Impact of phase retrieval on visualizing the lumen in angiographic phantoms with the use of polychromatic X-ray sources

Deep learning-based phase retrieval with SE-SwinUNet architecture in fringe projection 3D measurement

In the far-field approximation, an object’s diffraction field can be expressed as its Fourier transform multiplied by a phase factor. Here, we present a simple method with which to directly retrieve this phase factor from a single-shot off-axis interference pattern. By exploiting and adjusting its unique two-dimensional quadratic form, the quadratic contribution from the object’s Fourier transform can generally be neglected, particularly for amplitude-only objects and slowly varying phase objects. The phase factor is extracted by fitting a quadratic surface to the unwrapped phase obtained via Fourier-transform-based phase retrieval. Removing this factor enables precise reconstruction through a straightforward inverse Fourier transform, without requiring iterative computations. Compared with conventional far-field diffraction setups, our approach reduces system length and allows the use of smaller CCD sensors. Experimental validation using a modified Mach–Zehnder interferometer demonstrates high reconstruction accuracy and robustness. Overall, this method provides an efficient, practical, and real-time solution for object reconstruction, with the potential to simplify and miniaturize optical setups, offering an alternative approach to standard coherent diffraction imaging techniques.

Accurate 3D dynamic monitoring of thermosensitive hydrogel phase transitions remains challenging due to large deformations and high noise levels. We present a deep learning-enhanced dual-wavelength digital holographic method that overcomes noise amplification in synthetic-wavelength phase maps using an adapted multi-feature fusion unwrapping network, enabling robust phase retrieval under strong speckle noise. The experiments on hydrogels reveal the distinct contraction kinetics below and above the lower critical solution temperature, and a quantitative empirical model linking volume with temperature and time is established. This work provides a precise, wide-range, 3D dynamic measurement platform for soft matter studies and supports the design of hydrogel-integrated adaptive thermal-management systems.

The spatio-temporal coupling effect can temporally and spatially distort the ultrashort laser pulses after focusing, resulting in temporal stretching and decreased power density, and its characterization is of great significance for processes such as light field modulation, and pulse compression, and focusing. A single measurement of the spatio-temporal coupling effect of ultrashort laser pulses is technically challenging. In this paper, a global three-dimensional phase retrieval technique based on lens array and compressive sensing is proposed and applied to the quantitative measurement of spatio-spectral coupling distortion of ultrashort laser pulses. The known amount of pulse-front tilt (PFT) in ultrashort pulses is introduced with a wedge plate, and then compressive sensing is carried out through a deformed CASSI (coded aperture snapshot spectral imaging) system. The grating is the dispersion element of this system. In experiment, this method can fully characterize the spatio-spectral coupling effect of ultrashort laser pulses in a single-shot measurement, with good consistency between theoretical and measured results, which reveals potential applications in the field of ultrafast dynamics.

Abstract Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a novel robust sparse PR method that covers both real- and complex-valued cases. The core is to leverage the Huber function to measure the loss and adopt the ℓ 1 / 2 -norm regularization to realize feature selection, thereby improving the robustness of PR. In theory, we establish statistical guarantees for such robustness and derive necessary optimality conditions for global minimizers. Particularly, for the complex-valued case, we provide a fixed point inclusion property inspired by Wirtinger derivatives. Furthermore, we develop an efficient optimization algorithm by integrating the gradient descent method into a majorization–minimization framework. It is rigorously proved that the whole generated sequence is convergent and also has a linear convergence rate under mild conditions, which has not been investigated before. Numerical examples under different types of noise validate the robustness and effectiveness of our proposed method.

Two-frame randomly phase-shifted noisy interferograms phase retrieval based on intermediate frame generation network

Wave propagation modeling is fundamental to optics, facilitating diverse applications including lens design, computational imaging, and optical computing. However, existing approaches encounter a critical trade-off between computational accuracy and efficiency, primarily limited by numerical precision constraints. In this study, we establish the explicit numerical limits in wave propagation modeling and demonstrate that accurate simulations are achievable with reduced precision. Our analysis reveals that the limited significant decimal digits and dynamic range of floating-point arithmetic compromise phase and amplitude representation accuracy, thereby constraining the dimensions and space-bandwidth product of optical systems that can be reliably modeled. To address this challenge, we introduce a differentiable modeling scheme that maintains accurate phase representation through wrapping from double precision and appropriately prescales the amplitude to ensure the integral result remains within the representable dynamic range. We validate our approach by simulating point spread functions of optical systems, solving phase retrieval problems, and synthesizing holograms for light shaping. Our method achieves, on average, ∼20× acceleration in diffraction modeling while retaining accuracy comparable to double-precision implementations. Optical experiments further demonstrate our approach’s effectiveness. Specifically, our method successfully reconstructs complex amplitudes of laser beams from coded measurements and designs phase-only holograms for desired diffraction patterns. We envision that this technique will advance research in computational optics with enhanced computational efficiency.

