Abstract Three-dimensional (3D) images have become important information carriers in multimedia, medical treatment, and entertainment. However, existing 3D image hiding and watermarking schemes are mostly limited to single 3D image encryption, resulting in insufficient capacity, low security, and optimizable concealment. To address these issues, this paper proposes a highcapacity multi-3D image watermarking method based on multi-dimensional multiplexing holography and QZ embedding. Multiple 3D images are grouped and encoded into holographic watermarks using a multi-dimensional multiplexing hologram generation algorithm, where chaotic phase masks and spiral phase masks are adopted to expand the key space and enhance security. A contrast-guided embedding strategy is used to locate visually insensitive highcontrast regions in the two-dimensional host image, and the holographic watermarks are embedded into different wavelet sub-bands by combining discrete wavelet transform, singular value decomposition, and QZ embedding to achieve low distortion and strong robustness. Simulation results demonstrate that the proposed method can simultaneously embed sixteen 3D images with high imperceptibility proved by ultrahigh correlation coefficient and negligible entropy variation, good key sensitivity, and reliable robustness against noise and occlusion attacks. Compared with state-of-the-art hologram-based encryption schemes, the proposed method exhibits significant advantages in capacity, security, and concealment, showing potential for secure optical information hiding and copyright protection of 3D visual data.

In this paper, a three-dimensional (3D) image encryption method is proposed based on the phase wrapping principle and iterative phase retrieval algorithm in the Fresnel domain under structured light illumination. Original 3D plaintext is firstly converted into a converted amplitude via a low-complexity wrapping operation, which is further encrypted into a two-dimensional (2D) visible ciphertext with high imperceptibility. Meanwhile, a diffractive neural network composed of multiple phase-only masks (POMs) is generated. Optical parameters of structured light and all POMs are employed as decryption keys to ensure a large key space and high security. Numerical simulations verify that the proposed method has satisfactory feasibility, security, robustness and information concealment.

In this paper, a multiple-image encryption based on 3D face key and multiplexing holography with Kramers-Kronig relations is proposed. In the encryption process, the 3D face of the encryption user is collected by the 3D face acquisition device. Next the 3D face multiple-layer perceptron (FMLP) neural network and chaotic structured light phase mask generation algorithm are used to extract the high-order face vector (FV) of the encryption user and generate the face chaotic structured light phase mask (FCSPM), respectively. Subsequently, all plaintext images are divided into two groups, and the grating modulation, DRPE encoding in the Fresnel diffraction domain with FCSPM, and multiplexing digital holographic encoding (MDHE) technology are sequentially performed on each group, such that all plaintext images are encoded into a single amplitude type hologram. Finally, the hologram is hidden into the host image by the Discrete Wavelet Transform-Singular Value Decomposition (DWT-SVD) watermarking algorithm, thus the final ciphertext image is generated. The phase masks used in the DRPE process are FCSPM, generated through phase modulation technology combining the 3D face chaos mask (FCM) and structured phase mask (SPM), which undoubtedly expands the key space. Moreover, the DWT-SVD-based image watermarking technology can effectively hide all information of the plaintext image in a visible ciphertext image, thereby improving the imperceptibility of the valid information. In the decryption process, the user must first pass 3D face authentication. Once the authentication is successful, the correct digital keys should be input to obtain all decrypted images; otherwise, the decryption process is aborted. Notably, during the multiplexing digital holographic decoding (MDHD) process, the decryption object light wave is recovered using digital holographic decoding technology based on Kramers-Kronig relations. Compared to the traditional off-axis digital holography decoding technology, this method realizes multiple-image encryption with a single exposure and improves the utilization efficiency of the space-bandwidth product. In order to demonstrate the feasibility of the proposed multiple-image encryption method, a series of numerical simulations are performed, and the simulation results show that the proposed method exhibits high feasibility as well as level of security and the 3D face key possess high security and strong robustness.

Deep learning has shown significant promise for computer-generated holography (CGH), particularly in enabling real-time rendering. However, conventional U-Net-based methods exhibit critical limitations in computational resource efficiency and feature extraction capability, compromising both reconstruction quality and processing efficiency. To overcome this issue, this paper proposes a complex-valued efficient hybrid attention network (CEHAN) for high-quality hologram generation. The architecture comprises two specialized sub-networks: a complex amplitude inference network (CAIN) and a hologram encoding network (HEN). To enhance both reconstruction accuracy and computational efficiency, a complex efficient attention (CEA) mechanism is incorporated into the downsampling module. Furthermore, a hybrid attention block (HAB) integrates both channel and spatial attention mechanisms to optimize feature extraction. The proposed approach achieves a computational time of 16 ms per frame, while attaining an average PSNR of 35.71 dB and an SSIM of 0.944 on the DIV2K dataset, surpassing conventional methods. Numerical simulations and optical experiments demonstrate that the proposed method achieves superior detail reproduction and enhanced image quality while maintaining reduced computational demands. These results underscore the framework's strong potential for practical applications in holographic displays.

