Compact vari-focal augmented reality display based on ultrathin, polarization-insensitive, and adaptive liquid crystal lens

Compact vari-focal augmented reality display based on ultrathin, polarization-insensitive, and adaptive liquid crystal lens

Optics and Lasers in Engineering 128 (2020) 106006 Contents lists available at ScienceDirect Optics and Lasers in Engineering journal homepage: www...

3MB Sizes 0 Downloads 11 Views

Optics and Lasers in Engineering 128 (2020) 106006

Contents lists available at ScienceDirect

Optics and Lasers in Engineering journal homepage: www.elsevier.com/locate/optlaseng

Compact vari-focal augmented reality display based on ultrathin, polarization-insensitive, and adaptive liquid crystal lens Mareddi Bharath Kumar a, Daekyung Kang a, Jihoon Jung b, Hongsik Park b, Joonku Hahn b, Muhan Choi b, Jin-Hyuk Bae b, Hyunmin Kim c, Jonghoo Park a,∗ a

Department of Electrical Engineering, Kyungpook National University, Daegu 41566, Republic of Korea School of Electronics Engineering, Kyungpook National University, Daegu 41566, Republic of Korea c Companion Diagnostics & Medical Technology Research Group, DGIST, Daegu 42988, Republic of Korea b

a r t i c l e

i n f o

Keywords: Augmented reality Vergence-accommodation conflict Focus tunable lens Polarization-insensitive See-through near-eye display

a b s t r a c t Despite the recent advances in augmented reality (AR), which has shown the potential to significantly impact on our daily lives by offering a new way to manipulate and interact with virtual information, minimizing visual discomfort due to the vergence–accommodation conflict remains a challenge. Emerging AR technologies often exploit focus-tunable optics to address this problem. Although they demonstrated improved depth perception by enabling proper focus cues, a bulky form factor of focus–tunable optics prevents their use in the form of a pair of eyeglasses. Here, we propose a novel optical configuration for a compact vari-focal AR display which deliberately utilizes the zeroth and first diffraction orders of the LC lens to produce two foci: one for a real object and the other for a virtual object with addressable focal planes. The prototype AR glasses can adjust the accommodation distance of the virtual image, mitigating the vergence–accommodation conflict without substantially compromising the form factor or image quality. In addition, we describe the design, fabrication, and characterization of an ultrathin, polarization-insensitive focus-tunable liquid crystal (LC) diffractive lens with a large aperture, a low weight, and a low operating voltage. We show that the polarization dependence of the lens, which is an inherent optical property of LC lenses, can be insensitive using the trilayer birefringent materials and by aligning the optical axes of each birefringent material at a specific angle. The polarization insensitivity eliminates the need for a polarizer, thus further reducing the form factor of the optical system. This novel approach offers significantly reduced complexity for designing AR glasses with addressable focal planes. These technologies for ultrathin lens and AR display show promising potential for developing compact optical systems in various applications.

1. Introduction Augmented reality (AR) is a technology that overlays computer– generated virtual information on a real-world environment [1,2]. It allows users to manipulate and interact with virtual objects in the context of the real world around them. The interface between an AR system and a user has evolved to the form of a pair of eyeglasses, offering users a more immersive experience in various applications including entertainment, education, training, and marketing. However, conventional AR systems have been known to suffer from the vergence–accommodation conflict for the past decades [3,4], which causes visual discomfort such as visual fatigue [5] and depth perception error [4,6–9]. Vergence is a binocular eye movement wherein the eyes are rotated in opposite directions to direct the visual axis of each eye on the same object. Accommodation refers to the adjustment of the focal power (i.e., shape) of a crystalline lens to obtain a clear image at different depths. In a



natural environment, vergence and accommodation are strongly coupled. Therefore, the vergence distance, which is the distance between the eyes and a point where two visual axes intersect, coincides with the accommodation distance (i.e., the focal distance). In conventional AR systems, a virtual image is formed at different stereoscopic distances by displaying two slightly different images separately on each eye using see-through near-eye displays. This artificially induced binocular disparity leads to vergence, yielding a different vergence distance. However, the accommodation distance is fixed at the optical distance of the displays. Therefore, a user may not be able to see the real and virtual objects in focus simultaneously. This limitation is further exacerbated when augmenting a relatively close real object with a virtual image or information, such as in surgical training [10]. Among the various AR technologies that have been explored to address this problem [11–25], an interesting approach is the use of variable focal plane near-eye displays [10,26–32]. In these systems, the

Corresponding author. E-mail address: [email protected] (J. Park).

https://doi.org/10.1016/j.optlaseng.2020.106006 Received 22 October 2019; Received in revised form 21 November 2019; Accepted 3 January 2020 0143-8166/© 2020 Elsevier Ltd. All rights reserved.

M.B. Kumar, D. Kang and J. Jung et al.

focus-tunable optics, mostly a liquid lens [33,34], is placed in the optical path of the virtual image. The optical power of the focus-tunable lens is adjusted to match the focal distance of the virtual image with the vergence distance. Such systems exhibit improved depth perception [9,10,26–31,35] and significantly reduce the time required to fuse a pair of stereoscopic images [36] in a human visual system. However, their utility is compromised by the bulky form factor and high operating voltage of the tunable lenses. Thus, these systems are far from being suitable for practical use in the form of a pair of eyeglasses. An ideal focus-tunable lens for compact wearable AR glasses should be thin and lightweight while having a broad focus-tunable range, a large aperture, and a low operating voltage. The focus tunable lens technology that has best met these requirements to date is the liquid crystal (LC) diffractive lens [37–45]. It exhibits near-diffraction limit efficiency [39,40], optical power tunable range up to 10 diopter [45], aperture diameter up to 10 mm [38], and operating voltage lower than 2 Vrms [38]. However, it suffers from its inherent limitation of polarizationdependence. Although many approaches have been demonstrated for the fabrication of the polarization-insensitive liquid crystal diffractive lens [46–51], they are still facing challenges to meet the aforementioned requirements. Here, we present the design, fabrication, and characterization of an ultrathin (~266 𝜇m), polarization-insensitive, and focus-tunable LC diffractive lens with a large area (a diameter of 20 mm), a low weight (1.5 g), and a low operating voltage (< 2.1 V). We first introduce a novel approach to fabricate polarization-insensitive LC diffractive lens, implemented by trilayer birefringent structure consisting of a nematic LC as an active layer and thin birefringent films as substrates. We show that a proper alignment of the optical axes of the trilayer birefringent material makes the LC diffractive lens polarization-insensitive. In addition, we demonstrate the RGB imaging characteristics of the lens for 10 discrete, switchable optical powers ranging from −3 D to +3 D. Next, we demonstrate a monocular prototype of a near-eye see-through AR system implemented by integrating our focus-tunable lens with commercial AR glasses. The newly proposed AR display design deliberately utilizes the zeroth and first diffraction orders of the LC diffractive lens to pro-

