Search Results (67)

This study proposes a principal component analysis-based convolutional neural network (PC-CNN) to correct atmospheric turbulence-induced aberrations. Unlike traditional Zernike polynomials (ZPs)-based methods (ZP-CNN), PC-CNN avoids mode aliasing and cross-coupling via the strict orthogonality of principal components (PCs). A coefficient magnification strategy is incorporated to further enhance efficacy, maximally preserving the intrinsic physical information within the PCs coefficients. A series of systematic experiments was conducted under conditions from weak to strong turbulence, characterized by $D/r_0$ from 1 to 25, where $D$ is the pupil diameter and $r_0$ is the atmospheric coherence length. Quantitative results show PC-CNN achieves a lower mean relative error (MRE) in coefficient prediction than ZP-CNN under equivalent conditions. It also yields a higher Strehl ratio, reduced speckles, and enhanced spot clarity while requiring fewer basis terms, demonstrating high stability and robustness in strong turbulence. These findings emphasize that basis function orthogonality and physically informed preprocessing are critical design principles for deep-learning-based wavefront sensor-less adaptive optics (AO), establishing a robust foundation for real-time intelligent AO systems in astronomy and free-space optical communications. Full article

Zernike polynomials constitute an essential mathematical basis for representing functions defined over the unit disk. They are widely used in a diverse range of scientific and engineering disciplines, including adaptive optics for characterizing atmospheric distortions, ophthalmology for quantifying ocular aberrations, microscopy for instrument characterization and aberration correction, and optical metrology for surface profiling. This paper introduces ZernikeViewer, a software framework developed for the rapid calculation and visualization of fringe, phase, and point spread function (PSF) maps from Zernike coefficients. The framework leverages CPU multicore and multithreading capabilities through the .NET Task Parallel Library (TPL), augmented by codebase optimizations and the preloading of precomputed Zernike polynomial matrices. These optimizations reduce computation time by a factor of 7 to 10 compared to a conventional approach; for instance, from 1 ms to 0.1 ms for a radial order of n = 10 and from 700 ms to 80 ms for n = 100. Numerical error analysis confirms the accuracy of the computation, with an average root-mean-square (RMS) error of 0.11 ms observed in the timing measurements. Furthermore, it is demonstrated that implementing Jacobi recursion relations could potentially reduce the numerical calculation error by up to 5 orders of magnitude. Full article

Off-axis reflective telescopes are prone to component misalignment due to external environmental factors and mechanical vibrations. This misalignment introduces low-order aberrations, which severely degrade imaging quality. Thus, active misalignment correction is crucial for maintaining the imaging performance of off-axis reflective telescopes. Current computer-aided alignment technologies for optical systems mostly rely on wavefront sensors to acquire aberrations at multiple fixed fields of view (FOVs) or even the full FOV. This significantly increases system complexity and hinders practical engineering applications. To address this issue, this study first conducts sensitivity analysis of misaligned degrees of freedom (DOFs) using a mode truncation algorithm based on singular value decomposition (SVD). A compensation strategy is proposed to avoid the aberration coupling effect. Furthermore, two novel misalignment aberration compensation methods for off-axis reflective telescopes are presented. These methods require only a single focal spot image and eliminate the need for aberration detection and iterative calculations. One method directly solves component misalignment errors using a convolutional neural network (CNN) based on the system’s point spread function (PSF). To further improve compensation performance, an improved method fusing spot images and Zernike coefficients is proposed. In practical misalignment correction, both methods input a single acquired focal spot image into a well-trained model to obtain the misalignment compensation amount. Simulation experiments demonstrate that the improved method, which uses Zernike polynomial coefficients as an intermediate feature bridge, effectively establishes the mapping relationship between spot images and misalignment amounts. It achieves higher solution accuracy and better aberration compensation effect compared to the direct CNN method. This verifies the necessity of extracting Zernike polynomial coefficient features from spot images. Comparative experiments with the traditional sensitivity matrix method show that the two proposed methods outperform the sensitivity matrix method in aberration compensation accuracy over a large misalignment range. Comprehensive simulation results confirm the feasibility and effectiveness of the proposed methods. They overcome the limitations of existing methods, such as complex structure, high cost, and low efficiency, to a certain extent. Full article

