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Abstract
Digital holographic imaging has emerged as a transformative technology with significant implications for AR/VR devices. However, existing techniques often suffer from limitations such as restricted field of view (FOV), high power consumption, and contrast distortion. This paper introduces an innovative optical phased array (OPA)-based chip, integrating polarization, amplitude, and phase multiplexing for enhanced complex amplitude holographic imaging. A checkerboard-style staggered array is employed in the control strategy, substantially reducing power consumption and enabling the potential for large-scale array integration. To further enhance imaging quality, we introduce what we believe are two novel calibration strategies: one is to achieve super-resolution through block imaging methods, and the other is to image using sparse aperture methods. These advancements not only provide a robust foundation for high-quality holographic imaging, but also present a new paradigm for overcoming the inherent limitations of current active holographic imaging devices. Due to challenges in chip fabrication, the research is primarily simulation-based. Nevertheless, this work presents meaningful advancements in digital holographic imaging for AR/VR applications and provides a foundation for future experimental validations.
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1. Introduction
Virtual and augmented reality (VR/AR) are transforming various aspects of life and work. Novel holographic imaging methods can enrich VR/AR applications and improve user experiences. Current VR/AR headsets, based on stereoscopic vision, fail to mimic natural depth perception, leading to vergence-accommodation conflict. Holography, replicating light field characteristics through diffraction and interference, offers a more natural, depth-rich viewing experience.
Traditional holography can display objects in 3D but often involves complicated processes like exposure, development, and fixing. Unlike traditional optical holography, the generation of computational holography can be summarized as: information acquisition, processing, encoding storage, and reproduction. Initially, the complex simulated object wavefront is defined, followed by calculating its propagation to the holographic surface based on scalar diffraction theory, and then encoding the wavefront on the holographic surface, converting it into a hologram [1].
Computational holography can characterize any object's information, and the imaging optical path doesn't require the actual target. Researchers have proposed a meta-surface holographic imaging method [2]. Current research mainly focuses on modulating the amplitude [3], phase [4], frequency [5], polarization [6], and orbital angular momentum [7] of the input beam through on-chip microstructures, enabling multi-modal modulation for richer holographic images [8–10]. However, such meta-surface holography is passive, limiting its application in AR/VR devices.
Active holographic imaging can dynamically and real-time adjust the hologram pattern. Existing programmable holographic devices mainly include spatial light modulators, digital micromirrors, and programmable metasurfaces. Under control signals, spatial light modulators can modulate light wave properties, making them a major research direction in active holography, mainly consisting of acousto-optic modulators, digital micromirror devices, and liquid crystal spatial light modulators.
Researchers like Florian Willomitzer have combined acousto-optic modulators with their wavelength holography method, achieving holographic image reconstruction after scattering media [11]. Chonglei Zhang proposed a dynamic full-color 3D holography method based on a single digital micromirror, producing holograms with full-color, high refresh rates, and high fidelity [12]. Qiong-Hua Wang and Di Wang introduced adjustable liquid crystal gratings, overcoming conventional 3D holography's limitations with a narrow imaging field and small size [13].
However, there are still challenges in realizing final 3D displays with spatial light modulators based on discrete pixel structures. Stephen A. Benton pointed out that due to the pixel size and inter-pixel spacing of spatial light modulators, the viewing angle of the 3D hologram is limited, failing to meet direct-viewing requirements [14]. Some solutions increase system complexity, power consumption, and volume [15], while others face limitations in refresh rate [16] or practical application challenges [17]. Moreover, the diffraction effect of pixel units causes image distortion [14,15,17].
