An Economically Viable Minimalistic Solution for 3D Display Discomfort in Virtual Reality Headsets Using Vibrating Varifocal Fluidic Lenses

Abstract

Herein, we report a USB-powered VR-HMD prototype integrated with our 33 mm aperture varifocal liquid lenses and electronic drive components, all assembled in a conventional VR-HMD form-factor. In this volumetric-display-based VR system, a sequence of virtual images are rapidly flash-projected at different plane depths in front of the observer and are synchronized with the correct accommodations provided by the varifocal lenses for depth-matched focusing at chosen sweep frequency. This projection mechanism aids in resolving the VAC that is present in conventional fixed-depth VR. Additionally, this system can address refractive error corrections like myopia and hyperopia for prescription users and do not require any eye-tracking systems. We experimentally demonstrate these lenses can vibrate up to frequencies approaching 100 Hz and report the frequency response of the varifocal lenses and their focal characteristics in real time as a function of the drive frequency. When integrated with the prototype’s 120 fps VR display system, these lenses produce a net diopter change of 2.3 D at a sweep frequency of 45 Hz while operating at ~70% of its maximum actuation voltage. The components add a total weight of around 50 g to the off-the-shelf VR set, making it a cost-effective but lightweight minimal solution.

1. Introduction

Since the first report on stereoscopic systems by Wheatstone back in 1838 [1], the recent technological advances in electronic hardware and computational capabilities have transformed stereoscopy-based virtual reality (VR) head-mounted displays (HMDs) into a viable candidate for futuristic near-eye wearable gadgets that are both digitally interactive and capable of supporting time-intensive applications. This emerging technology of VR is based on stereoscopic observation of a simulated virtual environment in a near-eye HMD that facilitates interaction [2] and creates a sense of presence and immersion in this virtual environment, eliciting a heightened degree of “engagement” with the virtual world while being present in a different physical world [3,4,5]. Owing to its inclusive and interactive nature providing a sensory “stimuli” of virtual immersion, VR technology has proven to accelerate learning and training, as compared to two-dimensional (2D) display modules like desktops, tablets, mobile devices, etc. Jensen et al. recently reported that such an immersive experience [6] can positively affect the outcome of acquiring improved cognitive, psychomotor, and affective skills. In fact, a recent study suggests that virtual memory palaces in the VR HMD condition provide a 9% improvement in memory recall ability compared to the desktop condition [7]. Beyond gaming and entertainment, VR has many emerging applications in the areas of education, industrial design and manufacturing, retail, cinema, healthcare, sports, and aviation [8,9,10,11,12,13,14,15] to name a few. Stereoscopic VR displays, however, suffer from certain drawbacks and challenges. In terms of display performance, AR and VR face several common challenges to satisfy demanding human vision requirements, including field of view (FoV), angular resolution, dynamic range, eyebox, and correct depth cue, etc. Other considerations include ergonomics, user-friendly experience, weight and compactness, and affordability, amongst others. A detailed discussion on these challenges and trade-offs is reported elsewhere [16,17].

Perhaps the most critical of these challenges to have been widely studied till date is the absence of the appropriate depth cue for natural human viewing in 3D environments and the subsequent need to alter the conventional optical design and configuration. Of all the eight visual cues required for depth perception [18], VR stereoscopic displays offer all but one, the “convergence and accommodation” cue in the personal space (0.1~10 m). Hence, depth perception, which forms an integral part of a truly focused 3D immersive experience, is lost. Generally speaking, vergence and accommodation cues are synchronized by the brain–eye neural circuitry for disparity-free natural viewing; changes in one drive the other, and vice versa [19]. The situation changes while viewing the virtual objects in 3D stereoscopic displays. The observer’s eyes are focused on a fixed plane while the brain interprets those images originating from a different (farther or closer) plane. This mismatch between the focus cues and depth perception causes a disruption in the neural synchronization of the two cues and is commonly referred to as Vergence–Accommodation Conflict (VAC) [20,21], resulting in perceptual distortions and difficulty in fuse-focus of a stimuli, often manifesting as blurred, shifted, or double images inducing eye fatigue and dizziness after a short use of the VR HMDs [20,22,23,24,25]. Munafo et al. reported that incidences of motion sickness in commercially available VR devices can range anywhere from 33% for male participants all the way up to 78% for their female counterparts [26], with the experience worsening as the relative speed of object motion increases. This limits certain VR applications with objects up close that require accurately focused information, like aviation applications, diagnostic and surgical trainings, HAZMAT, etc. While gaming and entertainment are opt-in activities, the wider adoption of VR as a professional training or learning tool for extended periods of time by and large remains unrealized. Another drawback of these VR HMDs is the ability to provide refractive error corrections for a sizable user base that requires prescription eyeglasses [27].

