1. Introduction

Augmented reality (AR) combines computer-generated virtual images with surroundings. The optical engines in AR are designed to projected virtual images. Virtual reality (VR) is people who see projected virtual images when the distance between the projection lens and a display (a liquid crystal display or an organic light-emitting diode) is less than a focal length of the projection lens. In 2021 AR Optics Academic Forum, Meta FRL, chief scientist, Dr. Michael Abrash, said that the ultimate goal of AR and VR are eyeglass-looks, power consumption of the system less than 1 watt, light weight (<70 g), and socially acceptable appearance. However, AR or VR wearable devices still suffer from two main problems related to human eyes: vergence-accommodation conflict (VAC) and the vision corrections [1–6]. When human eyes intend to see a real object, the movement of both the eyes is triggered by the stereoscopic disparity, and the eyeballs start to rotate (vergence) toward the object of interest. Subsequently, the crystalline lenses of two eyes start to change their curvatures, which leads to a change in the focal length (i.e., accommodation) until the eyes see the object of interest clearly. Two dimensional images with disparity in AR and VR are generated for a binocular view to realize three dimensional experiences. When the mismatch between vergence and accommodation is large, people feel visual discomfort and fatigue [7]. In monovision, when the virtual image does not coincide with a real object, the eyes have to accommodate constantly in order to see both of the real object and the projected virtual image. This is so-called a registration problem (or focus rivalry). The registration problem occurs only in AR optical systems, and the solutions proposed to address this problem can also be used to help in the VAC problem [6]. Generally, the optical elements in the current AR and VR systems provide fixed optical properties, resulting in the virtual image located at a fixed location which leads to unavoidable VAC. Tunability in optical systems could help to achieve VAC-free AR/VR systems. As to vision correction, people have different eye conditions, but the designs of AR/VR systems are not tailored to all people. It needs tunable optics in AR/VR systems. Therefore, VAC-free AR/VR systems with vision correction should be developed.

In literatures, many research groups proposed tunable optics to solve VAC and vision correction in AR/VR. [5,6,8–11] The focal surface approach uses a spatial light modulator (SLM) as a freeform optics in order to provide arbitrary depth of image plane; however, the image quality of the projected image is limited by the resolution of the SLM [12]. A digitally switchable multi-focal lens is proposed by using SLM and freeform optics [13]. Both of the resolution of the SLM and the fabrication of the freeform lens limit the performance. Implementing a tunable plate can shift the image plane by changing the optical path length, but this approach generates limited range of the image depth as well as extra optical wavefront aberrations [14]. The light field approach provides a true 3 dimensional image, but its resolution degrades intrinsically [15–17]. For tunable lenses approach, the current gradient-index liquid crystal lenses present slow response time (∼1 sec) or small lens powers for shifting the image plane [6,18–23]. In 2009, G. D. Love et. al. cleverly proposed a high-speed switchable lens using two ferroelectric liquid-crystal(LC) polarization switches and two birefringent calcite lenses for the original purpose of a volumetric stereoscopic display [24]. The first polarizer produces vertically polarized light that is either rotated or not by the first ferroelectric LC polarization switch. The first lens focuses the two polarization states differently. A second ferroelectric LC switch and lens produce two more possible focal lengths for each of the first polarization states creating four focal states in all. Later on, many papers demonstrated different kind of tunable lenses based on the principle of a polarization controller combined with a passive anisotropic lens [25–30]. However, to date, no tunable optical elements could fit both AR/VR systems. In this paper, we develop a LC lens set whose focal length is rapidly tunable (<50 msec) and it shows 4 operating modes with 4 lens powers. The maximum lens power is ∼ 3.06 diopters. Moreover, it could be used in both of AR and VR systems to provide functions of VAC-free as well as vision correction. The design and mechanism of the LC lens set are discussed. The performance of AR and VR systems adopted with the LC lens set is also demonstrated for proof-of-concept. The impact of this study is to inspire researchers to develop tunable optics for AR/VR systems.

