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Holography|440 Article(s)
Computational Holographic Display Method Based on Error Diffusion
Pingping Wei, and Chao Han
ObjectivePhase-only hologram (POH) is favored by many researchers in holographic display technology due to its high diffraction efficiency and zero twin image. Common POH generation algorithms can be divided into iterative and non-iterative methods. The iterative methods require a lot of iterative optimization to obtain the required POH, which needs a large number of iterations and is time-consuming. The error diffusion algorithm does not require iteration and greatly improves the computational speed of POHs. In the traditional error diffusion method, the amplitude of all pixels on the complex amplitude hologram (CAH) is set to 1, and this hologram and its CAH are adopted to compute the error which will be diffused on the CAH to generate the POH. However, since different target images have various amplitude distributions, directly setting the CAH amplitude to 1 is not suitable for all images. Therefore, the quality of the generated POH is not high and the reconstruction image of the hologram cannot obtain a satisfactory display effect. Therefore, we call for a new error diffusion algorithm to improve the reconstructed image quality.MethodsTo improve the quality of the hologram reconstructed image generated by the error diffusion algorithm, we build a hologram error compensation model based on the bidirectional error diffusion algorithm by analyzing the relationship between the amplitude distribution of the target image and the generated hologram, and propose a new POH generation method. Firstly, the CAH of the target image is computed and its amplitude is set to 1. Secondly, the error between the POH and the original CAH is calculated by the error compensation model. Thirdly, the new error is adopted to generate a new POH by bidirectional error diffusion. Finally, a new error between this new POH and the original CAH is computed and the second error diffusion is carried out to obtain the final POH. Numerical simulations are conducted to compare the hologram reconstruction effect of the two methods. Additionally, the normalized correlation (NC) coefficient and the structural similarity index measure (SSIM) are employed to quantitatively compare and analyze the hologram reconstruction results. Meanwhile, the experimental schematic diagram is drawn and the optical imaging system is built, with the proposed method verified by optical experiments.Results and DiscussionsBy carrying out numerical simulation and optical experiments, the quality of hologram reconstructed images generated by different error diffusion methods is verified. The simulation results of the two error diffusion methods are shown in Fig. 6. The images of the first column in Fig. 6 are reconstructed ones by the traditional method, and contain obvious speckle noise. The images of the second column and third column in Fig. 6 are the reconstructed images of the holograms generated by the first improved error diffusion and second error diffusion respectively. Compared with the first column, the definition of the reconstructed images in the latter two columns is higher. The detail section of the images in the third column contains more information than the second column. For example, the detail part of Fig. 6(c) shows more information on the pepper stalk than that of Fig. 6(b). Additionally, for the detail part of the pirate, the hair of the man in Fig. 6(l) is more clear than that in Fig. 6(k), and the lines of the hair are more obvious. The NC coefficient and the SSIM are respectively adopted in Tables 2 and 3 to evaluate the quality of numerical simulation results of hologram reconstruction images quantitatively. After the first error diffusion, the NC coefficient and the SSIM increase by 0.05-0.14 and 0.036-0.09 respectively. After the second error diffusion, the NC coefficient and the SSIM increase by 0.01-0.026 and 0.025-0.036 respectively. Simulation results reveal that the reconstructed image quality of the proposed method is better than that of the original method. The similarity of the proposed method with the original image is higher, and reconstructed images of the proposed method are more in line with the visual quality requirements of human eyes. The comparison results of optical experiments on hologram reconstructed images by the traditional error diffusion method and the proposed error diffusion method are shown in Fig. 8. Fig. 8 indicates that for different target images, the hologram reconstructed images of the proposed algorithm can be displayed more clearly, but the hologram reconstructed images of the traditional error diffusion algorithm are obviously noisy and blurred. Comparison of the details of the two methods displays the sailboat in Fig. 8(e) and its reflection on the surface of the lake, while the sailboat in Fig. 8(e) is blurred. The pattern on the long spike behind the man’s hat in Fig. 8(g) is clear, while the pattern on the long spike in Fig. 8(h) is not clearly seen. The optical experiment results are consistent with those of simulations. The simulation and experimental results show that the proposed error diffusion algorithm is effective in improving the quality of hologram reconstructed images, with the feasibility and superiority of the proposed method verified.ConclusionsA bidirectional error diffusion compensation model is built by calculating the new error between CAH and POH. The hologram reconstructed images generated by the model contain more object light wave information. Additionally, the twice error diffusion algorithm is adopted to further improve the holographic display quality. Simulation results show that the reconstructed images generated by the improved method have higher resolution and more detailed information. The NC coefficient and SSIM serve as quantitative evaluation criteria for the simulation results. In Tables 2 and 3, the mean NC and SSIM values of the proposed method are 0.9743 and 0.8630 respectively, 0.0927 and 0.0848 higher than those of the traditional error diffusion method. The optical experiment results show that the reconstructed images generated by the improved algorithm have higher image quality and resolution in detail. Simulations and experimental results prove the effectiveness and feasibility of the improved algorithm, and this algorithm has application significance for computational holographic display. ObjectivePhase-only hologram (POH) is favored by many researchers in holographic display technology due to its high diffraction efficiency and zero twin image. Common POH generation algorithms can be divided into iterative and non-iterative methods. The iterative methods require a lot of iterative optimization to obtain the required POH, which needs a large number of iterations and is time-consuming. The error diffusion algorithm does not require iteration and greatly improves the computational speed of POHs. In the traditional error diffusion method, the amplitude of all pixels on the complex amplitude hologram (CAH) is set to 1, and this hologram and its CAH are adopted to compute the error which will be diffused on the CAH to generate the POH. However, since different target images have various amplitude distributions, directly setting the CAH amplitude to 1 is not suitable for all images. Therefore, the quality of the generated POH is not high and the reconstruction image of the hologram cannot obtain a satisfactory display effect. Therefore, we call for a new error diffusion algorithm to improve the reconstructed image quality.MethodsTo improve the quality of the hologram reconstructed image generated by the error diffusion algorithm, we build a hologram error compensation model based on the bidirectional error diffusion algorithm by analyzing the relationship between the amplitude distribution of the target image and the generated hologram, and propose a new POH generation method. Firstly, the CAH of the target image is computed and its amplitude is set to 1. Secondly, the error between the POH and the original CAH is calculated by the error compensation model. Thirdly, the new error is adopted to generate a new POH by bidirectional error diffusion. Finally, a new error between this new POH and the original CAH is computed and the second error diffusion is carried out to obtain the final POH. Numerical simulations are conducted to compare the hologram reconstruction effect of the two methods. Additionally, the normalized correlation (NC) coefficient and the structural similarity index measure (SSIM) are employed to quantitatively compare and analyze the hologram reconstruction results. Meanwhile, the experimental schematic diagram is drawn and the optical imaging system is built, with the proposed method verified by optical experiments.Results and DiscussionsBy carrying out numerical simulation and optical experiments, the quality of hologram reconstructed images generated by different error diffusion methods is verified. The simulation results of the two error diffusion methods are shown in Fig. 6. The images of the first column in Fig. 6 are reconstructed ones by the traditional method, and contain obvious speckle noise. The images of the second column and third column in Fig. 6 are the reconstructed images of the holograms generated by the first improved error diffusion and second error diffusion respectively. Compared with the first column, the definition of the reconstructed images in the latter two columns is higher. The detail section of the images in the third column contains more information than the second column. For example, the detail part of Fig. 6(c) shows more information on the pepper stalk than that of Fig. 6(b). Additionally, for the detail part of the pirate, the hair of the man in Fig. 6(l) is more clear than that in Fig. 6(k), and the lines of the hair are more obvious. The NC coefficient and the SSIM are respectively adopted in Tables 2 and 3 to evaluate the quality of numerical simulation results of hologram reconstruction images quantitatively. After the first error diffusion, the NC coefficient and the SSIM increase by 0.05-0.14 and 0.036-0.09 respectively. After the second error diffusion, the NC coefficient and the SSIM increase by 0.01-0.026 and 0.025-0.036 respectively. Simulation results reveal that the reconstructed image quality of the proposed method is better than that of the original method. The similarity of the proposed method with the original image is higher, and reconstructed images of the proposed method are more in line with the visual quality requirements of human eyes. The comparison results of optical experiments on hologram reconstructed images by the traditional error diffusion method and the proposed error diffusion method are shown in Fig. 8. Fig. 8 indicates that for different target images, the hologram reconstructed images of the proposed algorithm can be displayed more clearly, but the hologram reconstructed images of the traditional error diffusion algorithm are obviously noisy and blurred. Comparison of the details of the two methods displays the sailboat in Fig. 8(e) and its reflection on the surface of the lake, while the sailboat in Fig. 8(e) is blurred. The pattern on the long spike behind the man’s hat in Fig. 8(g) is clear, while the pattern on the long spike in Fig. 8(h) is not clearly seen. The optical experiment results are consistent with those of simulations. The simulation and experimental results show that the proposed error diffusion algorithm is effective in improving the quality of hologram reconstructed images, with the feasibility and superiority of the proposed method verified.ConclusionsA bidirectional error diffusion compensation model is built by calculating the new error between CAH and POH. The hologram reconstructed images generated by the model contain more object light wave information. Additionally, the twice error diffusion algorithm is adopted to further improve the holographic display quality. Simulation results show that the reconstructed images generated by the improved method have higher resolution and more detailed information. The NC coefficient and SSIM serve as quantitative evaluation criteria for the simulation results. In Tables 2 and 3, the mean NC and SSIM values of the proposed method are 0.9743 and 0.8630 respectively, 0.0927 and 0.0848 higher than those of the traditional error diffusion method. The optical experiment results show that the reconstructed images generated by the improved algorithm have higher image quality and resolution in detail. Simulations and experimental results prove the effectiveness and feasibility of the improved algorithm, and this algorithm has application significance for computational holographic display.