This paper introduces a color image encryption technique based on phase-only hologram (POH) encoding with dynamic constraint and phase retrieval under structured light illumination (SLI). During encryption, the color plaintext is first encoded into a POH. This hologram is then transformed into an amplitude distribution through phase-amplitude conversion. Subsequently, using an iterative phase retrieval algorithm under structured light, the amplitude is encrypted into a visible ciphertext image, while a POM set is produced. The resulting ciphertext exhibits a visible image pattern, rather than noise-like appearance, providing ultrahigh imperceptibility. Moreover, the dynamic constraint in hologram encoding ensures balanced quality across color channels, leading to high-quality decrypted images with correct keys. The incorporation of a structured phase mask and the POM set expands the key space and boosts security. In decryption, the decryption structured light (DSL) illuminates the ciphertext and the neural network sequentially to generate a reconstructed amplitude. This amplitude is converted into a phase distribution via amplitude-phase conversion, which then acts as the POH for color holographic reconstruction, yielding the decrypted image. Numerical simulations demonstrate the method’s feasibility, high security, and strong robustness.

This paper proposes a three-dimensional image hierarchical encryption method based on structured light holography and chained iris keys, aiming to address issues in the existing 3D image encryption techniques, such as low decryption quality, insufficient key security, inconvenient key management, and lack of hierarchical access control. The method first divides the 3D image into equidistant slices along the depth direction, generates encrypted structured light using a custom-designed structured light phase mask, and computes the structured light hologram for each slice layer via an iterative angular spectrum algorithm. Subsequently, user iris images are captured, and after preprocessing and feature extraction, user-specific chaotic phase masks are generated through a piecewise linear chaotic map, serving as keys for the hierarchical encryption. On this basis, a chained hierarchical encryption strategy is adopted, where the hologram of each level is coupled with the corresponding user's chaotic mask and the hologram from the previous level for the encryption, forming a dependent ciphertext sequence. During decryption, users must undergo iris authentication to obtain the chaotic key corresponding to their access level, followed by sequential chained decryption and optical reconstruction, thereby achieving identity- and authority-based hierarchical information access. Simulation experiments demonstrate that the method ensures high-quality 3D reconstruction while exhibiting high key sensitivity and robustness against noise, occlusion, and statistical attacks. Furthermore, the multi-parameter design in the structured light phase mask further expands the key space and enhances system security. This study provides a secure, practical, and manageable solution for the confidential transmission and hierarchical management of sensitive 3D visual data, with potential applications in fields such as medical imaging, military simulation, and virtual reality.

In this paper, we propose a complex-valued lightweight importance subspace attention network (CISANet) designed for the rapid generation of high-quality multi-depth holograms. The proposed framework incorporates two core modules: the complex-valued local importance-based attention (C-LIA) module and the complex-valued ultra-light subspace attention (C-ULSA) module. The C-LIA module optimizes phase information allocation by emphasizing salient spatial regions, whereas the C-ULSA module efficiently extracts multi-scale features within the complex domain. This design preserves high-frequency details while substantially reducing the network parameter count. Extensive numerical simulations and optical experiments demonstrate that the CISANet achieves an average PSNR of 32.98 dB and SSIM of 0.955, with a running time of only 18.3 ms per frame. These results validate the method's superiority in multi-depth reconstruction clarity and computational efficiency, underscoring its considerable potential for real-time 3D holographic display systems.

In this paper, a metasurface-enabled dual-channel optical image authentication based on polarization multiplexing is proposed. During encryption, authentication phases corresponding to dual-channel plaintext images are firstly calculated by using a sparse-constraint-driven authentication-holography (SCDAH) algorithm. Then, target transmission phase and geometric phase of metasurface to be designed are obtained accordingly by the composite phase modulation (CPM) principle. Next, the nanopillar-type metasurface unit is performed with parameter scanning to establish the transmission and geometric phase databases. Finally, the structural parameters of each nanopillar are determined on a pixel-by-pixel basis to complete the construction of polarization-multiplexing authentication metasurface (PMAM). During authentication, the PMAM are respectively illuminated by the left-handed circularly polarized (LCP) and right-handed circularly polarized (RCP) light to obtain pseudo-random images produced by far-field diffraction, and then the nonlinear correlation distribution between diffraction image and corresponding channel plaintext image is calculated, and the final authentication result of each channel is determined based on whether the signal-to-noise ratio of the nonlinear correlation distribution meets the standard. In fact, a new physical-characteristic-driven dual-channel optical image authentication technology is formed, where double identities of the user holding this PMAM can be simultaneously verified, breaking through the rigid constraint of conventional single metasurface-to-single image, meanwhile improving the capacity and efficiency for authentication metasurface from the perspective of physical mechanism. Numerical simulations are performed to demonstrate the feasibility of the proposed method, and the simulation results prove that the proposed method exhibits high feasibility and security as well as strong robustness against cropping attack, showing a promising application potential in the field of identity recognition and authentication.

