Large diameter electrically tunable lens for ophthalmic distance accommodation

Electrically tunable liquid crystal lens with 30 mm diameter is presented based on the refractive Fresnel concept. Relatively large optical power variation range (from – 0.74 to +0.71 Diopters) is demonstrated along with very low root mean square aberrations (≤0.15 µm). Optical characterizations, including with Snellen chart, show that good vision recovery may be obtained with fast response time (under 500 msec) and relatively low haze. The proposed design is very simple and may be fabricated by using single step lithography. Perspectives on its applications are discussed.


Introduction
Adaptive optical systems are gaining increasing importance in photonic applications.Among them, wearable or mobile systems, such as ophthalmic, augmented or virtual reality glasses, are particularly interesting (see, e.g., [1]).This type of application imposes severe requirements on the electrical power consumption, form factor, weight, the environmental reliability and robustness of the device.Traditional mechanical solutions are bulky, vibration and shock sensitive and exhibit rather high electric power consumption.They are thus not desirable for such applications.
However, until recently, several difficulties were prohibiting their widespread utilization.One of the fundamental difficulties was (and still is) the additional light scattering (or haze) when a TLCL is added on the optical path of the device.This scattering increases with the increase of the birefringence ∆n of the LC (∆n ≡ n ∥ -n ⊥ ) as well as of its thickness L [11].A related difficulty is the limited optical path difference (∆n L), and consequently, the limited achievable optical power (OP) variation ranges (OP ∝ ∆n L), when we try to reduce haze by reducing L or ∆n, [12].This limitation is particularly difficult to overcome in single aperture refractive type gradient index lenses when we attempt to increase their clear aperture (CA) due to the well-known inverted quadratic dependence OP ∝ CA −2 [3].Thus, many important applications, requiring large CAs, such as ophthalmology, have remained out of general reach until now.
Finally, while many interesting TLCL architectures have been proposed in the scientific literature, to the best of our knowledge, most of them require specific (non-standard) manufacturing conditions, which, for rather low quantities (compared to LCDs) is prohibiting their manufacturing on highly automated and high precision LCD factories.Some of the above-mentioned fundamental difficulties may be resolved by using approaches with non-uniform apertures.For example, diffractive Fresnel approach requires much smaller thicknesses L, which may reduce haze and enable faster operation (since LC's response times are ∝ L 2 ), [13].However, the micrometric precision manufacturing cost, chromatic aberrations and focus discretization are problems here that must be resolved first.Similar manufacturing problems persist for another very interesting approach (based on the refractive Fresnel concept) requiring multiple levels of high precision lithography [14,15].Other, promising approaches were reported as well, such as the so-called geometric-phase [16,17], refractive Fresnel [18] or Foveal type of TLCLs [19], which have good chances for mid-term applications in augmented reality and virtual reality devices (see also, [17,20]).However, the non-standard manufacturing requirements in most of these designs remain as serious problems yet to be resolved.
Recently, we have reported a particular TLCL design [21] that provided good optical performance for small aperture applications (CA ≈ 2 mm, [22,23]) and had the potential to enable larger diameter multi-zone or multi-segment (e.g., refractive Fresnel or Foveal type) approaches, while still using a standard single-step photo lithography.If this is proven to be true, then it might dramatically change the situation by allowing the use of widely available old-generation LCD manufacturing lines (without their noticeable modifications) to produce such lenses at low manufacturing cost.
In the present work, we describe a new electrode design, inspired by the one reported in [23], that allows the use of above-mentioned advantages, but for much larger CA values (up to 50 mm).We demonstrate the example of a lens with 30 mm diameter and characterize its OP's variation range as well as root mean square (RMS) aberrations.Its photographic characterizations, including the Snellen chart, show the possibility of good vision recovery.These results are described and discussed in view of the use of the developed lens in ophthalmic distance accommodation, as well as in augmented and virtual reality applications.

