Search Results (31)

Controlling light’s polarization through disordered media is crucial for advanced optical applications but remains challenging due to scattering and depolarization. Most existing approaches either require interferometric or multi-path measurements, or they recover only part of the polarization response. We present a comprehensive approach for spatially resolved polarization control by accurately retrieving the vector transmission matrix (VTM) of a scattering system from intensity-only, full-Stokes polarimetric measurements. Using a simple single-path setup comprising a liquid-crystal spatial light modulator (SLM) with a tunable retarder after it, we achieve spatial polarization modulation at the input, thereby enabling probing of the medium’s polarization–scattering characteristics. The VTM is retrieved with an adapted Gerchberg–Saxton procedure that enforces not only the measured output amplitudes but also the relative phase between the two orthogonal output polarization components obtained from the Stokes parameters. We show that a single retarder setting results in inter-block correlations in the retrieved VTM due to input coupling, while two linearly independent retarder settings decouple the intrinsic blocks and recover the full VTM. In our experiment, for a $16\times 16$ set of input–output spatial modes, the VTM is retrieved with about $90\%$ accuracy, enabling polarization-resolved focusing with up to $10\times$ enhancement for horizontal, vertical, arbitrary linear, and circular states. This work offers a compact framework for active polarization shaping and for polarimetric characterization of complex media, advancing our understanding of vectorial light–matter interactions. Full article

In this paper, the iterative Gerchberg–Saxton (GS) phase-retrieval algorithm is employed to reconstruct the amplitude spread function (ASF) of hololenses (HLs) recorded on a sustainable PVA/acrylate-based photopolymer, Biophotopol, when working with a CCD sensor. The main objective of this work is to characterize the spatial resolution of HLs, which are key components in a wide range of optical systems, including augmented reality (AR) glasses, combined information displays, and holographic solar concentrators. The GS algorithm, known for its efficiency in phase retrieval without prior knowledge of the phase of the optical system, is used to reconstruct the ASF, which is critical for mitigating information loss during imaging. Spatial resolution is quantified by convolving the ASFs obtained with two resolution tests (objective and subjective) and analyzing the resulting image using a CCD sensor. The convolution process allows an accurate assessment of lens performance, highlighting the resolution limits of manufactured lenses. The results show that the iterative GS algorithm provides a reliable method to improve image quality by recovering phase and amplitude information that might otherwise be lost, especially when using CCD or CMOS sensors. In addition, the recorded hololenses exhibit a spatial resolution of 8.9 lp/mm when evaluated with the objective Siemens star chart, and 30 cycles/degree when evaluated with the subjective Random E visual acuity test, underscoring the ability of Biophotopol-based HLs to meet the performance requirements of advanced optical applications. This work contributes to the development of sustainable high-resolution holographic lenses for modern imaging technologies, offering a promising alternative for future optical systems. Full article

The modeling of light propagation in scattering media is an important topic that has attracted considerable attention in recent decades. Coupling microscopic parameters such as particle concentration, particle size, and the refractive index of the medium can broaden the applicability of the model and improve simulation accuracy. In this work, these parameters are used to regulate the anisotropy factor and the mean free path. They are then integrated into a random phase screen model constructed using the Monte Carlo and the Gerchberg–Saxton algorithm. An optical experimental setup was established, in which a Laguerre–Gaussian beam was employed as the incident light source and diffusers with mesh numbers of 1500, 600, and 220 were used as the scattering media. The model was validated through comparative analysis between simulated and experimental results. Correlation coefficients between the simulated and experimental beam profiles exceeded 0.73, and the maximum relative error in power-in-the-bucket was only 4.9%, confirming the model’s accuracy and reliability. Numerical simulations were performed based on the established model to investigate beam propagation behavior. The results indicate that increasing particle concentration and particle size both lead to enhanced beam centroid shift and beam broadening. This modeling method provides a useful tool for analyzing beam propagation in complex scattering media and holds potential applications in wavefront correction and structured beam recognition. Full article