Acta Optica Sinica
- Publication Date: Apr. 10, 2024
- Vol. 44, Issue 8, 0809001 (2024)
Multiplane Color Holographic Display Based on Time-Division Multiplexing
Huadong Zheng, Zhen Wang, and Junchang Peng
ObjectiveDisplay technology is essential for human beings to obtain information. In display technology, holographic display is considered the most influential display technology, as it can reconstruct all the information of real or virtual scenes without visual fatigue. Color holographic display is a significant technology that can record and reconstruct the color and three-dimensional (3D) information of the original object. Compared with monochrome holograms, color holograms can reflect the real information of objects, having a more wide application. In this paper, we propose an iterative method for generating multiplane color phase-only holograms based on time-division multiplexing. This method is based on the Gerchberg-Saxon (GS) algorithm. When holograms are recorded, amplitude constraints are imposed on each channel plane, which is repeated. The red (R), green (G), and blue (B) channel information of color images is recorded in three phase-only holograms respectively. During reconstruction, RGB channels overlap at the same distances, and the target color images are reconstructed. The reconstruction results of one, three, and five color images are displayed. Compared with the deep-division multiplexing (DDM) method, the quality of reconstructed color images by the proposed method is improved, and the crosstalk between different channel planes is effectively avoided. Numerical simulation and optical reconstruction results prove the effectiveness of the proposed method.MethodsThe red, green, and blue channels of color images are set to the same distances when encoding in this study. When recording, we set the amplitude of the initial holograms of three-color channels as a constant of 1 and the phase as a random. When the wavefront propagates to the object plane through angular spectrum diffraction, its amplitude information is replaced by the amplitude of the object plane. The amplitude constraint is relaxed by applying a small nonzero value to the zero-intensity region of the object plane, and the phase is preserved. The wavefront continues to propagate backward, and the amplitude in the hologram plane is replaced by a constant of 1. The phase is preserved, and the process is repeated. Eventually, their three-color channel information is recorded in three holograms respectively. When reconstructing, the three-color channels of the color images are reconstructed at the same distances, and then the color images are reconstructed. When the wavefront propagates to the object plane through angular spectrum diffraction in holographic recording, a small nonzero value is applied to it to relax the amplitude constraint of the object plane. In holographic reconstruction, the original color images are reconstructed at a set distance. It can effectively reduce the speckle noise of the target color images by padding with zeros to the original images. As laser speckle often reduces the quality of the reconstructed images in optical experiments, we adopt the time averaging method. Through the time integration effect, the intensity information of reconstructed images of multiple holograms is superimposed to suppress speckle noise. For the optical reconstruction system, the chromatic aberration caused by the objective lens may lead to different image sizes in red, green, and blue channels. In this study, we construct an optical system with achromatic optical elements to avoid the problem of inconsistent size and distance of reconstructed images.Results and DiscussionsOur proposed method shows excellent performance in both numerical simulation and optical experiment (Fig. 6). The proposed method and DDM method can reconstruct the single-color image well. However, the original color image reconstructed by the DDM method has color deviation, which may be caused by the hologram recording images of different color channels during recording. The original color image can be reconstructed well by our method. We introduce the correlation coefficient as an index to measure the quality of color image reconstruction. The correlation coefficient values of our proposed method in reconstructing single and multiple color images are higher than those of the DDM method (Fig. 7). The DDM method reconstructing multiplane color images is very limited. When recording holograms, we need to keep multiple color channels at different distances, whereas this work will be very hard within a limited calculation distance. Eventually, crosstalk will inevitably occur between different channels, leading to color deviation. Because reconstructing n color images will eventually reconstruct n×3 channels, the possibility of crosstalk between different channels greatly increases. However, when we reconstruct n color images, only n channels will be reconstructed. Our method can reconstruct more color images, but we need to pay attention to the distance setting between different images to avoid crosstalk.ConclusionsIn this paper, we propose a phase-only hologram generation method for reconstructing multiplane color images. In holographic recording, the red, green, and blue color channels of color images are recorded in three holograms respectively, and finally, the original color images are reconstructed at the set distances. The traditional DDM method needs to record multiple information of different color channels when encoding. Therefore, the quality of the reconstructed images is poor and crosstalk occurs. Our method effectively avoids crosstalk between different planes by setting the distance between different planes reasonably during recording. When reconstructing multiplane color images, it can still maintain high quality. The correlation coefficients of our proposed method are significantly higher than that of the DDM method when reconstructing single and three images. Both numerical simulation and optical experiment results show the novelty and effectiveness of our proposed method. ObjectiveDisplay technology is essential for human beings to obtain information. In display technology, holographic display is considered the most influential display technology, as it can reconstruct all the information of real or virtual scenes without visual fatigue. Color holographic display is a significant technology that can record and reconstruct the color and three-dimensional (3D) information of the original object. Compared with monochrome holograms, color holograms can reflect the real information of objects, having a more wide application. In this paper, we propose an iterative method for generating multiplane color phase-only holograms based on time-division multiplexing. This method is based on the Gerchberg-Saxon (GS) algorithm. When holograms are recorded, amplitude constraints are imposed on each channel plane, which is repeated. The red (R), green (G), and blue (B) channel information of color images is recorded in three phase-only holograms respectively. During reconstruction, RGB channels overlap at the same distances, and the target color images are reconstructed. The reconstruction results of one, three, and five color images are displayed. Compared with the deep-division multiplexing (DDM) method, the quality of reconstructed color images by the proposed method is improved, and the crosstalk between different channel planes is effectively avoided. Numerical simulation and optical reconstruction results prove the effectiveness of the proposed method.MethodsThe red, green, and blue channels of color images are set to the same distances when encoding in this study. When recording, we set the amplitude of the initial holograms of three-color channels as a constant of 1 and the phase as a random. When the wavefront propagates to the object plane through angular spectrum diffraction, its amplitude information is replaced by the amplitude of the object plane. The amplitude constraint is relaxed by applying a small nonzero value to the zero-intensity region of the object plane, and the phase is preserved. The wavefront continues to propagate backward, and the amplitude in the hologram plane is replaced by a constant of 1. The phase is preserved, and the process is repeated. Eventually, their three-color channel information is recorded in three holograms respectively. When reconstructing, the three-color channels of the color images are reconstructed at the same distances, and then the color images are reconstructed. When the wavefront propagates to the object plane through angular spectrum diffraction in holographic recording, a small nonzero value is applied to it to relax the amplitude constraint of the object plane. In holographic reconstruction, the original color images are reconstructed at a set distance. It can effectively reduce the speckle noise of the target color images by padding with zeros to the original images. As laser speckle often reduces the quality of the reconstructed images in optical experiments, we adopt the time averaging method. Through the time integration effect, the intensity information of reconstructed images of multiple holograms is superimposed to suppress speckle noise. For the optical reconstruction system, the chromatic aberration caused by the objective lens may lead to different image sizes in red, green, and blue channels. In this study, we construct an optical system with achromatic optical elements to avoid the problem of inconsistent size and distance of reconstructed images.Results and DiscussionsOur proposed method shows excellent performance in both numerical simulation and optical experiment (Fig. 6). The proposed method and DDM method can reconstruct the single-color image well. However, the original color image reconstructed by the DDM method has color deviation, which may be caused by the hologram recording images of different color channels during recording. The original color image can be reconstructed well by our method. We introduce the correlation coefficient as an index to measure the quality of color image reconstruction. The correlation coefficient values of our proposed method in reconstructing single and multiple color images are higher than those of the DDM method (Fig. 7). The DDM method reconstructing multiplane color images is very limited. When recording holograms, we need to keep multiple color channels at different distances, whereas this work will be very hard within a limited calculation distance. Eventually, crosstalk will inevitably occur between different channels, leading to color deviation. Because reconstructing n color images will eventually reconstruct n×3 channels, the possibility of crosstalk between different channels greatly increases. However, when we reconstruct n color images, only n channels will be reconstructed. Our method can reconstruct more color images, but we need to pay attention to the distance setting between different images to avoid crosstalk.ConclusionsIn this paper, we propose a phase-only hologram generation method for reconstructing multiplane color images. In holographic recording, the red, green, and blue color channels of color images are recorded in three holograms respectively, and finally, the original color images are reconstructed at the set distances. The traditional DDM method needs to record multiple information of different color channels when encoding. Therefore, the quality of the reconstructed images is poor and crosstalk occurs. Our method effectively avoids crosstalk between different planes by setting the distance between different planes reasonably during recording. When reconstructing multiplane color images, it can still maintain high quality. The correlation coefficients of our proposed method are significantly higher than that of the DDM method when reconstructing single and three images. Both numerical simulation and optical experiment results show the novelty and effectiveness of our proposed method.
