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Abstract
Optical devices like virtual reality (VR) headsets present challenges in terms of vergence-accommodation conflict that leads to visual fatigue for the user over time. Lenses available to meet these challenges include liquid crystal (LC) lenses, which possess a response time in the millisecond range. This response time is slow, while accessing multiple focal lengths. A ferroelectric liquid crystal (FLC) has a response time in the microsecond range. In this article, we disclose a switchable lens device having a combination of the fast FLC-based polarization rotation unit and a passive polarization-dependent LC lens. A cascaded combination of three such lens units allows access to eight different focal points quite rapidly and can be a convenient device for VR applications.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The need to drive lenses without any moving parts and come out with a possible solution has been felt for a long time. However, for the VR application, we need a fast-switchable lens to avoid any optical defects. A review of the progress of LC lenses has been published by Lin et al. in 2011 [1]. The intrinsic speed of Nematic Liquid Crystals (NLCs) is extremely slow for the VR application [2,3]. Thus, the response times of the lenses built using NLCs are in the order of 100 ms [4]. Various approaches have been reported recently to improve the response time. A snapshot for some of these approaches has been shown in Table 1. One approach is lenses made of Dual Frequency LC (DFLC) materials. These materials exhibit a positive dielectric anisotropy (Δɛ) at low-frequency, and show negative dielectric anisotropy, at a high frequency [5]. However, the high frequency may result in dielectric heating causing performance degradation. The response time reported is around 433 ms, the operating voltage is ∼ 15 and 90 V. The aperture is small ∼2 mm, and the focal length varies between -0.25 m to +0.25 m. Diffractive lenses using the dual-frequency LC have been studied as well. But diffractive lenses suffer from low light efficiency. Also, the aperture is only around 400 µm, and the voltage required is still high, around 25 V. The response time, in this case, is 680 µs for the raise time and 550 µs for the relaxation time [6]. Furthermore, diffractive lenses show serious color dispersion.
Table 1. Snapshot of various switching modes for LC lenses.
Another approach is to use optically isotropic materials like blue phase LC (BPLC) [7,11,18–22]. A lens built using the BPLC requires a high voltage of 80 V, which has an aperture ∼450 µm and a focal length ranging from ∞ to 4 cm [13,14,23–27]. They are self-assembled microstructures and do not require an alignment layer. Even though their switching is in the sub-millisecond range, they are still not the fastest. Polymer stabilized LC lenses [28] have also been reported. It, however, has a switching time in the range of milliseconds and requires a low driving voltage of ∼10 V. The aperture, however, is only around 400 µm and has a small focal length of 4 mm. Polymer Dispersed Liquid Crystal (PDLC) with nanodroplets demonstrates better results. The switching time is in the range of hundreds of microseconds. But the switching voltage is high ∼ 80 V [29]. It can, however, produce large-aperture lenses, and the focal length ranges between ∞ to 0.484 m. PDLC lens with hole patterned electrodes has also been studied as a lens candidate [30]. It requires a high voltage of 50 V and shows a small focal length around 20 µm, with a switching time in the ms range.
The idea of a polarization-dependent passive LC lens along with a polarization rotation unit, where the combination is characterized by a low switching voltage, fast switching time, large aperture, and a large focal length range. One approach is to use the TN cell as a polarization rotation unit [9,31,32]. The TN cell used as a polarization rotator, for a polarization-dependent passive LC cell, was reported to show a response of 12 ms of raise time and 40 ms of the relaxation time [9]. Using an LC of lower viscosity, the response time of TN cells reported is around 2 ms [8]. Using an LC cell with a smaller cell gap of 1.6 µm, the response time is further reduced. The rise time reported is 70 µs, and the relaxation time is 1.71 ms at 25°C. At an elevated temperature of 50°C the rise time is 30 µs, and the relaxation time is 690 µs [10]. For the Optically compensated bend (OCB) mode, the switching time is in the range of µs [33]. The switching voltage is 30 V. The aperture, however, is very small, 100 µm, and the minimum focal length is also around 16 mm only. Changing the polarization unit to chiral sematic A, SmC* [12], has reported extremely fast switching in the scale of a few µs. But it is not stable.