Learning-based computer-generated holography has emerged as a promising approach for three-dimensional (3D) visualization. However, current methods typically extract multi-depth information from two-dimensional (2D) images using single-diffraction models, which lack sufficient physical constraints and consequently degrade the quality of reconstructed images. To overcome this limitation, we propose a dynamic large kernel attention network (DLKAN) for 3D hologram generation. The network integrates a multi-depth diffraction (MDD) model within a dual U-Net architecture and employs a dynamic large kernel attention (DLKA) module to produce high-quality 3D holograms. The MDD mechanism enables effective capture of holographic information across different depths, while the DLKA module combines large kernel convolutions, residual connections, and depthwise convolutions to efficiently aggregate both local and global information. Through the synergistic design of these components, the network accurately extracts complex amplitude information at varying depths and generates high-fidelity 3D holograms. Both numerical and optical reconstructions demonstrate that the proposed method outperforms existing approaches in 3D hologram generation, significantly improving the quality of the reconstructed imagery.

In this paper, an optical color zero-watermarking scheme based on robust bimodal biometric keys and phase-shifting digital holography is proposed. The color watermark is first encrypted into three amplitude ciphertexts through an optical encryption framework combining grating modulation, Fresnel-domain double random phase encoding (DRPE), and phase-shifting digital holography, where the phase masks are generated from biometric keys derived from the iris and three-dimensional (3D) face features of the encryption user. These high-level biometric features are extracted by a bimodal biometric high-order feature extraction network (BBHEN), including an iris high-order data extraction network and a 3D face high-order data extraction network. The extracted features of the color host image are then XORed with the corresponding ciphertexts, and the results are merged to construct a single zero-watermark image containing both host and watermark information. During extraction, biometric authentication is first performed to verify the identity of the decryption user. Only authorized users can recover the original watermark through zero-watermark reconstruction and extraction; otherwise, the process is terminated. Numerical simulations demonstrate the effectiveness, security, and robustness of the proposed scheme, particularly the strong protection capability of the bimodal biometric keys.

This study presents a multi-scale attention-integrated network (MSAINet) for generating high-fidelity phase-only holograms. Performance is enhanced through the integration of two key components: an adaptive spatial attention unit (ASAU) and a multi-scale feature aggregation module (MFAM). Specifically, the ASAU enhances optical patterns and suppresses speckle noise through channel-wise gating and independent processing of complex-valued components while preserving the essential phase-amplitude relationships. The MFAM adopts a multi-branch architecture that employs dilated convolutions and a channel expansion-reduction scheme. This design efficiently captures interdependent local and global features across multiple receptive fields, facilitating hierarchical multi-scale fusion. Numerical simulations demonstrate that the MSAINet achieves an average peak signal-to-noise ratio (PSNR) of 35.22 dB and a structural similarity index measure (SSIM) of 0.95 at a resolution of 1920 & times; 1072, surpassing conventional complex-valued convolutional networks. Furthermore, optical experiments confirm its capability to produce high-quality holograms with substantially suppressed speckle noise, underscoring its strong potential for next-generation virtual and augmented reality displays.

In this paper, a security-enhanced 3D image encryption method based on a multiple-dimensional multiplexing phase hologram (MMPH) is proposed. In the encryption process, 3D multiple images are encrypted into an MMPH by the iterative layer-oriented angular-spectrum algorithm and multiple-dimensional parameter selective phase hologram generation technology with different chaotic spiral phase masks (CSPMs). In the decryption process, the topological charge number key and chaotic parameter keys corresponding to different 3D image plaintexts need to be input by the decryption user; the 3D decryption result can be reconstructed correctly. This undoubtedly expands the key space and enhances the key sensitivity, thereby significantly increasing the security of the encryption system. In order to demonstrate the feasibility and advancement of the proposed 3D multiple-image encryption method, a series of computational simulations and optical experiments were conducted. The experimental verification is carried out using a holographic imaging system based on spatial light modulators (SLMs). The experimental data show that the simulation results are highly consistent with the experimental results, which effectively verify the reliability of the encryption method in practical applications. The security analysis shows that the proposed encryption method has a large key space. In addition, the experimental results also show that the proposed encryption method exhibits high feasibility and security, as well as strong robustness.

