5° C.). Alternatively, other sorts of achiral dimer molecules of the type CBnCB (of which CB7CB is one example) may be used to form chiral heliconical liquid crystal materials, as reported by Chen et al., in “Chiral heliconical ground state of nanoscale pitch in a nematic liquid crystal of achiral molecular dimers,”  Proceedings of the National Academy of Sciences of the U.S.A.  110(40), pages 15931-15936 (2013). 
     Another example of a liquid crystal that can be used in material  24  is UD68, wherein the liquid crystal is achiral but the twist-bend nematic phase is chiral, as reported by Chen et al., in “Twist-bend heliconical chiral nematic liquid crystal phase of an achiral rigid bent-core mesogen,”  Physical Review E  89, page 22506 (2014). 
     Alternatively, other mixtures of liquid crystals with or without chiral additives (left- or right-handed) may be used to create heliconical liquid crystal materials with pitch in the desired range, and such mixtures are considered to be within the scope of the present invention. 
     Applying an electrical field along helicoidal axis  38  has the effect of decreasing both tilt angle θ and pitch P, thus modifying the effective refractive index. However, as opposed to CLC, the helical structure of heliconical liquid crystal material  24  is preserved under the applied electrical field, and the material exhibits a polarization-independent optical path length, which varies with the varying electrical field. This feature enables a continuous and polarization-independent phase modulation in optical device  20 . 
     An additional advantage of heliconical liquid crystal material  24  is that, by decreasing pitch P by an applied electrical field, the wavelength λ Bragg  for Bragg-reflections, mentioned above, may be moved to ultraviolet (UV) wavelengths in case the zero-field pitch results in Bragg-reflection in the visible spectrum. 
     Polarization-Independence Using Multiple Lenses 
     As noted earlier, a polarization-independent lens may be assembled by stacking two polarization-dependent lenses. The two polarization-dependent lenses are designed to affect polarized light in polarizations P 1  and P 2  respectively, wherein P 1  and P 2  are orthogonal. The first lens operates as a lens for P 1  polarized light, but does not affect light in the orthogonal P 2  polarization. Similarly, the second lens operates as a lens for P 2  polarized light, but does not affect light in the orthogonal P 1  polarization. Therefore, the combination of the two lenses operates as one polarization-independent lens. 
     A lens positioned opposite an eye causes a magnification M of the image on the retina, compared to an image created on the retina without a corrective lens. For positive lenses the image is magnified (M&gt;1), while for negative powers the image size is reduced (M&lt;1). The magnification depends not only on the focal length of the lens, but also on the distance between the pupil and the lens. A larger distance between the pupil and the lens, as well as a shorter focal length of the lens, will result in a larger effect on the magnification. 
     When the polarization-independent lens described above is placed opposite an eye, the two lens elements composing the device are positioned at different distances from the pupil. Therefore, the image on the retina will be constructed of P 1  polarized light focused by the first lens element with magnification M 1 , and P 2  polarized light focused by the second lens element with magnification M 2 . If M 1  and M 2  are not equal, this can result in a doubling of the image of the retina, thus lowering the perceived sharpness and overall quality of the image. 
     In an embodiment of the present invention, the focal lengths of the two lenses are controlled so that their difference compensates for the distance separating the lenses so as to equalize the magnifications M 1  and M 2  for the retinal images at the two polarizations P 1  and P 2 , respectively. Since magnification cannot be controlled independently from focus, equalizing the magnifications M 1  and M 2  implies that one or both of the retinal images at the two polarizations P 1  and P 2  are not in a sharp focus. Equalizing the magnifications rather than focusing both polarizations is preferable, as a slight loss of image resolution (with equal magnifications) is tolerated better by the human visual perception than a sharp double image. 
       FIG. 3  is a schematic perspective view of a polarization-independent optical device  120 , in accordance with another embodiment of the present invention. Optical device  120  comprises two polarization-dependent lenses  121   a  and  121   b , each comprising an optical phase modulator  122  and control circuitry  123 . Although control circuitry  123  is shown as a unitary component, it could as well comprise a separate component for each of the two lenses  121   a  and  121   b . Optical phase modulator  122  comprises an electro-optical layer  124 , which typically comprises nematic or other birefringent liquid crystal material, sandwiched between an upper substrate  126  and a lower substrate  127 , wherein the substrates comprise a transparent material, for example, glass. The inner surfaces of upper substrate  126  and lower substrate  127  can be coated with an alignment layer, such as polyimide, as referred to above. 
     Optical phase modulator  122  of lens  121   b  is similar to the optical phase modulator of lens  121   a . Electro-optical layer  124  is typically contained by suitable encapsulation, as is known in the art. 
     Light impinges on optical device  120  as an incident light  130 , and exits the phase modulators as a transmitted light  132 . The optical phase of transmitted light  132  is locally modified, with respect to the optical phase of incident light  130 , by the local optical path through electro-optical layers  124 . The local optical path is modified in response to applied control voltage waveforms, as will be detailed below. As electro-optical layers  124  are typically birefringent, the modification of the optical phase in each of lenses  121   a  and  121   b  affects only one polarization of transmitted light  132 . Therefore, lenses  121   a  and  121   b  are arranged so that the respective electro-optical layers  124  operate on orthogonal polarizations of light. 