In high-precision optical systems such as laser optics, astronomical observation, and semiconductor lithography, anti-reflection coatings are crucial for light transmittance, imaging quality, and stability, but traditional designs face modeling challenges in balancing ultralow reflectivity, high wavefront quality, and manufacturability amid multi-dimensional parameter coupling and multi-objective constraints. This study addresses these by proposing a unified mathematical modeling framework integrating a Symmetric five-layer high-low refractive index alternating structure (V-H-V-H-V) with dual-scale nanostructures, employing a constrained quasi-Newton optimization algorithm (L-BFGS-B) to minimize reflectivity, wavefront root-mean-square (RMS) error, and surface roughness root-mean-square (RMS) in a six-dimensional parameter space. The Sellmeier equation is adopted to calculate wavelength-dependent material refractive indices, the model uses the transfer matrix method for the Symmetric five-layer high-low refractive index alternating structure’s reflectivity, incorporates nano-surface height function gradient correction, sub-wavelength modulation, and radial optimization, applies Zernike polynomials for low-order aberration correction, quantifies surface roughness via curvature proxies, and optimizes via a weighted objective function prioritizing low reflectivity. Numerical results show the spatial average reflectivity at 632.8 nm reduced to 0.13%, the weighted average reflectivity across five representative wavelengths in the 550–720 nm range to 0.037%, the reflectivity uniformity to 10.7%, the post-correction wavefront RMS to 11.6 milliwavelengths, and the surface height standard deviation to 7.7 nm. This framework enhances design accuracy and efficiency, suits UV nanoimprinting and electron beam evaporation, and offers significant value for high-power lasers, lithography, and space-borne radars. Full article

In freeform optical metrology, wavefront fitting over non-circular apertures is hindered by the loss of Zernike polynomial orthogonality and severe sampling grid distortion inherent in standard conformal mappings. To address the resulting numerical instability and fitting bias, we propose a unified framework curve-shortening flow (CSF)-guided progressive quasi-conformal mapping (CSF-QCM), which integrates geometric boundary evolution with topology-aware parameterization. CSF-QCM first smooths complex boundaries via curve-shortening flow, then solves a sparse Laplacian system for harmonic interior coordinates, thereby establishing a stable diffeomorphism between physical and canonical domains. For doubly connected apertures, it preserves topology by computing the conformal modulus via Dirichlet energy minimization and simultaneously mapping both boundaries. Benchmarked against state-of-the-art methods (e.g., Fornberg, Schwarz–Christoffel, and Ricci flow) on representative irregular apertures, CSF-QCM suppresses area distortion and restores discrete orthogonality of the Zernike basis, reducing the Gram matrix condition number from >900 to <8. This enables high-precision reconstruction with RMS residuals as low as $3\times {10}^{-3}\lambda$ and up to 92% lower fitting errors than baselines. The framework provides a unified, computationally efficient, and numerically stable solution for wavefront reconstruction in complex off-axis and freeform optical systems. Full article

The use of large-aperture scanning mirrors for high-resolution and wide-swath imaging represents a major trend in Earth observation technology. However, to improve dynamic response performance, scanning mirror assemblies are highly lightweighted, resulting in reduced overall stiffness. This makes the mirror surface susceptible to thermal and inertial loads during operation, leading to degraded surface accuracy and poor imaging quality. Moreover, dynamic scanning mirror has the multi-disciplinary coupling effects and non-circular structural characteristics. It poses significant challenges for surface figure analysis. To address these issues, this paper proposes a surface analysis method for high-dynamic scanning mirrors under multi-physics coupling in non-circular domains. First, a finite element model of the mirror assembly is established based on the minimum aperture and angular velocity parameters. Through finite element analysis, the surface response of the scanning mirror assembly under thermal loads, dynamic inertial loads, and their coupled effects is quantitatively investigated. Subsequently, an analytical approach, which combines rigid-body displacement separation and Gram–Schmidt orthogonalization, is developed to construct non-circular Zernike polynomials, enabling high-precision fitting and reconstruction of the mirror’s dynamic surface distortions. Numerical experiments validate the accuracy of the model. Results show that for a scanning mirror with an aperture of 466 mm × 250 mm under the coupled condition of a 5 °C temperature rise and 50 N·mm torque, the surface figure achieves RMS < 2 nm and PV < 22 nm, with a fitting accuracy achieves 10⁻⁶. These results verify the accuracy and reliability of the proposed method. The surface analysis approach presented in this study provides theoretical guidance and a design framework for subsequent image quality evaluation and assurance. Full article

In adaptive optics systems, most methods rely on reconstruction techniques centered on regional or global orthogonal bases, which struggle to accommodate the multi-scale characteristics of atmospheric turbulence wavefronts. This paper adopts a hybrid basis wavefront reconstruction method based on mutual information sorting, combining Zernike modes with Daubechies wavelet modes for mutual information calculation and sorting. The modes with the highest correlation are selected for reconstruction, effectively reducing the scale of the reconstruction matrix while considering both global and local features. The reconstruction results show that when the number of modes is 20, the root mean square (RMS) of the wavefront residual error of the hybrid basis reconstruction drops to 0.14 rad, outperforming 0.19 rad of the Zernike mutual information method and 0.33 rad of the Zernike expansion method. The peak-to-valley (PV) value after wavefront correction converges to 0.057 μm at the 39th iteration, demonstrating a faster convergence speed and smaller residual error; the RMS value converges to 0.027 μm at the 77th iteration after correction. Full article