Electrically suppressed helix ferroelectric liquid crystals (ESHFLCs) show extremely fast switching [15–17,34,35] with no hysteresis, no fringe field effect, good electro-optic performance, and shock stability [36–39]. These benefits offer it a promising potential to be used as polarization rotator or shutter in different applications in combination with a polarization-dependent passive LC lens. The ESHFLC show binary electro-optical operations and need small driving voltage of ∼5 V. The switching time for the half waveplate ESHFLC at this driving voltage is in the range of 50-100 µs. Thus, the ESHFLC unit may work for the polarization rotation unit. The polarization rotation unit works as a half-wave plate that can rotate the polarization azimuth of the impinging light in one state and does not affect the polarization azimuth in the other state. The out-going light from the ESHFLC cell and polarization-dependent lens in the two states (i.e., Eout1 and Eout2) can be written in the form of Jones matrix [40]-
Fig. 1. The polarization dependent focusing of light for two different switching states of the FLC cell are shown in (a) and (b). Our proposed design showing a combination of a FLC cell acting as a polarization rotation unit and a polarization dependent passive LC lens. Two such units in combination with a polarizer placed in front produces three focal points and an infinite focal length condition.
2. Device fabrication and material properties
Fabrication of the lens has been shown in Fig. 2. The lens is fabricated using a PDMS mold, which was fabricated using the glass lens. Three different concave glass lenses of the focal length of 1 m, 3 m, and 5 m have been used to fabricate the mold. The UV glue (NOA 71) is poured onto the mold, and a glass plate is placed on the top to ensure the flatness of the external lens surfaces. The UV glue is cured at 365 nm for 5 min. The thickness of the fabricated lens is maintained at 1.3 mm. Later, the fabricated lens is coated with an alignment layer of 1% Sulphonic dye (SD1) (from Dai-Nippon Ink and Chemicals) dissolved in ethylene glycol. The ramp-up speed is 800 rpm for 5 s, and the spin speed is 2000rpm for 30 s. (Figure 2(a)) The coated lens is then heated on a hot plate for 30 min at 40°C to dry the surface. A glass plate of 1 cm square, another substrate of the lens, is processed in the same way. First, treated with UV ozone for 40 min, coated with SD1, and dried (Fig. 2(b)). The glass plate with the coated surface inside is placed on the top of the lens and glued (Fig. 2(c)). After the lens assembling, the SD1 is aligned through UV irradiation using a wire grid polarizer at 360 nm (65 mW/cm2) for one hour (Fig. 2(d)). Later, the nematic LC was filled in the cavity using the vacuum (Figs. 2(e)–2(f)). The NLC material used in the lens is E90 + 0.1% ZLI 811. It has a birefringence Δn = 0.2063 and ne = 1.7313. It has a clearing point of 69°C.
Fig. 2. The fabrication steps have been shown. (a) SD1 is spin coated on both the glass substrates and the lens made using UV curable glue. (b) Both the substrates are dried using the hot plate at 40°C. (c) The lens is assembled using the coated glass and cured UV glue substrates. (d) Alignment of SD1 is done using UV of wavelength 360 nm. (e) The assembled lens is filled with LC under vacuum. (f) The filled LC lens. (g) SD1 in both the coated glass substrates are aligned using UV of wavelength 360 nm. (h) The substrates are assembled with the coated surfaces facing each other. (i) The cell is filled with FLC. (j) The filled FLC cell.
The ESHFLC polarization rotation unit is similarly fabricated by coating both the glass substrates with SD1 after exposing the substrates to UV ozone (Fig. 2(g)). The cell is then assembled. The thickness of the cell is maintained at 1.5 µm by the glass spacers (Fig. 2(h)). Lastly, the cell is filled with ESHFLC based on capillary phenomenon (Fig. 2(i)). The FLC mixtures used in the present studies is FLC-595. At T = 22°C, FLC-595 has a spontaneous polarization PS = 40 nC.cm-2, tilt angle θ=21.3°, rotational viscosity γϕ = 0.022 Pa. s. The ESHFLC is characterized by high contrast ratio and fast microsecond response. When the applied voltage is less than the voltage required for helix unwinding, it acts as deform the helix ferroelectric liquid crystal [17]. The FLC helix unwinds at the higher electric field, and thus, provide high optical quality. The critical field of the helix unwinding in the present case is 0.7 V, hence one can achieve good optical quality, without any defects, at the electric field higher than 1 V [17,35,36].
The schematics of the lens unit consisting of the LC polarization-dependent lens, FLC polarization rotation cell, and the polarizer is shown in Fig. 3(a). When the ESHFLC cell is switched under the electric field, the FLC molecules switch between the two states (Fig. 3(b)). These two states are symmetric along the alignment directions. To achieve the 0 to $\pi /2$ phase difference, one of the two switching positions is aligned with the polarization azimuth of the impinging light. Thus, in one state, the ESHFLC cell works as a half waveplate and rotates the polarization azimuth of the impinging light by 90°, while in the second state, it does not affect the impinging light [39]. Under crossed polarizers, both the states can be seen in Fig. 3(c). Similarly, the polarization dependent lens unit have been characterized under crossed polarizers where the optical axis of the lens is at an angle of 45° from the polarization axis of the polarizer and when the optical axis of the lens is parallel to the polarizer (Fig. 3(d)). The response time of the FLC has been characterized. At 500 Hz frequency, switching time of the FLC is ∼15 µs at the driving voltage of 10 V (Fig. 3(e)). It is much faster than any other available device, see Table 1.