The immersive experience of holographic displays is fundamentally limited by their space–bandwidth product (SBP), which imposes an inherent trade-off between the field of view (FOV) and eyebox size. This paper proposes a method to extend the SBP by employing cascaded modulation with a dynamic spatial light modulator (SLM) and a passive high-resolution binary random phase mask (BRPM). We find that the key to unlocking this extension of SBP lies in a sophisticated algorithmic optimization, grounded in a physically accurate model of the system. We identify and correct the Nyquist undersampling problem caused by high-frequency scattering in standard diffraction models. Based on this physically accurate model, we employ a gradient descent optimization framework to achieve efficient, end-to-end solving for complex light fields. Simulation and experimental results demonstrate that our method achieves an approximately 16-fold SBP extension (4-fold FOV) while delivering significantly superior reconstructed image quality compared to the traditional Gerchberg–Saxton (GS) algorithm. Furthermore, this study quantitatively reveals the system’s extreme sensitivity to sub-pixel level alignment accuracy, providing critical guidance for the engineering and implementation of our proposed method. Full article

Atomic magnetometers (AMs), recognized for their ultra-high magnetic sensitivity, demand highly uniform pump light fields to maximize measurement accuracy. In this paper, a phase modulation-based method using convolutional neural networks (CNN) and the Gerchberg–Saxton (GS) algorithm is proposed to generate the pumping light field, and the model was trained using a supervised learning approach with a custom dataset. The specific training settings are as follows: the backpropagation algorithm was adopted as the training algorithm, and the Adam optimization method was used for network training, with a learning rate of 0.001 and a total of 100 training epochs, utilizing a liquid crystal spatial light modulator (LCSLM) to regulate the light field phase distribution dynamically. By transforming Gaussian beams into flat-top beams, the method significantly enhances polarization uniformity within vapor cells, leading to improved magnetometric sensitivity. The proposed hybrid algorithm reduces the mean square error from 35% to 19% and peak non-uniformity from 21% to 7.6%. A reflective LCSLM-based optical setup is implemented to produce circular and square flat-top beams with a measured non-uniformity of 5.1%, resulting in an enhancement of magnetic sensitivity from 14.54 fT/Hz^1/2 to 7.80 fT/Hz^1/2. Full article

Atmospheric and oceanic turbulence can severely degrade the orbital angular momentum (OAM) mode purity of vortex beams in cross-media optical links. Here, we propose a hybrid correction framework that fuses multiscale phase-screen modeling with a lightweight U-Net predictor for phase-distortion—driven solely by measured optical intensity—and augments it with a feed-forward, Gaussian-reference subtraction scheme for iterative compensation. In our experiments, this approach boosts the l = 3 mode purity from 38.4% to 98.1%. Compared to the Gerchberg–Saxton algorithm, the Gaussian-reference feed-forward method achieves far lower computational complexity and greater robustness, making real-time phase recovery feasible for OAM-based communications over heterogeneous channels. Full article

A metasurface capable of flexibly manipulating electromagnetic waves to realize holograms presents significant potential in millimeter-wave imaging systems and data storage domains. In this study, full-space three-dimensional holograms are realized from a reflection–transmission integrated reconfigurable metasurface, which can achieve nearly 360° phase coverage in reflection space and 180° phase coverage in transmission space. By adjusting the voltage applied to the constituting electronically tunable meta-atoms of the metasurface, an octahedron hologram constituted by three hologram images in different focal planes is generated in the reflection space at 6.25 GHz. Moreover, a diamond hologram, also composed of three hologram images in different focal planes, is achieved in the transmission space at 6.75 GHz. Both the numerical simulation and experimental measurement are performed to validate the full-space holograms implemented by the modified weighted Gerchberg–Saxton (WGS) algorithm with specific phase distribution in different imaging planes. The obtained results pave the way for a wide range of new applications, such as next-generation three-dimensional displays for immersive viewing experiences, high-capacity optical communication systems with enhanced data encoding capabilities, and ultra-secure anti-counterfeiting solutions that are extremely difficult to replicate. Full article