2. Background

In order to resolve the VAC problem, the projection system must be able to project virtual images at various distances and, therefore, the projection optics of the HMD must be tunable. Three-dimensional displays with variable image distances have been proposed and constructed in various approaches [27,28]. Some of the proposed solutions to the problem of providing such depth cues attempt to approximate focus cues. Varifocal displays, monovision displays, and even some implementations of multifocal displays fall in this category. As an alternative to focus tuning, a simpler approach of monovision has also been proposed [29,30]. Monovision has, however, been reported to reduce sharpness with only a marginal change in fusion or accommodation compared to conventional near-eye displays [27]. Since only one eye is offered with digital images, this approach is more suited to AR applications than immersive VR [16]. Software approaches like retinal blur or gaze-contingent disparity rendering [29,30,31,32] neither provide natural focus cues or refractive error corrections.

Volume-sweeping varifocal and multifocal displays are the most straightforward approach to project 3D images in a volumetric space by using tunable lens optics which project corresponding virtual images at different depths [33,34]. In this approach, the 3D volume in front of the observer is swept periodically and planar images of objects at different depths are projected at different times. Fundamentally, this method of rendering is the most natural, and it is able to render object slices at any distance away from the observer. Varifocal near-displays have a single image plane where the vergence and focus cues match, and this plane is moved by using focus-tunable lenses [27,35], or deformable membrane mirrors [36], or by actuating fixed-focus optical components [37]. In a varifocal display, all pixels are at the same focal plane, and therefore virtual pixels that do not lie on the plane of focus need to be synthetically blurred in proportion to their distance from the plane of focus. Varifocal displays need to track the accommodation state of the pupil [27] or assume that the pupils are accommodated to the eye convergence distance [27,36]. Multifocal near-eye displays, first proposed by Akeley et al. [38], display a small number of images at different depths; the images are perceived additively [34,38,39,40,41]. In Akeley et al. [38] and MacKenzie et al. [41], subregions of an LCD panel were mapped to different focal planes using beam splitters. Liu and Hua [40] and Love et al. [34] proposed a lens that is switchable to multiplex between the multiple focal planes. Several variations of the varifocal schemes have been reported that partially overcome the disadvantages of the time multiplexing approach. Hu and Hua [42,43] proposed using high-speed optical components to achieve a larger number of focal planes. Because a relatively small number of depth planes are used to represent objects occupying a large volume, multifocal plane displays need scene decomposition algorithms to optimally represent a 3D scene using a few 2D image planes. Content generated by these scene decomposition algorithms provide synthetic focus cues to represent objects that lie in between the focal planes. MacKenzie et al. [41] propose a per-pixel linear blending approach. Narain et al. [44] proposed an optimized blending algorithm that can demonstrate occlusion, reflection, and non-Lambertian effects, while Mercier et al. [45] and Lee et al. [46] proposed new scene decomposition techniques that are tolerant to eye movements. While scene decomposition algorithms help to depict imagery that lies between the focal planes, the spatial frequency of the fused image is inversely related to the focal plane separation [39,47]. Recently, swept-volume displays that utilize fast-moving lenses (~60 Hz) coupled with a DMD light projection systems have been implemented. Recently, Chang et al. [48] and Rathinavel et al. [49] reported volumetric displays that have a large number of focal depths, i.e., 40 and 280, respectively. Although, depth scan-based volume-sweeping method is very simple, this scheme however has several disadvantages. First, the tunable lens must be swept at very high frequencies in order for the eye not to notice gradual focus changes; hence, a fast lens is needed. Second, the duty cycle of the image for any given depth is small, thus proportionally reducing the object brightness. Third, when a virtual image is projected only when the volume is swept, one can also see the objects in front or behind it. This renders the objects with a ghostly appearance in the absence of software object occlusion checks. Temporal multiplexing can introduce perceived flicker and requires display refresh rates higher than the flicker-fusion threshold frequency.