MIT pioneered the theoretical foundation and experimental validation of optical phased arrays (OPAs) in holographic imaging, as demonstrated in studies [18–20]. Due to its capability for high-speed and precise beam control, OPA demonstrates great potential in the field of digital holographic imaging, particularly in enhancing imaging speed and quality. Subsequent developments have focused on algorithms to mitigate thermal effects in phased arrays and sparse OPA techniques for reduced power consumption [21,22]. Despite the high frame rates achieved by photonic waveguide phased arrays, they still rely on conventional phase modulation methods. However, the ongoing advancements in silicon-based photonic waveguide technology, integrating OPAs with on-chip light modulators, are opening new avenues in digital holography. Leading institutions like MIT, Intel, and Columbia University have contributed unique designs and low-power solutions [23–25]. OPA phase shifters offer a wide range and faster modulation speeds compared to traditional spatial light modulators [26,27]. Research has extended OPA applications from the near-infrared to the visible light spectrum, particularly in SiN materials [28–30], broadening the scope for holographic imaging. Additionally, OPAs show promising potential in correlation imaging and optical communication, as highlighted by studies from the University of Tokyo [31,32]. Nonetheless, the challenge of achieving on-chip compound beam modulation in OPAs remains an area of active research.
In silicon photonics, on-chip modulators are increasingly crucial for high-quality digital holography, with significant progress made recently. Phase modulators, altering waveguide refractive indices to shift light field phases, utilize acousto-optic, thermo-optic, and electro-optic effects [20,24]. Notable techniques include Jie Sun's thermo-optic phase shifting [23], Yubing Wang's graphene nano-heater approach [33], and carrier-injected electro-optic modulation. Intensity modulators, leveraging electric field modulation in micro-ring resonators, offer compactness and energy efficiency, ideal for large-scale photonic chips. Polarization modulators, focusing on beam splitting and rotating, transform polarization states [34–39], with innovative designs from Zhejiang University's team enhancing photonic phased arrays [39]. This research underpins photonic phased arrays’ growing role in AR/VR devices, highlighting their potential in core holographic imaging technologies.
Given the mature spatial light modulation holography and the emerging waveguide phased array holography, existing challenges in active digital holography include:
- • Narrow imaging fields and image distortion with active diffractive wavefront encoders.
- • Waveguide phased array holography can enhance imaging frame rates, but limited integration capabilities hinder high-resolution holographic imaging.
- • Most digital holographic wavefront encoding methods rely on single light parameter modulation, limiting image quality improvement.
Grounded in imaging mechanisms and wavefront coding technology, we will deeply analyze the principles of multidimensional complex amplitude digital holography. By utilizing on-chip beam polarization multiplexing and sparse aperture coding strategies, we aim to expand the holographic imaging field. Along with compensatory algorithms, we intend to overcome image distortions caused by diffractive wavefront encoders. This approach promises not only a significant improvement in imaging frame rate but also the flexible control of the output light field's complex amplitude from each beam-emitting antenna, producing high-quality holographic images tailored to various environmental needs, providing a theoretical basis for the optimal realization of holographic imaging.
2. Method
This paper presents a complex amplitude holographic imaging approach based on high-performance optical modulators, as depicted in Fig. 1. The OPA produces two diverging beams differentiated by their polarization states. Following this, informed by the information of the imaging target, a targeted calibration is applied to the OPA's output light field using the appropriate wavefront encoding algorithm, leading to the reconstruction of images in distinct sub-block regions. Harnessing the swift on-chip beam modulation of the OPA, images from each sub-block are sequentially outputted, enabling the high-quality reconstruction of the desired target.
This method enhances field of view (FOV) by controlling the polarized light beams and temporally alternating the output of different polarization states from the OPA's antennas. Concurrently, through the utilization of the specific wavefront encoding techniques, it adeptly mitigates distortion challenges in holographic imaging. Furthermore, by employing on-chip beam wavelength-division multiplexing control, the scope of holographic imaging control is extended.
The methodology adopted in this study ensures superior quality in holographic imaging on two fronts. Firstly, at the chip level, the design based on the OPA architecture incorporates stable and efficient on-chip components. Through structural innovation, it achieves the multiplexing of output light polarization, amplitude, and phase under low-power conditions, laying a solid foundation for high-quality holographic imaging. Secondly, from the control strategy perspective, this paper introduces and validates a beam control technique. This approach fully harnesses the advantages of complex amplitude holographic imaging, markedly enhancing the quality of holographic captures, providing assurance at the software level for high-quality holographic imaging. The feasibility of the proposed solution will be discussed in detail from these two angles in the subsequent sections.