Acta Optica Sinica
- Publication Date: Feb. 10, 2024
- Vol. 44, Issue 3, 0309001 (2024)
Holographic Near-Eye Display System with Expanded Eyebox Based on Waveguide
Chao Yu, Xiangyu Meng, Li Jiang, Hong Cai, Hui Mao, Rui Wang, and Shiliang Pu
ObjectiveHolographic near-eye displays (NEDs) have attracted ever-increasing attention in recent years. Through wavefront modulation of the incident beam by the spatial light modulator (SLM), a holographic NED can achieve multiple functions that are not within the reach of conventional two-dimensional (2D) displays, such as controlling the depth of the displayed image and dynamically correcting the aberration. However, due to the limited space-bandwidth product of the SLM, the etendue of the entire system is small, leading to a long-standing trade-off between the field of view (FOV) and the eyebox. For example, Microsoft reported at the SIGGRAPH conference in 2017 that they had achieved a FOV of 80°, but the eyebox was small. Two main types of methods have been proposed to expand the eyebox, i.e., active methods and passive methods. The active methods utilize a pupil-tracking system and move the eyebox subject to the position of the user's eye. Their energy efficiency can be high, contributing to lower power consumption of the system, longer battery life, and simpler thermal design. However, the main challenge for achieving high immersion in augmented reality (AR) use cases is low motion-to-photon latency, which is more difficult to obtain when the process of eye-tracking is incorporated. The passive solutions generally provide multiple discrete eyebox points simultaneously to expand the entire eyebox. However, they are exposed to the risk that no or two eyebox points may enter the pupil at a certain position as the user's eye moves. In such a case, missing of fields, low brightness uniformity, or ghost artifact occurs. In this paper, a holographic NED system with an expanded eyebox based on a surface relief grating (SRG) waveguide is investigated, showcasing a continuously and two-dimensionally expanded eyebox.MethodsIn the calculation of holograms, the angular spectrum method (ASM) and the stochastic gradient descent (SGD) algorithm are adopted because they can provide much better image quality than that offered by the traditional Gerchberg-Saxton (GS) algorithm. This advantage is confirmed by the comparison result of the peak signal-to-noise ratio (PSNR). To increase the etendue of the holographic NED, this paper utilizes a waveguide incorporating an in-coupling grating and a 2D surface relief out-coupling grating. The beam width corresponding to each image point in the holographic image is expanded two-dimensionally and continuously, and a two-dimensionally expanded eyebox is thereby obtained. Furthermore, the influence of pupil expansion on holographic display is assessed. By calculating the optical path difference between adjacent out-coupling beams, the paper finds that the angular period of the interference pattern is too small to be observed, and its impact on image quality is thus negligible.Results and discussionsAn experimental prototype (Fig. 6) is built to verify the effectiveness of the investigated system. Firstly, the display performance of the system on a monochromatic image verifies that the fine details of the resolution pattern can be reconstructed (Fig. 7). Then, the system's capability of displaying color images is demonstrated. Since the principle of the system's display of color images is time-division multiplexing, the monochromatic images of three colors are acquired independently and then synthesized (Fig. 8). The color image looks reasonably well despite a certain amount of stray light. Next, the paper verifies the aim of the 2D expansion of the eyebox. The baseline case without the waveguide is assessed first. The results (Fig. 9) reveal that when the eye relief is 20 mm, only a small part of the target image can be captured at each position within the range of 4 mm×4 mm. In contrast, when the waveguide is added to the system, the entire image can be observed across an eyebox range of 8 mm×6 mm (Fig. 10). In this range, 15 points are sampled continuously and uniformly, with the horizontal sampling points located at 0, ±2 mm, ±4 mm and the vertical sampling points at 0, ±3 mm, respectively. Furthermore, an AR display test (Fig. 11) is conducted, and the results demonstrate that the user can observe virtual and real scenes simultaneously. After that, the stray light and uniformity of the system are discussed. The stray light in the upper part of the displayed image is mainly due to the scattering at the defects on the waveguide and the higher energy of the beam transmitting in the waveguide in the upper part. A uniformity of 39.47% is obtained by evaluating the average grayscale of nine points uniformly sampled in the display area. Finally, the possibility of displaying 3D scenes is discussed.ConclusionsTo mitigate the challenge of obtaining a sufficiently large eyebox under a proper FOV for holographic NEDs, this paper investigates a holographic NED system with an expanded eyebox. A waveguide incorporating a 2D surface relief out-coupling grating is utilized to expand the beam width of the holographic image two-dimensionally and continuously. Experiments confirm that when the eye relief is 20 mm and the FOV is 38.6°, an eyebox of 8 mm×6 mm can be obtained. The problem of the incompetence of the FOV is thereby effectively mitigated. In the follow-up work, research will be conducted on deep learning-based computer-generated holography (CGH) algorithms, which can provide suitable pre-compensation of phase for the image coupled into the waveguide, to achieve the high-quality reconstruction of 2D and three-dimensional (3D) scenes. ObjectiveHolographic near-eye displays (NEDs) have attracted ever-increasing attention in recent years. Through wavefront modulation of the incident beam by the spatial light modulator (SLM), a holographic NED can achieve multiple functions that are not within the reach of conventional two-dimensional (2D) displays, such as controlling the depth of the displayed image and dynamically correcting the aberration. However, due to the limited space-bandwidth product of the SLM, the etendue of the entire system is small, leading to a long-standing trade-off between the field of view (FOV) and the eyebox. For example, Microsoft reported at the SIGGRAPH conference in 2017 that they had achieved a FOV of 80°, but the eyebox was small. Two main types of methods have been proposed to expand the eyebox, i.e., active methods and passive methods. The active methods utilize a pupil-tracking system and move the eyebox subject to the position of the user's eye. Their energy efficiency can be high, contributing to lower power consumption of the system, longer battery life, and simpler thermal design. However, the main challenge for achieving high immersion in augmented reality (AR) use cases is low motion-to-photon latency, which is more difficult to obtain when the process of eye-tracking is incorporated. The passive solutions generally provide multiple discrete eyebox points simultaneously to expand the entire eyebox. However, they are exposed to the risk that no or two eyebox points may enter the pupil at a certain position as the user's eye moves. In such a case, missing of fields, low brightness uniformity, or ghost artifact occurs. In this paper, a holographic NED system with an expanded eyebox based on a surface relief grating (SRG) waveguide is investigated, showcasing a continuously and two-dimensionally expanded eyebox.MethodsIn the calculation of holograms, the angular spectrum method (ASM) and the stochastic gradient descent (SGD) algorithm are adopted because they can provide much better image quality than that offered by the traditional Gerchberg-Saxton (GS) algorithm. This advantage is confirmed by the comparison result of the peak signal-to-noise ratio (PSNR). To increase the etendue of the holographic NED, this paper utilizes a waveguide incorporating an in-coupling grating and a 2D surface relief out-coupling grating. The beam width corresponding to each image point in the holographic image is expanded two-dimensionally and continuously, and a two-dimensionally expanded eyebox is thereby obtained. Furthermore, the influence of pupil expansion on holographic display is assessed. By calculating the optical path difference between adjacent out-coupling beams, the paper finds that the angular period of the interference pattern is too small to be observed, and its impact on image quality is thus negligible.Results and discussionsAn experimental prototype (Fig. 6) is built to verify the effectiveness of the investigated system. Firstly, the display performance of the system on a monochromatic image verifies that the fine details of the resolution pattern can be reconstructed (Fig. 7). Then, the system's capability of displaying color images is demonstrated. Since the principle of the system's display of color images is time-division multiplexing, the monochromatic images of three colors are acquired independently and then synthesized (Fig. 8). The color image looks reasonably well despite a certain amount of stray light. Next, the paper verifies the aim of the 2D expansion of the eyebox. The baseline case without the waveguide is assessed first. The results (Fig. 9) reveal that when the eye relief is 20 mm, only a small part of the target image can be captured at each position within the range of 4 mm×4 mm. In contrast, when the waveguide is added to the system, the entire image can be observed across an eyebox range of 8 mm×6 mm (Fig. 10). In this range, 15 points are sampled continuously and uniformly, with the horizontal sampling points located at 0, ±2 mm, ±4 mm and the vertical sampling points at 0, ±3 mm, respectively. Furthermore, an AR display test (Fig. 11) is conducted, and the results demonstrate that the user can observe virtual and real scenes simultaneously. After that, the stray light and uniformity of the system are discussed. The stray light in the upper part of the displayed image is mainly due to the scattering at the defects on the waveguide and the higher energy of the beam transmitting in the waveguide in the upper part. A uniformity of 39.47% is obtained by evaluating the average grayscale of nine points uniformly sampled in the display area. Finally, the possibility of displaying 3D scenes is discussed.ConclusionsTo mitigate the challenge of obtaining a sufficiently large eyebox under a proper FOV for holographic NEDs, this paper investigates a holographic NED system with an expanded eyebox. A waveguide incorporating a 2D surface relief out-coupling grating is utilized to expand the beam width of the holographic image two-dimensionally and continuously. Experiments confirm that when the eye relief is 20 mm and the FOV is 38.6°, an eyebox of 8 mm×6 mm can be obtained. The problem of the incompetence of the FOV is thereby effectively mitigated. In the follow-up work, research will be conducted on deep learning-based computer-generated holography (CGH) algorithms, which can provide suitable pre-compensation of phase for the image coupled into the waveguide, to achieve the high-quality reconstruction of 2D and three-dimensional (3D) scenes.