2. Operating principles

The structure and operating principle of the LC lenses are depicted in Figs. 1(a) to 1(c). The structure of a LC lens consists of three glass substrates, two indium-tin-oxide (ITO) layers, four alignment layers, a layer of nematic LC, a lens (i.e., plano-convex glass lens) and one LC polymeric layer, as illustrated in Fig. 1(a). The LC layer, so-called twisted nematic (TN) LC cell or TN cell, functions as a tunable half-wave plate for the purpose of switching polarizations of light. In the LC layer, the LC molecules near the top and bottom glass substrates are aligned along x-direction and z-direction, respectively. The LC molecules are then rotated gradually from x-direction to z-direction from top to bottom of the TN cell. Without the external electric field, the z-linearly polarized light incident to the LC layer is converted to x-linearly polarized light. This is because the excitation of linearly polarized x-eigen-mode in the twist of LC molecules when the incident light is linearly polarized z-eigen-mode. The x-linearly polarized light then propagates to the LC polymeric layer. The lens power of the LC polymeric layer is related to the polarization of light. The x-linearly polarized light is diverged because of a negative lens power (P_LC) resulting from the summation of a positive lens power of the lens and a negative lens power of the LC polymeric layer. P_LC then equals to (n_g-n’_e)/R < 0, where R is the radius of curvature of the lens, n’_e is extraordinary refractive index of LC polymeric layer, and n_g is refractive index of the lens (n_g < n’_e). The LC lens then functions as a negative lens at V = 0. When the voltage(V) exceeds the threshold voltage (V_th) a lot, the LC molecules are reoriented along y-direction and then the z-linearly polarization remains. For the z-linearly polarized light, P_LC then equals to (n_g-n’_o)/R, where n’_o is ordinary refractive index of LC polymeric layer. The z-linearly polarized light is still collimated because n_g ∼n’_o, as depicted in Fig. 1(c). Thus, no focusing effect at V>>V_th. The difference of the lens powers between V = 0 and V>>V_th is Δn’/R, where Δn’ is the birefringence of the LC polymeric layer (i.e., Δn’ = n’_e-n’_o). Therefore, the LC lens has two different lens powers.

 

Fig. 1. (a) Structure of the LC lens. Red arrows indicate the rubbing direction of the alignment layers. (b) The LC lens is a negative lens at V = 0. (c) No focusing effect of the LC lens at V>>V_th. The LC polymeric layer functions as a passive anisotropic lens. When three LC lenses stack together, 4 LC modes are displayed: (d) LC mode 0, (e)LC mode 1, (f) LC mode 2, and (g) LC mode 3.

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Four LC modes could be operated when we use three LC lenses and one polarizer (we call “LC lens set”). Three LC lenses (Lens A, Lens B and Lens C) are stacked together, and one polarizer is attached for the purpose of z-linearly polarized incident light, as depicted in Figs. 1(d)–1(g). In Fig. 1(d), three LC lenses turn on (V>> V_th), the z-linearly polarized light propagates through three LC lenses without changing polarization and then the LC lens set exhibits no focusing effect. In Fig. 1(e), only lens C turns on, z-linearly polarized light is switched to x-linearly polarization after passing through lens A and then is switched back to z-linearly polarization. The lens power equals (n_g-n’_e)/R. Similarly, when only the lens B turns on, z-linearly polarized light is switched to x-linearly polarization after passing through two lenses (lens A and lens B) and then is switched back to z-linearly polarization. The lens power is 2x(n_g-n’_e)/R (Fig. 1(f)). When both of lens B and lens C turn on, z-linearly polarized light is switched to x-linearly polarization, the lens power is 3x(n_g-n’_e)/R (Fig. 1(g)). Here, the operation modes in Figs. 1(d)–1(g) are called “LC mode 0”, “LC mode 1”, “LC mode 2”, and “LC mode 3”, respectively.