Multifocal displays present multiple focal image planes simultaneously, allowing the viewer to refocus on any object, while varifocal displays utilize eye vergence to determine the observer object distance, refocusing or blurring object images. A key disadvantage of the varifocal scheme is that it must sense the eye vergence correctly; hence, multifocal displays fundamentally provide a more realistic display experience. The oldest and most common VAC-resolved multifocal display scheme utilizes a fixed-distance projection screen that is observed through a varifocal lens placed at a fixed distance from the screen that is smaller than its focal distance. This produces a virtual image in front of the observer at a depth that depends on the lens power. In order to produce a 3D display, the lens power must oscillate at high frequency, thus producing a periodic series of virtual images projected at different depths. Such a scheme has been implemented in both HMD and 3D display applications, utilizing both mechanical shape-changing varifocal lenses and solid-state digital polarization and tunable Fresnel varifocal lenses. In a third approach that is more suitable for augmented reality (AR), a similar effect is achieved, utilizing solid-state waveguide multi-plane displays. Light field displays [50,51,52,53,54,55,56,57] and holographic displays [58,59,60] have also been proposed as a potential fix for VAC since they can approximate the wave front perceived by the observer for different views and provide relatively accurate focus cues. Light field display approaches are interesting as they do not require tunable optical elements or tunable lenses, but they require high-resolution displays and are computation-intensive. Current implementations of light field displays are either diffraction-limited [51,56] or have poor resolution due to spatial-angular resolution trade-offs [50,57]. Current implementations of holographic near-eye displays have a very small eyebox [58] and, similar to light field displays, have high computational requirements. In addition, phase-only spatial light modulator (SLM) technologies that holographic displays are based on also need improvement for practical implementation in near-eye VR HMDs. These devices are fundamentally very complex in nature and currently are at an early development stage. The multifocal approaches have many trade-offs. Solid-state approaches offer both low weight and very high reliability and drop resistance, but universally the complexity and cost of these devices are not volume-scalable, resulting in very high production unit costs. Thus, these devices are only practical in high-end, high-cost applications. Solid-state multifocal display devices are, in general, very fast, with some implementations reaching kHz image frame rates, but they suffer from strong chromatic aberration and consequently poor image quality. On the other hand, mechanical varifocal lens approaches are less reliable than solid-state devices and can lead to higher set weights and unwanted vibrations, but they provide polarization-independent imaging and can deliver higher-quality images with larger apertures and low chromatic aberration. Mechanical varifocal schemes also are much simpler than the solid-state approaches, thus leading to much lower unit costs.

In order to synchronize the virtual object depth with the appropriate focus for normal visual cues, several research studies have reported on the use of gaze detection technology in combination with either optically tunable lenses or movable mechanical display systems to address these discomforts. While the use of tunable varifocal optics has emerged as a viable solution, a vast majority of these varifocal systems have apertures in the range of 20 mm or less. Digital crosstalk between gaze detection and tunable actuation modules usually make current varifocal VR techniques computation-intensive, sometimes adding noticeable lag to these adaptive systems. Additionally, eye-tracking sensory systems do not provide the desirable accuracy of depth-sensing, especially for high-frequency depth variations and surfaces of varying transparency and/or reflectivity [61,62]. Ebner et al. [63] has recently reported a video see-through mixed reality system with full support for focus cues using an eye-tracking module. Out of the methods discussed above, the most realistic images are produced by the varifocal technique, which, when combined with very bright light sources, high-speed projection systems, and appropriate signal processing, can produce very realistic 3D scenery images. The major problem that remains to be solved is the practical implementation of these methods in a manner that is inexpensive and computationally balanced for a given application. In this paper, we present the implementation of a low-cost VAC-free multifocal display that utilizes a single-plane screen and an oscillating varifocal mechanical lens producing a sequence of virtual images at a volume sweep rate of 30 Hz and a frame rate of 90 fps. This true-focus system does not require an eye-tracking module, hence negating additional complexity and inaccuracies, as reported previously [63]. Sections below describe the system construction, the low-cost varifocal mechanical lens, multifocal display design parameters, and the experimental performance.