Acta Optica Sinica
- Publication Date: May. 10, 2023
- Vol. 43, Issue 9, 0909001 (2023)
Compact Phase-Only Holographic Near-Eye 3D Display
Xiaofeng Cai, Gongyu Song, Xin Yang, Zengyao Wang, Qing Wen, Fuyang Xu, and Zhijun Ren
ObjectiveAs a virtual 3D space parallel to reality, metaverse can greatly enrich human life and work and has received extensive attention. Augmented reality (AR) and virtual reality (VR) are considered the gateway to the metaverse. True 3D display without visual fatigue caused to human eyes is the key to AR and VR displays. Among the 3D displays such as light field 3D display, the holographic 3D display is the only way to completely reconstruct the phase and amplitude information of 3D scenes.The phase-only hologram is more attractive for its higher diffraction efficiency. The spatial light modulator (SLM), especially the phase-only liquid crystal on silicon (LCoS), is an ideal display panel for dynamic holographic 3D displays with phase-only holograms. However, due to the pixel structure of the LCoS, there are zero-order and high-order lights, which are inevitable and very annoying for holographic near-eye 3D displays and are always filtered with 4f optical systems. The enlarged virtual 3D image is viewed with an eyepiece and the presence of 4f optical systems increases the size of the display system. Since the complex amplitude distribution of diffracted 3D scenes is difficult to be fully described by phase-only data, the computation of phase-only holograms is a big challenge. Different optimization algorithms including Gerchberg-Saxton (GS) algorithm, patterned phase-only hologram, double phase method, gradient descent algorithm and deep learning algorithm have been proposed for the phase-only hologram calculation. The above algorithms have their advantages and disadvantages. Most of the algorithms are not related to the display systems and cannot be employed to reduce the volume of the display system.MethodsThis paper demonstrates a compact holographic near-eye 3D display only with one projection lens and one eyepiece after the SLM, thereby avoiding the utilization of 4f optical systems and reducing the display system. In the hologram calculation, an interactive method by considering the parameters of holographic near-eye display systems is designed and implemented. The quadratic phases related to the focal length of the projection lens and the depth of each layer of the 3D model are adopted as compensation phase factors, and only the Fourier transform and inverse Fourier transform are leveraged in the iterations to obtain the 3D phase-only hologram. Finally, the 3D image with multiple layers can be projected near the focus plane of the projection lens and the enlarged virtual image can be watched with the eyepiece for VR near-eye 3D display and an extra beam splitter for AR near-eye 3D display.Results and DiscussionsFour layers with a resolution of 1080 pixel×1080 pixel non-overlapped 3D model are designed, and the phase-only holograms with random phase and quadratic phase as initial phase are calculated and reconstructed. The peak signal-to-noise ratio (PSNR) and correlation coefficient (CC) are employed to evaluate the proposed calculation method and point out that when the initial phase is random, the speckle noise of the reproduced image is worse but the 3D effect of out-of-focus focusing is more obvious. However, when the quadratic phase is used as the initial phase, the speckle noise can be suppressed under certain circumstances, but the out-of-focus change is not obvious for the 3D display. In addition, a simulation study is conducted on the multi-depth images with front and back occlusion, which proves that the proposed algorithm is also effective in this case. The optical reconstructions of the phase-only holograms are implemented and the holographic near-eye VR and AR 3D display results are verified with experiments in the proposed compact display system.ConclusionsIn this paper, a compact holographic near-eye display is proposed for holographic near-eye VR and AR 3D displays. The proposed iterative algorithm is a display system-related algorithm, which is conducive to reducing the volume of the holographic near-eye display system. The effectiveness of the proposed method is proved by simulations and optical experiments. The combination of the proposed method and the optical waveguide has the potential to be applied to the waveguide-type holographic AR 3D display to promote the early arrival of the metaverse. ObjectiveAs a virtual 3D space parallel to reality, metaverse can greatly enrich human life and work and has received extensive attention. Augmented reality (AR) and virtual reality (VR) are considered the gateway to the metaverse. True 3D display without visual fatigue caused to human eyes is the key to AR and VR displays. Among the 3D displays such as light field 3D display, the holographic 3D display is the only way to completely reconstruct the phase and amplitude information of 3D scenes.The phase-only hologram is more attractive for its higher diffraction efficiency. The spatial light modulator (SLM), especially the phase-only liquid crystal on silicon (LCoS), is an ideal display panel for dynamic holographic 3D displays with phase-only holograms. However, due to the pixel structure of the LCoS, there are zero-order and high-order lights, which are inevitable and very annoying for holographic near-eye 3D displays and are always filtered with 4f optical systems. The enlarged virtual 3D image is viewed with an eyepiece and the presence of 4f optical systems increases the size of the display system. Since the complex amplitude distribution of diffracted 3D scenes is difficult to be fully described by phase-only data, the computation of phase-only holograms is a big challenge. Different optimization algorithms including Gerchberg-Saxton (GS) algorithm, patterned phase-only hologram, double phase method, gradient descent algorithm and deep learning algorithm have been proposed for the phase-only hologram calculation. The above algorithms have their advantages and disadvantages. Most of the algorithms are not related to the display systems and cannot be employed to reduce the volume of the display system.MethodsThis paper demonstrates a compact holographic near-eye 3D display only with one projection lens and one eyepiece after the SLM, thereby avoiding the utilization of 4f optical systems and reducing the display system. In the hologram calculation, an interactive method by considering the parameters of holographic near-eye display systems is designed and implemented. The quadratic phases related to the focal length of the projection lens and the depth of each layer of the 3D model are adopted as compensation phase factors, and only the Fourier transform and inverse Fourier transform are leveraged in the iterations to obtain the 3D phase-only hologram. Finally, the 3D image with multiple layers can be projected near the focus plane of the projection lens and the enlarged virtual image can be watched with the eyepiece for VR near-eye 3D display and an extra beam splitter for AR near-eye 3D display.Results and DiscussionsFour layers with a resolution of 1080 pixel×1080 pixel non-overlapped 3D model are designed, and the phase-only holograms with random phase and quadratic phase as initial phase are calculated and reconstructed. The peak signal-to-noise ratio (PSNR) and correlation coefficient (CC) are employed to evaluate the proposed calculation method and point out that when the initial phase is random, the speckle noise of the reproduced image is worse but the 3D effect of out-of-focus focusing is more obvious. However, when the quadratic phase is used as the initial phase, the speckle noise can be suppressed under certain circumstances, but the out-of-focus change is not obvious for the 3D display. In addition, a simulation study is conducted on the multi-depth images with front and back occlusion, which proves that the proposed algorithm is also effective in this case. The optical reconstructions of the phase-only holograms are implemented and the holographic near-eye VR and AR 3D display results are verified with experiments in the proposed compact display system.ConclusionsIn this paper, a compact holographic near-eye display is proposed for holographic near-eye VR and AR 3D displays. The proposed iterative algorithm is a display system-related algorithm, which is conducive to reducing the volume of the holographic near-eye display system. The effectiveness of the proposed method is proved by simulations and optical experiments. The combination of the proposed method and the optical waveguide has the potential to be applied to the waveguide-type holographic AR 3D display to promote the early arrival of the metaverse.