X-ray holographic microscopy is a three-dimensional (3D) imaging technique for nanoscale-resolution imaging of morphological features and phase contrast in biological samples and solid-state materials. However, it is challenging to recover phase and absorbance information from shot-noise-limited (SNL) X-ray holograms acquired under weak illumination. In this study, we propose a deep learning model, named MorpHoloNet-X, for single-shot phase and absorbance retrieval from SNL X-ray holograms using a physics-driven neural network. By incorporating physics-based prior knowledge and wave propagation principles into the neural network, MorpHoloNet-X can directly reconstruct 3D complex wavefield, phase, and absorbance distributions in a simulated 3D volume. The performance of the proposed MorpHoloNet-X is validated using synthetic and experimental SNL holograms, and the results are compared with those of conventional methods. The proposed technique would be utilized to reconstruct phase and absorbance information from hard X-ray holograms acquired under rapid acquisition or weak illumination.

Abstract This paper addresses the problem of achieving quadratic convergence in quaternion phase retrieval. To this end, we propose a novel augmented quaternion Gauss–Newton (AQGN) framework for recovering quaternion signals from magnitude-only measurements. The method is developed based on the generalized Hamilton–real (GHR) calculus, which rigorously preserves the intrinsic quaternion algebraic structure while enabling efficient second-order optimization without component-wise decomposition. The main contributions are threefold. \textit{i)} We derive the AQGN update rule within the GHR calculus framework. \textit{ii)} We prove that the resampled AQGN achieves quadratic convergence under spectral initialization with high probability, provided $\mathcal{O}(n \log n)$ quaternion Gaussian measurements. \textit{iii)} We further show that the algorithm attains an $\epsilon$-accurate solution within $\mathcal{O}(\log_2 \log_2 \epsilon^{-1})$ iterations, demonstrating a substantial reduction in iteration complexity compared with existing quaternion-based optimization methods. Extensive numerical experiments on both synthetic datasets and real-world images demonstrate that the proposed method generally outperforms state-of-the-art approaches in terms of recovery accuracy, convergence speed, and computational efficiency. Overall, the proposed framework establishes a provably efficient second-order method for hypercomplex phase retrieval, providing both theoretical guarantees and practical scalability for high-dimensional quaternion signal recovery.

Quaternionic reweighted amplitude flow for phase retrieval in image reconstruction

Adaptive distance joint optimization for multi-distance phase retrieval

We employ Bragg coherent diffractive imaging to reconstruct the three-dimensional [102] displacement field and strain within individual grains of ferroelectric LiNbO3 thin films. By directly imaging buried nanoscale ferroelastic and ferroelectric textures, this approach provides a nondestructive route to resolve internal electromechanical structure in technologically relevant oxide energy materials. Coherent diffraction around the (102) Bragg peak reveals twin-like features, despite classical deformation twinning being symmetry-forbidden in LiNbO3 by its R3c structure and absence of a {102} glide plane. Iterative phase retrieval achieves sub-20 nm spatial resolution, resolving inversion-type ferroelectric domains with domain-wall widths of ∼50–60 nm. Landau phase-field simulations of coupled polarization and strain reproduce the observed domain morphology and strain profiles. This combined experimental–theoretical framework establishes a nondestructive approach to probe nanoscale polarization–strain coupling, with direct implications for the design and optimization of ferroelectric thin films for electro-optic, piezoelectric, and energy-conversion applications.

Abstract. Contrails – thin ice clouds formed by aircraft – are a major contributor to aviation-induced climate forcing, yet their observational characterization remains limited. We present a manually labeled contrail dataset derived from observations of the Meteosat Second Generation (MSG) SEVIRI instrument over Europe and the North Atlantic, comprising 140 scenes of 256 × 256 pixels at 3 km nominal resolution. The dataset covers the time period in which Meteosat-10 was the operational satellite (from January 2013 through February 2018 and from March 2023 through March 2024) and scenes are distributed randomly over the whole SEVIRI disk. Each scene was independently annotated by three labelers, with ground truth established via majority consensus. To provide additional context, the dataset includes outputs from two satellite retrievals: CiPS (Cirrus Properties from SEVIRI) and ProPS (Probabilistic Cloud Top Phase retrieval), offering information on cloud cover and cloud top phase, cirrus probability, ice optical thickness, and ice cloud top height. These complementary variables enable detailed investigations, such as factors influencing contrail visibility. The dataset supports analyses of contrail detection, contrail characteristics, cloud-contrail interactions, and environmental conditions affecting detection. By providing high-quality labeled data with auxiliary cloud information, this resource facilitates the development and evaluation of contrail studies, contributes to improved understanding of aviation-related cloud effects, and informs strategies for climate impact mitigation. The full dataset is available under: https://doi.org/10.5281/zenodo.17669443 (Santos Gabriel et al., 2025) with version v2 presented in this study.