3. Electro-Optical Design

3.1. Optical Layout

Figure 1 below shows a schematic of our minimalistic low-cost multifocal VR set. It consists of a high-speed, high-brightness screen placed in front of a varifocal lens set, one per eye. A pair of convex lenses of fixed optical power (~16D) are placed 20 mm away from the observer eyes, and a mobile smartphone screen projecting stereoscopic images of an object is placed 58 mm away from the lens. Because the screen is closer than the focal point of the lens (62.5 mm), the screen and lens system produces a virtual image in front of the observer at about 0.8 m away from the lens. In conventional VR HMDs, the virtual image distance is always fixed no matter where the object is placed in the virtual space. Most inexpensive fixed-lens virtual reality sets use a virtual image projected between 0.8 and 3 m away from the observer. The root of the VAC conflict in conventional VR sets is the inability to project virtual images of objects at different distances. In order to resolve the VAC problem, the projection optics of the set must be tunable. For the particular distances used, a virtual image location between 25 cm (reading distance) and infinity requires utilization of a varifocal lens that ranges between 13D and 17D, or a 4D change in the lens power. In order to display a realistic volumetric image, the varifocal lens power is periodically swept between these two power limits while the image of the objects at each virtual depth is virtually projected by the smartphone screen with consistent object occlusions.

Fundamentally, for the observer to disregard screen flickering, the frequency of the periodic display of virtual images should be at least 60 Hz or more, and preferably 90 Hz. Thus, we have chosen the sweep frequency of the varifocal lenses to be 30 Hz with 3 or more periodic virtual image display. Within that 30 Hz sweeping scene, we can send multiple frames for different object depths. In this prototype, we used three frames per scene with 90 Hz frame rate (using a display system of 120 fps refresh rate) at this sweep frequency of 30 Hz. The faster this oscillation is and the higher the number of images displayed to approximate the 3D volume scenery in front of the observer, the smaller the time available to present the images. Therefore, as the number of images presented per period increases, one conversely needs a progressively brighter and faster screen. This is a limitation of the multifocal imaging scheme that needs careful selection of display hardware.

3.2. Piezoelectric Varifocal Tunable Liquid Lenses and Drive Electronics

We have selected lightweight piezoelectric liquid VTL that has been demonstrated elsewhere by the authors [64]. Figure 2 shows a schematic diagram and photographs of the VTLs used in the VAC-free VR set. We drive the lenses using periodic harmonic sinusoidal excitation; hence, the full multifocal range is swept in the sinusoidal cycle = (0.25 m-infinity). Since the dynamics of the liquid lenses are linear to the first order, the corresponding sinusoidal VTL power dynamic range is thus somewhat increased by driving the lenses near resonance. The piezoelectric sinusoidal drive for the lenses is generated utilizing low-cost amplifier electronics.

Figure 3 below shows a simplified schematic of the lens’ driving electronics. Each piezoelectric lens is driven differentially between the outputs of two single-ended high-voltage (HV) dual operational amplifier chips (PA79DK) connected to the lens in a bridge configuration. This permits the generation of a bipolar lens driven from a single-ended high-voltage supply. The two high-voltage op-amps gains for each chip are set to −10x and −1x correspondingly. The (−) input of the −10x PA79DK op-amp is connected to the output of a cascade level shifter preamplifier, while the (+) input is set to a fixed preset voltage VR2. The level shifter preamplifier input is driven by a single-ended op-amp that both provides a high input impedance and produces linear −5x preamplifier gain. A common-gate high-voltage signal MOSFET is utilized to shift the preamplifier output near +VR2. The preamp input is connected to the output of a digital to analog converter (DAC). The DAC is driven by a microcontroller which synthesizes the sinusoidal excitation waveforms in sync with the mobile screen cycle. The varifocal lens voltage is thus 100x larger than the DAC output signal. In the current HV amplifier configuration, the high-voltage amplifier board is driven by a single 120 V DC power supply generated from a 5 V supply using a miniature high-voltage DC converter (EMCO-A series). All electronic components were purchased from www.digikey.com (accessed on 10 June 2023).