In this paper, we propose an innovative complex-valued subpixel convolutional neural network for the generation of high-fidelity phase-only holograms. This novel approach integrates complex-valued convolution with subpixel convolution, enhancing the quality of reconstructed images while reducing the running time. The complex-valued convolution is capable of effectively capturing the phase and amplitude information of light waves, enriching the details of holograms. The subpixel convolution resolves the inherent limitations of conventional upsampling methods by substituting zero-padding with learnable pixel rearrangement. This zeropadding-free architecture maintains phase-amplitude consistency and suppresses high-frequency spectral attenuation, enhancing the visual fidelity of reconstructed images while operating at lower computational cost. The proposed methodology presents superior performance with an average PSNR of 33.43 dB and SSIM of 0.93, while operating at 71.4 frames per second. These results surpass those of conventional methods in both reconstruction quality and computational efficiency. Numerical simulations and optical experimental results further confirm the efficacy of this method in effectively reducing speckle noise, enhancing the quality of reconstructed images with reduced computation time. The proposed method shows promising prospects in real-time holographic display applications where rapid and high-quality image reconstruction is crucial.

In this paper, we propose a novel complex-valued hierarchical multi-fusion neural network (CHMFNet) for generating highquality holograms. The proposed architecture builds upon a U-Net framework, incorporating a complex-valued multi-level perceptron (CMP) module that enhances complex feature representation through optimized convolutional operations and advanced activation functions, enabling effective extraction of intricate holographic patterns. The framework further integrates an innovative complex-valued hierarchical multi-fusion (CHMF) block, which implements multi-scale hierarchical processing and advanced feature fusion through its specialized design. This integration of complex-valued convolution and specialized CHMF design enables superior optical information representation, generating artifact-reduced high-fidelity holograms. The computational results demonstrate the superior performance of the proposed method, achieving an average peak signal-to-noise ratio (PSNR) of 34.11 dB and structural similarity index measure (SSIM) of 0.95, representing significant improvements over conventional approaches. Both numerical simulations and experimental validations confirm CHMFNet's enhanced capability in hologram generation, particularly in terms of detail reproduction accuracy and overall image fidelity.

In this paper, we propose a complex-valued attention feature distillation network (CAFDN) that incorporates a novel lightweight module (CAFDN_Lite) within dual U-Net architectures for phase-only hologram (POH) generation. The proposed network architecture employs simplified upsampling and downsampling layers to enhance computational efficiency, while the CAFDN_Lite module implements hierarchical feature extraction through integrated local attention mechanisms, multi-scale analysis, and channel pruning. This synergistic design enables progressive feature refinement across successive network layers, achieving optimal balance between representational capacity and computational efficiency through systematic feature distillation. The proposed method achieves an average peak signal-to-noise ratio (PSNR) of 32.52 dB and an average structural similarity index (SSIM) of 0.861 within a running time of 36 ms, outperforming conventional approaches. Both numerical reconstructions and optical experiments confirm superior detail reproduction and image quality while reducing computational demands. These advancements highlight the framework's potential for practical holographic display applications, especially in real-time and high-fidelity reconstruction scenarios.

In this paper, we propose, to our knowledge, a new complex-valued dense atrous neural network (CDANN) for phase-only hologram (POH) generation. The network architecture integrates a complex-valued partial convolution (C-PConv) module into the down-sampling stages of dual U-Net structures, enhancing computational efficiency through selective channelwise processing. To improve feature extraction, we introduce a novel complex-value dense atrous convolution (DAC) module, which employs four cascaded branches with multi-scale atrous convolutions to capture intricate features while maintaining spatial resolution. Additionally, we integrate a spatial pyramid pooling (SPP) module into the U-Net architecture to encode multi-scale contextual features derived from the DAC module. This hierarchical integration expands the U-Net's receptive field while facilitating cross-layer feature fusion. The proposed method achieves an average peak signal-to-noise ratio (PSNR) of 32.19 dB and an average structural similarity index measure (SSIM) of 0.892 within a running time of 24 ms, outperforming conventional approaches. Experiments confirm significant improvements in both reconstruction quality and computational efficiency, making the CDANN suitable for real-time holographic displays.