Optics and Lasers in Engineering 128 (2020) 106006

duce two foci: one for a real object and the other for a virtual object. It can adjust the accommodation distance of the virtual image, providing improved depth perception without substantially compromising the form factor or image quality. Fig. 1a shows a schematic of the trilayer birefringent structure of the lens. The homogeneously aligned nematic LC is sandwiched between two birefringence substrates, polyethylene terephthalate (PET) films, for which the optical axes are in-plane and oriented ± 45° relative to the optical axis of the LC. The PET is one of the most popular materials as a substrate for flexible electronics, however, its anisotropic optical property, birefringence, has not been fully utilized for many applications. The proper alignment of optical axes of the trilayer birefringent materials provides advanced functionality, polarization insensitivity. The fabrication of the bottom substrate started from the indium tin oxide (ITO)-coated 127 𝜇m-thick PET film (see Appendix A for a detailed fabrication procedure). The 130 nm-thick ITO was patterned to form Fresnel zone pattern electrodes by photolithography. The Fresnel zone pattern electrodes consist of 46 Fresnel zones, with each Fresnel zone divided into 12 subzones with a 1 𝜇m gap. The outer radii of each Fresnel zone [52] and subzone [53] were determined corresponding to an optical power of 0.5 D and a phase difference of 2𝜋 at each Fresnel zone boundary for a wavelength of 543 nm. As shown in Fig. 1b, the subzones with the same indices in all the Fresnel zones are electrically connected by an aluminum interconnect line (black lines) through via holes (red dots) on a SU-8 insulation layer. The Al lines are then extended to the contact pads. The top substrate consists of 130 nm-thick ITO coated on a PET as the ground electrode and poly (vinyl alcohol) (PVA) as an LC alignment layer. The PVA layers on the top and bottom substrates were rubbed in an antiparallel direction using a velvet cloth. The two substrates were bonded using 10 𝜇m-thick adhesive spacers placed on the rim of one substrate. A commercial nematic LC (E7) was filled between the two substrates by capillary action. The thickness of the LC was uniformly maintained over the lens area using bead spacers (diameter: 10 𝜇m) sprayed between the two substrates. Fig. A.1 shows the fabricated ultrathin, polarization-insensitive, and focus tunable LC diffractive lens with the total thickness of 266 𝜇m.

Fig. 1. Schematics of the ultrathin, polarization-insensitive liquid-crystal diffractive lens. (a) Orientations of the extraordinary axes of the top and bottom PETs and the LC. Explored view of the LC lens highlighting the different components and thicknesses of the multilayer architecture. The first and second layers from the bottom illustrate a Fresnel zone-patterned ITO on a PET substrate and the aluminum interconnect lines patterned on a SU-8 layer, respectively. A nematic LC layer is sandwiched between the PVA layers rubbed in antiparallel directions. The unpatterned ITO on the top PET substrate is grounded. (b) Detailed view of the Fresnel zone-patterned electrodes, interconnect lines, and via holes. The subzones with the same indices are connected by an Al interconnect line through via holes.

M.B. Kumar, D. Kang and J. Jung et al.

Optics and Lasers in Engineering 128 (2020) 106006

Fig. 2. The voltage-dependent optical transmission and the diffraction efficiencies of the lens for different polarization directions of the incident light. (a) Maximum (red line) and minimum (blue line) values of the voltage-dependent optical transmission of the PET(0°)/LC(45°)/PET(90°) structure in crossed polarizer for different angles between the extraordinary axis of the LC and the optical axis of the polarizer (𝜑) under the homogeneous electric field. It exhibits electro-optic effects for all polarization directions while the conventional structure (dotted line), glass/LC/glass, shows electro-optic effects only at angles near odd number multiplies of 45°. (b) The diffraction efficiency of the LC lens with +1.0 D, +1.5 D, and +2 D optical powers for the different angles between the extraordinary axis of the LC and the polarization direction of the incident light, showing the polarization-insensitive characteristic of the lens. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

2. Results To demonstrate the polarization-insensitive characteristics of the lens, the voltage-dependent optical transmission of the LC sandwiched between the PET substrates under the homogeneous electric field was measured. The measurements were performed in crossed polarizers for different angles (𝜑) between the extraordinary axis of the LC and the optical axis of the polarizer while varying the intensity of the electric field to the LC (see in Appendix B). Fig. B.2a–c shows the voltage-dependent optical transmission of the lens for the polarizer azimuth angle (polarization direction) of 0°, 45°, and 90° with respect to the extraordinary axis of the LC, respectively. The optical transmission, which is translated into the effective phase modulation of the PET(0°)/LC(45°)/PET(90°), oscillates between the minimum and maximum value as a function of the voltage as the effective birefringence of the PET(0°)/LC(45°)/PET(90°) structure goes through full and half wave plate conditions. The optical transmission varies depending on the polarization direction under the same voltage, however, the phase difference between Fresnel zones for each of the polarization directions remains 2𝜋 for a given voltage range, as shown in Fig. B.2d. Fig. 2a shows the maximum (red line) and minimum (blue line) values of the voltage-dependent optical transmission of the PET(0°)/LC(45°)/PET(90°) for all the angles. For a direct comparison, the same measurement was performed for a conventional structure comprising a LC layer sandwiched between two ITO-coated glass substrates (dotted lines). For the conventional structure, the electro-optic effects only arise for certain polarization directions of the incident light, i.e., at angles of odd number multiplies of 45°. For the angles of 𝜑 that are even number multiples of 45°, the optical transmission remains zero, regardless of the voltage applied to the LC. Unlike that in the conventional structure, the electro-optic effects in the proposed structure are induced for all angles of 𝜑, indicating polarization-insensitive of the structure. The main difference between these two structures is that the proposed structure was designed to have the extraordinary ray of the LC, which feels the change in the extraordinary refractive index induced by the voltage applied to the LC, regardless of the polarization direction of the incident light. When the light enters the PET with the polarization