3. Device preparation
Current digital holographic imaging predominantly relies on spatial light modulators and metamaterials for wavefront encoding. Spatial light modulator-based holography often faces limitations such as single-mode modulation, slower speeds, and restricted fields of view. Metamaterial-based holography, while innovative, struggles with the inflexibility of plate production, making dynamic image transformation challenging. Additionally, introducing wavelength-division multiplexed holography complicates the optical path, demanding further advancements for practical use. As the saying goes, ‘To do a good job, one must first sharpen one's tools.’ Therefore, developing a wavelength-division multiplexing wavefront encoder that offers a wide FOV, high frame rates, and high-quality imaging is crucial.
Benefitting from the maturity of the complementary metal-oxide-semiconductor process, silicon-based photonic phased array chips, boasting low production costs, high integration, and superior processing accuracy, have increasingly attracted the attention of researchers. With ongoing efforts, there's a plethora of silicon-based light modulators, all comprehensive in functionality, laying the groundwork for digital holographic imaging wavefront encoding devices. This paper intends to augment traditional silicon-based photonic phased array designs with amplitude and polarization modulators to craft novel integrated wavefront encoding devices tailored to application needs.
Figure 2 presents a schematic of the chip designed for this study. Key on-chip structures include: an on-chip Mach-Zehnder interferometer combined with a polarization beam splitter/rotator, guiding different polarizations into waveguide devices; a power splitter array of cascaded 1 × 2 multimode interferometers for distributing light across multiple paths; a microring modulator array for adjusting the output light intensity of antennas, crucial for holography; a phase shifter array to modify the output light's phase; and a transmission antenna array, arranged in alternating rows and columns, coupled via directional couplers. This structure is not only practical but also employs on-chip components that have been proven highly reliable in existing silicon photonic integrated chip design technologies.
3.1 Polarization multiplexing modulator
This paper proposes to use a polarization multiplexer controller comprised of PBS/PR + MZI. Components of this device are standard on silicon-based chips, and researchers worldwide have delved deeply into their principles and experimentation. Researchers such as Yaocheng Shi and Jingye Chen were the first to apply this device to OPAs, conducting both simulations and experimental verifications [39]. The device operates as follows: By controlling the optical field phase of the Mach-Zehnder modulator, the input TE0 light is directed to either the upper or lower path of the device. Integrating a polarization rotator on this path allows the conversion of TE0 to TM0. Subsequently, by integrating a reverse polarization rotator, both outputs can be directed towards the same waveguide, facilitating arbitrary switching of the input light's polarization state with minimal loss. Incorporating this device significantly aids the paper in achieving wavelength-division multiplexing and wide-field imaging. Furthermore, the waveguide structures employed are standard components on silicon chips, ensuring a short production cycle and reduced costs.
3.2 Crossed structure and principles of output field's phase and intensity
Advancements in laser technology have led to rapid modulation in OPAs, typically involving independent phase controllers for each channel. However, this approach, especially in larger chip integrations, results in high power consumption. Managing instantaneous temperature with thermo-electric coolers becomes challenging, increasing the number of on-chip heating electrodes and bonding wires, thus complicating chip packaging. Building on Farshid Ashtiani's method to reduce OPA power consumption [40], which controls an N × N OPA with just 2N phase shifters by intersecting each antenna's input waveguide, our study introduces a novel waveguide structure. We propose a checkerboard-style design for efficient optical parametric modulation, minimizing power usage.