Fig. 3. (a) The structure and the alignment direction of a single unit consisting of a FLC cell, a LC lens and a polarizer. (b) The switching of the FLC molecules with respect to the polarizer. (c) Corresponding bright and dark states of the FLC cells kept between crossed polarizers. The binary electro-optic switching of the FLC is shown in the waveform driven at 500 Hz frequency. (d) The polarization dependent lens unit under the crossed polarizer where the optical axis of the lens is at an angle of 45° from the polarization axis of the polarizer and when the optical axis of the lens is parallel to the polarizer. (e) The response time for the switching between the two states for the FLC molecules. For around 10 V, the measured time is 15 µsec. (f) The transmittance vs. wavelength plot showing the effect of glue as a refractive index matching material between the glass surface and the flat surface of the lens made of cured UV glue.
The proposed device uses a multiple stack structure that intrinsically shows huge reflection losses at every interface. To suppress the reflection losses, the ESHFLC cell and the LC lens are glued using the index-matching liquid. The refractive index of the glue is 1.44. The refractive index of glass is 1.5, and the refractive index of the cured UV glue is 1.56. Figure 3(f) shows the optical spectrum of the glass-glue-lens system, which confirms the greatly reduced reflection losses after the application of the index matching glue. The transmission is 100% for the bare glass. The single lens and ESHFLC interface, through the air, shows the transmission of around 85%. The addition of index matching liquid between the two units improves the reflection losses and results in the transmission of ∼96%.
The ESHFLC polarization rotation units are driven using Arduino Mega. The combination consists of a polarizer, 3 FLC cells and 3 polarization dependent passive LC cells. Each FLC cell is individually driven and the driving signals are as shown in Figs. 4(a)–4(c). The output signal obtained when light moves through the combination is shown in Fig. 4(d). Specifically, for one lens unit consisting of the LC polarization-dependent lens, FLC polarization rotation cell, and the polarizer. When the ESHFLC cell is switched under the electric field, the FLC molecules switch between the two states which are symmetric along the alignment directions. To achieve the 0 to $\pi /2$ phase difference, one of the two switching positions is aligned with the polarization azimuth of the impinging light. Thus, in one state, the ESHFLC cell works as a half waveplate and rotates the polarization azimuth of the impinging light by 90°, while in the second state, it does not affect the impinging light. In a nutshell, when 3 units are combined together and driven individually according to the Figs. 4(a)–4(c), the light passes through with 7 focuses and 1 unfocused state.
Fig. 4. The driving signal of 3 FLC rotation units are illustrated as (a) driving signal 1, (b) driving signal 2 and (c) driving signal 3. (d) The output when light propagate through the 3 rotation units. According to the mechanism described, 3 rotation units are driven to generate 8 different combinations.
3. Results and discussion
The mechanism of lensing for a combination of a polarizer, ESHFLC polarization rotation unit and the polarization dependent LC lens has been shown previously in Figs. 1(a)–1(b). The unpolarized light gets polarized after passing through the polarizer. As the polarized light impinges onto the ESHFLC cell, based on the states of the ESHFLC molecule, the polarization azimuth of light could be tuned at a fast speed. If this polarization is aligned with the optic axis of the polarization-dependent LC molecules in the lens, the refractive index is 1.732. This is the extraordinary refractive index, ne and is different from the refractive index of the LC lens material which is cured UV glue. The refractive index of cured UV glue is 1.56. This higher refractive index results in the lens effect. The focal length of the lens is given by $\textrm{f} = {\; }{\textrm{r}^2}/2\textrm{d}\Delta \textrm{n}$ [41,42]. Where, f is the focal length, r is the radius of curvature, d is the thickness of the lens and $\Delta n{\; }$is the birefringence.