The HV board and additional digital microcontroller boards fit inside the VR system shell. The VAC-compensated VR prototype integrates two varifocal tunable eyepiece lenses and specialized associated hardware (mounts, drivers, display and communication interfaces) necessary to display 3D virtual imagery. The VAC-compensated VR is shown in Figure 4 integrated within a conventional Google cardboard-type VR HMD set (dimensions of 18.42 × 12.07 × 9.14 cm). These utilize a mobile phone CPU to produce stereoscopic images and the phone screen as the object which is virtually projected in the front of the observer. Note that, in our prototype, our tunable lenses and the drive electronics fit within the void space between the lenses and the mobile phone screen. In this experimental implementation, the electronics driving the lenses is connected to the phone via a wifi connection, and the phone executes a simple scene render app using Unity and the Google cardboard SDK. The phone app adjusts the location of the virtual images as the objects in the scene are sequentially displayed. For this experimental prototype set, we utilized three different depth zones for the virtual images displayed at 90 frames/s.

Figure 5a shows examples of virtual images of far and close objects projected by this set at two different vergence distances. Note that the blurring of objects is different on both images indicative of the VAC compensation in action. In the left image, the vergence is near and, in the right, the vergence is further. This simple image set example demonstrates that VAC compensation can be realized inexpensively with our piezo lenses. Figure 5b shows examples of images captured by a simulated eye camera system consisting of a 35 mm SLR camera and focus adjustable lens, as projected through the variable virtual image system using three different virtual image distances. The complete image is obtained by projecting at each virtual depth the objects corresponding to a virtual distance zone centered at the range, while other objects are blacked out. The system is cycled through all the depth zones and objects in a repeating cyclic manner. The left and right images were obtained by adjusting the camera lens focus to near and middle distances. Two challenges are evident in the photographs that affect the image quality. The first is the compensation of magnification differences between projection zones as the virtual image size is a function of the virtual image depth, thus necessitating projected image scaling and accurate image registration. The second is the overall darkening effect of the images as the more zones the virtual space is divided into, the lower the image brightness.

From these preliminary tests performed on the prototype set, we learned the features that can be improved for realization of commercial grade prototypes. Namely, two improvements are required to enhance the quality of the 3D virtual image projection. The first consists of the utilization of faster lenses. The second is the utilization of faster, brighter screens. Faster tunable lens operation translates into smoother projected images and improved display quality. Faster displays permit the projection of more image planes per cycle resulting in less flickering and smoother, more natural images.

3.3. Lens Vibration Frequency, Virtual Image Frame Rate and Visual Perception

Central to the volumetric display are the vibrating lens frequency and the determination of the number of image planes needed to represent the scenery with a good quality. Since depth binning is used with virtual images displayed at specific distances, the tunable lens must first reach and settle the correct power, and then, the image of the object is flashed in focus, with all other objects that fit in other bins displayed out of focus. The settling of the lens power can lead to lower frame rates, for example. Lee et al. [65] recently showed that a more efficient way to drive the 3D display is by not driving the lens to the right power but instead having the lens motion continuously excited at resonance, while the correct images with proper occlusion are displayed on the object screens. Using this concept, Rathinavel et al. [49] displayed low-flicker 3D images at 280 different depths. We believe the continuous sweep approach used is effective in producing excellent 3D images, but it is not necessary to project such a large number of depths to produce reasonable good-quality 3D images.

There are two major known effects for this reasoning, both of them being consequences of the working and limitations of the human visual system. First, there is the flicker-fusion threshold. The flicker-fusion threshold, or flicker-fusion rate, is a concept in the psychophysics of vision. It is defined as the frequency at which an intermittent light stimulus appears to be completely steady to the average human observer. Flicker-fusion threshold is related to persistence of vision. Although flicker can be detected for many waveforms representing time-variant fluctuations of intensity, it is conventionally, and most easily, studied in terms of sinusoidal modulation of intensity. Flicker fusion is important in all technologies for presenting moving images, nearly all of which depend on presenting a rapid succession of static images (e.g., the frames in a cinema film, TV show, or a digital video file). If the frame rate falls below the flicker-fusion threshold for the given viewing conditions, the flicker will be apparent to the observer, and movements of objects on the film will appear jerky. For the purposes of presenting moving images, the human flicker-fusion threshold is usually between 60 and 90 Hz.