In this work, we explored, for the first time, to the best of our knowledge, the potential of stochastic gradient descent (SGD) to optimize random phase functions for application in non-iterative phase-only hologram generation. We defined and evaluated four loss functions based on common image quality metrics and compared the performance of SGD-optimized random phases with those generated using Gerchberg–Saxton (GS) optimization. The quality of the reconstructed holograms was assessed through numerical simulations, considering both accuracy and computational efficiency. Our results demonstrate that SGD-based optimization can produce higher-quality phase holograms for low-contrast target scenes and presents nearly identical performance to GS-optimized random phases for high-contrast targets. Experimental validation confirmed the practical feasibility of the proposed method and its potential as a flexible alternative to conventional GS-based optimization. Full article

Wavefront sensing is an essential technique in optical imaging, adaptive optics, and atmospheric turbulence correction. Traditional wavefront reconstruction methods, including the Gerchberg–Saxton (GS) algorithm and phase diversity (PD) techniques, are often limited by issues such as low inversion accuracy, slow convergence, and the presence of multiple possible solutions. Recent developments in deep learning have led to new methods, although conventional CNN-based models still face challenges in effectively capturing global context. To overcome these limitations, we propose a Transformer-based single-shot wavefront sensing method, which directly reconstructs wavefront aberrations from focal plane intensity images. Our model integrates a Normalization-based Attention Module (NAM) into the CoAtNet architecture, which strengthens feature extraction and leads to more accurate wavefront characterization. Experimental results in both simulated and real-world conditions indicate that our method achieves a 4.5% reduction in normalized wavefront error (NWE) compared to ResNet34, suggesting improved performance over conventional deep learning models. Additionally, by leveraging Walsh function modulation, our approach resolves the multiple-solution problem inherent in phase retrieval techniques. The proposed model achieves high accuracy, fast convergence, and simplicity in implementation, making it a promising solution for wavefront sensing applications. Full article

As a programmable optical device, a liquid crystal optical phased array (LCOPA) has many unique applications. Multi-beam fan-out is one of the novel application cases. However, currently commercially available liquid crystal optical phased array devices typically use reflective structures and are operated on desktop software. This can be inconvenient for the construction of the optical path and the manipulation of the device. On the other hand, multi-beam fan-out capability alone may not be sufficient in some application scenarios. The additional function of focusing might bring some new advantages. Thus, we developed a transmissive liquid crystal optical phased array device based on a fully embedded human–computer interaction control method. It does not require the installation of computer desktop software and only needs a touch screen for easy human–computer interaction. This not only brings convenience to control, but also reduces the cost of devices. Meanwhile, based on the Gerchberg–Saxton algorithm (GS algorithm) and the method of lens phase superposition, we achieved a composite function of multiple-beam fan-out with focusing function by simulation and experiment. This composite function may have unique application value for some special application scenarios. Full article

In the current study, we address the phase retrieval of one-dimensional phase objects from near-field diffraction patterns using the multiple-plane Gerchberg–Saxton algorithm, which is still widely used for phase retrieval. The algorithm was implemented in a low-cost digital signal processor capable of fast Fourier transform using Q15 arithmetic, which is used by the previously mentioned algorithm. We demonstrate similarity between one-dimensional phase objects, i.e., vectors cut out of a phase map of the tertiary spherical aberration retrieved by the multiple-plane Gerchberg–Saxton algorithm, and these vectors are measured with a non-contact profiler. The tertiary spherical aberration was induced by a phase plate fabricated using grayscale lithography. After subtracting the vectors retrieved by the algorithm from those measured with the profiler, the root mean square error decreased, while a corresponding increase in the Strehl ratio was observed. A single vector of size 64 pixels was retrieved in about 2 min. The results suggest that digital signal processors that are capable of one-dimensional FFT and fixed-point arithmetic in Q15 format can successfully retrieve the phase of one-dimensional objects, and they can be used for applications that do not require real-time operation, i.e., analyzing the quality of cylindrical micro-optics. Full article

Holographic displays are an upcoming technology for AR and VR applications, with the ability to show 3D content with accurate depth cues, including accommodation and motion parallax. Recent research reveals that only a fraction of holographic pixels are needed to display images with high fidelity, improving energy efficiency in future holographic displays. However, the existing iterative method for computing sparse amplitude and phase layouts does not run in real time; instead, it takes hundreds of milliseconds to render an image into a sparse hologram. In this paper, we present a non-iterative amplitude and phase computation for sparse Fourier holograms that uses Perlin noise in the image–plane phase. We conduct simulated and optical experiments. Compared to the Gaussian-weighted Gerchberg–Saxton method, our method achieves a run time improvement of over 600 times while producing a nearly equal PSNR and SSIM quality. The real-time performance of our method enables the presentation of dynamic content crucial to AR and VR applications, such as video streaming and interactive visualization, on holographic displays. Full article