The Zernike polynomial method is extensively used for atmospheric phase screen generation but is limited by insufficient high-frequency components. Calculating higher-order terms introduces challenges in computational efficiency and numerical instability when using the direct method. This paper analyzes these issues and proposes replacing the direct method with recursive radial formulas. We evaluate four recursive algorithms (Barmak’s, q-recursive, Prata’s and Kintner’s) for their performance in phase screen generation, focusing on computational speed and numerical stability. Our results demonstrate that recursive methods achieve a 10–20-times improvement in computational efficiency and maintain numerical stability even for high-order expansions. The main novelty of this study lies in the comprehensive comparison and validation of these recursive strategies for high-accuracy atmospheric phase screen simulation. Full article

Background/Objectives: Ocular wavefront aberrations are clinically relevant for optimizing vision correction and predicting surgical outcomes. This study aimed to establish normative reference ranges for a Korean population by quantifying wavefront aberrations using a Hartmann–Shack wavefront sensor and Zernike coefficients, and to assess correlations with age, sex, and spherical equivalent (SE). Methods: Wavefront aberrations were measured in 98 Koreans (196 eyes) using a Hartmann–Shack aberrometer without cycloplegia. Five repeated measurements per eye at a 6 mm pupil size were averaged. Parameters included Zernike coefficients (Z3–Z20), higher-order aberration (HOA) root mean square (RMS, Z6–Z20), and total RMS (Z3–Z20). Associations with age, sex, and SE were assessed using univariable and multivariable linear mixed-effects models. Second-order polynomial regression assessed nonlinear relationships. Interocular symmetry was evaluated using mirror-symmetry-adjusted Spearman’s correlation and intraclass correlation coefficients (ICCs). Results: Vertical coma (Z7, 0.208 ± 0.174 μm) and spherical aberration (Z12, 0.200 ± 0.161 μm) were the largest contributors to HOA RMS. Mean HOA RMS and total RMS were 0.51 ± 0.21 μm and 3.03 ± 2.51 μm, respectively. HOA RMS increased with age (β = 0.003 μm/year, p = 0.010), whereas total RMS decreased with SE (β = −0.678 μm/D, p < 0.001). Most Zernike coefficients showed positive interocular correlations, with ICCs of 0.75 for total RMS and 0.64 for HOA RMS. Conclusions: In normal Korean eyes, HOAs increased with age and exhibited significant interocular symmetry. Vertical coma and spherical aberration were predominant components. While the pattern was similar to that in Western populations, the absolute values were greater. These normative values may aid future wavefront-guided refractive surgery and presbyopia correction procedures. Full article

The implementation of efficient free-space channels is fundamental for both classical and quantum free-space optical (FSO) communication. This can be challenging for fiber-coupled receivers, due to the time variant inhomogeneity of the refractive index that can cause strong fluctuations in the power coupled into the single-mode fiber (SMF), and requires the use of adaptive optics (AO) systems to correct the atmospheric-induced aberrations. In this work, we present two adaptive optic systems, one using a fast-steering prism (FSP) for the correction of tip-tilt and a second one based on a multi-actuator deformable lens (MAL), capable of correcting up to the third order of Zernike’s polynomials. We test both systems at telecom wavelength both with artificial turbulence in the laboratory and on a free-space channel, demonstrating their effectiveness in increasing the fiber coupling efficiency. Full article

The demand for high-spatial-resolution optical remote sensing applications is increasing, while conventional high-resolution optical payloads face limitations in widespread application due to their large size and high manufacturing costs. With the rapid development of image processing technology, we adopt a method combining small-pixel detector sampling with image deblurring algorithms to obtain high-spatial-resolution remote sensing images. In this work, we use Zernike polynomials to simulate diffraction-blurred small-pixel images under various aberration modulations, ensuring the simulation data follow solid physical principles. Furthermore, we propose a new weighted sparse model ℓ_we that combines the Welsch-weighted ℓ₁-norm with ℓ₀-norm constraints, and further applies ℓ_we regularization to both gradient fidelity terms and image gradient terms to enhance fidelity constraints and improve latent structure preservation. Compared with other sparse models, our model produces results with fewer residual structures and stronger sparsity. Comprehensive evaluations on both simulated small-pixel remote sensing datasets and real-world remote sensing images demonstrate that the proposed weighted sparse image quality restoration algorithm achieves more desirable results with excellent robustness. Compared to other methods, the proposed approach improves PSNR by an average of 2.5% and SSIM by 2.2%, while reducing ER by 20.7%. This provides an effective technical solution for image quality restoration of small-pixel remote sensing data. Full article