direction either parallel or perpendicular to the optical axis of the PET, it travels through the PET without changing the polarization direction. Therefore, when subsequently entering the LC, it has a polarization direction of 45° relative to the extraordinary axis of the LC. When the light is incident on the PET with the polarization direction that is oblique with respect to the optical axis of the PET, the light is decomposed into the ordinary and extraordinary ray of the PET. These rays travel at different velocities through the PET and enter the LC with the polarization directions of ± 45° with respect to the extraordinary axis of the LC. Therefore, the polarization direction of the light entering the LC is always ± 45° relative to the extraordinary axis of the LC regardless of the polarization direction of the light incident on the PET. The light entering the LC is further split into the ordinary and the extraordinary ray of the LC, and each ray travels at different velocities through the LC. The extraordinary ray of the LC experiences the effective refractive index which changes from the extraordinary refractive index (ne ) to the ordinary refractive index (no ) as a function of voltage applied to the LC, whereas the ordinary ray of the LC always feels the refractive index of no . The extraordinary and ordinary ray of the LC is then incident on the PET with 45° azimuth angle and will be decomposed into the extraordinary and ordinary ray of the PET. Since the phase of the extraordinary ray of LC can be modulated by the voltage, the phase of both extraordinary and ordinary ray of the PET can also be modulated by the voltage. Therefore, the extraordinary and ordinary ray of the PET that coming from different subzones can constructively interfere at the focal length by applying the appropriate voltages on each subzone in the Fresnel zones. This optical configuration always generates the extraordinary ray of LC that gives rise to the electro-optic effects regardless of the polarization direction of the incident light. The theoretical expression for the voltage-dependent optical transmission for PET(0°)/LC(45°)/PET(90°) under the crossed polarizer can be obtained by Jones matrix (see in Appendix C): { ( ) } Δ Δ Δ1 Δ 𝐼𝑐𝑟𝑜𝑠𝑠 = 4 × sin2 1 cos2 1 + cos2 2 cos2 2(𝛾) sin2 2 (1) 2 2 2 2 where Δ1 = 2𝜋 ⋅ 𝛿𝑛 ⋅ dPET ∕𝜆 is the phase retardation of PET, 𝛿n and dPET are the birefringence and thickness of the PET, Δ2 = 2𝜋 ⋅

M.B. Kumar, D. Kang and J. Jung et al.

𝛿𝑛(𝑉 ) ⋅ 𝑑∕𝜆 is the phase retardation of the LC, δn(V) = 𝑛ef f (𝑉 ) − 𝑛0 , 1/𝑛2ef f (V) = cos2 𝜃(V)/𝑛2𝑒 + sin2 𝜃(V)/𝑛2𝑜 , ne and no are extraordinary and ordinary refractive index of a LC, respectively. 𝛾 is the angle between the ordinary axis of the PET and the optical axis of the polarizer. 𝜃(V) is a tilt angle between the plane perpendicular to the propagating direction of the ray and the extraordinary axis of the LC, V is the voltage across the LC, d is the thickness of the LC, and 𝜆 is the wavelength of the incident light. The measured birefringence of the PET (𝛿n) for wavelengths of 680 nm, 543 nm, and 450 nm are 0.01268, 0.02215, and 0.04664, respectively. This yields the phase retardation (Δ1 ) of 132.5°, 65°, and 58.6° for the wavelengths of 680 nm, 543 nm, and 450 nm, respectively. Fig. C.2 shows the numerical calculation of the maximum and minimum values of the voltage-dependent optical transmission of the PET(0°)/LC(45°)/PET(90°) based on Eq. (1) and using the measured values of Δ1 for different wavelengths. The result for the wavelength of 543 nm agrees well with the measured data. The optical transmission slightly changes with wavelengths. The polarization insensitivity of the lens was further characterized by measuring the first order diffraction efficiency for different polarization directions of the incident light. The first order diffraction efficiency was obtained by measuring the ratio of diffracted power at the first order focal spot to the total power in the focal plane [38,45,54,55]. The diffracted power was measured with lens on and a small aperture was placed in front of the optical power meter to isolate the first order of the diffracted light. The total power was measured with lens off and without an aperture. (see Appendix D). Fig. 2b shows the first order diffraction efficiencies of the lens. The measured efficiencies are weakly change with the polarization direction. The maximum and minimum diffraction efficiencies were obtained with polarization direction of 0° and 90°, respectively. The maximum (minimum) diffraction efficiency of the lens for ++1.0 D, ++1.5 D, and +2.0 D are 65% (53%), 62% (50%), and 54% (43%), respectively. These results experimentally prove that the lens can focus any polarization direction of the incident light. We attribute the discrepancy in diffraction efficiencies between the measured and theoretical values to the opaque aluminum bus lines, and the abrupt phase change in 1 𝜇m gap between subzones. We speculate that the slight diffraction efficiency variation with respect to the polarization direction can be minimized if the PET fulfills the quarter wave plate condition. Although the lens was designed to provide an optical power of 0.5 D with 12 discrete phase levels per a phase difference of 2𝜋, it can be electrically reconfigured to provide optical powers of ± 1.0 D with six phase levels, ± 1.5 D with four phase levels, ± 2.0 D with three phase levels, and ± 3.0 D with two phase levels, as shown in Fig. E.1. To demonstrate the focus tunability of the lens, the images of a target located at different distances were captured using a model eye comprising an achromatic refractive lens (with a focal length of 19.0 mm) and a charge coupled device (CCD). The LC lens was placed in front of the model eye. The images were taken under white light illumination without a wavelength filter or a polarizer. Fig. 3a shows the images of the USAF target printed in RGB colors on a photo paper, captured when the LC lens was turned off (i) and on (ii–v) with different optical powers. The target, which was placed at 48, 62, 93, and 193 cm away from the model eye, was brought into focus when the lens was on for optical powers of 2.0, 1.5, 1.0, and 0.5 D, respectively (see Fig. F.1 for images with optical power of ± 3.0 D). To obtain images for a negative LC lens power, a meniscus lens with an opposite power was placed in front of the LC lens. The target located at a fixed distance of 60 cm away from the model eye is first focused using the model eye and then defocused by placing a positive power meniscus lens in front of the LC lens, as shown in the first image (i) in Fig. 3b. Finally, the target is brought into focus again by compensating for the optical power of the meniscus lens using the negative power LC lens, as shown in Fig. 3b (ii–v). Fig. 3c shows the luminance modulation transfer function, the weighted sum of RGB values (Y = 0.3 × R + 0.59 × G + 0.11 × B), of the entire optical system