Design
To build the proposed TLCL, two glass substrates were assembled in the form of a sandwich by using a peripheral UV curable glue.This glue was containing spacers with 50 µm diameter to maintain the desired gap between substrates.The gap was filled with a home-made nematic LC (NLC) mixture, with optical birefringence ∆n ≈ 0.263.One of the substrates had a uniform transparent indium tin oxide (ITO) electrode on its inner surface.The second substrate was treated lithographically to obtain a spiral-serpentine shaped electrode (see also [23]).The microphotography of the central zone of the obtained ITO pattern is presented in Fig. 1(a), as an example.The open-colored rings here represent ITO lanes and the darker rings are the area where the ITO was removed.The CA = 30 mm of the lens was composed of 14 such Fresnel segments (Fig. 1(b), see next section for details).We have followed the same approach, described in [23], in the choice of values of the width w of ITO spiral coil lanes and of the gap g between them to keep the residual diffraction effect at low level.
Before the final assembly of the sandwich, a layer of polyimide (SE-150 material from Nissan Chemicals) was spin coated on inner surfaces of both substrates, baked, and rubbed in so-called antiparallel directions [24], to uniformly align NLC molecules almost parallel to substrates (with a small pretilt angle of α ≈ 3°).
The proposed structure allows applying higher voltage either to the inner electrode or to the outer electrode of each Fresnel zone, enabling thus a bipolar operation (providing positive or negative OP, see also [23,25]).Indeed, the operation principle of the lens is as follows (see also [23]): the electric field profile inside the NLC volume is generated by applying pairs of voltages to inner (V j in ) and outer (V j out ) electrode contacts of each Fresnel segment j (j changes from 1 to 14).These are square-shaped AC electrical potentials with frequency F j .The serpentine character of the electrode serves to gradually distribute the electric potential in the transverse plane of the TLCL.The frequency of the signal F j is also used to control the profile of this distribution within each Fresnel segment.Homemade electronic board was developed to control the lens from a computer.It generates 14 pairs of drive signals.The driver is powered by a 12VDC-2A power supply.Four microchip controllers (one master and three slaves) receive commands via the USB bus input, and generate 14 sets of timing, phase and enable signals.The controller also sends data (through I2C bus) to 28 DACs to set amplitudes of drive signals.By using this driver, we can activate different contacts, select the required amplitudes and frequencies of the signal, and we can thus control the distribution of the electric potential in the working area of the device, which allows us to generate many spatial phase retardation profiles.Among others, we can obtain a spherical lens (both positive and negative) or even an aspherical (ex: Mexican hat type) profiles, [23].