Lens-free imaging technology shows great potential in biomedical detection due to its simple structure, low cost, and strong portability. However, its imaging accuracy and practical applications are limited by twin-image interference in coaxial optical systems and the difficulty in precise reconstruction distance determination. This study proposes a portable cell detection method based on multiwavelength illumination, using a tricolor LED source (red: 630 nm, green: 520 nm, blue: 470 nm) combined with a CMOS image sensor and computational reconstruction algorithms to achieve high-resolution phase imaging of cells. A multiwavelength iterative phase retrieval algorithm with sub-pixel displacement correction effectively suppresses twin-image artifacts, whereas an automatic multiwavelength reconstruction distance search method based on phase gradient standard deviation enables adaptive and precise reconstruction within 0.5 to 1 mm. Experimental results show that this method can successfully image animal and plant cells (5 to 40 μm) with clear three-dimensional morphology and distribution patterns, providing an effective technical solution for portable cell detection.

Modern microscopy methods incorporate computational modeling as an integral part of the imaging process, either to solve inverse problems or optimize the optical system design itself. These methods often depend on differentiable optics simulations, yet no standardized framework exists—forcing computational optics researchers to repeatedly and independently implement simulations with limited reusability and performance. These common problems limit the potential impact of computational optics as a field. Here we present Chromatix: an open-source, GPU-accelerated, differentiable wave optics simulation library. Chromatix builds on JAX to democratize fast, parallelized simulation of diverse optical systems and expand the design space in computational optics. Chromatix standardizes a growing collection of optical elements and propagation methods allowing a broad range of applications, which we demonstrate here for snapshot microscopy, holography, and phase retrieval. We demonstrate speed improvements of 2-6× on a single GPU and up to 22× on 8 GPUs.

Accurate and high-speed characterization of transient flow fields is vital for advancing aerospace, combustion, and plasma science. Yet, existing optical and probe-based diagnostics face an inherent trade-off between spatial coverage and temporal resolution, hindering the capture of rapidly evolving phenomena. Here, we introduce ultrafast multipoint flow sensing based on optical time-stretch interferometry, which implements a time-frequency-space mapping to convert spatial distributions into temporal waveforms, enabling simultaneous monitoring of hundreds of points with a spatial resolution of 7.81 μm at a 100 MHz sampling rate. Through absolute phase retrieval, the system quantitatively resolves flow perturbations from ∼10 m/s to ∼300 m/s, achieving root-mean-square deviations of 14.38% and 3.14% compared with hot-wire and Pitot measurements, respectively. Validated against high-speed schlieren imaging, this technique circumvents the long-standing spatiotemporal trade-off, providing a powerful, nonintrusive platform for real-time diagnostics of turbulence, combustion instabilities, and laser–plasma interactions under extreme conditions.

A new mathematical framework, to our knowledge, for phase recovery from a single two-beam interferogram is presented. Conventional approaches, relying on trigonometric inversion followed by phase unfolding and unwrapping, are hindered by discontinuities typically addressed through intricate algorithms. Our approach bypasses the unfolding and unwrapping, instead formulating a first-order differential equation directly relating the phase to the interferogram. Integration of this equation enables continuous retrieval of phase along any straight path. Representing a new class of analytical tools for single-interferogram phase retrieval, this approach is derived from first principles and accommodates both Newton-type and Fizeau-type interferograms. Its performance is demonstrated on multiple idealized synthetic interferograms of increasing complexity, validating against the known seed phase.

Untrained neural networks (UNNs) have recently emerged as a promising approach for solving inverse problems without the need for large-scale datasets or extensive training. In this work, we systematically investigate the performance of UNNs in the context of phase retrieval from free-space propagation of intensity. We focus on two distinct architectures: the deep decoder and U-Net, evaluating their ability to reconstruct phase information from intensity measurements. Through simulation and experiment, we compare the reconstruction robustness of both architectures under various noise levels and propagation distances. Our findings highlight the strengths and limitations of each architecture, offering insights into the design of effective UNN-based phase retrieval algorithms and guiding future work toward more efficient imaging solutions.

Quantitative phase imaging of transparent samples with large phase variations is fundamentally challenged by the nonconvex nature of phase retrieval from intensity-only measurements. In this regime, conventional algorithms with random initialization often converge to nonphysical solutions and fail to recover meaningful phase information, even when the forward model is accurately known. Here, we present a phase-gradient-based initialization strategy for coded ptychographic imaging that exploits the fact that local phase gradients remain stably encoded as lateral displacements in coded intensity patterns. By extracting displacement-derived phase-gradient information from measured intensities and constructing a globally consistent initial phase, the proposed initialization introduces essential first-order physical constraints prior to optimization. Simulations and experiments demonstrate that this strategy enables stable and physically correct reconstruction in large-phase regimes where random initialization breaks down, without increasing measurement redundancy.