The basic of AR or VR systems is the image formation. Assume the system has a lens and a LC lens set as depicted in Fig. 2. The objective distance is p, image distance is q, the focal length of the lens is f and the focal length of the LC lens set is f_LC. The image formation for such a system follows Eq. (1) [6]:

We project the virtual image in a AR or VR system which means q < 0. When f_LC is infinite (i.e. lens power = 1/ f_LC =0), the image formation turns out:

 

Fig. 2. The image system consists of a lens and a LC lens.

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Because of the virtual image in a AR or VR, q’<0 and that requires p < f. From Eqs. (1) and (2), we could obtain Eq. (3):

When the lens power of the LC lens set (1/ f_LC) > 0, this means: $\frac{1}{q} - \frac{1}{{q\mathrm{^{\prime}}}}\mathrm{> }0$ which also indicates $|q |\mathrm{> }|{q^{\prime}} |$ . When we operate the LC lens set as a positive lens, the virtual image is away from the lens ($|q |\mathrm{> }|{q^{\prime}} |$). Similarly, When we operate LC lens set as a negative lens, the virtual image is close to the lens ($|{q^{\prime}} |\mathrm{> }|q |$). This means the virtual images in AR or VR system are going to move close to the eyes when the LC lens set is operated from LC mode 0 to LC mode 3. For the vision correction in AR or VR system, the LC lens set is operated as a negative lens for myopia. Thus, the LC lens set could help in varifocal images in both of AR and VR systems and vision correction for myopia.

The fabrication of sample in Fig. 1(a) includes two parts: one is fabrication of TN cell and the other one is the part of the LC polymeric layer. For the TN LC cell, the nematic LC (Merck, E7, Δn = 0.2255) was sandwiched between two ITO glass substrates coated with rubbed polyimide layers (Nissan 7492) which were mechanically buffed and the glass substrates were assembled in an anti-parallel fashion with respect to the rubbing direction. The thickness of the LC layer was 8 microns. As to the LC polymeric layer, we prepared a flat glass substrate and a plano-convex glass lens (BK7) with a lens power of + 4.75 diopters (D) and a radius of curvature of 108 mm. The flat glass substrate and a plano-convex glass lens were coated with mechanically buffered polyimide layers as alignment layers. The rubbing directions at the flat glass substrate and a plano-convex glass lens were arranged in an anti-parallel fashion. We then used the one drop filling method [31] to sandwich nematic LC (Merck, MLC-2144, Δn = 0.2493 for λ = 589.3 nm at 21°C,), reactive mesogen (RM257, Δn = 0.18 for λ = 633nm, Merck) and photoinitiator (IRG-184, Merck) at a ratio of 20:79:1 wt% between the flat glass substrate and the plano-convex glass lens. We exposed the UV light (λ = 365 nm) to the sample for photo-polymerization. After photo-polymerization, we attached the TN cell with the sample of the LC polymeric layer. The thicknesses in the center of the LC polymeric layer and in the peripheral region were around ∼10 µm and ∼ 473 µm, respectively. The aperture size of the LC lens is 20 mm. After we prepared three LC lenses, we stacked them together with a polarizer as a LC lens set. The calculated the lens powers are -0.037 D at V>>V_th and -1.35D at V = 0 based on the parameters of sample fabrication: n_g = 1.514, n’_e = 1.66, and n’_o = 1.518, R = 0.108 m.