Characterization methods
We have used several well-known methods to characterize our lenses.It is important to mention that, in this work, we have tested "full" TLCLs, composed of two NLC layers having their molecules oriented at 90°one with respect to the other.Thus, the focusing was obtained for unpolarized light.Two TLCLs with single NLC layers, focusing only the extraordinary polarized light (the reason why we call them "half lenses"), were used only for the initial characterization stage, and then, they were laminated together with 90°rotation, see [5].
Usually, we start the lens characterization with the polarimetric set-up since it is more visual and intuitive.It allows us to quickly (but approximately) identify the driving conditions corresponding to the desired wavefronts.We also use these polarimetric data to roughly reconstruct the corresponding wavefront profiles (see next section for details) and even to estimate the level of aberrations.To perform the polarimetric imaging, the "half" TLCL was placed between two cross oriented linear polarizers.The ground state optical axis of the NLC, named director [11], was oriented (by the rubbing direction) at 45°relative to transmission axes of polarizers.A beam from a fluorescence illumination source (EXFO X-Cite 120) passed through a narrow bandpass filter (Thorlabs, FLH532-10) to create relatively monochromatic illumination.The same bandpass filter was later used for OP and aberrations measurements.Different wavelengths were not tested as the dispersion of lens materials is not high.Transmitted images were recorded by a Microscope Digital Camera (AmScope MU1000-HS).
When the "half" TLCL is activated, then, at its output, the relative phase retardation between the ordinary and extraordinary polarization modes generates various polarization states at different radial positions x (from the center of the lens), which are visualized (behind the analyzer) as concentric (bright and dark) rings or lines (fringes), Fig. 1(b).The distance between two bright (or dark) fringes corresponds to the transverse positions where the extraordinary polarized light's wavefront undergoes 2π phase shift (see, e.g., [26]).
The OP and RMS wavefront error (aberrations) of our "full" TLCLs were also studied by using a Shack-Hartmann (SH) wavefront sensor (Imagine Optic HASO 3-42).As a probe beam, we have used the same (described above) light source.A static imaging lens was used to project the exiting (from the TLCL) wavefront of light on the SH sensor's plane.It is worth mentioning 3 important elements here (see also the discussion section for details).First, neither SH sensor nor Zygo interferometer were adapted to characterize such large area lenses with such large dynamic range of OP variation.This is the reason why only the central 5 zones were characterized with 17.93 mm diameter, while the remaining part of the lens was characterized by using the above-mentioned polarimetric approach.The second element also is related to the metrology limitations: due to the limited sensor area of the SH, we could not use 4f configuration and we were using M < 1 magnification.Third, we were measuring the relative wavefront values by extracting (numerically, by the software of the wavefront sensor) the contribution of the imaging lens from the total wavefront.
Based on the measured Zernike coefficients, we have reconstructed the wavefronts and calculated the lens power and aberrations (see next section for details).
The EOS 60D 18MP professional camera in combination with 100 mm focal camera lens (from Canon) was used for all photographic tests.During these tests, the "full" TLCL was closely positioned in front of the commercial Canon camera.Photographic images were analysed for two different camera aperture stop diameters of 29 mm and 9 mm, which correspond approximately to f -numbers: 3.5 and 11.The 9 mm case is rather close to the maximal human eye pupil diameter, and 29 mm almost fits the active diameter of our Fresnel lenses.Images taken from the Snellen chart were used for human visual perception estimations only and don't represent a real human visual perception.The Snellen chart was placed at 103 cm from the Canon camera.At this distance the 20/20 line on the chart is associated with human normal visual acuity of 20/20 with 1 arcmin angular resolution.Images recorded without activating our lens were used as reference.The first reference image was recorded when the chart was brought in focus mechanically.Then an out-of-focus image was recorded.Finally, the image was brought into focus with the activation of the TLCL (see next section for details).We think that this is the right way to characterize the performance of any TLCL since it shows also the impact of the haze, which is usually higher for moderately activated TLCL.Using these data, we have analyzed the contrast enhancement thanks to our lenses.