Optics and Lasers in Engineering 128 (2020) 106006

comprising the LC lens, a refractive lens, and a CCD with a resolution of 1024 × 768 pixels. The luminance MTFs for different optical powers were determined by analyzing the images of slanted edges in the ISO 12,233 resolution chart obtained under each LC lens power. The luminance MTF 50 slightly decreases with the increase in the optical power, as shown in Fig. 3d. This is because of the higher the optical power, the lower the diffraction efficiency. Because the lens is designed for a wavelength of 543 nm, other wavelengths produce focal planes at different locations, resulting in chromatic aberration. The focal lengths for other wavelengths are determined by 𝑓 (𝜆) = 𝑓0 𝜆0 ∕𝜆, where f0 and 𝜆0 are the design focal length and wavelength, respectively. Although the focal lengths of the LC lens for a red and a blue wavelengths deviate from that of a green wavelength substantially, the chromatic aberration becomes less pronounced when the LC lens is combined with a relatively high power refractive lens such as a human crystalline lens. Fig. 3e shows the depth of field of the combination of the LC lens (2D) and the model eye (52.6 D) for the wavelengths of red (680 nm), green (543 nm), and blue (450 nm) (see Appendix F for the depth of field calculation). The measured planes of focus for R, G, and B locate within the overlapped depth of field. Fig. 4a shows the prototype of compact near-eye see-through AR glasses capable of controlling the depth of a virtual image. It is noteworthy that only one ultrathin diffractive LC lens was placed at the eye side, the common optical path for both real and virtual image, of the commercial AR glasses (BT-300, Epson). Conventionally, a focus tunable lens is placed in the optical path of the virtual image so that the AR glasses maintain the accommodation distance of the real object while correcting that of the virtual image using the LC lens. However, in this prototype, we placed the LC lens in the common optical path for virtual and real image and deliberately utilized the zeroth and first diffraction orders of the LC lens to produce two foci: one for a real object and one for a virtual object. When the lens is turned on, the zeroth-order energy of the incident light is directed at the focal point of the refractive lens, whereas the first-order energy is directed at the effective focal point formed by the combination of the refractive and LC lens. With a negative LC lens power, the real (near) image is formed by high power refractive lens, whereas the virtual (far) object is formed by the combination of the refractive lens and LC lens. The optimal light distributions between far and near vision have been investigated in the field of the diffractive bifocal intraocular lens (IOL) designs [56]. The energy distributions between far and near vision of a number of IOLs used in clinics are 40/40, 70/20, and 77/13 [57]. The maximum (minimum) first diffraction order efficiencies of the LC lens corresponding to optical powers of 1.0 D, 1.5 D, and 2.0 D are 65% (53%), 62% (50%), and 54% (43%), respectively, as shown in Fig. 2b. These are within the range of the amount of the light distributed to far vision of the IOLs. To simulate an AR training task performed within arm’s reach, for example in surgical training, a real object (a teddy bear) was placed 45 cm away from the AR glasses. The virtual image (a heart) was displayed by the commercial near-eye see-through AR glasses at a focal distance of 310 cm. As shown in Fig. 4b, the real object is seen in focus when focusing the model eye on the real object with the LC lens turned off, whereas the virtual image is out of focus because of the mismatch between their accommodation distances. When the lens is turned on with an optical power of −2 D, the focal distance of the virtual image is decreased to 45 cm, bringing both the real and virtual objects in focus. Fig. 4c shows the depth control of the virtual image at other positions for LC lens powers of −1.5 and −1 D, respectively. Three real targets were placed at 50 (K in red), 69 (N in green), and 97 cm (U in blue) away from the AR glasses as references to the depth of the virtual image. When focusing the model eye at 69 and 97 cm, respectively, both the real and virtual toruses were seen in focus for LC lens power of −1.5 and −1 D, respectively. The insets show the images captured when the LC lens was turned off; the virtual torus is out of focus while the real target (K, N, U) is in focus.

M.B. Kumar, D. Kang and J. Jung et al.

Optics and Lasers in Engineering 128 (2020) 106006

Fig. 3. RGB images with different positive and negative powers of the lens under white light illumination without a polarizer or a wavelength filter. (a) Images of USAF resolution with different positive powers of the lens. (i and ii) Images of the target placed at a reading distance (48 cm) when the lens is turned (i) off and (ii) on with +2.0 D. (iii–vi) Images of the target placed at 62, 93, and 193 cm, when the lens is turned on; the corresponding lens powers for focusing are +1.5D, +1.0D, and +0.5 D, respectively. (b) Images of USAF target with different negative powers of the lens. The target is located at 60 cm away from the model eye, and a meniscus lens with opposite power is placed in front of the LC lens. (c) The luminance modulation transfer function of the lens for different optical powers. (d) The MTF 50, showing a slight decrease with increasing the lens power. (e) Depth of fields of the combination of LC lens and the model eye for R, G, and B color with the LC lens power of 2.0 D. The planes of focus for R, G, and B color locate within the overlapped depth of filed, resulting in mitigated chromatic aberration. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

3. Materials and methods Details regarding the lens fabrication are given in the Appendix information. The commercial nematic LC (E7) and SU-8 2000.5 were purchased from INSTEC, Inc (USA) and Micro Chem (USA), respectively. The ITO-coated PET and Poly(vinyl alcohol) were purchased from Sigma

Aldrich (USA). The birefringence of the PET was measured using a retardation film and material evaluation system (RETS-100, Otsuka Electronics Co., Ltd.) with a wavelength of 550 nm. The images were captured using the model eye comprising an achromatic refractive lens (with a focal length of 19.0 mm) and a CCD camera (DCU223C, Thorlabs) with a resolution of 1024 × 768 pixels. The 12 voltage waveforms used to drive

M.B. Kumar, D. Kang and J. Jung et al.

Optics and Lasers in Engineering 128 (2020) 106006

Fig. 4. Schematic of a compact monocular prototype of a see-through near-eye AR system and AR images obtained using the same: (a) Schematic of the compact near-eye see-through AR system. The ultrathin lens is placed between the model eye and the commercial AR glasses. (b) AR images obtained using the AR glasses. (left) AR image when the model eye focuses on the real object and the LC lens is turned off. The virtual image is out of focus because of the accommodation distance mismatch between the real and virtual objects placed at 45 and 310 cm, respectively, (right). When the LC lens is turned on with a power of −2 D, both the real and virtual objects are in focus. (c) AR images when the model eye focuses on the real object “N” placed at 69 cm with an LC lens power of −1.5 D. The inset shows the AR image when the LC lens is turned off. (d) AR image when the model eye focuses on the real object “U” placed at 97 cm with a lens power of −1.0 D. The inset shows the AR image when the LC lens is turned off. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