The second effect is the inability of the human eye to resolve distances accurately. Intrinsically the human eyes accommodate for the vergence of the object or projected virtual image. This vergence is proportional to the inverse of the image distance. Therefore, as the distances become increasingly larger, the lens power adjustments become progressively smaller. Physiologically, the human eye cannot distinguish refractive errors that produce wavefront errors smaller than the average aberration of the eyes themselves. The average human eye’s RMS aberration is 0.35 µm [66]. This aberration can be translated to an equivalent defocusing [67]:

$${∆P}_{eye}={\displaystyle \frac{4\pi \sqrt{3}·a_{rms}}{A_p}}$$

(1)

where a_rms is the average RMS aberration (in microns), and A_p is the pupil area in mm². For a typical pupil diameter of 3 mm, this translates into a defocusing error equivalence of 0.28D. The smaller is the area of the pupil and the larger the equivalent defocusing for a fixed RMS aberration. The pupil diameter is also a function of the object distance [68]. The closer the object (or virtual image) is, the smaller the pupil size. If a good volumetric VR set projects virtual images from reading distance (0.25 m = 4D) to infinity (=0D), then, from Equation (1), the diopter accuracy of the tunable lens should be between 0.28D and 0.6D as the aberrated eye behaves as a low-pass power averaging filter. For the calculated tunable power diopter range of 4D of the VAC-corrected set, the number of frames at which images should be projected is 7 to 15. A higher number of projected depth images would be perceived no different than ~10 images per cycle in the volumetric sweep for the majority of the population. The number of displayed frames is also dependent on the visual acuity of the subject as well as the level of illumination. An additional frame number-reducing effect is the depth of field:

$$DOF={\displaystyle \frac{2u^{2}Nc}{f^2}}$$

(2)

where u is the distance of the object, N is the lens system f-number, c is the circle of confusion radius and f is the system focal length. In optics and photography, the depth of field is the distance between the nearest and the farthest objects that are in acceptably sharp focus in the image. In our system, the f-number is determined as the ratio of the system focal distance over the pupil aperture diameter. The depth of field is entirely dependent upon what level of sharpness is considered to be acceptable based on the selected radius of the circle of confusion, but it helps to narrow down the number of image planes [63] as the observer would perceive all objects in focus on a depth bin that is equal to the depth of field. The tolerable error for the limit of circle of confusion diameter is traditionally set at 0.05 mm. Since we are using a finite number of virtual image frames projected at different depths, for a varifocal range of 4D, about eight virtual images and above are sufficient to produce a reasonable representation of the 3D scenery. At a 30 Hz periodic lens drive cycle, an effective virtual image frame rate of 240 fps+ is thus required in the display screen. For experimental and viability study purposes, we have used a 120 fps display system (Samsung S20), but the cost addition of high-fps-display systems is justifiable for bulk commercial manufacturing. A third important consideration is the screen brightness setting. The total energy of the optical light emitted per frame is proportional to the display time for that frame. Since the position and power change sinusoidally, the speed of the virtual image is not constant. One must either reduce or increase the display time to normalize the object brightness accordingly for different virtual image depth bin volume.

4. VTL Dynamics Experiments

The faster the VTL is vibrated, the smoother is the 3D image produced. It is therefore of extreme importance to utilize a high-frequency lens. For our low-cost system, we measured both the frequency response of the lens’ central deflection and the power vs. time under sinusoidal excitation. These two measurements are discussed below.

4.1. Varifocal Lens Frequency Response

In this experiment, we utilized the HV amplifier driven by an audio signal generator to vibrate a single varifocal lens at different frequencies under low voltage amplitude. The mechanical deflection vs. time of the lens at its apex was measured and recorded using a high-frequency laser spot distance probe (Micro-Epsilon optoNCDT 1420, Micro-Epsilon, Ortenburg, Germany) sampled at 2 k Hz. The amplitude of the lens peak deflection is related to the power of the lens by the relation. To the first order, the optical power for this type of fluid lens is only dependent on the membrane dimensions, liquid index, and the lens peak deflection Δh: wherein

$$∆P={\displaystyle \frac{4(n-1)·r_r^2·∆h}{r_o^4}}$$

(3)