This innovative design facilitates complex amplitude modulation via waveguide intersections, combined with dual micro-ring intensity and phase modulators, as illustrated in Fig. 2. The design features a diagonal array of micro-ring modulators, each comprising dual micro-ring units. The checkerboard waveguide pattern, divided by a power splitter array, positions these modulators diagonally to modulate light intensity in adjacent waveguides effectively. This arrangement requires only n intensity modulators to control light intensity across N 2 paths. Additionally, we incorporate 2N thermo-optic phase shifters for independent phase control, each governing a row or column's phase. This synergistic integration of micro-ring modulators and thermo-optic phase shifters enables the chip to modulate the optical field's complex amplitude emitted from N 2 antennas with enhanced efficiency and reduced power consumption
Overlooking the influence of the phase shifter array on the phase modulation of the optical field in the waveguide, n rows and n columns of waveguides intersect to form a checkerboard emission antenna area, with each square on the board having an emission antenna. The light energy of the emission antenna array is inputted from its corresponding row and column through a directional coupler. Assuming the optical field expression entering the m th row is ${E_m} = {a_m}{e^{j{\xi _m}}}$ and that entering the nth column is ${E_n} = {b_n}{e^{j{\eta _n}}}$ where ${a_m}\Delta {b_n}$ represent the optical field amplitude of the m th row and n th column, and ${\xi _m}\Delta {\eta _n}$ represent the optical field phase of the m th row and n th column respectively. As shown in the Figure 3, the emission antenna is placed at the intersection of rows and columns, combined via directional couplers and Y-shaped waveguides [41], then transmitted into space through an antenna.
Assuming, based on structural optimization, that the optical field entering the emitting antenna has not been modulated by the amplitude and phase modulators. At this moment, the phase difference between the optical field entering the antenna at row m, column n, and the antenna at m th row, n + 1th column of the grating emission antenna input end can be expressed as:
3.3 Study and simulation of dual polarized antenna
This paper aims to use waveguide grating couplers to project the internal optical beam of the chip into external space. According to the optical waveguide transmission theory, the phase difference generated by the grating cycle will affect the optical field passing through this grating. Since the incident light of each grating cycle shares the same origin, when the emitted light of different grating cycles meets the phase matching conditions, coherent superposition of the emitted light from each unit will occur in space, resulting in optical field distributions of different diffraction orders.
Based on the optical waveguide mode theory, under the condition of identical waveguide widths, as its thickness increases, the effective refractive indices of TE0 and TM0 modes gradually converge. Concerning the emission angle of the transmitting antenna, the difference in emission angles between the two polarization modes diminishes with increasing waveguide thickness. On the other hand, with identical waveguide width, the effective refractive indices of both polarization modes tend to converge as the thickness grows. However, when both the waveguide height and width are reduced simultaneously, guided modes propagating within the waveguide become difficult to confine, leading to relatively high insertion losses across the entire chip. To address the FOV of the dual-polarized optical beam, this paper proposes using a binary grating structure to replace the traditional periodic etched waveguide structure.
Each cycle of the binary grating comprises several sub-cycles, with each sub-cycle having a distinct duty cycle within a single grating period. Suppose each grating cycle contains M sub-cycles; then, the width of each sub-cycle is $T = {\Lambda / M}$. If the ridge widths of each sub-cycle are w 1,w 2,…,w n, their corresponding duty cycles are ${f_1} = {{{w_1}} / \Lambda },{{{f_2} = {w_2}} / \Lambda },\ldots {f_3} = {{{w_3}} / \Lambda }$. The binary grating belongs to the category of sub-wavelength gratings, where the size of its sub-cycles is much smaller than the wavelength. Thus, equivalent medium model theory can be applied during analysis. According to this theory, we have:
Modeling was conducted in Lumerical, and simulation results were derived. Using the finite-difference time-domain (FDTD) method, the authors established the following simulation model. Subsequent results were obtained, relevant antenna configurations were crafted, and the transmission efficiency of the antenna with different polarization inputs was tested. Based on the simulation results shown in Fig. 4, it can be observed that, when using appropriate parameters, the binary grating can maintain a high antenna emission efficiency in both TE and TM modes. Furthermore, examining the far-field distribution of the output light from both, they can achieve optical field stitching, thus realizing the proposed idea in this paper of enlarging the holographic imaging FOV through on-chip beam polarization multiplexing.