3. Experiments and discussion

Before we assembled TN cell to the sample of the LC polymeric layer, we measured the voltage-dependent transmission of the TN cell. The light source was He-Ne laser (Meredith Instruments, HNH-10-633, λ= 633 nm). The TN cell was placed between two crossed polarizers in which one of the transmissive axes was parallel to z-axis and a photodetector (Newport, model 2031) was used to record corresponding transmission. The measured result is shown in Fig. 3(a). The transmission starts to drop after the applied voltage exceeds the threshold voltage (V_th= 0.5 V_rms, f= 1000 Hz). The transmission drops to 0 as V> 2.5 V_rms which means the z-linearly polarized light is converted to x-linearly polarized light. The small up and down between 0.5 V_rms and 1.3 V_rms is because the TN cell does not satisfy the Mauguin condition [31,32]. Mauguin parameter(u): $u = 2 \cdot d \cdot {{\Delta \textrm{n}} / \lambda }$=5.67. To satisfy the Mauguin condition, $u$ should >>1. The measured response times of TN, rise time and decay time, are depicted in Figs. 3(b) and 3(c). We turned on and off applied voltage from 0 to 10 V_rms and 10 V_rms to 0. The rise time is around 1.5 ms and decay time is around 45 ms. Such response times are fast enough to switch varifocal images of AR and VR which could help solving VAC problem. After we assembled TN cell to the sample of the LC polymeric layer in order to construct the LC lens in Fig. 1(a), we measured the lens power of the LC lens by converting the measured wavefronts. The system of wavefront measurement consists of a laser (a diode pumped solid state laser, λ = 532 nm), a single mode fiber to form a point source, a solid lens with a focal length of 20 cm for converting the point source into a collimated light, a linear polarizer to control the polarization of incident plane wave, a pair of homogeneous index lenses (focal length: 26.7 cm and 6.3 cm) as relay optics, and a Shack-Hartmann wavefront sensor (WFS150-7AR, Thorlabs). The samples of the LC lens were placed at the front focal plane of the relay optics. In the measurement, the results from the wavefront sensor were fitted using the first 21 Zernike polynomials (i = 0-20) corresponding to 5^th order Zernike coefficients with ANSI (American National Standards Institute) standard. The lens power is obtained using equation: ${\bar{P}_{LC}} ={-} {{4\sqrt {3 \cdot } {c_4}} / {{r^2}}}$, where c₄ is the Zernike coefficient for i = 4 [33]. The lens power is defined as a reciprocal of a focal length with the unit of diopter (D) or m^-1. The measured wavefronts of the LC lens at V = 0 and V = 10 V_rms (f = 1kHz) are shown in Figs. 3(d) and 3(e). The measured lens powers are -1.12 D at V = 0 and +0.09 D at 10 V_rms. The change of the lens power is 1.21 D. This sample denotes as Lens B. We prepared two more LC lenses which changes to the lens power are 1.09 D (–0.96 D at 0V and +0.13 D at 10 V_rms) and 1.06 D (-0.98 D at 0V and +0.08 D at 10 V_rms). These two lenses are denoted as Lens A and Lens C, respectively. The lens powers are smaller than the theoretical calculation due to fabrication errors of the polymeric layers. The corresponding optical path differences (OPD) of three LC lenses from cross sections of wavefront measurements are depicted in Fig. 3(f). When the TN cell turns off, the z-lineay polarized light is converted to x-linearly polarized light which is an extraordinary wave(e-wave) to the LC polymeric layer. Similarly, the z-linearly polarized light is ordinary wave(o-wave) to the LC polymeric layer as the TN cell turns off. In Fig. 3(f), we can see three LC lenses have closed OPD (50∼55 microns) at 10 V_rms but slight difference at V = 0. This is due to the variations in thickness of the polymeric layers.

 

Fig. 3. (a) Voltage dependent transmission of TN cell. (b) is rise time and (c) is decay time of the TN cell. Measured wavefronts of the LC lens at (d)V = 0 and (e)V = 10 V_rms. (f) Optical path difference of three LC lenses from cross sections of wavefront measurements. e-wave means V = 0 of a TN cell (solid lines) and o-wave means V = 10 V_rms of a TN cell (dotted lines).

