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Abstract
This study proposes a novel computational imaging system that integrates a see-through screen (STS) with volume holographic optical elements (vHOEs) and a digital camera unit. Because of the unique features of the vHOE, the STS can function as a holographic waveguide device (HWD) and enable the camera to capture the frontal image when the user gazes at the screen. This system not only provides an innovative solution to a high-quality video communication system by realizing eye-contact but also contributes to other visual applications due to its refined structure. However, there is a dilemma in the proposed imaging system: for a wider field of view, a larger vHOE is necessary. If the size of the vHOE is larger, the light rays from the same object point are diffracted at different Bragg conditions and reflect a different number of times, which causes blurring of the captured image. The system imaging process is analyzed by ray tracing, and a digital image reconstruction method was employed to obtain a clear picture in this study. Optical experiments confirmed the effectiveness of the proposed HWD-STS camera.
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1. Introduction
Currently, the demand for high-quality video communication systems is increasing. The conventional video communication system is shown in Fig. 1, including a display and a separately placed camera. When the user views the display, it is difficult for the camera to capture from the front view of the user. In this case, eye contact is not possible, which is an important evaluation feature for high-quality video communication [1–5]. Some published works focused on solving the eye contact problem in video communication systems for a realistic viewing experience based on hardware and software approaches. However, in the hardware approach [5–8], the system requires a half-mirror and/or a separately aligned camera. The bulky size of the solutions limits the applications of the system to mobile devices. In the software approach, the eyes are detected using a computer vision approach, and the angle of gaze direction is adjusted using a computer graphics technique [9]. The software approach is low-cost and easy to apply; however, the image is artificially altered.
Recently, “under-display camera” or “in-display sensor” technology has been actively developed [10]. Holes were made in the display panels, and an image sensor was placed under it. The primary purpose of the under-display camera is to remove the camera lens from the smartphone surface to achieve a truly full-screen display. Although they can also be used for frontal image capture or fingerprint sensors, the holes affect the display’s pixel density. A thin “see-through” lens-less camera [11] can be applied for frontal image capturing. However, this camera’s light efficiency is low, and the resolution and image quality are severely restricted for practical applications.
Holographic optical elements (HOEs) can simultaneously perform several optical functions based on a thin and see-through film by selective angular and wavelength characteristics [12]. HOEs have been widely used in different types of visual display systems, such as head-mounted displays (HMD) [13–16], near-eye displays [17,18], and three-dimensional (3D) displays [19]. The devices can also be used in image-capturing optical systems [20]. Previous research [1,4] proposed an off-axis virtual imaging system using a volume HOE (vHOE), which can capture the frontal image of the user’s face. However, this system requires separate placement of the holographic mirror and camera, and the size and calibration of the system restrict the expanded functionality.
A holographic waveguide device (HWD)-based see-through screen (STS) camera is proposed in this study. The HWD has been used in thin illumination devices [21,22], AR displays [23], and eye-gaze detection [24] and is also being considered for HUD applications [25,26]. Because of the wavelength selectivity of the volume-reflection holograms, most of the light from the backside transmits to the screen. In contrast, the light from the object of a specific wavelength is diffracted and captured by the camera. Due to the integrated design, the proposed HWD-based STS camera has a much smaller and more compact structure compared to previous research [1,4–8], so that it can be used in a mobile display that enables eye-contact video communication, near-screen gesture sensing, biometric image acquisition on the display surface, and image acquisition through a glass window.
An issue with the HWD-based STS camera is that a larger vHOE is needed to achieve a wider field of view; however, images with different counts of total reflection superposed with shifts on the image sensor if the size of the vHOE is large. Therefore, vertical discrete blur significantly degrades the quality of the captured image. In [27], only the subject located at infinity was considered, in which images with different counts of total reflection perfectly matched. Thus, they are challenging to apply in practice, and no experimental results have been reported. An image reconstruction technique was used to solve this issue. In addition, the acquisition of a deblurred image was demonstrated experimentally. There are no previous studies on the experimental presentation of image capturing using STS with a waveguide HOE.