the lens were generated using a PCI-6723 analog output module (NI). Each channel generates a 100 Hz bipolar pulse with zero DC bias. The MTF was calculated using Imatest Master 5.1.22 (Imatest LLC). Commercial AR glasses (BT-300, Epson) was used for the prototype. The image of the heart was purchased from 123rf.com. 4. Conclusion Despite the recent advancements in resolving the vergence– accommodation conflict in AR display using focus-tunable optics, reducing their form factor remains a key challenge for developing consumergrade AR platforms. We report a substantial progress in the development of the compact vari-focal AR display and the focus tunable lens that significantly reduces the form factor of AR systems by not only reducing the thickness of the lens but also by eliminating the need for a polarizer and a wavelength filter. Our initial study suggests that the proposed optical configuration for AR display and focus-tunable lens offer advances in AR glasses for improved depth perception without substantially compromising the form factor or image quality. In the future, we plan to develop compact gaze-contingent and adaptive focusing AR glasses by integrating the lens with a gaze tracker. Moreover, time-multiplexed operating of the lens will be explored. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment This work was supported by Samsung Research Funding & Incubating Center of Samsung Electronics under project number SRFCIT1301-51, SAMSUNG Research of Samsung Electronics Co., Ltd, and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2017R1A4A1015565 and NRF2015R1D1A1A04060083). Appendix A. Lens fabrication The lens fabrication started from cleaning an ITO coated PET substrate with acetone, IPA, and DI water in an ultrasonic bath for 5 min

Fig. A.1. Image of the lens.

each. The sample was cleaned in UV ozone chamber for 10 min. A photoresist GXR 601 was spin-coated on the sample with 3500 rpm for 30 s and soft baked at 110 °C for 50 s. The photoresist was exposured to UV wavelength of 350 nm with an energy of 18 mJ under the mask for Fresnel zone pattern electrode in the mask aligner (MIDAS MDA-8000B). The UV exposed area of the photoresist was developed by AZ300 developer for 50 s. The photoresist pattern was then hard baked at 110 °C for 2 min. The ITO films not covered by the photoresist was etched by using LCE 12 K diluted by DI water with 1:3 ratio. After rinsing with DI water, a 500 nm thick SU8 2000.5 layer was spin coated on the sample with 4000 rpm for 30 s. The SU8 was exposured to UV with energy of 26 mJ under the mask for via holes. The exposed area of the SU8 was developed by SU8 developer for 1 min 10 s. The sample was then exposured to UV with a power of 10 mJ/sec for 5 min without a mask (flood exposure). The sample was rinsed with acetone, IPA, and DI. A negative image reversal photoresist AZ 5214 was spin coated on the sample with 3500 rpm for 30 s and baked at 110 °C for 1 min. The sample was exposured by UV light with an energy of 25 mJ under the mask for aluminum bus lines followed by hard baking at 110 °C for 1 min 45 s. The photoresist was developed in AZ300 developer. The aluminum bus lines were formed by depositing 600 nm thick aluminum layer by using thermal evaporation followed by a lift-off process. The 2wt% of polyvinyl alcohol (PVA) was prepared and mixed with diameter of 10 μm bead spacers. The PVA was then spin coated on the sample and baked at 90 °C for 1 h. The PVA was also spin coated on ITO coated PET to fabricate a top substrate. The

M.B. Kumar, D. Kang and J. Jung et al.

Optics and Lasers in Engineering 128 (2020) 106006

Fig. B.1. Measurement setup for the voltage– dependent optical transmission.

PVA layers on top and bottom substrates were rubbed by using a velvet cloth. A 10 μm thick adhesive spacers were placed on the rim of the bottom substrate. The top and bottom substrates were then bonded in antiparallel rubbing direction. A commercial E7 liquid crystal was filled into the cell by capillary action at 60 °C. Appendix B. Voltage–dependent optical transmission measurement Fig. B.1 shows the measurement setup for voltage–dependent optical transmission of the homogeneously aligned LC between PET substrates. The setup is comprising a 543 nm wavelength He-Ne laser, an attenuator (ATT), a half wave plate, a spatial filter, a refractive lens (with focal length of 200 mm), an aperture, a polarizer, the LC lens, and an analyzer. The intensity of the light incident on the PET(0°)/LC(45°)/PET(90°) structure was monitored by the optical power meter. The intensity kept constant regardless of the orientation of optical axes of the polarizer by adjusting an attenuator and a half wave plate. The spatial filter consists of a microscope objective, a pinhole aperture, and a positioning mechanism. The refractive lens was used to collimate the beam. The angle

between the optical axes of the polarizer and the LC was changed by rotating the optical axes of the polarizer and the analyzer. The angle between the polarizer and the analyzer is perpendicular to each other during rotation. The optical transmission was measured for the different angles (𝜑) between the optical axes of LC and the polarizer as a function of the voltage applied to the LC. All 12 electrodes were electrically connected during the measurement. Fig. B.2a–c shows the voltage–dependent optical transmission of the PET(0°)/LC(45°)/PET(90°) structure with angle between polarizer and LC lens of 0°, 45°, and 90°, respectively. The optical transmission oscillates between the minimum and maximum value as a function of the voltage applied to the LC as the effective birefringence of the PET(0°)/LC(45°)/PET(90°) structure goes through full and half wave plate conditions. The voltage–dependent optical transmission (Icross) can be translated into the effective phase modulation of the PET(0°)/LC(45°)/PET(90°) structure, and the relation between the optical transmission and the phase retardation in crossed polarizers is described in Eq. (8) in Appendix C. Fig. B.2.d shows the effective phase modulation of the PET(0°)/LC(45°)/PET(90°) structure as a function of voltage.

Fig. B.2. Voltage–dependent optical transmission between polarizer and LC lens of (a) 0˚, (b) 45˚, (c) 90˚, and (d) Effective phase modulation as a function of voltages applied to the LC.

M.B. Kumar, D. Kang and J. Jung et al.

Optics and Lasers in Engineering 128 (2020) 106006

Δ ⎡ cos Δ − 𝑖sin Δ cos2𝛾 − 𝑖sin sin2𝛾 2 2 2 T=⎢ Δ Δ ⎢ −𝑖sin Δ sin2𝛾 cos + 𝑖sin cos2𝛾 ⎣ 2 2 2

⎤ ⎥ ⎥ ⎦

(3)

where T is the transmission of the light. R(𝛾) and R(-𝛾) are the rotation and reverse rotation matrix, respectively. The reverse rotation matrix is used to refer back to the original reference axis (X, Y). The optical transmission for the structure of PET(0°)/LC(45°)/PET(90°), Eout , can be calculated by multiplying Jones matrix for PET1, LC, and PET2: Fig. C.1. The orientation of extraordinary and ordinary axes of the retarder with respect to the reference axis.