Acta Optica Sinica
- Publication Date: Mar. 10, 2023
- Vol. 43, Issue 5, 0509002 (2023)
Microchannel Detection Based on Dual-Wavelength Image-Plane Digital Holographic Microscopy
Siqin Tao, Ming Kong, Wei Liu, Jianan Xu, Fuxia Cheng, Kaixuan Liu, and Zeqiu Yang
ObjectiveThe microfluidic chip is composed of a micro-nano-scale channel network. The microfluidic effect of biological, chemical, medical, and other samples is generated by the microchannel which carries the function of the "container" in the reaction. The dimensional accuracy such as the structure, shape, and size of the microchannel will directly impact the sample type, sample throughput, and sample injection rate in the microfluidic system. Therefore, it is of great significance to detect the three-dimensional topography of microfluidic chip channels. In recent years, scholars have continuously introduced new imaging detection methods for microfluidic chips, but most of the research focuses on the surface morphology of the reaction solution in the microchannel of the microfluidic chip or samples to be tested. There is little literature introduction on the measurement of microchannels. In this paper, digital holographic microscopic detection technology is combined with microfluidic technology. It provides a new imaging detection method for the microfluidic channel and has important application value for improving the quality of the chip.MethodsThis paper proposes a method for measuring the microchannels of microfluidic chips based on dual-wavelength image-plane digital holographic microscopy to meet the requirements of three-dimensional topography visualization of microfluidic chip channels. A reflective off-axis dual-wavelength image-plane digital holographic microscopic measurement system is built. Firstly, the lateral and vertical resolution and the magnification of the system are calibrated by the resolution target and standard sample. The results show that the dual-wavelength holographic microscope system has good accuracy and feasibility in the measurement of lateral and vertical depth. Then the straight channel of the polydimethylsiloxane (PDMS) microfluidic chip, the circular liquid phase chamber with vertical height transition, and the microchannel of the silicon-based microfluidic chip are measured. The phase distribution of the measurement surface is quantitatively recovered by combining the two-step phase division method and the 2π compensation method.Results and DiscussionsFirstly, a reflective off-axis dual-wavelength image-plane digital holographic microscopy experimental system is built (Fig. 1). To analyze and verify the accuracy and feasibility of the measurement system, this study adopts the 1951USAF resolution target, one-dimensional grid standard template, and segment difference standard film to calibrate the system respectively. The lateral resolution of this digital holographic microscope system can reach 2.2 μm (Fig. 4), and the actual magnification of the system is 13.5 times (Fig. 2). At the same time, the 20.79 μm segment difference standard film is measured, and the longitudinal depth is 19.9 μm with a relative error of 4.2% (Fig. 5). In addition, the three-dimensional morphology of the straight channel of the PDMS microfluidic chip, the circular liquid phase chamber with vertical height transition, and the microchannel of the silicon-based microfluidic chip are reproduced. Microchannels with different structures are obtained. The depth and the width of the straight channel and the circular chamber microchannel are 48.6 μm & 75.8 μm (Fig.9) and 48.5 μm & 76.6 μm (Fig. 10), respectively; the channel depth of silicon-based microfluidic chip is 61.6 μm (Fig. 11). Finally, the experimental results are well consistent with the white-light interferometry results (Table 1 & Table 2), which illustrates the reliability and accuracy of the dual-wavelength holographic microscope system, providing a new imaging detection method for the microchannel detection of microfluidic chips.ConclusionsIn this paper, a reflective off-axis dual-wavelength image-plane digital holographic microscopy measuring device is constructed based on digital holographic microscopy. The research on the three-dimensional topography measurement of microfluidic chip channels is carried out. The experimental results show that the lateral resolution of the system can reach 2.2 μm. The error range of the channel width and depth measurement is less than 4%, and the phase and plane distributions of the microchannel are accurately reproduced, indicating that the system has certain accuracy and feasibility. This research greatly expands the application field of digital holographic microscopic measurement, especially for closed microfluidic channels, meeting the needs of non-contact and label-free detection. In addition to the research on the structure of the chip channel itself, digital holographic microscopy can be extended to study the characteristics of the reaction solution, biological cells, and biological slice samples in the channel of the microfluidic chip. This study broadens the application scope of digital holographic microscopy and lays a foundation for the research on microfluidic-related technologies. ObjectiveThe microfluidic chip is composed of a micro-nano-scale channel network. The microfluidic effect of biological, chemical, medical, and other samples is generated by the microchannel which carries the function of the "container" in the reaction. The dimensional accuracy such as the structure, shape, and size of the microchannel will directly impact the sample type, sample throughput, and sample injection rate in the microfluidic system. Therefore, it is of great significance to detect the three-dimensional topography of microfluidic chip channels. In recent years, scholars have continuously introduced new imaging detection methods for microfluidic chips, but most of the research focuses on the surface morphology of the reaction solution in the microchannel of the microfluidic chip or samples to be tested. There is little literature introduction on the measurement of microchannels. In this paper, digital holographic microscopic detection technology is combined with microfluidic technology. It provides a new imaging detection method for the microfluidic channel and has important application value for improving the quality of the chip.MethodsThis paper proposes a method for measuring the microchannels of microfluidic chips based on dual-wavelength image-plane digital holographic microscopy to meet the requirements of three-dimensional topography visualization of microfluidic chip channels. A reflective off-axis dual-wavelength image-plane digital holographic microscopic measurement system is built. Firstly, the lateral and vertical resolution and the magnification of the system are calibrated by the resolution target and standard sample. The results show that the dual-wavelength holographic microscope system has good accuracy and feasibility in the measurement of lateral and vertical depth. Then the straight channel of the polydimethylsiloxane (PDMS) microfluidic chip, the circular liquid phase chamber with vertical height transition, and the microchannel of the silicon-based microfluidic chip are measured. The phase distribution of the measurement surface is quantitatively recovered by combining the two-step phase division method and the 2π compensation method.Results and DiscussionsFirstly, a reflective off-axis dual-wavelength image-plane digital holographic microscopy experimental system is built (Fig. 1). To analyze and verify the accuracy and feasibility of the measurement system, this study adopts the 1951USAF resolution target, one-dimensional grid standard template, and segment difference standard film to calibrate the system respectively. The lateral resolution of this digital holographic microscope system can reach 2.2 μm (Fig. 4), and the actual magnification of the system is 13.5 times (Fig. 2). At the same time, the 20.79 μm segment difference standard film is measured, and the longitudinal depth is 19.9 μm with a relative error of 4.2% (Fig. 5). In addition, the three-dimensional morphology of the straight channel of the PDMS microfluidic chip, the circular liquid phase chamber with vertical height transition, and the microchannel of the silicon-based microfluidic chip are reproduced. Microchannels with different structures are obtained. The depth and the width of the straight channel and the circular chamber microchannel are 48.6 μm & 75.8 μm (Fig.9) and 48.5 μm & 76.6 μm (Fig. 10), respectively; the channel depth of silicon-based microfluidic chip is 61.6 μm (Fig. 11). Finally, the experimental results are well consistent with the white-light interferometry results (Table 1 & Table 2), which illustrates the reliability and accuracy of the dual-wavelength holographic microscope system, providing a new imaging detection method for the microchannel detection of microfluidic chips.ConclusionsIn this paper, a reflective off-axis dual-wavelength image-plane digital holographic microscopy measuring device is constructed based on digital holographic microscopy. The research on the three-dimensional topography measurement of microfluidic chip channels is carried out. The experimental results show that the lateral resolution of the system can reach 2.2 μm. The error range of the channel width and depth measurement is less than 4%, and the phase and plane distributions of the microchannel are accurately reproduced, indicating that the system has certain accuracy and feasibility. This research greatly expands the application field of digital holographic microscopic measurement, especially for closed microfluidic channels, meeting the needs of non-contact and label-free detection. In addition to the research on the structure of the chip channel itself, digital holographic microscopy can be extended to study the characteristics of the reaction solution, biological cells, and biological slice samples in the channel of the microfluidic chip. This study broadens the application scope of digital holographic microscopy and lays a foundation for the research on microfluidic-related technologies.