Section 2 presents the analysis of the imaging model using ray tracing. A deblurring reconstruction method was proposed in this section. Section 3 presents the setup and results of optical experiments to verify the effectiveness of the proposed system with the reconstruction method. Finally, Section 4 concludes the study.
2. Holographic waveguide device (HWD)-based see-through-screen (STS) camera
2.1 Proposed system
The optical system of the proposed HWD-based STS camera is illustrated in Fig. 2(a). Two volume-reflection HOEs with a large diffraction angle are attached to the different surfaces of transparent glass plates. The diffraction angle of the vHOE was larger than the critical angle of the glass plate, as recorded by the optical system shown in Fig. 2(b). This screen can function as a waveguide device. The Bragg-matched incident light from the object is diffracted by the bottom backside vHOE, propagates within the screen as a total reflection to the top vHOE, and diffracted to the image sensor by the other vHOE on the top front surface. Therefore, the proposed HWD-based STS camera can capture the frontal image of a user gazing at the screen. The STS camera could be a solution for eye-contact telecommunication systems by placing a display behind the screen, which is convenient and no need for strict optical calibration. In addition to its application in video communication systems, the proposed STS camera can also be employed in various visual media applications owing to its compact and thin size, which shows the versatile ability of our design. The under-display camera is a current trend in smartphones, and the existing design aims to expand the distance between pixels, allowing the sensor to capture images. The proposed STS camera can be used in this case without spacing between pixels. Another application of the proposed system is in near-screen gesture recognition or non-contact touch interface displays [Fig. 3]. Conventional touchless user interface systems are based on infrared or capacitive sensing; however, the types of gestures that these sensors can detect are limited. A camera-based gesture recognition system cannot easily sense near-screen gestures because the camera’s field of view is narrow, as shown in Fig. 3(a). However, the proposed system does not have this restriction, as shown in (b).
Fig. 2. (a) Optical system of the proposed HWD-based STS camera. (b) Optical system for recording the vHOE used in the HWD.
Fig. 3. (a) Conventional gesture recognition system; (b) near-screen gesture recognition using the proposed system.
In the proposed optical system shown in Fig. 4(a), the incident light rays represented by the dashed and solid lines are from different object points with varying numbers of total reflections received by the same sensor pixel after diffraction by the top vHOE. The blurred image is observed in the experimentally captured image, as shown in Fig. 4(b), caused by multiplexing images with different total reflection counts. In addition, color variation appears where the top is red, the middle is green and the bottom is blue, even though we use a vHOE recorded at a single wavelength, as the image in Fig. 4(b) shows. It is due to the received wavelength varies in the vertical direction because the diffraction wavelength depends on the incident angle from the object under Bragg diffraction law [28]. To better show the vertical blur caused by different total reflection counts, a small size image with 64 $\times$ 64 pixels (17 mm $\times$ 17 mm) is used as an object shown on the LCD monitor. As shown in Fig. 4(c), we can easily observe the separation between images, and four shifted patterns. It means four times total reflections are captured in the imaging process. The distance between the adjacent separated images on the sensor plane is almost 26 pixels, which corresponds to about 7.3 mm on the vHOE plane. Since the glass thickness $w$ is about 2 mm and the diffraction angle is about $61.2^{\circ }$ inside the glass plate, we can confirm the separation distance $d$ agrees with the theoretical estimation, i.e., $d=2\times w \times \tan {61.2^{\circ }}\approx 7.3 {\rm mm}$. The maximum count of total reflections depends on the size of the bottom-backside vHOE, which is 50 mm height in this case. However, the attenuation during the propagation in the waveguide also affects the count of shifted patterns, then only four-times total reflections are observed in Fig. 4(c). In this study, the optical phenomenon that causes image blurring was characterized, and digital image reconstruction was applied to solve this problem.