Fig. 4. Dual-polarized antenna simulation results. (a) Simulation model; (b) Simulation results of emission efficiency under TE/TM modes; (c) Far-field distribution in TE mode at 1550 nm wavelength; (d) Far-field distribution in TM mode at 1550 nm wavelength.
In conclusion, this device meets the requirements for polarization control, complex amplitude control, and also achieves low power consumption. A minor drawback is that the control achieved by this chip isn't entirely independent. However, its primary advantage lies in the ultra-fast modulation speed of the OPA, enabling the overlay of multiple frames to achieve high-quality imaging through compensatory methods.
4. Discussion and conclusion
4.1 Application scenarios and principles of the algorithm
The image corresponding to the complex amplitude light field generated by the wavefront coding device on the image plane can be represented by the Fourier transformation of the emitted light field. Assuming that the complex amplitude of the output light field from the integrated OPA can be expressed as ${E_s}(x,y) = S \cdot {e^{i\phi s}}$, then the light field on the image plane at a distance Z from the emission plane can be expressed as:
For complex amplitude holographic imaging involved in this paper, it can be equated to computing the amplitude and phase of the emitting plane, ensuring that the light field interferes coherently in the far field to match the desired imaging target. Specifically, the following formula can be used:
where ${\cal L}({\bullet} )$ represents an error function, quantifying the error between the reconstructed and original images. Furthermore, solving the optimization problem entails iterative adjustments of amplitude and phase values for each antenna in the emission plane to minimize the discrepancy between the reconstructed hologram and the original image.As illustrated in Fig. 5, there is a comparative diagram of the simulation effects between complex amplitude holographic imaging and traditional holographic imaging. In the experiment, we utilized a 16 × 16 OPA to optimize and calibrate holographic imaging for the 60 × 60 pixel letters “X” and “XDU”. Specifically, the letter “X” and “XDU” were set with a grayscale gradient ranging from 0-255. For the imaging results of the letter X, the peak signal-to-noise ratio (PSNR) of the complex amplitude holographic image is 23.12 dB, and that of the phase holographic image is 22.44 dB. For the imaging results of the letters XUD, the PSNR of the complex amplitude holographic image is 31.19 dB, and that of the phase holographic image is 27.35 dB. Upon analyzing the simulation results, it becomes evident that the imaging quality of complex amplitude holographic imaging is superior when processing intricate graphics compared to phase holographic imaging results.
Fig. 5. OPA Holography Simulations - Complex Amplitude vs. Phase. (a) “X” in complex amplitude: optimized image, phase, and amplitude; (b) “X” in phase holography: optimized image and iterative evaluation; (c) “XDU” in complex amplitude: optimized image, phase, and amplitude; (d) “XDU” in phase holography: optimized image and iterative evaluation.
4.2 Potential for super-resolution imaging and the resolving imaging contrast distortion
Existing digital holography employs discrete antenna arrays to encode beams, creating holographic images via diffraction. The output light field distribution of the antenna array can be represented as:
where $U({\theta _x},{\theta _y})$ is the diffraction envelope determined by a single antenna, and $M({\theta _x},{\theta _y})$ is the array factor influenced by the arrangement of antennas. Utilizing MATLAB and inputting relevant parameters, the results are shown in Fig. 6 (a) and (b). Analysis indicates that the far-field beam produced by the diffraction array is inherently restricted by an envelope determined by the individual antenna.Fig. 6. Simulation results of the OPA light beam output. (a) Far-field distribution of the array with an antenna size of 3µm and the far-field distribution of the array with an antenna size of 3.8µm; (b) Maximum intensity peak achievable by the OPA output light field within the FOV
In our simulation, we used an antenna array with 11µm spacing, with antennas of 3µm and 3.8µm width. Figures 6(c) and (d) show the far-field patterns from these antennas, revealing a quasi-Gaussian intensity distribution. This pattern can cause contrast distortions in holographic images, as diffraction-like wavefront coding devices typically reproduce only central or focal regions accurately.