In this paper, a security-enhanced optical image authentication method is proposed based on cascaded geometric-phase metasurfaces. In the encryption process, an original plaintext image is first encoded into an authentication amplitude by using a sparse constraint encoding algorithm. Subsequently, the Fourier phase-only hologram of the authentication amplitude is calculated by employing an iterative Fourier transform algorithm, and then it is decomposed into a ciphertext phase and a key phase. Finally, the ciphertext phase and the key phase are, respectively, constructed as the ciphertext metasurface and the key metasurface through a geometric-phase metasurface unit structure, thus forming two physically separated metasurfaces. During authentication, the ciphertext metasurface and the key metasurface need to be cascaded to achieve the authentication of user identity, overcoming a common problem that the current metasurface-based authentication methods lack physical security keys. Numerical simulations are performed to demonstrate the proposed method, and the simulation results show that the proposed method exhibits high feasibility and strong security-enhanced effect as well as large key space.

In this paper, a color image encryption method based on finger vein key and off-axis digital holography with phase-modulated reference light is proposed. In the encryption process, firstly the channel separation operation is performed on the color plaintext image, and the “red”, “green” and “blue” channels grayscale data of the color plaintext image are obtained respectively. Subsequently, the finger vein quantum matrix of the encryption user is generated through the quantum matrix generation program and used as the scrambling index key, mask key, and phase mask keys in the next encryption steps. The grayscale data of each channel of the original color plaintext image is then encrypted using the DNA coding encryption operation, and these encrypted results are embedded into the carrier image, thus the encryption watermark image is obtained. After, the encryption watermark image is executed image encryption operation based on double random phase coding (DRPE) in the Fresnel transform domain, so that the encryption object light is obtained. Finally, the off-axis digital holography encoding technology (ODHE) with phase-modulated reference light is performed on encryption object light, so that the finally holographic ciphertext is generated. In the decryption process, the decryption user’s finger vein must first be authenticated. If the authentication is successful, the system proceeds with the subsequent decryption steps, so that the correct decrypted color image can be obtained; otherwise, the decryption process is terminated. In order to demonstrate the feasibility of the proposed color image encryption method, a series of numerical simulations are performed, and the simulation results show that the proposed method exhibits high feasibility as well as high security level, large key space, contactless authentication, strong portability of ciphertext, strong robustness and security of finger vein key.

In this paper, an optical image encryption using multimodal biometric keys under the framework of three-step phase-shifting digital holography is proposed. In the encryption process, first, the grayscale image is encrypted into the DNA compilation result by using DNA encoding with an iris chaotic mask; then, the DNA compilation result is encrypted into the three ciphertext holograms using phase-shifting digital holography and modified double random phase encoding (MDRPE) with the fingerprint and finger vein chaotic masks. In the decryption process, first, authentication is performed by decrypting and verifying three types of biometric features: iris, fingerprint, and finger vein; if the authentication is successful, the iris chaotic mask for subsequent decryption and the conjugate chaotic masks for both fingerprint and finger vein are generated by the decryption system. Finally, the final decryption image is obtained by utilizing digital holographic reconstruction technology and DNA decoding technology. To demonstrate the feasibility of the proposed method, a series of numerical simulations are performed, and the simulation results confirm that the proposed method shows high feasibility and robustness against various attacks, and the integration of multimodal biometric keys contributes to a high level of security, where each biometric key exhibits strong robustness against potential attacks.

The holographic Maxwellian display, as a promising technique, offers a potential solution to the vergence–accommodation conflict in see-through near-eye displays for augmented reality applications. However, traditional holographic Maxwellian displays primarily rely on iterative or non-iterative algorithms, which face the challenge of balancing image quality and computational efficiency. To address this issue, we propose a lensless phase-only holographic Maxwellian display based on a complex-valued convolutional neural network algorithm. The complex-valued convolutional approach captures both the phase and amplitude information of light waves, enriching the holographic details and significantly improving the quality of the reconstructed images. Simulation results demonstrate that the quality of the reconstructed image can be significantly enhanced while maintaining high computational efficiency compared to conventional algorithms. Furthermore, by multiplying the phase hologram with a convergent spherical wave at the hologram plane, the virtual target image is focused on the viewer's pupil, ensuring a consistent perception of all-in-focus images at the pupil's location. To expand the size of the eyebox, multiple digital spherical waves were employed in the holographic Maxwellian display. Finally, experimental results validate that our proposed near-eye display system successfully generates see-through virtual images, effectively eliminating the vergence–accommodation conflict. The demonstrated capabilities of the proposed method underscore its considerable potential for applications in holographic near-eye displays.