In order to meet the increasing requirements of speed and distance, an advanced digital signal processing (DSP) algorithm is preferred without changing the system structure in intensity modulation and the direct detection (IM/DD) system. As the transmission distance increases, the power fading induced by dispersion must be mitigated. In addition, linear and nonlinear inter symbol interference (ISI) introduced by bandwidth limitation and device imperfections becomes an obstacle to achieving higher capacity. The Gerchberg–Saxton (GS) algorithm was recently used to compensate for dispersion. In this paper, GS-based pre- and post-compensation schemes in the IM/DD system with nonlinearity were investigated. We investigated and compared the performance of the GS-based pre- and post-compensation algorithm in a 28 GB aud four-level pulse amplitude modulation (PAM-4) transmission over 40 km standard single-mode fiber (SSMF). The bit error rate (BER) achieved a threshold of 3.8 × 10⁻³ using look-up-table (LUT), FFE, and the GS-based pre-compensation algorithm without iterations. Turning to the GS-based post-compensation scheme, 80 iterations are needed. However, the demand for FFE is reduced. The algorithm selection depends on the tolerance of the transmitter or receiver complexity in specific scenarios. The joint LUT and GS-based pre-compensation algorithm may be a preferable approach in scenarios where a low-complexity receiver is desired. Full article

In detecting the rotation velocity of an object employing the rotational Doppler effect of vortex beams, atmospheric turbulence can easily cause phase distortion and spiral spectrum dispersion, consequently reducing velocity measurement accuracy. This study combines adaptive optical intelligence algorithms with polarization compensation information to propose a novel approach, the Stokes–Particle swarm optimization Gerchberg–Saxton (Stokes-PSO GS) algorithm, which integrates Stokes polarization information assistance and PSO for GS phase retrieval. The algorithm adjusts the phase and amplitude of the pre-compensated phase screen of the GS algorithm utilizing Stokes information of polarized vortex beam (with l_L = 5 and l_R = −5) before and after distortion. The PSO is then employed to optimize the pre-compensated phase screen and perform compensations. Simulation results at z_S-T = 200 m and $C_n^2$ = 1 × 10⁻¹⁴ m^−2/3, demonstrate that the Stokes-PSO GS algorithm exhibits strong stability (small angular spectrum purity deviation, σ_{p, Stokes-PSO GS} = 0.005675% < σ_{p, GS} = 11.62%), superior optical field recovery (well-recovered Stokes optical field, up to 33.76% improvement in angular spectrum purity), and high-velocity measurement accuracy (25.93% improvement) compared to the GS algorithm. This approach enables precise measurement of the rotation velocity of the vortex beam, demonstrating its potential in practical applications. Full article

The paper studies the influence of coherent noises on the quality of images of particles reconstructed from digital holograms. Standard indicators (for example, signal-to-noise ratio) and such indicators as the boundary contrast and boundary intensity jump previously proposed by the authors are used to quantify the image quality. With the use of these parameters, for examples of some known methods of suppressing coherent noises in a holographic image (eliminating the mutual influence of virtual and real images in in-line holography, and time averaging), the features and ranges of applicability of such correction were determined. It was shown that the use of the complex field amplitude reconstruction method based on the Gerchberg–Saxton algorithm and the spatial-frequency method improves the quality of determining the particle image boundary (by boundary intensity jump) starting from the distance between a hologram and a particle, which is about twice the Rayleigh distance. In physical experiments with model particles, averaging methods were studied to suppress non-stationary coherent noises (speckles). It was also shown that averaging over three digital holograms or over three holographic images is sufficient to provide a quality of particle image boundary suitable for particle recognition. In the case of multiple scattering, when it is necessary to impose a limit on the working volume length (depth of scene) of the holographic camera, the paper provides estimates that allow selecting the optimal working volume length. The estimates were made using the example of a submersible digital holographic camera for plankton studies. Full article