Appendix C. Jones matrix equation The retardation in birefringent material can be modelled as a retardation matrix. We consider a PET and LC as retarders that introduce a phase difference (Δ) between ordinary and extraordinary rays. The retardation could be considered as − Δ2 along the slow axis and + Δ2 along the fast axis. Thus, the incident light on a retarder can be represented by following complex number notation; Δ

⎡ e−𝑖 2 P=⎢ ⎢ ⎣ 0

0 Δ

e+𝑖 2

⎤ ⎥ ⎥ ⎦

(1a)

Eout

Δ1 Δ1 Δ ⎡ − 𝑖sin 1 sin2𝛾 ⎢ cos 2 − 𝑖sin 2 cos2𝛾 2 PET1 = ⎢ Δ Δ1 Δ1 ⎢ −𝑖sin 1 sin2𝛾 cos + 𝑖sin cos2𝛾 ⎣ 2 2 2

⎤ ⎥ ⎥ ⎥ ⎦

( ) ( )⎤ Δ2 (V) Δ2 (V) Δ (V) ⎡ ◦ sin2 𝛾 + 45◦ ⎥ − 𝑖sin 2 ⎢ cos 2 − 𝑖sin 2 cos2 𝛾 + 45 2 LC = ⎢ ( ) ( ) ⎥ Δ (V ) Δ (V ) Δ (V ) ⎢−𝑖sin 2 sin2 𝛾 + 45◦ cos 2 + 𝑖sin 2 cos2 𝛾 + 45◦ ⎥ ⎣ ⎦ 2 2 2 (5) ( ) ( ) Δ1 Δ1 Δ ⎡ ◦ − 𝑖sin 1 sin2 𝛾 + 90◦ ⎢ cos 2 − 𝑖sin 2 cos2 𝛾 + 90 2 PET2 = ⎢ ( ) ( ) Δ Δ Δ ⎢ −𝑖sin 1 sin2 𝛾 + 90◦ cos 1 + 𝑖sin 1 cos2 𝛾 + 90◦ ⎣ 2 2 2

Δ2 (V) Δ2 (V) Δ Δ Δ (V ) Δ (V ) ⎡ 2sin 1 cos 1 sin 2 − 𝑖sin 2 cos2𝛾cosΔ1 ⎢ cos 2 + 𝑖sin 2 sin2𝛾cosΔ1 2 2 2 2 = ⎢ Δ1 Δ1 Δ2 (V) Δ2 (V) Δ2 (V) Δ2 (V) ⎢ −2sin cos sin − 𝑖sin cos2𝛾cosΔ1 cos − 𝑖sin sin2𝛾cosΔ1 ⎣ 2 2 2 2 2 2

A retarder introduces a rotation (𝛾) and retardation (Δ), where 𝛾 is the angle between the ordinary axis of the PET and optical axis of the incident light. The orientation of extraordinary and ordinary axes of the retarder with respect to the optical axis of incident light can be represented as in Fig. C.1. Jones matrix for a retarder can be represented by following matrix: ][ [ ][ Δ ] cos(𝛾) −sin(𝛾) e−𝑖 2 0 cos(𝛾) sin(𝛾) T = R(−𝛾) P R(𝛾) = Δ sin(𝛾) cos(𝛾) 0 e+𝑖 2 −sin(𝛾) cos(𝛾) (2)

(4)

⎤ ⎥ ⎥ ⎥ ⎦

⎤ ⎥ ⎥ (6) ⎥ ⎦

(7)

The optical transmission in crossed polarizers (Icross ) and the phase retardation (Δ) is described in the following equation: ( ) Δ Δ Δ1 Δ Icross = {4 × sin2 1 cos2 1 + cos2 2 cos2 2(𝛾)} sin2 2 (8) 2 2 2 2 where i is the imaginary unit, Δ1 = 2π ⋅ δn ⋅ dPET ∕λ is the phase retardation of the PET, 𝛿n and dPET are the birefringence and thickness of the PET, Δ2 = 2π ⋅ δn(V) ⋅ d∕λ is the phase retardation of the LC, δn(V) =nef f (V) − n0 , 1/n2ef f (V) = cos2 𝜃(V)/n2e + sin2 𝜃(V)/n2o , 𝜃(V) is a tilt angle between the plane perpendicular to the propagating direction of the ray and the optical axis of the LC, V is the voltage across the LC, d is the thickness of the LC, and 𝜆 is the wavelength of incident light, 𝛾 is the angle between the ordinary axis of PET1 and polarization of incident light. Fig. C.2 shows the numerical calculation of the maximum and Fig. C.2. The maximum and minimum voltagedependent optical transmission of the PET (0°)/LC (45°)/PET (90°) structure calculated based on Jones matrix using the measured birefringence values of PET for red, green and blue wavelengths.

M.B. Kumar, D. Kang and J. Jung et al.

Optics and Lasers in Engineering 128 (2020) 106006

Fig. D.1. Diffraction efficiency measurement setup. Table 1 The depth of field calculations for +2D powered LC lens with different wavelengths.

minimum optical transmission of the PET(0°)/LC(45°)/PET(90°) structure based on Eq. (8) and the measured values of Δ1 for different wavelengths. The optical transmission for a wavelength of 543 nm agrees well with the measured data shown in Fig. 2a. Appendix D. Diffraction efficiency measurement setup Fig. D.1 shows the diffraction efficiency measurement setup for the LC lens. The setup is comprising a 543 nm He-Ne laser, an attenuator (ATT), a half wave plate, a polarizer, a spatial filter, a refractive lens (with a focal length of 200 mm), an aperture 1, a LC lens, an aperture 2, and a power meter. The spatial filter consists of a microscope objective lens and a pinhole aperture. The refractive lens was used to collimate the beam. The lens was placed between the polarizer and the optical power meter. The power meter was placed in the focal plane of the LC lens. The optical axes of the PET1, LC, and PET2 are aligned 45° to each other in anti-clock wise direction as shown in Fig. D.1. The power of the light in the focal plane was measured with the lens on and off for different angles (𝜑) between the extraordinary axis of the LC and the optical axis of the polarizer. The ratio of power between the lens on and off is calculated for the diffraction efficiency. The angle between the optical axes of the polarizer and the LC was changed by rotating the optical axis of the polarizer. The power of the light with lens off was kept constant during the rotation by adjusting the attenuator and the half wave plate. The aperture 2 placed in front of the power meter was used to isolate the first-order diffracted light when the LC lens was on. Appendix E. Electrically reconfigurable phase profile for different optical powers