When the ESHFLC molecule is switched to the first switching position (Fig. 3(b)), since the ESHFLC cell acts as a half wave plate, a nearly 90° rotation of the polarization azimuth direction is achieved. The polarization direction is now almost perpendicular to the optic axis of the LC molecules in the polarization-dependent lens unit that manifest the ordinary refractive index, (no). The no of the NLC used is 1.52. This is close to the refractive index of the cured UV glue. The light passing through the device sees the NLC and the lens as one refractive index and hence no lensing occurs. The above device is used to capture the image of an object kept at 5 m from the lens. This and other objects used in the study are commercially available toy cars. When the FLC lens is switched ON, two states, one focused (Fig. 5(a) see Visualization 1) and the other defocused state (Fig. 5(b)) are obtained. The still images are single frame excerpts from video recordings generated during this study. As discussed before each unit of a FLC and a lens produces 2N states. Using a combination of 3 FLC cells and 3 LC lens successively in a cascading pattern, along with a polarizer, 8 focuses can be obtained. When lenses with focal length of 2 m, 3 m, and 5 m are used, the corresponding focal lengths can be obtained from the truth table (Fig. 5(c)). To evaluate the performance of the combination, three objects at distances of 1.2 m, 1.9 m and 5 m have been placed. Three focal planes have been separately accessed. In Fig. 5(d), the first object at 1.2 m is in focus, while other objects are in defocus. The second object at 1.9 m is shown to be in focus in Fig. 5(e) and the third object is in focus in Fig. 5(f). Using the same truth-table (Fig. 5(c)), five objects have been kept at distances of 1 m, 1.2 m, 1.9 m, 3 m, and 5 m. For each focal length one of the objects are in focus while others are in defocus. This is shown in Figs. 5(g)–5(k).
Fig. 5. The defocusing and focusing effect of a single unit consisting of a FLC polarization rotation unit and a polarization dependent passive LC lens of 5 m focal length, along with a polarizer are shown in (a) and (b). Here, (a) is the focused state and (b) the defocused state. (c) Truth table showing various focal lengths that can be produced using three lens combination of different focal lengths. Successive focusing and defocusing is obtained using a combination of 3 FLC cells, 3 polarization dependent passive LC lens, a polarizer and three objects are shown in (d)-(f). The objects are placed at distances of 1.2 m, 1.9 m and 5 m. Using the same combination, successive focusing and defocusing of five objects placed at 1 m, 1.2 m, 1.9 m, 3 m and 5 m are shown in (g)-(k). (Media-1). The objects used in the study are commercially available toy cars. The pictures are single-frame excerpts from video recordings generated during the study,
4. Conclusion
We have developed a fast-switchable lens unit, which can provide several accurate vergence cues to the user. It utilizes a combination of polarization rotation unit based on the Ferroelectric liquid crystals and a polarization-dependent passive LC lens. It shows promising performance in three aspects; firstly, the switching time of the device is in the low microsecond range as compared to the high micro-second range or millisecond range for the other alternatives (Table 1). Secondly, the entire device requires low driving voltages (∼ 10 V or less). Thirdly, 8-tunable focus lengths switching at µs speed enable the ability to detect enriched 3D information at a high frame rate. Also, the aperture of the device is 1 cm, which compares very positively with existing devices. The focal length of the device is in the range of 1-5 m, which makes this device stand out while trying to access the large-focal-length, and thus, focus objects far away. Also, because of the refractive index matching glue used, the light losses are reduced. These advantages over other existing devices can help to meet the accommodation-vergence challenges being faced by the user while using VR devices.
The size of the lens in the present device can be increased more than 1cm square but is limited by the thickness of the LC lens. It is necessary to ensure that a strong surface anchoring is imposed by both the substrates, which is needed to preserve a strong alignment. Going by these conditions, these lenses find enhanced applications in VR devices as well as possible device attachments for cell phone cameras. The ability to access several focal planes rapidly, opens up the possibility to use these devices to capture a wide range of focal points in a single image. This can have significant applications for outdoor imaging, opening the possibility to virtually visit tourist locations with realistic effect. It can also reduce the cost for data storage significantly as each image can hold more information. Another possible application can be to provide enhanced vision during robotic surgery helping the automation process. While the device has several positive features, which we have reported previously, we have not characterized the lenses for optical aberrations. Such aberrations can be overcome through optical compensation. Also, the device being polarization dependent, it does lead to light losses. The lens material here is made of UV curable glue and stacking several lenses can make it bulky. However, this can be improved with a rigid, transparent material, allowing 16 and 32 focal planes to be accessed using a stack of 4 and 5 devices in the future.
Funding
Innovation and Technology Commission (PRP/049/19FX).
Acknowledgments
We acknowledge the support of The State Key Laboratory of Advanced Displays and Optoelectronics through the Innovations and Technology Commission of Hong Kong and Innovations and Technology Commission of Hong Kong grant number PRP/049/19FX.
Disclosures
The authors declare no conflicts of interest.
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