     Excitation electrodes  128  and  129  are disposed over substrates  126  and  127 , respectively. Control circuitry  123  is coupled to excitation electrodes  128  and  129 , and is configured to apply control voltage waveforms to the excitation electrodes, modifying the local optical path through electro-optical layers  124  according to the local control voltage waveform. The features of electrodes  28  and  29  and control circuitry  23  that were described above are likewise applicable, mutatis mutandis, to electrodes  128  and  129  and control circuitry  123 . 
       FIGS. 4A-B  are schematic side views of the use of two polarization-dependent lenses  140  and  142  as a polarization-independent ophthalmic lens  144 , in accordance with an embodiment of the present invention. Lenses  140  and  142  are constructed and operate, for example, in accordance with the principles of device  120  described above. 
       FIG. 4A  shows an eye  146  viewing an object point  148  with the aid of polarization-independent ophthalmic lens  144 . In the present example, object point  148  is located 33 cm to the left from a pupil  150  of eye  146 , and 3 cm above an optical axis  152  of the eye, although other distances and heights of the object point may be handled in similar fashion. Polarization-independent ophthalmic lens  144 , comprising polarization-dependent lenses  140  and  142  (shown in  FIG. 4B ), is located in front of eye  146 . Optical rays  154  travel from object point  148  through polarization-independent ophthalmic lens  144  into eye  146  through its pupil  150 , and image the object point onto a retina  151  of the eye. Polarization-independent ophthalmic lens  144  is, through its component lenses  140  and  142 , coupled to control circuitry  156 . 
       FIG. 4B  is a schematic raytrace of optical rays  154  from object point  148  (outside  FIG. 4B , but shown in  FIG. 4A ) traversing polarization-dependent lenses  140  and  142  and continuing to eye  146 . Polarization-dependent lenses  140  and  142 , with orthogonal polarization axes, together make up polarization-independent ophthalmic lens  144 , shown by a double dotted line. Lens  140  refracts rays of polarization P 1  and lens  142  refracts rays of polarization P 2 . For clarity, polarization-dependent lenses  140  and  142  are drawn schematically as thin lenses, and eye  146  is represented schematically as a pupil plane  158  (representing pupil  150 ) and retina  151 . 
     In the present example, polarization-dependent lenses  140  and  142  are located at respective distances of 2.2 cm and 2.0 cm to the left of pupil plane  158 . The optical centers of both polarization-dependent lenses  140  and  142  are shifted to 1 cm below optical axis  152  of eye  146 , defining an optical axis  160  for polarization-independent ophthalmic lens  144 . Rays  154 , shown as double solid lines, arrive from object point  148  impinging first on lens  140 . Lens  140  refracts rays of polarization P 1 , which then pass through lens  142  without refracting. Rays of polarization P 2  are not refracted by lens  140 , but are refracted by lens  142 . Rays  154  are, through refraction, separated by lenses  140  and  142  into rays  162  of polarization P 1  (drawn as dotted lines) and rays  164  of polarization P 2  (drawn as solid lines). Rays  162  and  164  are refracted at pupil plane  158 , and image object point  148  onto retina  151 . 
     Control circuitry  156  has adjusted the optical powers of lenses  140  and  142  to 3.25 D (D=diopters) and 3.3 D, respectively. With these optical powers object point  148  is imaged with the same magnification for the two polarizations P 1  and P 2 . Imaging of object point  148  is shown in greater detail by expanding an area  166  to an area  168 . Rays  162  of polarization P 1  arrive at a point  172  on retina  151  in a sharp focus. Rays  164  of polarization P 2  arrive at point  172  with a slight defocus. Both rays  162  and  164  are centered at or around point  172 , which is equivalent to equal magnification of imaging for both polarizations P 1  and P 2 . Due to its small value, the blur of rays  164  (polarization P 2 ) has no significant effect on the visual perception of object point  148 . Alternatively, the blur diameter could be further reduced by adjusting the optical powers of lenses  140  and  142  so that the images at both polarizations P 1  and P 2 , still having equal magnification, are defocused by the same amount. However, were the optical powers of both lenses  140  and  142  adjusted by control circuitry  156  for a sharp focus on retina  151  (in the disclosed embodiment to 3.25 D for lens  140  and to 3.22 D for lens  142 ), the lateral distance between the two sharp images of object point  148  on the retina would be 15 μm, which would be perceived as an objectionable double image. 
     Polarization-independent ophthalmic lens  144 , as well as polarization-dependent lenses  140  and  142 , are described in the disclosed embodiment as positive lenses. Alternatively, lenses  140  and  142  may similarly be configured as negative lenses, and the principles explained above may similarly be applied in adjusting the respective optical powers. 
     It will be appreciated that the embodiments described above are cited by way of example, and that the present invention is not limited to what has been particularly shown and described hereinabove. Rather, the scope of the present invention includes both combinations and subcombinations of the various features described hereinabove, as well as variations and modifications thereof which would occur to persons skilled in the art upon reading the foregoing description and which are not disclosed in the prior art.