Fig. 4. (a) Schematic of the overlapping in the HWD-based STS camera; (b) captured image from the optical experiment using Pointgray color camera with RGB module. The alphabet shown on the monitor is used as the object; (c) left is the binary image used as object and right is the captured image from the optical experiment using Pointgray camera with RGB module.
2.2 Model of blurred imaging by ray-tracing
The blur in the system is caused by the multiplexing of images from different counts of total reflections. The ray-tracing method is employed to analyze the optical transfer function in the proposed system quantitatively. The relationship between the object and captured image can be calculated by tracing the light ray obtained by the sensor pixel based on the Bragg condition [29,30]. As shown in Fig. 5, the Cartesian coordinate system is assumed to be centered in the middle of the image sensor, where the sensor is in the x-y plane; the z-axis is perpendicular to the STS plane. The camera lens is placed at a distance of $d_{1}$ mm from the top vHOE with a focal length of $f$ mm. The distance from the lens to the sensor is $d_{0}$ mm. The object is located at a distance of $d_{2}$ mm from the see-through screen, which has a width of $w$ mm. The light propagation can be described by the azimuth angle $\phi$ and elevation angle $\theta$. The propagation in the horizontal $(x)$ direction follows the law of reflection, and the propagation in the vertical $(y)$ direction contains Bragg diffraction and total reflection. A side view of the imaging system is shown in Fig. 5(b) to explain the light propagation in the vertical direction.
Calculating from a pixel point ${\rm P_{0}}(x_{0},y_{0},0)$ on the sensor, it receives the incident light ray $U_{C}$ from the point ${\rm Q_{1}}(j_{1},k_{1},l_{1})$ on the top vHOE through the point ${\rm Q_{1}^{'}}(j_{1}^{'},k_{1}^{'},l_{1}^{'})$ on the glass surface of the HWD with an elevation angle $\theta$ and an azimuth angle $\phi$, given by,
From the geometrical relationship, the following equations are derived:
As shown in Fig. 2, the vHOE is recorded as the interference of the two plane waves. The close-up in Fig. 5(b) shows the recording of vHOE, where the green dashed lines represent the recording waves of the vHOE. The object wave $U_{O}$ enters the photopolymer vertically with the incident angle $\varTheta _{\rm O}=0$, and the reference wave $U_{R}$ enters with an angle $\varTheta _{\rm R}$, where both $U_{O}$ and $U_{R}$ travel perpendicular to the x-axis. The capital $\varTheta$ with suffix will be used for the angle inside the medium. Subsequently, the grating vector $\textbf {K} = [K_{x},K_{y},K_{z}]^{\rm T}$ becomes
From the diffraction formula of a thick grating, the diffracted and incident beams satisfy the Bragg condition, given by
Equation (5) represents the Bragg condition, as illustrated in Fig. 6. The wavelength and angles of the beam diffracted at point ${\rm Q}_{1}$ can be determined from this relationship. Based on the previous explanation, the location of the diffraction point ${\rm Q}_{2}$ at the bottom vHOE can be calculated by
The top and bottom vHOEs are from the same fabrication process and follow the same Bragg condition. Therefore, the diffraction angles of the bottom vHOE at ${\rm Q}_{2}$ are $\varTheta ^{'}_{\rm C}$ and $\phi ^{'}_{\rm C}$ , which means that ${\rm Q}_{2}$ receives the incident light from the object with the angles $\varTheta _{\rm C}$ and $\phi _{\rm C}$. The location of the object point ${\rm P}_{1}$ can be calculated by:
In the case where the total reflection is included, as shown in Fig. 5, ${\rm Q}_{2}$ will also receive the light after a one-time total reflection from object point ${\rm P}_{2}$. Based on the above analysis, the location of ${\rm P}_{2}$ can be calculated by