To mitigate this, we developed an angle-weighted strategy based on a detailed amplitude response analysis of the OPA. This strategy globally optimizes holographic images to maintain consistent contrast with the original image. By mapping the imaging target onto our imaging FOV and considering the OPA's maximum light intensity outputs at various angles, we calculate amplitude weighting values for each FOV position. This global optimization approach moves beyond maximizing local amplitude to enhance overall contrast.
Additionally, by slicing the FOV finely and reassembling these slices, we not only optimize contrast but also explore super-resolution potential. This method, focusing on small-range slices, suggests the possibility of achieving higher resolution with the same hardware.
The following presents a pseudocode used in this paper. During the implementation of this program, we first compare the target area with the light intensity distribution at the predefined regions of the OPA. Subsequently, the target image is segmented and inversely weighted based on this distribution. Based on this, the Adam optimizer is employed with necessary modifications to calibrate each sub-region accordingly. Leveraging the rapid scanning capability of the OPA, these sub-fields are overlaid to form the final desired imaging target.
As depicted in Figs. 7 and 8, Fig. 7 illustrates the holographic imaging calibration results for various small segments within the OPA's FOV, showcasing the potential of our proposed method in achieving super-resolution imaging. Figure 8 contrasts our approach with conventional methods under similar conditions, showing the progression of the evaluative function through iterations. We used a grayscale gradient of the letter ‘X’ as the target image. This comparison reveals that, despite using a large-scale OPA chip, conventional methods fall short in achieving high-quality holographic imaging. In contrast, our approach significantly enhances imaging resolution. By leveraging complex amplitude holography, our method allows for flexible intensity modulation within each sub-imaging segment, effectively minimizing visible boundaries between segments. Although this approach may reduce the imaging frame rate, the inherent modulation speed of the OPA chip in holographic imaging compensates for this [25,27]. Additionally, a detailed analysis of the three-dimensional distribution of imaging results in Figs. 7 and 8 shows that our advanced algorithm, based on inverse weighting according to the amplitude distribution of the zero-phase field, effectively corrects contrast aberrations at the edges of the imaging FOV.
Fig. 7. Simulation results of the algorithm proposed in this study. In this simulation, the FOV was segmented into a 4 × 4 grid, and after compensation based on weights, the optimized holographic imaging outcome was achieved.
Fig. 8. (a) Target image; (b) Imaging results obtained from our study; (c) Imaging outcome derived from direct optimization of the target using OPA; (d) Evolution curve of the evaluation function with iteration numbers using our proposed method; (e) Evolution curve of the evaluation function using the conventional approach.
4.3 Possibility of holographic imaging with sparse apertures
In addition to our primary research, we also explore the integration of sparse aperture methods into holographic imaging. Susmija Jabbireddy's team at the University of Maryland has theoretically suggested that sparse apertures could reduce the control power consumption in OPAs [22]. However, this concept, while promising, lacks practical validation in the context of OPA architecture. Traditional OPAs face challenges in implementing sparse aperture imaging due to the inherent design of antenna arrays, which emit light fields uniformly. Optimizing the array layout for specific spectral targets introduces two major issues: the optimized array may only be suitable for imaging certain targets, and as the array scale increases, the resulting non-uniform and irregular patterns complicate design and fabrication processes [42–44]. Despite these challenges, our study indicates the feasibility of high-quality holographic imaging using sparse aperture OPAs with current technology.
In our proposed OPA architecture (Sec. 3), we can precisely control the light amplitude output of each antenna, enabling the creation of a sparse aperture antenna array. This array can be dynamically adjusted to meet specific imaging needs, offering high flexibility in beam control. We also introduce pseudocode for our algorithm, which differs from [22] by employing a well-established particle swarm optimization algorithm. This approach avoids the use of Gaussian weighting for image reconstruction, commonly used in optimizing OPA sparse aperture arrays [22,45].