Acta Optica Sinica
- Publication Date: Mar. 10, 2023
- Vol. 43, Issue 5, 0509001 (2023)
Improved Weighted Iterative Multi-Plane Holographic Display Method
Chi Hu, Guobin Sun, Shilei Jiang, Yan Zhou, Yanyan Liu, and Jin Zhang
ObjectiveThe continuous development of 3D display technology has brought society a new research field. Since 3D display technology based on computer generated hologram (CGH) features flexibility, repeatability, and convenience, most universities and research organizations have conducted in-depth research on it. With the increasing research on CGH theory and improving the performance of spatial light modulator (SLM) device structures, applications based on SLM have gradually become a research hotspot in holographic projection, holographic displays, virtual reality/augmented reality (AR/VR) displays, dynamic holography, and color holography. In 3D display, there is a multi-plane display method whose essence is between 2D and 3D, and the method employs a hologram that can display the same or different results at multiple locations. However, there are two main problems in the multi-plane holographic display. One is that the decreased reconstruction quality will accompany the increased number of planes in a multi-plane holographic display, and the other is the non-uniform distribution of the reconstruction image quality among each plane. The main reason is that the planes will interfere with each other, and the interference is random and relatively difficult to control. To improve multi-plane holographic display quality, we propose an improved weighted iterative multi-plane holographic display method. Meanwhile, to reduce the mutual influence among the planes in designing holograms, we introduce weights to control the constraints, and thus the quality distribution of the reconstructed images among multiple planes is more uniform and of higher quality by the constant correction of the weights during the calculation. The results show that the introduction of this method not only does not reduce the calculation speed but also leads to a more uniform quality distribution of the reconstructed image in the multi-plane holographic display. Additionally, the quality is improved to some extent, which provides a new idea for high-quality multi-plane display.MethodsOur design idea is based on the Gerchberg-Saxton (GS) iterative algorithm and is further improved by introducing weights on the holographic plane. Firstly, the output plane complex amplitude is composed according to the amplitude information of the known multi-plane target with random phases. Then, the inverse diffraction is carried out into the holographic plane at a known distance, and all complex amplitudes in the holographic plane are summed up in the weights. The total complex amplitude distribution of the holographic plane is obtained, and the weights are distributed in a weighting. In assigning the weights, the sum of all the weights should be 1. Initially, the weights of each plane are set to be equal. Then, the weights are corrected iteratively by the iterative optimization algorithm according to the CC value changes, and the purpose of setting the weights is to reduce the mutual influence among the planes. After summing up the weights, we ensure that the influences of the planes are balanced to make the distribution among the planes more uniform. Then we take the phase, keep it unchanged, and combine it with the plane wave amplitude to get the complex amplitude distribution of the holographic plane. Meanwhile, forward diffraction is conducted again to obtain the complex amplitude distribution of the output plane, then its phase is taken and combined with the target amplitude. This process is repeated until the results are satisfied.Results and DiscussionsOur core content is the weight correction for each plane, the specific correction idea is shown in Fig. 2, and the specific formulas for the correction are Eqs. (3)-(6). For two-plane holography, the quality of reconstructed images in each plane without introducing weights will be randomly distributed, and the reconstructed images in each plane will be qualitatively different when the introduction of the weights among various planes makes the reconstruction of the image distribution quality uniform (Figs. 4 and 12). It is discussed that for each plane with the same or different target images (Fig. 9), the quality of the reconstructed images of various target image types is different. Specifically, the quality of reconstructed images is relatively high under the same target images, and the quality of reconstructed results is poor when the target images are not the same. The differences between the two will become increasingly larger with the rising number of planes. Under the small number of planes, whether the target image is the same has little effect on the quality of the reconstructed image, and under the large number of planes, the quality of the reconstructed image is affected by whether the target images are the same or not (Figs. 6 and 10). For multi-plane holography, the most significant influence is the target image type, the number of planes, and the distance between neighboring planes (Figs. 13 and 14).ConclusionsTo reduce the mutual influence among the planes in the multi-plane display, we propose an improved weighted iterative multi-plane holographic display method by employing the weights. Finally, the control among the planes is controlled according to the interactions among the planes in the process of designing the holograms, and the distribution of the reconstruction image quality among the planes is more uniform. Additionally, without reducing the quality of the reconstructed image, the calculation speed will not be affected. The method is compared and analyzed by the simulation analysis and experimental verification of two to six different target images and the same target image to achieve a more uniform distribution of the reconstructed image quality among the planes. The quality of the reconstructed image is affected by the target image type, in which the quality is relatively high under the same target image, and it is poorer under different target images. The difference between them will become increasingly larger with the rising number of planes. In conclusion, introducing this method reduces mutual interference among reconstructed images in multi-plane holographic displays and their more uniform quality distribution. ObjectiveThe continuous development of 3D display technology has brought society a new research field. Since 3D display technology based on computer generated hologram (CGH) features flexibility, repeatability, and convenience, most universities and research organizations have conducted in-depth research on it. With the increasing research on CGH theory and improving the performance of spatial light modulator (SLM) device structures, applications based on SLM have gradually become a research hotspot in holographic projection, holographic displays, virtual reality/augmented reality (AR/VR) displays, dynamic holography, and color holography. In 3D display, there is a multi-plane display method whose essence is between 2D and 3D, and the method employs a hologram that can display the same or different results at multiple locations. However, there are two main problems in the multi-plane holographic display. One is that the decreased reconstruction quality will accompany the increased number of planes in a multi-plane holographic display, and the other is the non-uniform distribution of the reconstruction image quality among each plane. The main reason is that the planes will interfere with each other, and the interference is random and relatively difficult to control. To improve multi-plane holographic display quality, we propose an improved weighted iterative multi-plane holographic display method. Meanwhile, to reduce the mutual influence among the planes in designing holograms, we introduce weights to control the constraints, and thus the quality distribution of the reconstructed images among multiple planes is more uniform and of higher quality by the constant correction of the weights during the calculation. The results show that the introduction of this method not only does not reduce the calculation speed but also leads to a more uniform quality distribution of the reconstructed image in the multi-plane holographic display. Additionally, the quality is improved to some extent, which provides a new idea for high-quality multi-plane display.MethodsOur design idea is based on the Gerchberg-Saxton (GS) iterative algorithm and is further improved by introducing weights on the holographic plane. Firstly, the output plane complex amplitude is composed according to the amplitude information of the known multi-plane target with random phases. Then, the inverse diffraction is carried out into the holographic plane at a known distance, and all complex amplitudes in the holographic plane are summed up in the weights. The total complex amplitude distribution of the holographic plane is obtained, and the weights are distributed in a weighting. In assigning the weights, the sum of all the weights should be 1. Initially, the weights of each plane are set to be equal. Then, the weights are corrected iteratively by the iterative optimization algorithm according to the CC value changes, and the purpose of setting the weights is to reduce the mutual influence among the planes. After summing up the weights, we ensure that the influences of the planes are balanced to make the distribution among the planes more uniform. Then we take the phase, keep it unchanged, and combine it with the plane wave amplitude to get the complex amplitude distribution of the holographic plane. Meanwhile, forward diffraction is conducted again to obtain the complex amplitude distribution of the output plane, then its phase is taken and combined with the target amplitude. This process is repeated until the results are satisfied.Results and DiscussionsOur core content is the weight correction for each plane, the specific correction idea is shown in Fig. 2, and the specific formulas for the correction are Eqs. (3)-(6). For two-plane holography, the quality of reconstructed images in each plane without introducing weights will be randomly distributed, and the reconstructed images in each plane will be qualitatively different when the introduction of the weights among various planes makes the reconstruction of the image distribution quality uniform (Figs. 4 and 12). It is discussed that for each plane with the same or different target images (Fig. 9), the quality of the reconstructed images of various target image types is different. Specifically, the quality of reconstructed images is relatively high under the same target images, and the quality of reconstructed results is poor when the target images are not the same. The differences between the two will become increasingly larger with the rising number of planes. Under the small number of planes, whether the target image is the same has little effect on the quality of the reconstructed image, and under the large number of planes, the quality of the reconstructed image is affected by whether the target images are the same or not (Figs. 6 and 10). For multi-plane holography, the most significant influence is the target image type, the number of planes, and the distance between neighboring planes (Figs. 13 and 14).ConclusionsTo reduce the mutual influence among the planes in the multi-plane display, we propose an improved weighted iterative multi-plane holographic display method by employing the weights. Finally, the control among the planes is controlled according to the interactions among the planes in the process of designing the holograms, and the distribution of the reconstruction image quality among the planes is more uniform. Additionally, without reducing the quality of the reconstructed image, the calculation speed will not be affected. The method is compared and analyzed by the simulation analysis and experimental verification of two to six different target images and the same target image to achieve a more uniform distribution of the reconstructed image quality among the planes. The quality of the reconstructed image is affected by the target image type, in which the quality is relatively high under the same target image, and it is poorer under different target images. The difference between them will become increasingly larger with the rising number of planes. In conclusion, introducing this method reduces mutual interference among reconstructed images in multi-plane holographic displays and their more uniform quality distribution.