where r_r and r_o are the piston and membrane aperture radii, and n is the index of refraction of the liquid lens [64]. Equation (3) indicates that the optical power is independent of any other system parameters. The audio signal driving the HV amplifier was swept between 10 and 100 Hz. Figure 6 shows the normalized frequency response amplitude vs. frequency under a sinusoidal lens excitation voltage of 75 V peak to peak. The lens experienced a pole with amplitude dropping 6 dB (50% in amplitude) at about 45 Hz. While the drop is steep, the lens can be driven at higher frequencies, utilizing a higher drive voltage. A significant effect of the resonance peak is the phase shift change near resonance. This implies that, near the peak, the motion of the lens is out of phase with respect to the drive signal. The amount of phase shift thus must be measured and compensated by the microcontroller in order to ensure that the lens power corresponds to the actual object virtual image distance. The phase shift is measured as described in the following section.

4.2. Stroboscopic Varifocal Lens Power vs. Time Profile

The previous measurement provides a measure of the lens peak deflection vs. drive frequency, but it does not ensure that the lens surface is not distorted or mode switched during the periodic lens excitation. In this experiment, we utilized the HV amplifier driven by a dual-output signal generator as shown in Figure 7 below. The HV amplifier signal is a sinusoidal voltage of frequency f with a DC offset. The amplified sinusoidal voltage V_D(t) drives one piezoelectric lens. The second output of the dual signal generator is used to produce a narrow voltage strobe pulse V_S(t), typically 1% of the duty cycle of the sinusoidal signal but offset by a fixed phase ϕ, as shown on the upper right insert of Figure 7. The narrow strobe pulse generated by a DDS signal generator (Koolertron GH-CJDS66, Koolertron, Hong Kong, China) is used to drive and strobe a collimated LED light source (ThorLabs M625L3-C1, ThorLabs, Newton, NJ, USA) with the intensity modulator (ThorLabs LEDD1B, ThorLabs, Newton, NJ, USA). This light passes through the VTL and is captured by a Shack–Hartmann wavefront sensor (SHS) (Thorlabs WFS150-7AR, ThorLabs, Newton, NJ, USA). Since the phase of the pulse is fixed, the wavefront produced at the SHS is static; hence, it can easily be captured by the SHS. The power of the lens at phase ϕ can be determined from the wavefront radius of curvature (ROC). The lens is placed 55 mm away from the SHS sensor. When the ROC is measured in mm, the power of the lens is then $P\left(\varphi \right)=1000{(ROC-55-13.6)}^{-1}$. Figure 8 shows an example screenshot of the wavefront captured by the SHS sensor. By sweeping the phase ϕ between 0 and 360 degrees while keeping the same frequency, one can observe the actual P(t). Figure 9 (Top) shows the waveform of P(ϕ) for different drive frequencies. Note that the waveform is not exactly a sinusoid, indicating a possible partial excitation of higher-order modes or nonlinearities in the lens. Also note that the waveforms are shifted in phase due to the resonant nature of the piezoelectric VTL. Figure 9 (Bottom) shows the relationship between phase and the excitation frequency. At a drive voltage of 104 V driven at 45 Hz, the lens experiences a diopter change of 2.3 D, sufficient to span a VAC-free virtual depth range of 43.5 cm–infinity in the VR set.

5. Summary

We present the implementation of a swept-volume VAC-free VR headset that utilizes low-cost components consisting of two lightweight VTL lenses and an HV-amplifier driven by a conventional smartphone screen. The set tested can present multiple depth virtual images at a swept-volume frequency of 30 Hz with frame rates determined by the mobile device’s maximum frame rate (120 fps for a Samsung S20) without the need for any tracking sensory system. Our tunable lenses can be tuned for higher operation frequencies subject to aperture modifications. We also present dynamical measurements of the VTL characteristics utilizing time-domain and stroboscopic measurement setups. The field of view (FoV) for this large-aperture-lens VR system is 105 degrees with 1520 × 1440 AMOLED display pixels per eye. The depth range of 43.5 cm–infinity driven at around 100 V can be improved with higher drive voltages (up to 150 V and depending on the maximum application voltage of piezo material). A magnetometer-based feedback circuitry mechanism [69] can be integrated with the tunable lens system for enhancing long-term system performance and stability.