In general, the pixel point ${\rm P}_{0}(x_{0},y_{0},0)$ on the sensor receives the light ray from the object point ${\rm P}(x_{i},y_{i},z_{i})$, which is modeled as
2.3 Deblurring method for image reconstruction
From the ray-tracing analysis of the relationship between the object and captured image, a linear model of the imaging system is described as
where $\textbf {g}=[g_{1},\ldots g_{M^2}]^{\rm T}$ is an $M^2$-dimensional column vector containing the captured image of size $M\times M$. $\textbf {f}=[f_{1},\ldots f_{N^2}]^{\rm T}$ is an $N^2$-dimensional column vector representing the intensity of the original object of size $N\times N$. $\textbf {H}$ is an $M^2\times N^2$ matrix describing the system transform model, and $\textbf {n}$ is an $N^2$-dimensional column vector that represents the noise. This study used the alternating direction method of multiplier (ADMM) with TV regularization [31] to reconstruct the image $\hat {f}$ as:3. Experiment
3.1 Fabrication of the vHOE
The optical system used in this study for the fabrication of the reflection-type vHOE is shown in Fig. 2(b). A diode-pumped, solid-state (DPSS) continuous-wave laser (Samba 100 mW, Cobolt) operating at 532 nm was used as the light source. A photosensitive material (Bayfol HX200, Covestro) was used for the volume hologram recording. For the HOE exposure, a right-angled prism was used to inject parallel light as the object light such that it was perpendicular to the photopolymer. The reference light was refracted through the oblique side of the right-angle prism and entered the photopolymer at an angle of $61.2^{\circ }$, exceeding the critical angle of the glass. Interference fringes were then recorded in the photopolymer. The dimensions of the vHOEs were 20 mm $\times$ 50 mm, and 50 mm $\times$ 50 mm. The field of view (FOV) of the system is $34.3^{\circ }$.
3.2 Experimental setup for image capturing
In the optical experiment, a liquid crystal display (LCD) monitor (HP ZR2440W) was used to show the 2D targets. The size of the monitor was $1920\times 1200$ pixels, with a pixel pitch of 0.27 mm. The Pointgray camera (CM3-U3-13Y3C-CS) with monochrome mode was used for capturing the images, with a sensor size of $1280\times 1024$ pixels, pixel pitch of 4.8 µm, and focal length of 6 mm. As shown in Fig. 7(a), the display was placed 550 mm before the see-through screen camera. Black tape was used to cover the top vHOE to prevent the camera from capturing the environment scene. The captured images on the sensor were cropped to $440\times 440$ pixels for processing. The system transform matrix was measured using the Hadamard basis patterns, as described in the next subsection. The actual experiment is shown in Figs. 7(b) and (c).
Fig. 7. (a) Configuration of measuring the system matrix; optical experiment of (b) measuring the system matrix and (c) capturing the target.
3.3 Measurement of the system transform matrix
The $N\times N$ Hadamard basis patterns were used as input images [32] to measure the system matrix of the imaging system, as shown in Fig. 8. The imaging process of the Hadamard patterns can be expressed as:
The system matrix $\textbf {H}$ is calculated and applied to the ADMM-TV reconstruction method in the next step.
In this experiment, 4,096 Hadamard basis patterns with a size of $64\times 64$ pixels were displayed on the monitor at $640\times 640$ pixels. The images captured on the sensor were cropped to $440\times 440$ pixels for processing. $\textbf {u}_{i}$ is a $4096\times 1$ column vector, $\textbf {v}_{i}$ is a $193600\times 1$ column vector, and the calculated system transform matrix, H, is a $193600\times 4096$ vector.