Acta Optica Sinica
- Publication Date: Dec. 10, 2023
- Vol. 43, Issue 23, 2309001 (2023)
Study on Improving Quality of Liquid Crystal Spatial Light Modulator Holographic Reproduction Images by Phase Compensation Method of Reproduction Domain Model
Chi Hu, Jin Zhang, Guobin Sun, Shilei Jiang, and Yanyan Liu
ObjectiveWith the continuous development of spatial light modulators, it has been widely applied in many fields, such as light field control, beam shaping, beam deflection, and holographic reproduction, with unparalleled advantages. However, due to limitations of process conditions, it also has many defects. The existence of zero-order spots and multi-order diffraction images caused by its own "black-matrix effect" will exert certain effects on the quality of the output light field, which leads to a low utilization rate of light energy and poor uniformity of reproduced images. However, most studies nowadays are conducted from the perspective of algorithm design to improve the reproduced image quality of holographic display. But when the liquid crystal spatial light modulator (LC-SLM) is employed for holographic display, due to the influence of the "black-matrix effect", the light energy distribution of the reproduced results follows the sinc function distribution, so that the energy distribution of the reproduced images is not uniform. We propose a method to improve the uniformity of the reproduced images through digital blazed grating to deviate the reproduced images and combine with the phase compensation method of the holographic reproduction domain model. This method provides theoretical assistance to improve the quality of reproduction results when LC-SLMs are leveraged for holographic reproduction.MethodsBased on the principle of Fresnel hologram calculation, our main design principle is analyzing the influence of zero-order spots and multi-order diffraction images produced by the "black-matrix effect" of the LC-SLM adopted for holographic reproduction on the results. Then with an aim at avoiding the offset of the zero-order spots on the reproduced images by digital blazed grating superimposed on the hologram, and finally to compensate for the uneven distribution of light energy, the phase is compensated according to the proposed reproduction domain model. The steps are as follows. First, the reproduction domain is determined according to the size of the reproduction image, and after loading a certain period of digital blazed grating based on the original design hologram, the compensation amount is inverted according to the light intensity distribution of the reproduction domain reproduction results and then synthesized with the original light wave. Recalculating the hologram can achieve the adjustment of the reproduction results. The quality of the holographic reproduction results is improved by avoiding the influence of zero-order spots on the reproduction results.Results and DiscussionsDue to the influence of the grid structure when LC-SLM performs holographic reproduction (Fig. 2), when the hologram is loaded, the reproduction results shown in Fig. 4 will have multi-order diffraction images and zero-order spots, which seriously affects the quality of the reproduction results. We propose the phase compensation method of the reproduction domain model (Fig. 6) according to the digital blazed grating deviation from the reproduction image and then compensate the phase according to the light energy of the reproduction domain, which can improve the uniformity of reproduction results. the calculation flow chart is shown in Fig. 8(b). Through the optimization calculation and simulation verification of the phase compensation amount and the construction of the holographic reproduction optical path (Fig. 14), the phase after compensation calculation is loaded onto the SLM for reproduction experimental verification and tests. The experimental results show that the uniformity of the reproduced image after compensation is twice as much as that of the original one, and the utilization rate of light energy is also improved to a certain extent, as shown in Figs. 16 and 17.ConclusionsWe analyze the light energy distribution of the reproduced image when the LC-SLM performs holographic reproduction, and propose a phase compensation method through the reproduction domain model to compensate for its phase. The results show that after adding a certain period of digital blazed grating to the design hologram, the compensation amount is inverted according to the distribution of light energy in the reproduction domain, and then synthesized with the original light wave and redesigned to calculate the hologram. The uniformity of the reproduced results is twice as much as that of the unimproved one, and the utilization rate of light energy is also improved. The experimental results prove that the method can effectively improve the uniformity and light energy utilization of holographic reproduction results while avoiding the effect of zero-order spots when LC-SLMs are employed for holographic reproduction. The results of this study are useful for improving the quality of output results when spatial light modulators are adopted for light field modulation and holographic reproduction. ObjectiveWith the continuous development of spatial light modulators, it has been widely applied in many fields, such as light field control, beam shaping, beam deflection, and holographic reproduction, with unparalleled advantages. However, due to limitations of process conditions, it also has many defects. The existence of zero-order spots and multi-order diffraction images caused by its own "black-matrix effect" will exert certain effects on the quality of the output light field, which leads to a low utilization rate of light energy and poor uniformity of reproduced images. However, most studies nowadays are conducted from the perspective of algorithm design to improve the reproduced image quality of holographic display. But when the liquid crystal spatial light modulator (LC-SLM) is employed for holographic display, due to the influence of the "black-matrix effect", the light energy distribution of the reproduced results follows the sinc function distribution, so that the energy distribution of the reproduced images is not uniform. We propose a method to improve the uniformity of the reproduced images through digital blazed grating to deviate the reproduced images and combine with the phase compensation method of the holographic reproduction domain model. This method provides theoretical assistance to improve the quality of reproduction results when LC-SLMs are leveraged for holographic reproduction.MethodsBased on the principle of Fresnel hologram calculation, our main design principle is analyzing the influence of zero-order spots and multi-order diffraction images produced by the "black-matrix effect" of the LC-SLM adopted for holographic reproduction on the results. Then with an aim at avoiding the offset of the zero-order spots on the reproduced images by digital blazed grating superimposed on the hologram, and finally to compensate for the uneven distribution of light energy, the phase is compensated according to the proposed reproduction domain model. The steps are as follows. First, the reproduction domain is determined according to the size of the reproduction image, and after loading a certain period of digital blazed grating based on the original design hologram, the compensation amount is inverted according to the light intensity distribution of the reproduction domain reproduction results and then synthesized with the original light wave. Recalculating the hologram can achieve the adjustment of the reproduction results. The quality of the holographic reproduction results is improved by avoiding the influence of zero-order spots on the reproduction results.Results and DiscussionsDue to the influence of the grid structure when LC-SLM performs holographic reproduction (Fig. 2), when the hologram is loaded, the reproduction results shown in Fig. 4 will have multi-order diffraction images and zero-order spots, which seriously affects the quality of the reproduction results. We propose the phase compensation method of the reproduction domain model (Fig. 6) according to the digital blazed grating deviation from the reproduction image and then compensate the phase according to the light energy of the reproduction domain, which can improve the uniformity of reproduction results. the calculation flow chart is shown in Fig. 8(b). Through the optimization calculation and simulation verification of the phase compensation amount and the construction of the holographic reproduction optical path (Fig. 14), the phase after compensation calculation is loaded onto the SLM for reproduction experimental verification and tests. The experimental results show that the uniformity of the reproduced image after compensation is twice as much as that of the original one, and the utilization rate of light energy is also improved to a certain extent, as shown in Figs. 16 and 17.ConclusionsWe analyze the light energy distribution of the reproduced image when the LC-SLM performs holographic reproduction, and propose a phase compensation method through the reproduction domain model to compensate for its phase. The results show that after adding a certain period of digital blazed grating to the design hologram, the compensation amount is inverted according to the distribution of light energy in the reproduction domain, and then synthesized with the original light wave and redesigned to calculate the hologram. The uniformity of the reproduced results is twice as much as that of the unimproved one, and the utilization rate of light energy is also improved. The experimental results prove that the method can effectively improve the uniformity and light energy utilization of holographic reproduction results while avoiding the effect of zero-order spots when LC-SLMs are employed for holographic reproduction. The results of this study are useful for improving the quality of output results when spatial light modulators are adopted for light field modulation and holographic reproduction.
