Pixel super-resolution phase retrieval algorithms for digital holography

Single beam phase retrieval techniques [1-8] allow the reconstruction of the object phase information of a general volume speckle field for single beam devices such as optical microscopes. These techniques are well-suited for simple optical setups and recover the phase using the intensity recorded at a single or multiple planes. Deterministic Phase Retrieval techniques, as e.g. approaches based on the Transport of Intensity Equation [4-6] or the Contrast Transfer Function [7,8] allow recovering directly the phase of a wavefront, but are limited either to the paraxial case or impose restrictions on the phase to be estimated. Available Iterative Phase Retrieval (IPR) techniques as the Single-Beam-Multiple-Intensity-Reconstruction (SBMIR) algorithm [1-3] overcome this problem and are applicable to the non-paraxial case without imposing restrictions on the object to be investigated. However, this family of IPR techniques are subject to varying levels of performance or stagnate after few numbers of iterations. The stagnation is a result of the slow elimination of the remaining low frequency error components usually in form of a phase tilt, a bell-shaped error, or other low frequency artefacts. This problem results in a poor reconstruction for the case of slow-varying objects or the measurement of aberrations.

In this work the stagnation problem in iterative single beam multiple intensity reconstruction algorithms is reduced by combining deterministic and iterative phase retrieval techniques in order to compensate for paraxial artifacts. This combined technique has a better convergence, because it suppresses better the stagnation problem present in iterative phase retrieval techniques. The reported hybrid deterministic-iterative phase retrieval techniques can be successfully employed for cases where an iterative solver is trapped in a local minimum, and moreover, allows increasing the convergence of iterative solvers.

Pixel super-resolution (PSR) techniques have been developed to overcome the sampling limit in lensless digital holographic imaging. However, the inherent non-convexity of the PSR phase retrieval problem can potentially degrade reconstruction quality by causing the iterations to tend toward a false local minimum. Furthermore, the ill posedness of the up-sampling procedure renders PSR algorithms highly susceptible to noise. In this Letter, we propose a heuristic PSR algorithm with adaptive smoothing (AS-PSR) to achieve high-fidelity reconstruction. By automatically adjusting the intensity constraints on the estimated field, the algorithm can effectively locate the optimal solution and converge with high reconstruction quality, pushing the resolution toward the diffraction limit. The proposed method is verified experimentally within a coherent modulation phase retrieval framework, achieving a twofold improvement in resolution. The AS-PSR algorithm can be further applied to other phase retrieval methods based on alternating projection.

This paper investigates experimental means of measuring the transmission matrix (TM) of a highly scattering medium, with the simplest optical setup. Spatial light modulation is performed by a digital micromirror device (DMD), allowing high rates and high pixel counts but only binary amplitude modulation. On the sensor side, without a reference beam, the CCD camera provides only intensity measurements. Within this framework, this paper shows that the TM can still be retrieved, through signal processing techniques of phase retrieval. This is experimentally validated on three criteria : quality of prediction, distribution of singular values, and quality of focusing.

Phase retrieval is a highly useful technique that allows the calculation of the complex electric field of a beam of spatially coherent radiation based only on recordings of intensity profiles with a camera. In this work, we demonstrate what we believe, to the best of our knowledge, is a new technique for single-beam multiple-intensity phase retrieval based on simultaneous propagations that provides improved fidelity results compared to standard methods (0.9931 compared to 0.9646) and a 34 dB reduction in background noise level. The implementation is fast, open source, user friendly, and can be run on either CPUs or GPUs. It is available for download at https://gitlab.gbar.dtu.dk/biophotonics/PhaseRetrieval.

Phase-contrast x-ray computed tomography (PCCT) is currently investigated as an interesting extension of conventional CT, providing high soft-tissue contrast even if examining weakly absorbing specimen. Until now, the potential for dose reduction was thought to be limited compared to attenuation CT, since meaningful phase retrieval fails for scans with very low photon counts when using the conventional phase retrieval method via phase stepping. In this work, we examine the statistical behaviour of the reverse projection method, an alternative phase retrieval approach and compare the results to the conventional phase retrieval technique. We investigate the noise levels in the projections as well as the image quality and quantitative accuracy of the reconstructed tomographic volumes. The results of our study show that this method performs better in a low-dose scenario than the conventional phase retrieval approach, resulting in lower noise levels, enhanced image quality and more accurate quantitative values. Overall, we demonstrate that the lower statistical limit of the phase stepping procedure as proposed by recent literature does not apply to this alternative phase retrieval technique. However, further development is necessary to overcome experimental challenges posed by this method which would enable mainstream or even clinical application of PCCT.

Due to its low complexity and acceptable accuracy, phase retrieval technique has been proposed as an alternative to solve the classic optical surface measurement task. However, to capture the overall wave field, phase retrieval based optical surface measurement (PROSM) system has to moderate the CCD position during the multiple-sampling procedure. The mechanical modules of CCD movement may bring about unexpectable deviation to the final results. To overcome this drawback, we propose a new PROSM method based on spatial light modulator (SLM). The mechanical CCD movement can be replaced by an electrical moderation of SLM patterns; thus the deviation can be significantly suppressed in the new PROSM method. In addition, to further improve the performance, we propose a new iterative threshold phase retrieval algorithm with sparsity-constraint to effectively reconstruct the phase of wave field. Experimental results show that the new method provides a more simple and robust solution for the optical surface measurement than the traditional techniques and achieves higher accuracy.