Wavelength (𝜆)

S0

S

c

DoF

680 nm 543 nm 450 nm

58 cm 60 cm 62 cm

48 cm 50 cm 51 cm

0.0784 0.0726 0.0756

17.1 cm 17.3 cm 18.8 cm

Appendix F. Depth of field calculations Depth of field (DoF) is the distance between nearest and furthest objects are in focus [58].The approximate depth of field can be given by the following equation [59,60]: DoF =

2S2 Nc f2

(9)

where f is the focal length (19.03 mm) of a combination of the achromatic lens and +2D LC lens, N is F-number (1.73), S is the measured focused object distance and c is circle of confusion. Table 1 shows the parameters used in the DoF calculation. The circle of confusion (c) is used to calculate depth of field. To calculate the circle of confusion, the blur circle (C) at object plane was calculated first by, C = A

(S0 − S) S0

(10)

where S0 is the far unfocused object distance. The values are shown in Table 1, and A is the diameter of the aperture (11 mm). The circle of confusion is calculated by multiplying the magnification (m) of the system with the blur circle C. The magnification in terms of the focused

Fig. E.1. Electrically reconfigurable phase profile of the lens for different optical powers.

M.B. Kumar, D. Kang and J. Jung et al.

Optics and Lasers in Engineering 128 (2020) 106006

Fig. F.1. RGB imaging of the lens. (a) Images of USAF resolution target placed at 31 cm when the LC lens was turned off (left) and on (right) with optical power of + 3.0 D. (b) Images of USAF resolution target placed at 60 cm when the LC lens was turned off (left) and on (right) with optical power of −3.0 D. The meniscus lens with optical power of + 3.0 D was placed in front of the LC lens.

object distance and the focal length is as follows: f (11) S−f The circle of confusion (c = C × m) is given by the following equation [59]: m =

c = A

(S0 − S) f × S0 S−f

(12)

To calculate Hyperfocal distance, near acceptable and far acceptable sharpness are calculated by the following equations [58,59]: Hyperfocal distance H: f2 +f Nc Near distance of acceptable sharpness Dn :

H =

S(H − f ) H + S − 2f Far distance of acceptable sharpness Df :

Dn =

Df =

S(H − f ) H−S

(13)

(14)

(15)

References [1] Rolland JP, Hua H. Head-mounted display systems. Encycl Opt Eng. New York, NY: Marcel Dekker; 2005. p. 1–13. [2] Cakmakci O, Rolland J. Head-worn displays: a review. J Disp Technol 2006;2:199–216. [3] Mon‐Williams M, Warm JP, Rushton S. Binocular vision in a virtual world: visual deficits following the wearing of a head‐mounted display. Ophthalmic Physiol Opt 1993;13:387–91. [4] Wann JP, Rushton S, Mon-Williams M. Natural problems for stereoscopic depth perception in virtual environments. Vis Res 1995;35:2731–6. [5] Hoffman DM, Girshick AR, Akeley K, Banks MS. Vergence–accommodation conflicts hinder visual performance and cause visual fatigue. J Vis 2008;8:33. [6] Frisby JP, Buckley D, Horsman JM. Integration of stereo, texture, and outline cues during pinhole viewing of real ridge-shaped objects and stereograms of ridges. Perception 1995;24:181–98.