Figure 9 illustrates our application of this method. In Fig. 9(a), we calibrate a 16 × 16 OPA using the sparse aperture algorithm. Figure 9(b) shows the amplitude distribution of the OPA, demonstrating the effective calibration of sparse aperture holographic imaging by the optimization algorithm. The phase distribution in Fig. 9(c) further supports this, indicating that where the amplitude is 0, the phase value is also 0.
Fig. 9. Illustration of calibration using a 16 × 16 OPA with sparse aperture algorithm. (a) Calibration results; (b) Amplitude distribution of OPA; (c) Corresponding phase distribution, indicating zero phase at zero amplitude positions.
This section emphasizes that the imaging technique discussed in Section 4.3 is a sophisticated approach designed to optimize sparse aperture configurations for holographic imaging. By selectively activating specific OPA antennas, we can capture the entire image without losing resolution. While this method appears distinct, it can be seamlessly integrated with the approach in Section 4.2, which focuses on enhancing contrast and achieving high-quality imaging through segmentation. Section 4.3's method excels in sparse imaging, whereas Section 4.2 effectively tackles contrast-related distortions, enabling super-resolution imaging. It's noteworthy that under certain conditions, the methods from Sections 4.2 and 4.3 could be combined for enhanced results. However, this integration poses practical engineering challenges, and relying solely on simulations for validation is a limitation. Therefore, this paper does not delve into this combined approach in depth.
For the validations in this chapter, we align closely with the OPA imaging process, using Eq. 6 for all beam calibrations. The imaging targets are primarily simple letters, with grayscale variations included to demonstrate the benefits of complex amplitude modulation.
5. Conclusion
The primary objective of this paper is to enhance the application performance of AR/VR devices in the realm of holographic imaging. Initially, based on the existing optical phased array architecture, we designed an optical chip capable of achieving complex amplitude holographic imaging. This chip integrates polarization multiplexing, amplitude multiplexing, and phase multiplexing techniques. Furthermore, a checkerboard-style staggered array was adopted in its control strategy, significantly reducing the chip's control power consumption, and paving the way for large-scale array integration. Simultaneously, we specifically designed transmitting antenna structures with adjacent far-field characteristics in both TE and TM modes. This chip design provides a solid foundation for high-quality holographic imaging, offering a new direction to address the limitations of current active holographic imaging devices.
Furthermore, in this paper, we introduced two distinct calibration strategies for holographic imaging beams. The first strategy focuses on achieving high-quality complex amplitude holographic imaging. It primarily employs a block imaging approach to realize super-resolution in holographic imaging and combines it with amplitude modulation techniques to counteract contrast distortion inherent in holography. In tandem with our specially designed complex amplitude optical chip, we also proposed a method for sparse aperture holographic imaging. We believe that the combined application of these two methods can further enhance the quality of holographic imaging significantly. We aim to validate this hypothesis in our future endeavors.
Regrettably, due to the challenges of integrating both TE and TM modes with the chip manufacturers we have access to, the research in this paper is primarily based on simulations. It's essential to clarify that the ideas and concepts presented in this paper were previously disclosed during our funding application processes and related review meetings. Unfortunately, we did not secure the necessary funding, which has accelerated our need to publish this work to ensure the originality of our contributions is recognized. As a result, we couldn't proceed with chip fabrication and had to rely on simulations for this paper. In the future, we will strive to collaborate with relevant manufacturers to complete the actual chip fabrication and validation, further refining this research experimentally, hoping to contribute to the high-quality development of digital holographic imaging.
Funding
Fundamental Research Funds for the Central Universities (ZYTS23129); Natural Science Foundation of Shaanxi Province (2019JQ-648); 2021 Open Project Fund of Science and Technology on Electromechanical Dynamic Control Laboratory; National Natural Science Foundation of China (62005207).
Acknowledgments
We extend our sincere gratitude to the engineers at Chongqing United Microelectronics Center for their invaluable advice and guidance on the chip architecture proposed in this paper. We also wish to express our deep appreciation to the responsible editors and anonymous reviewers who have offered valuable comments and suggestions, contributing significantly to the enhancement of this paper.
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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