Experimental results
The polarimetric technique allowed us to adjust the excitation signals to obtain a good spherical profile, Fig. 2. As we can see, an excellent fit is obtained for a parabola (shown by the black dashed line in Fig. 2) at both positive (+ 0.5 D, Fig. 2(a)) and negative (-0.5 D, Fig. 2(b)) OP ranges.We can even estimate the RMS aberrations by fitting these experimental points with a polynomial, but the SH measurements provide an easier (and more accurate) way of measuring them (see hereafter).
More detailed measurements (performed by the SH wavefront sensor; measured clear aperture of the lens was 17.93 mm) show that we can reach a total OP variation range of about 1.5 D while keeping very low total RMS aberrations (Fig. 3(a)).In many optical designs, the RMS spherical aberration is important.This is the reason why we show it (Fig. 3(a)) along with total aberration.Interestingly, the RMS aberrations for positive and negative optical powers are non-symmetrical.We think that this is related to the director's pretilt angle, which creates the asymmetry with respect to the tilt angle of the electric field (different for positive and negative OPs).As we can see (Fig. 3(b)), other significant contributions to the RMS aberration are coming from astigmatism and coma, which are related to the manual manufacturing technique and the possible misalignment of optical components during our measurements -thus, we can reduce them in the future.A haze-gard by BYK-Gardner was used for haze measurements of our lenses.Two lenses with the same ITO pattern design but with different NLC gaps (30 µm and 50 µm) were tested.Each lens was placed in the close proximity to the haze-port.Then haze measurements were taken for the entire range of OP of each lens and for the unpowered states (Fig. 4).We can notice that, as mentioned before, the OP and the haze of TLCLs is proportional to the thickness L of the NLC layer.Thus, for the 30 µm cell, the ground state haze is below 3%, while we must keep in mind that the achievable range of OPs is also narrower compared to the 50 µm cell.However, it is important to mention that even with this level of haze, the image quality is greatly improved as it is demonstrated in Fig. 5.
Indeed, the results of our experiments with the Snellen chart (for human visual perception estimations only) are presented in Fig. 5 for EOS camera two aperture stop diameters: 9 mm (upper images) and 29 mm (lower images).The example when the OP of our lens is -0.5 D summarizes these results.The image of the Snellen chart, put in focus mechanically (without activating our lens), is shown as a reference (Fig. 5, left images).Then, the out of focus image is recorded (Fig. 5, central images).Finally, this image is brought into focus by the activation of our lens (Fig. 5, right images).As we can see, the quality improvement of right images (with respect to the central images) is obvious.The impact of the haze can be seen if we compare left and right images.However, for functional comparison, we should obviously compare the right and central images.A corresponding quantitative contrast comparison, demonstrating the image quality improvement after the lens activation, is shown in Fig. 6.The analyses here was done along the letter "U" in the chart row corresponding to 20/20 visual acuity (second raw from the bottom, Fig. 5).As we can see, the relative contrast of pixel grey values (measured as (I max -I min )/(I max + I min )) is approximately 21.6% for the case of mechanical adjustment (in focus image, Fig. 5, left), it drops only to 18.9% in the electrically tuned (by our TLCL) case (Fig. 5, right), while it is ≈ 0% for the case of the out of focus image (in the middle of Fig. 5).In other words, the relative contrast drop is below 15% for mechanical and electronic focused cases, while the drop is 100% without the focusing.The optical transparency of these lenses is also important.Thus, we have performed corresponding measurements (for the main lens, having 50 µm NLC thickness).Both glass substrates, forming the NLC cell, were coated with basic index matched ITO.The substrate with patterned ITO had also a basic anti-reflective coating on the outer side.The Cary 5000 UV-Vis-NIR spectrophotometer was used to perform the measurements.The beam of spectrophotometer had a rectangular shape of approximately 10 mm X 3 mm.Although the lens had 14 Fresnel zones -the beam of spectrophotometer was passing only through the central Fresnel zone of the lens and the first transition zone.Since transmission losses are mostly defined by the electrode, reflections and the NLC material, we think that this is rather representative data.The measurements were carried out in the unpowered state, and for both minimal and maximal OPs of the lens within the visible range of the spectrum.As we can see (from Fig. 7) the transmission of the lens is rather good in the entire visible spectrum.The excited state slightly increases haze, but it does not degrade noticeably the transmission for either positive or negative OPs.
Finally, the transition times were shortly studied also.To accelerate the speed of electro-optical response, we have used voltage kicks and have achieved the speed acceleration from few seconds to below 500 ms.To further accelerate the operation of the lens, we can use a so-called Dual Frequency NLC mixture [27].A short transitory electrical pulse of appropriate frequency should be then sent to the lens segments during the switching between two stationary OP values.The pulse duration and its amplitude should be optimized for the operation temperature range, but this is a subject for a separate study.