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Thereafter, we attached three LC lenses with a polarizer together as a LC lens set and then the wavefronts for operating 4 different modes are shown in Figs. 1(d)–1(g). The results are shown in Figs. 4(a) to 4(d). Four LC modes display -2.75 D for the LC mode 3, -1.80D for the LC mode 2, -0.79D for the LC mode1, and +0.32D for the LC mode 0. When we add the results of three LC lenses directly from Fig. 3(f), the calculated four LC modes are -3.06 D for the LC mode 3, -2.00 D for the LC mode 2, -0.79D for the LC mode1, and +0.30D for the LC mode 0. Figure 4(e) shows OPD of the LC lens set from cross sections of wavefront measurements (solid lines) and OPD from adding the results of three LC lenses in Fig. 3(f) (dotted lines). Compared the lens powers of the LC lens set and the lens powers from addition of three individual LC lens, the lens powers, calculated from the Zernike coefficient c₄, are slightly different. From Fig. 4(e), we can see the variation of wavefronts and this results from the assembly error of three lenses.

 

Fig. 4. Measured wavefront of the LC lens set (three LC lenses). (a) LC Mode 3: V = 0 in Lens A, and V = 10 V_rms in both of Lens B and Lens C. (b) LC Mode 2: V = 0 in both Lens A and Lens C, and V = 10 V_rms in Lens B. (c) LC Mode 1: V = 0 in both Lens A and Lens B, and V = 10 V_rms in Lens C.(d) LC Mode 0: V = 10 in three lenses.(e) Optical path difference (OPD) of the LC lens set from cross sections of wavefront measurements(solid lines) and from adding the results of three LC lenses in Fig. 2(f) (dotted lines).

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To further demonstrate that the LC lens set could provide electrically tunable varifocal virtual image and vision correction in both of AR and VR system, we set up a simple VR system for proof-of-concept. We used a camera, a solid lens with a lens power of 20 D (i.e. focal length of 5 cm), the LC lens set and a cell phone (Apple, iphone 12). The cell phone was placed 4.65 cm (less than focal length of the solid lens) away from the LC lens set. We input many “NYCU” on the cell phone screen. In order to identify the locations of virtual images at different LC modes, we also placed several papers printed with words and then adjusted the locations of the papers till the camera saw the clear images on the papers. Figures 5(a) to 5(d) exhibit the performance of the virtual images at four LC modes. The locations of four virtual images are 68.17 cm for LC mode 0, 38.97 cm for LC mode 1, 25.47 cm for LC mode 2, and 19.67 cm for LC mode 3. The changes of lens power is 3.62 D (1/0.1967-1/0.6817 = 3.62) which is larger than the measurement of 3.06 D. This is because the effective aperture size we see from camera is less than 20 mm. The effective aperture size is calculated∼ 18.4 mm based on lens power inversely proportional to squared aperture size. From Figs. 5(a) to 5(d), the 4 virtual image planes are electrically switchable with fast response time (∼50 ms). The fast-switching varifocal images are able to solve the VAC problem. In Fig. 5, the image sharpness could be further optimized by reducing the image ghost caused by multiple reflections, which mainly originates from between air and glass interface (see Figs. 1(d)–1(g)), with anti-reflection coating. In addition, since the TN cell does not well satisfy the Mauguin condition for λ= 633 nm), it is prone to high wavelength dispersion caused by internal reflections and causes the color shifting effect. As a result, we can observe color-dependent magnification in Fig. 5 . The aberration in Fig. 5 is from large lens power of the solid lens (20D).

 

Fig. 5. Varifocal testing of VR. Recorded images at (a) LC mode 0, (b) LC mode 1, (c) LC mode 2, and (d) LC mode 3.