Acta Optica Sinica
- Publication Date: Oct. 10, 2023
- Vol. 43, Issue 19, 1909001 (2023)
Research Progress of Real-Time Holographic 3D Display Technology
Juan Liu, Dapu Pi, and Yongtian Wang
SignificanceHolographic three-dimensional (3D) display technology can effectively reconstruct the wavefront of 3D objects and provide whole depth cues for human eyes, so it has become a research hotspot in the 3D display field. Compared with optical holography, computer-generated holography simulates the recording process of the hologram by computers and adopts the refreshable spatial light modulator instead of holographic recording material as the hologram-carrying media. Due to the above characteristics, computer-generated holography becomes an ideal technology to realize real-time holographic 3D displays and has a broad application prospect in military navigation, industrial manufacturing, medical treatment, education, and entertainment fields. At present, the development of real-time holographic 3D displays is hindered by the huge data of 3D objects, the insufficient modulation capacity of spatial light modulators, and the low display degree of holographic 3D display systems. In order to overcome these problems, researchers have made many innovations from both algorithm and hardware aspects.ProgressWe review the progress of real-time holographic 3D displays. Firstly, the basic principle and development history of holography are outlined. Next, the fast calculation methods of computer generated holograms (CGHs) and wavefront coding methods for current spatial light modulators are introduced in detail. Then, the contribution of deep learning to real-time holographic 3D displays is discussed, and some typical holographic display systems are introduced. Finally, the future development of real-time holographic 3D displays is prospected. The fast calculation methods can be classified into algorithm optimization and hardware acceleration. The algorithm optimization mainly simplifies the calculation complexity and reduces the redundant computation of traditional calculation methods, including point-based method, polygon-based method, and layer-based method. Hardware acceleration mainly speeds up the CGH calculation by designing fast calculation algorithms adapted to the hardware platform and optimizing hardware system architectures. The wavefront coding methods for current spatial light modulators can be mainly classified into iterative methods and non-iterative methods. Iterative methods solve the desired phase-only hologram by iterative calculation between the image plane and the hologram plane or pixels in the hologram plane, which are time-consuming. Non-iterative methods convert the diffracted complex wavefront to an intensity-constant distribution analytically. Compared with iterative methods, non-iterative methods are more efficient and suitable for real-time holographic 3D displays. In recent years, deep learning is also introduced into the computer-generated holography field. Deep learning completes the CGH calculation and wavefront coding through the trained neural network, which shows great potential for realizing real-time holographic 3D displays. Furthermore, with the development of algorithms, devices, and systems, the holographic display system is gradually developing towards large size, large field of view, and real-time color display.Conclusions and ProspectsReal-time holographic 3D display is the ultimate goal of the holographic 3D display. Although there is still a long way to go, it is believed that there is great potential for the further development of real-time holographic 3D displays in both software (algorithms) and hardware (devices and systems). It is expected that holographic 3D displays will eventually achieve real-time display and come gradually into the market and daily life, thus bringing revolutionary changes to our future life. SignificanceHolographic three-dimensional (3D) display technology can effectively reconstruct the wavefront of 3D objects and provide whole depth cues for human eyes, so it has become a research hotspot in the 3D display field. Compared with optical holography, computer-generated holography simulates the recording process of the hologram by computers and adopts the refreshable spatial light modulator instead of holographic recording material as the hologram-carrying media. Due to the above characteristics, computer-generated holography becomes an ideal technology to realize real-time holographic 3D displays and has a broad application prospect in military navigation, industrial manufacturing, medical treatment, education, and entertainment fields. At present, the development of real-time holographic 3D displays is hindered by the huge data of 3D objects, the insufficient modulation capacity of spatial light modulators, and the low display degree of holographic 3D display systems. In order to overcome these problems, researchers have made many innovations from both algorithm and hardware aspects.ProgressWe review the progress of real-time holographic 3D displays. Firstly, the basic principle and development history of holography are outlined. Next, the fast calculation methods of computer generated holograms (CGHs) and wavefront coding methods for current spatial light modulators are introduced in detail. Then, the contribution of deep learning to real-time holographic 3D displays is discussed, and some typical holographic display systems are introduced. Finally, the future development of real-time holographic 3D displays is prospected. The fast calculation methods can be classified into algorithm optimization and hardware acceleration. The algorithm optimization mainly simplifies the calculation complexity and reduces the redundant computation of traditional calculation methods, including point-based method, polygon-based method, and layer-based method. Hardware acceleration mainly speeds up the CGH calculation by designing fast calculation algorithms adapted to the hardware platform and optimizing hardware system architectures. The wavefront coding methods for current spatial light modulators can be mainly classified into iterative methods and non-iterative methods. Iterative methods solve the desired phase-only hologram by iterative calculation between the image plane and the hologram plane or pixels in the hologram plane, which are time-consuming. Non-iterative methods convert the diffracted complex wavefront to an intensity-constant distribution analytically. Compared with iterative methods, non-iterative methods are more efficient and suitable for real-time holographic 3D displays. In recent years, deep learning is also introduced into the computer-generated holography field. Deep learning completes the CGH calculation and wavefront coding through the trained neural network, which shows great potential for realizing real-time holographic 3D displays. Furthermore, with the development of algorithms, devices, and systems, the holographic display system is gradually developing towards large size, large field of view, and real-time color display.Conclusions and ProspectsReal-time holographic 3D display is the ultimate goal of the holographic 3D display. Although there is still a long way to go, it is believed that there is great potential for the further development of real-time holographic 3D displays in both software (algorithms) and hardware (devices and systems). It is expected that holographic 3D displays will eventually achieve real-time display and come gradually into the market and daily life, thus bringing revolutionary changes to our future life.
Acta Optica Sinica
- Publication Date: Aug. 10, 2023
- Vol. 43, Issue 15, 1509001 (2023)
Dispersion of Cloud Droplet Based on Pulsed Digital Holographic Interferometry
Yangzi Gao, Jun Wang, Jiabin Tang, Jingjing Liu, Qing Yan, and Dengxin Hua
In order to study the correlation between cloud droplet spectrum dispersion and cloud microphysical parameters, an observation technique based on short pulse modulated laser based on field programmable gate array, high resolution microscopic optical system, and coaxial digital holographic interferometry is proposed. The minimum size of cloud droplet detected by proposed technique is 2 μm, and the complete spectrum width data of cloud droplet can be obtained. Under different aerosol concentrations for three consecutive days in an expanding cloud chamber, the three-dimensional positions and diameters of cloud droplets during the generation and elimination process are observed, and the cloud microphysical parameters are calculated by using the observation results. Furthermore, the positive correlation between the dispersion of cloud droplet spectrum and cloud microphysical parameters in the process of generation and dissipation is analyzed. By comparing the dispersion distribution of cloud droplet spectrum under different aerosol number concentrations, it is concluded that with the increase of cloud droplet concentration, the value range of the dispersion will gradually decrease, and the dispersion will decrease relative to the fitting line. In order to study the correlation between cloud droplet spectrum dispersion and cloud microphysical parameters, an observation technique based on short pulse modulated laser based on field programmable gate array, high resolution microscopic optical system, and coaxial digital holographic interferometry is proposed. The minimum size of cloud droplet detected by proposed technique is 2 μm, and the complete spectrum width data of cloud droplet can be obtained. Under different aerosol concentrations for three consecutive days in an expanding cloud chamber, the three-dimensional positions and diameters of cloud droplets during the generation and elimination process are observed, and the cloud microphysical parameters are calculated by using the observation results. Furthermore, the positive correlation between the dispersion of cloud droplet spectrum and cloud microphysical parameters in the process of generation and dissipation is analyzed. By comparing the dispersion distribution of cloud droplet spectrum under different aerosol number concentrations, it is concluded that with the increase of cloud droplet concentration, the value range of the dispersion will gradually decrease, and the dispersion will decrease relative to the fitting line.
Acta Optica Sinica
- Publication Date: Mar. 07, 2022
- Vol. 42, Issue 6, 0609001 (2022)
Computer Generated Half-Circle Viewable Color Rainbow Holographic Stereogram
Fuyang Xu, Xin Yang, Zimo Liu, Qiang Song, Guobin Ma, and Zhijun Ren
Holographic stereogram (HS) is a kind of hologram that can accelerate calculation, which can realize the monochromatic holographic three-dimensional (3D) display, and combining it with the color rainbow hologram and realizing the half-circle viewable color rainbow holographic 3D display which can be watched by many people have practical application value. Based on the HS calculation principle, the side angle of view and the field of view of the elemental hologram are designed, and the spectrum of the elemental hologram containing red, green, and blue information through frequency domain multiplexing is achieved. The elemental hologram is obtained by taking the real part of the complex amplitude from the inverse Fourier transform of the spectrum. The high-resolution half-circle viewable color rainbow HS can be achieved by combining all elemental holograms. A high resolution half-circle viewable color rainbow HS with a resolution of 200800 pixel×200800 pixel and a size of 64 mm×64 mm is calculated only within 15.15 min by parallel acceleration. Reflective illumination is used for optical reproduction and a clear color holographic 3D display that can be viewed by multiple people is achieved, which is expected to be applied to 3D military maps, 3D sand tables, and other fields. Holographic stereogram (HS) is a kind of hologram that can accelerate calculation, which can realize the monochromatic holographic three-dimensional (3D) display, and combining it with the color rainbow hologram and realizing the half-circle viewable color rainbow holographic 3D display which can be watched by many people have practical application value. Based on the HS calculation principle, the side angle of view and the field of view of the elemental hologram are designed, and the spectrum of the elemental hologram containing red, green, and blue information through frequency domain multiplexing is achieved. The elemental hologram is obtained by taking the real part of the complex amplitude from the inverse Fourier transform of the spectrum. The high-resolution half-circle viewable color rainbow HS can be achieved by combining all elemental holograms. A high resolution half-circle viewable color rainbow HS with a resolution of 200800 pixel×200800 pixel and a size of 64 mm×64 mm is calculated only within 15.15 min by parallel acceleration. Reflective illumination is used for optical reproduction and a clear color holographic 3D display that can be viewed by multiple people is achieved, which is expected to be applied to 3D military maps, 3D sand tables, and other fields.
Acta Optica Sinica
- Publication Date: Jan. 28, 2022
- Vol. 42, Issue 4, 0409001 (2022)
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