Discussions and conclusions
The reported approach of making large diameter lenses using single step lithography ensures very low cost of manufacturing and, as we saw here, with a rather good optical performance.This is the reason why we think that it can dramatically change the situation and enable the widespread utilization of TLCLs in ophthalmic distance accommodation, as well as in augmented and virtual reality applications (see, e.g., [20]).Indeed, already in these first prototypes, we have excellent aberrations (≤0.15 µm) with almost 1.5 D of total OP variation range.This can "eliminate" the need of 6 ophthalmic glass corrections (since the OP values of these glasses are usually changing by the steps of 0.25 D).The distance accommodation times are also quite reasonable and the optical transmission is good over the entire visible spectrum (further improvements are certainly possible with better index matching and antireflection coatings).
To this list, we should add also other, typical advantages of TLCLs, mentioned already in the introduction (low power consumption, very thin, robust, etc.).
Obviously, for the moment, this work addresses one of the most important problems of TLCLs -their manufacturability problem.We did not address yet the scattering (haze) problem, which is inherent to most LC-based solutions.We know its origins (NLC fluctuations, transition zones, etc.), we are currently working on their reduction and we are confident that we can further improve it.The corresponding results will be reported as soon as available.
However, our results, obtained by the Snellen chart, already clearly show that the vision recovery is very efficient.
We are currently working also on the development of a metrology system that would allow us to fully characterize our lenses by using SH wavefront sensors (e.g., for the entire CA as well as for the off-axis performances).Surprisingly enough we were not able to find such commercial systems that can measure (even on-axis) the performances of lenses with such large apertures and such tunable OP ranges.To the best of our knowledge, with ZYGO interferometer or with Imagine Optics' latest model, to characterize the lens under test (LUT), the so called autocollimation mode is used.In both cases the incident diverging or converging beam should be collimated after traversing the LUT.Depending upon the power of the LUT (positive or negative OP), the incident light beam should be diverging or converging, respectively.The focal points of LUT and converging or diverging beams focuses (real or imaginary) must match together to obtain autocollimation regime after the LUT.In the case of small OPs, this approach requires larger distances between the LUT and incident beam's forming optics and makes it difficult to realize in normal laboratory conditions.The second inconvenience is the need for large aperture and/or specially designed optics (especially in the case of LUT's negative OPs) to form converging or diverging incident beams.
It is important however to mention that we are very confident for the performance of the entire CA since we already have the polarimetric tool, but also, because the specific design, reported here, allows an extraordinarily rich variety of wavefronts to be "dialed-in" by using the couples of voltages and frequencies of electrical control signals.
Funding.Canada Research Chairs (230212); Natural Sciences and Engineering Research Council of Canada (05888).

Fig. 1 .
Fig. 1.(a) Microphotography of the patterned spiral-serpentine ITO in the central Fresnel segment (the bus line is oriented vertical) and (b) the polarimetric microphotography of the entire lens.The bus line is visible on the left (horizontal).

Fig. 2 .
Fig. 2. Polarimetric reconstruction of phase profiles for (a) + 0.5 D and (b) -0.5 D OP values.Dotted lines represent the perfect parabolic profile and blue rectangles are experimental measurement points.

Fig. 3 .
Fig. 3. (a) Total (solid line) and spherical (dotted line) RMS aberrations in µm versus the optical power (lines are for eye-guiding only) and (b) details of some key contributions in aberrations for various optical power values, where 3 rd , 5 th and 7 th orders of aberrations were considered for calculation of RMS.

Fig. 5 .
Fig. 5. Demonstration of a possible vision correction by using the developed TLCL: left images -mechanical focusing, central images -out of focus, right images -electrically focused (see text for details).Upper images correspond to 9 mm aperture stop diameter, and lower images are for 29 mm aperture stop diameter.

Fig. 6 .
Fig.6.Pixel gray value histograms along the horizontal yellow line (across the letter "U" of 20/20 vision acuity raw) with the following conditions: without LC lens activation, but with mechanical focus on target (solid curve); target out of focus (dotted curve); and with the TLCL activated (dashed curve).Spatial coordinate represents the image pixels along the letter "U" in the Snellen chart row corresponding to 20/20 vision.

Fig. 7 .
Fig. 7. Spectral dependence of transmission of the lens measured in the range from 425 nm to 650 nm in the unpowered state (a) and in two excited states (b) for OP = -0.75D and (c) for OP = + 0.73 D.