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To demonstrate the LC lens set is able to help in vision correction in VR, we also set up the similar VR system, depicted in Fig. 6(a). The LC lens set was attached to the solid lens and a convex lens was placed in front of the camera. At first, without the convex lens, we adjusted the camera till we saw the clear image on the cell phone. Then we placed a convex lens in front of camera in order to mimic myopia eye. We used a convex lens with lens powers of +1D and then the blurred image was observed in Fig. 6(b). Thereafter, we observed clear image in Fig. 4(e) after the LC lens set was operated in LC mode 1. This means the LC lens set at LC mode 1 could correct myopia with 1D and it indicates the lens power of the LC lens set at LC mode 1 is around -1D. Similarly, we used different convex lenses with lens powers of +2.5D, and +3.5D while the LC lens set was at LC mode 0. The images were shown in Figs. 6(c) and 6(d). The images are more blurred as the lens power of the convex lens increases (Figs. 6(b) to 6(d)). Then the LC lens set was operated in LC mode 2, and LC mode 3, the images turned out clear in Figs. 6(f) and 6(g), respectively. This means the lens powers of the LC lens set at LC mode 2 and LC mode 3 are around -2.5D and -3.5 D, respectively. We can see that the LC lens set could be used for vision correction. From Figs. 6(b) to 6(g), the lens powers of the LC lens set (-1D, -2.5, and -3.5D) are larger than those from the wavefront measurement. This is also because of the effective aperture size is around 18.4 mm, not 20 mm. When we calculate the lens powers for the aperture size of 18.4 mm, the lens powers turn out 3.61 D for LC mode 3, 2.36 D for LC mode 2, 0.93 D for LC mode 1 which are close to the lens powers of the convex lenses used in Fig. 6.

 

Fig. 6. (a) Experimental setup for vision correction of VR. We use a camera and a convex lens to mimic a myopia eye. In LC mode 0, the recorded images as convex lens is (b) + 1D, (c) +2.5D, and (d) +3.5D. The blurred images in (b), (c), and (d) are corrected after the LC lens set is operated at (e) LC mode 1, (f) LC mode 2, and (g) LC mode 3, respectively.

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To demonstrate the varifocal imaging of the LC lens set in AR, we set up a simple AR system, as illustrated in Fig. 7(a). The AR system consists of a microLED display (JBD, JBD5UM720PG, active area: 0.31 inch, resolution: 1280 × 720, 5000ppi, λ=525nm), the LC lens set, a solid lens with lens power of 20 D, a beam splitter, and a camera. The distance between the microLED and the solid lens should be less than the focal length of the solid lens in order to satisfy the image formation of a virtual image. We placed several targets at 532 cm (new year scroll), 76, cm(tiger), 38 cm (cabbage) and 26 cm(dolls). In Fig. 7(b), the camera was set to see the images located at 532 cm away from the beamsplitter without the LC lens set. When we put the LC lens set to the setup and the LC lens set was at LC mode 0, the camera saw both the new year scroll and projected virtual image “NYCU 534cm” clearly. The image distance was 534 cm by adding 2 cm, the distance between the beamsplitter and the solid lens. We then adjusted the camera in order to see the dolls at 26 cm clearly (Fig. 7(c)). Since the virtual image was still located at the 532 cm, the virtual image was blurred in Fig. 7(c). After the LC lens set was operated at LC mode 3 and we input words “NYCU 28 cm” to the microLED display, we saw both of cabbage and “NYCU 28 cm” were clear in Fig. 7(d). This indicates both of the cabbage and “NYCU 28 cm” (the real object and the virtual image) were located in 26 cm away from the beamsplitter. The image distance was 28 cm. The change of the lens power of the LC lens set is 3.38D (1/0.28-1/5.34 = 3.38) which is close to the experimental result of 3.06 D. In Figs. 7(e) to 7(h), we adjusted camera to see the real objects at 4 locations and then the LC lens set were operated at LC mode 0, LC mode 1, LC mode 2, and LC mode 3, respectively. From Figs. 7(e) to 7(h), we were able to rapidly switch virtual images at 4 locations to realize the varifocal function in AR.

 

Fig. 7. (a)Experimental setup for varifocal testing of AR. (b) Recorded images at LC mode 0. The real image and virtual image(“NYCU 534 cm”) located at 532 cm are clear. (b) We adjust camera till the dolls are clear, but the virtual image is blurred. (d) To see the clear virtual image, LC lens set is operated at LC mode 3. Both of the dolls and the virtual image(“NYCU 28cm”). The virtual image is at 532 cm, 76 cm, 38 cm, and 26 cm as the LC lens set is operated at (e)LC mode 0, (f) LC mode 1, (g) LC mode 2, and (h) LC mode 3, respectively.