[7] Interrante V, Ries B, Anderson L. Distance perception in immersive virtual environments, revisited. In: Proceedings of the IEEE virtual reality conference (VR 2006). IEEE; 2006. p. 3–10. [8] Thompson WB, Dilda V, Creem-Regehr SH. Absolute distance perception to locations off the ground plane. Perception 2007;36:1559–71. [9] Watt SJ, Akeley K, Ernst MO, Banks MS. Focus cues affect perceived depth. J Vis 2005;5:7. [10] Liu S, Cheng D, Hua H. An optical see-through head mounted display with addressable focal planes. In: Proceedings of the 7th IEEE/ACM international symposium on mixed and augmented reality. IEEE; 2008. p. 33–42. [11] Westheimer G. The Maxwellian view. Vis Res 1966;6:669–82. [12] Rolland JP, Krueger MW, Goon A. Multifocal planes head-mounted displays. Appl Opt 2000;39:3209–15. [13] Akeley K, Watt SJ, Girshick AR, Banks MS. A stereo display prototype with multiple focal distances. In: Proceedings of the ACM transactions on graphics (TOG). ACM; 2004. p. 804–13. [14] Schowengerdt BT, Murari M, Seibel EJ. 44.1: volumetric display using scanned fiber array. In: Proceedings of the SID symposium digest of technical papers. Wiley Online Library; 2010. p. 653–6. [15] Lippmann G. Epreuves reversibles donnant la sensation du relief. J Phys Theor Appl 1908;7:821–5. [16] Xiao X, Javidi B, Martinez-Corral M, Stern A. Advances in three-dimensional integral imaging: sensing, display, and applications. Appl Opt 2013;52:546–60. [17] Lanman D, Luebke D. Near-eye light field displays. ACM Trans Graph 2013;32:220. [18] Hua H, Javidi B. A 3D integral imaging optical see-through head-mounted display. Opt Express 2014;22:13484–91. [19] Song W, Wang Y, Cheng D, Liu Y. Light f ield head-mounted display with correct focus cue using micro structure array. Chin Opt Lett 2014;12:060010. [20] Peterka T, Kooima RL, Sandin DJ, Johnson A, Leigh J, DeFanti TA. Advances in the dynallax solid-state dynamic parallax barrier autostereoscopic visualization display system. IEEE Trans Vis Comput Graph 2008;14:487–99. [21] Urey H, Chellappan KV, Erden E, Surman P. State of the art in stereoscopic and autostereoscopic displays. Proc IEEE 2011;99:540–55. [22] Maimone A, Fuchs H. Computational augmented reality eyeglasses. In: Proceedings of the IEEE international symposium on mixed and augmented reality (ISMAR). IEEE; 2013. p. 29–38. [23] Hua H. Enabling focus cues in head-mounted displays. Proc IEEE 2017;105:805–24. [24] Marran L, Schor C. Multiaccommodative stimuli in VR systems: problems & solutions. Hum Factors 1997;39:382–8. [25] Wetzstein G, Lanman D, Hirsch M, Raskar R. Tensor displays: compressive light field synthesis using multilayer displays with directional backlighting. ACM Trans Graph 2012;31:1–11. [26] Suyama S, Date M, Takada H. Three-dimensional display system with dual-frequency liquid-crystal varifocal lens. Jpn J Appl Phys 2000;39:480. [27] Liu S, Hua H. Time-multiplexed dual-focal plane head-mounted display with a liquid lens. Opt Lett 2009;34:1642–4. [28] Love GD, Hoffman DM, Hands PJ, Gao J, Kirby AK, Banks MS. High-speed switchable lens enables the development of a volumetric stereoscopic display. Opt Express 2009;17:15716–25. [29] Konrad R, Cooper EA, Wetzstein G. Novel optical configurations for virtual reality: evaluating user preference and performance with focus-tunable and monovision near-eye displays. In: Proceedings of the CHI conference on human factors in computing systems. ACM; 2016. p. 1211–20. [30] Padmanaban N, Konrad R, Stramer T, Cooper EA, Wetzstein G. Optimizing virtual reality for all users through gaze-contingent and adaptive focus displays. Proc Natl Acad Sci 2017;114:2183–8. [31] Liu S, Hua H, Cheng D. A novel prototype for an optical see-through head-mounted display with addressable focus cues. IEEE Trans Vis Comput Graph 2009;16:381–93. [32] Wang Y-J, Chen P-J, Liang X, Lin Y-H. Augmented reality with image registration, vision correction and sunlight readability via liquid crystal devices. Sci Rep 2017;7:433. [33] Kuiper S, Hendriks B. Variable-focus liquid lens for miniature cameras. Appl Phys Lett 2004;85:1128–30. [34] Ren H, Wu S-T. Variable-focus liquid lens. Opt Express 2007;15:5931–6. [35] Held RT, Cooper EA, Banks MS. Blur and disparity are complementary cues to depth. Curr Biol 2012;22:426–31. [36] So RH, Wong W, Yip R, Lam AK, Ting P. Benefits of matching accommodative demands to vergence demands in a binocular head-mounted display: a study on stereo fusion times. Presence Teleoper Virtual Environ 2011;20:545–58. [37] Ren H, Fan Y-H, Wu S-T. Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals. Appl Phys Lett 2003;83:1515–17. [38] Li G, Mathine DL, Valley P, Äyräs P, Haddock JN, Giridhar M, Williby G, Schwiegerling J, Meredith GR, Kippelen B. Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications. Proc Natl Acad Sci 2006;103:6100–4. [39] Li L, Bryant D, Van Heugten T, Bos PJ. Near-diffraction-limited and low-haze electro-optical tunable liquid crystal lens with floating electrodes. Opt Express 2013;21:8371–81. [40] Li L, Bryant D, Van Heugten T, Duston D, Bos PJ. Near-diffraction-limited tunable liquid crystal lens with simplified design. Opt Eng 2013;52:035007. [41] Jamali A, Bryant D, Zhang Y, Grunnet-Jepsen A, Bhowmik A, Bos PJ. Design of a large aperture tunable refractive Fresnel liquid crystal lens. Appl Opt 2018;57:B10–19. [42] Li G, Valley P, Äyräs P, Mathine DL, Honkanen S, Peyghambarian N. High-efficiency switchable flat diffractive ophthalmic lens with three-layer electrode pattern and two-layer via structures. Appl Phys Lett 2007;90:111105.

M.B. Kumar, D. Kang and J. Jung et al. [43] Lee C-R, Lo K-C, Mo T-S. Electrically switchable Fresnel lens based on a liquid crystal film with a polymer relief pattern. Jpn J Appl Phys 2007;46:4144. [44] Fan Y-H, Ren H, Wu S-T. Switchable Fresnel lens using polymer-stabilized liquid crystals. Opt Express 2003;11:3080–6. [45] Valley P, Mathine DL, Dodge MR, Schwiegerling J, Peyman G, Peyghambarian N. Tunable-focus flat liquid-crystal diffractive lens. Opt Lett 2010;35:336–8. [46] Lin Y-H, Chen H-S, Lin H-C, Tsou Y-S, Hsu H-K, Li W-Y. Polarizer-free and fast response microlens arrays using polymer-stabilized blue phase liquid crystals. Appl Phys Lett 2010;96:113505. [47] Ren H, Lin Y-H, Fan Y-H, Wu S-T. Polarization-independent phase modulation using a polymer-dispersed liquid crystal. Appl Phys Lett 2005;86:141110. [48] Li Y, Wu S-T. Polarization independent adaptive microlens with a blue-phase liquid crystal. Opt Express 2011;19:8045–50. [49] Patel JS, Rastani K. Electrically controlled polarization-independent liquid-crystal Fresnel lens arrays. Opt Lett 1991;16:532–4. [50] Lin L-C, Jau H-C, Lin T-H, Fuh AY-G. Highly efficient and polarization-independent Fresnel lens based on dye-doped liquid crystal. Opt Express 2007;15:2900–6. [51] Kim D-W, Yu C-J, Kim H-R, Kim S-J, Lee S-D. Polarization-insensitive liquid crystal Fresnel lens of dynamic focusing in an orthogonal binary configuration. Appl Phys Lett 2006;88:203505.

Optics and Lasers in Engineering 128 (2020) 106006 [52] Kress B, Meyrueis P. Digital diffractive optics. John Wiley & Sons Ltd; 2000. [53] America O. Handbook of optics, vol. 2: devices, measurements, and properties. McGraw-Hill Professional; 1994. [54] Chen WT, Zhu AY, Sisler J, Bharwani Z, Capasso F. A broadband achromatic polarization-insensitive metalens consisting of anisotropic nanostructures. Nat Commun 2019;10:355. [55] Huang B-Y, Lin T-H, Jhuang T-Y, Kuo C-T. Electrically tunable Fresnel lens in twisted-nematic liquid crystals fabricated by a Sagnac interferometer. Polymers (Basel) 2019;11:1448. [56] Davison JA, Simpson MJ. History and development of the apodized diffractive intraocular lens. J Cataract Refract Surg 2006;32:849–58. [57] Millán MS, Vega F, Ríos-López I. Polychromatic image performance of diffractive bifocal intraocular lenses: longitudinal chromatic aberration and energy efficiency. Invest Ophthalmol Vis Sci 2016;57:2021–8. [58] Salvaggio NL, Salvaggio N, Stroebel LD, Zakia RD. Basic photographic materials and processes. Taylor & Francis; 2009. [59] Allen E, Triantaphillidou S. The manual of photography and digital imaging. Focal Press; 2012. [60] B. Wikipedians, FPC terminology, PediaPress.