3.4 Results
Three binary images (apple, bee, and face) and three grayscale images (cameraman, clock, and text) were used as targets in the optical experiment, as illustrated in Fig. 9. The images were then resized to $64\times 64$ pixels before being displayed on the monitor at $640\times 640$ pixels to match the size of the Hadamard basis pattern. The blurred vertical shift can be observed significantly in the captured images, particularly in the horizontal patterns. The blurred pattern is the same as in the theoretical analysis described in the Section 2. The ADMM-TV method ($\tau$=5) was used for reconstruction with 50 iterations, and the results were converged to the threshold value. For comparison, the conjugate gradient method (CGM) was also used for image reconstruction. The results are shown in Fig. 9.
Fig. 9. Original objects (1st column), captured images (2nd column), and reconstructed images by the CGM (3rd column) and the ADMM-TV (4th column) of (a) Apple, (b) Bee, (c) Face, (d) Cameraman, (e) Clock and (f) Text in the experiment.
From the reconstruction results, the blurred parts of the captured images were removed, and the original objects were reconstructed using the CGM and ADMM. Although the CGM shows a similar performance to the ADMM, some noise still appear at the top and bottom of the images in the binary image reconstruction. The ADMM eliminates noise in the grayscale image reconstruction. The reconstruction results are smoother and clearer compared with the results from the CGM. The peak signal-to-noise ratio (PSNR) was also used to evaluate the image quality. The details of the evaluation are shown in Table 1. The ADMM shows a more powerful denoising ability than the CGM based on numerical comparison.
Table 1. Evaluation indicators of the experiment’s reconstruction images.
The results of the optical experiment verified the concept of the proposed frontal imaging system using the deblurring method. However, it took a long time for the CGM and ADMM to reconstruct the images, which is not suitable for a real-time communication system. In future work, more efficient image reconstruction algorithm will be considered to reduce the reconstruction time.
4. Conclusion
A novel computational imaging system called the HWD-STS camera is proposed in this study. The STS is composed of a piece of transparent glass and two reflection vHOEs attached to different sides of the glass. The vHOE functions as a large-angle off-axis mirror that diffracts the Bragg-matched object light to the waveguide, which carries the diffracted light to the camera set behind the screen. Therefore, the user’s frontal image can be captured while the user is gazing at the screen. This feature makes eye-contact possible in a telecommunication system by combing it with a display behind the screen. The proposed computational camera can also be used in various visual devices because of its compact size and integrated design. Potential applications include near-window gesture recognition and a transparent communication system in combination with a transparent display. The system’s imaging process was analyzed by ray tracing to remove the vertical multiplexed blur caused by the larger size of the vHOE. Subsequently, the ADMM-TV method was used for image reconstruction based on the system transform matrix measured from the Hadamard matrix. Compared with the see-through lensless camera [11], the proposed structure can achieve a higher light efficiency, can employ an easier image reconstruction method, and has a significant potential to realize better image quality. A prototype camera was proposed and tested in an optical experiment. Binary and grayscale images were used as the targets for testing, and the evaluation results proved the validity and practicality of the theory. Although the reconstruction quality is not so high, we believe that higher image quality will be possible in the future if we use a more advanced reconstruction method.
This study has several limitations. The image reconstruction process took a long time in the CGM and ADMM. However, because the proposed camera is expected to be used in real-time communication systems, higher-speed image reconstruction needs to be implemented in the future. In addition, only grayscale images were used in the experiemnt. The use of full-color vHOE is considered for full-color image reconstruction in the future works. Furthermore, the measured system matrix for image reconstruction was obtained at a certain distance; if the optical conditions change, the system matrix must be remeasured. For the reconstruction of objects at multiple depths, it is necessary to characterize the system matrix at different distances. There has been reported work that implemented multiple-depth image recovery, e.g., [33] and it will be possible to adopt a more robust reconstruction system that considers distance with higher image quality in the future.
Funding
Japan Society for the Promotion of Science (18H03256); Japan Science and Technology Agency (JPMJSP2106, JST SPRING); Tokyo Institute of Technology (TAC-MI scholarship).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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