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To demonstrate LC lens set is also able to perform vision correction in AR, we used the same AR setup, but we changed the position of the LC lens set (Fig. 8(a)). In addition, we also placed a convex lens in front of camera for the purpose of mimicking an eye with myopia. In the beginning, we set camera to see the object located at 532 cm (new year scroll). The images of new year scroll and the virtual image (“NYCU 534 cm”) were blurred in Fig. 8(b) after we put the convex lens of +1D to the experimental setup. However, the tiger became clear because the image plane shifted to where the tiger is. After we turned on the LC lens set at LC mode 1, the blurred images of the new year scroll and “NYCU 534 cm” became clear again. Similarly, the blurred images at 532 cm would become clear again by operating of LC lens set at LC mode 2 and LC mode 3 (Figs. 8(f) and 8(g)) when the images were blurred causing by convex lenses in Figs. 8(c) and 8(d). From above, the vision correction in this AR system could be realized. From Figs. 8(b) to 8(g), it indicates the LC lens set are around -1D, -2.5D and -3.5D when the LC lens set is operated at LC mode 1, LC mode 2, and LC mode 3, respectively. This is close to the results in Fig. 6.

 

Fig. 8. (a) Experimental setup for vision correction of AR. We use a camera and a convex lens to mimic a myopia eye. In LC mode 0, the recorded images as convex lens is (b) + 1D, (c) +2.5D, (d) +3.5D. The blurred images in (b), (c), and (d) are corrected after the LC lens set is operated at (e) LC mode 1, (f) LC mode 2, and (g) LC mode 3, respectively.

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From above, the LC lens set with 4 operated modes could be applied to both of AR and VR systems for varifocal images as well as vision corrections. The response time is less than 50 msec which is faster than the response time of the typical response time of GRIN LC lens ∼ couple hundreds msec to 1 sec [19]. Fast response time is a requirement of varifocal images for the purpose of solving VAC. To further understand how tunable optics with fast response time could improve viewer comfort (or solve VAC), the paper published by Paul V. Johnson et. al. explained the mechanism well [8]. As to how large of the lens power of a tunable lens is enough for varifocal images in VR, X. Hu and H. Hua also explained that the lens power of 3D is enough for varifocal images in VR to solve VAC [34]. In terms of the vision corrections, according to statistical analysis of European Eye Epidemiology Consortium, the lens power of -3D already covers 81.6% of myopia people in Europe [35]. As a result, the LC lens set we proposed in this paper is good for solve VAC in AR/VR as well as vision problem for most of myopia people. To further enlarge the lens powers, more LC lens could be used in a LC lens set, but the tradeoff is the transmittance due to multiple interfaces. To achieve a certain lens power, we can use more LC cells to reduce the thickness of each LC layer for increasing the order parameter of LC and then reduce the light scattering effect. However, when we keep cascading the LC cells for a larger lens power, the overall scattering effect could increase.

4. Conclusion

We design a LC lens set consisting of three LC lenses for varifocal images and vision corrections in both of AR and VR systems. Four operating modes of such a LC lens set could exhibit electrically tunable three lens powers: 0 diopter, -0.79 diopter, -2 diopters, and -3.06 diopters by means of manipulation of polarization of incident light using tunable half wave plate (i.e., TN cell). The response time is fast < 50 ms compared to the typical GRIN LC lens (∼1 sec). We also demonstrate how to apply the LC lens set to both of AR and VR systems to display functions of varifocal images and vision corrections. The tunable range and the response time are suitable for varifocal images. The range of lens powers could cover most of population of myopia in Europe. The fast-switching LC lens set has great potential not only in applications of AR/VR, but also applications of detection in Advanced Driver Assistance Systems (ADAS) and surveillance system.