High aspect ratio (HAR) sample-induced aberrations seriously affect the topography measurement for the bottom of the microstructure by coherence scanning interferometry (CSI). Previous research proposed an aberration compensating method using deformable mirrors at the conjugate position of the pupil. However, it failed to compensate for the shift-variant aberrations introduced by the HAR hybrid trench array composed of multiple trenches with different parameters. Here, we propose a computational aberration correction method for measuring the topography of the HAR structure by the particle swarm optimization (PSO) algorithm without constructing a database and prior knowledge, and a phase filter in the spatial frequency domain is constructed to restore interference signals distorted by shift-variant aberrations. Since the aberrations of each sampling point are basically unchanged in the field of view corresponding to a single trench, each trench under test can be considered as a separate isoplanatic region. Therefore, a multi-channel aberration correction scheme utilizing the virtual phase filter based on isoplanatic region segmentation is established for hybrid trench array samples. The PSO algorithm is adopted to derive the optimal Zernike polynomial coefficients representing the filter, in which the interference fringe contrast is taken as the optimization criterion. Additionally, aberrations introduce phase distortion within the 3D transfer function (3D-TF), and the 3D-TF bandwidth remains unchanged. Accordingly, we set the non-zero part of the 3D-TF as a window function to preprocess the interferogram by filtering out the signals outside the window. Finally, experiments are performed in a single trench sample and two hybrid trench array samples with depths ranging from 100 to 300 μm and widths from 10 to 30 μm to verify the effectiveness and accuracy of the proposed method. Full article

A multi-order combined diffraction spatial filter, integrated with a set of Zernike phase functions (representing wavefront aberrations) and Zernike polynomials, enables the simultaneous formation of multiple aberration-transformed point spread function (PSF) patterns in a single plane. This is achieved using an optical Fourier correlator and provides significantly more information than a single PSF captured in focal or defocused planes—all without requiring mechanical movement. To analyze the resulting complex intensity patterns, which include 49 diffraction orders, a convolutional neural network based on the Xception architecture is employed. This model effectively identifies wavefront aberrations up to the fourth Zernike order. After 80 training epochs, the model achieved a mean absolute error (MAE) of no more than 0.0028. Additionally, a five-fold cross-validation confirmed the robustness and reliability of the approach. For the experimental validation of the proposed multi-order filter, a liquid crystal spatial light modulator was used. Optical experiments were conducted using a Fourier correlator setup, where aberration fields were generated via a digital micromirror device. The experimental results closely matched the simulation data, confirming the effectiveness of the method. New advanced aberrometers and multichannel diffractive optics technologies can be used in industry for the quality control of optical elements, assessing optical system alignment errors, and the early-stage detection of eye diseases. Full article

Simulating atmospheric turbulence phase screens is essential for optical system research and turbulence compensation. Traditional methods, such as multi-harmonic power spectrum inversion and Zernike polynomial fitting, often suffer from sampling errors and limited diversity. To overcome these challenges, this paper proposes an improved denoising diffusion probabilistic model (DDPM) for generating high-fidelity atmospheric turbulence phase screens. The model effectively captures the statistical distribution of turbulence phase screens using small training datasets. A refined loss function incorporating the structure function enhances accuracy. Additionally, a self-attention module strengthens the model’s ability to learn phase screen features. The experimental results demonstrate that the proposed approach significantly reduces the Fréchet Inception Distance (FID) from 154.45 to 59.80, with the mean loss stabilizing around 0.1 after 50,000 iterations. The generated phase screens exhibit high precision and diversity, providing an efficient and adaptable solution for atmospheric turbulence simulation. Full article

Neural networks have significantly advanced adaptive optics systems for telescopes in recent years. Future adaptive optics systems, especially for extremely large telescopes, are expected to predominantly employ pyramid wavefront sensors, which offer good sensitivity but suffer from a non-linear response under certain conditions. This non-linearity limits the performance of traditional linear reconstruction methods, such as matrix–vector multiplication, leading to suboptimal performance. Convolutional Neural Networks offer a promising alternative, as they can model complex non-linear relationships and extract spatial patterns from sensor images. While CNN-based reconstruction has shown success in closed-loop systems, this study investigates their application in open-loop wavefront reconstruction. A custom network architecture and training strategy are developed, using realistic training data from end-to-end atmospheric turbulence simulations. CNNs are trained to reconstruct Zernike polynomial coefficients representing optical aberrations, enabling a tomographic estimation of turbulence. The proposed approach demonstrates significant improvements over conventional open-loop methods, underscoring the potential of CNNs to enhance wavefront reconstruction in next-generation AO systems. Full article