This paper presents the Pixel Super Resolution with Axial Scanning (PSR-AS) technique to enhance the resolution of Lensless Digital In-line Holographic Microscopy (LDHM). By utilizing multiple holograms captured at different axial distances, PSR allows for the recovery of high-resolution information, improving the image clarity and information content. Experimental results demonstrate a twofold lateral resolution enhancement, achieving the resolution of 1.23 μm in amplitude imaging and significantly augmenting phase reconstruction quality. The integration of PSR-AS into LDHM systems leads to notable reductions in noise and artifacts, offering a promising approach for high-resolution imaging in applications such as biomedical diagnostics and environmental monitoring. Full Text: PDF References Y. Park, C. Depeursinge, and G. Popescu, "Quantitative phase imaging in biomedicine," Nature Photon, 12(10), 578 (2018). CrossRef D. Gabor, "A New Microscopic Principle," Nature, 161(4098), 777 (1948). CrossRef K. Matsushima and T. Shimobaba, "Band-Limited Angular Spectrum Method for Numerical Simulation of Free-Space Propagation in Far and Near Fields," Opt. Express, 17(22), 19662 (2009). CrossRef Y. Wu and A. Ozcan, "Lensless digital holographic microscopy and its applications in biomedicine and environmental monitoring," Methods, 136, 4 (2018). CrossRef J. Zhang, J. Sun, Q. Chen, and C. Zuo, "Resolution Analysis in a Lens-Free On-Chip Digital Holographic Microscope," IEEE Transactions on Computational Imaging, 6, 697 (2020). CrossRef Gerchberg, R. W.. “A practical algorithm for the determination of phase from image and diffraction plane pictures.” Optik 35, 237 (1972). CrossRef H. Lee, J. Kim, J. Kim, P. Jeon, S. A. Lee, and D. Kim, "Noniterative sub-pixel shifting super-resolution lensless digital holography," Opt. Express,29(19), 29996 (2021). CrossRef A. Greenbaum and A. Ozcan, "Maskless imaging of dense samples using pixel super-resolution based multi-height lensfree on-chip microscopy," Opt. Express, 20(3), 3129 (2012). CrossRef J. Zhang, J. Sun, Q. Chen, J. Li, and C. Zuo, "Adaptive pixel-super-resolved lensfree in-line digital holography for wide-field on-chip microscopy," Sci Rep, 7(1), 11777 (2017). CrossRef L. I. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D: Nonlinear Phenomena, 60(1), 259 (1992). CrossRef

A new efficient method for broadband antenna characterization from phaseless acquisitions in the frequency-domain (FD) is presented. The phase-retrieval technique is based on an extrapolation of the off-axis indirect holography. In common with the conventional approach, the power of the interferometric field of the antenna under test (AUT) and a reference antenna, whose field is known in advance, as well as the power of the AUT alone, is measured at the desired frequencies. Nevertheless, the phase retrieval is accomplished independently at each spatial point by filtering in the time-domain (TD) rather than in the k -space. Thus, the dependency of the phase retrieval on the position accuracy is reduced and it can be accomplished simultaneously at all frequencies without resorting to iterative schemes. Moreover, it yields a less dense sampling and a phase-retrieval algorithm not dependent on the geometry of the acquisition. The method is illustrated with a numerical example in the $W$ -band as well as with two near-field (NF) measurement examples in the $K_a$ - and $W$ -bands.

After nearly a century of specialized applications in optics, remote sensing, and acoustics, the near-field (NF) electromagnetic (EM) propagation zone is experiencing a resurgence in research interest. This renewed attention is fueled by the emergence of promising applications in various fields, such as wireless communications, holography, medical imaging, and quantum-inspired systems. Signal processing within NF sensing and wireless communications environments entails addressing issues related to extended scatterers, range-dependent beampatterns, spherical wavefronts, mutual coupling effects, and the presence of both reactive and radiative fields. Recent investigations have focused on these aspects in the context of extremely large arrays and wide bandwidths, giving rise to novel challenges in channel estimation, beamforming, beam training, sensing, and localization. While NF optics has a longstanding history, advancements in NF phase retrieval (PR) techniques and their applications have lately garnered significant research attention. Similarly, utilizing NF localization with acoustic arrays represents a contemporary extension of established principles in NF acoustic array signal processing. This article aims to provide an overview of state-of-the-art signal processing techniques within the NF domain, offering a comprehensive perspective on recent advances in diverse applications.

We present a phase coefficient optimization technique for determining the vortex charge of a high-power orbital angular momentum beam. This high-power vortex beam is generated by transmitting a Gaussian-like beam emitted by a gyrotron with an output power of 25 kW through a spiral phase plate (SPP), which introduces a vorticity at the center of the beam characterized by the geometrical parameters of the SPP. One rigorous, intensity-measurement-based, phase retrieval technique, known as the Gerchberg–Saxton algorithm, does not converge to a correct solution because of the presence of a phase singularity in the high-power vortex beam. Here, we introduce a new phase retrieval algorithm that chooses an appropriate initial phase estimate. This technique yields successful vortex charge determination for both low- and high-power vortex beams. The retrieved intensity profiles show 99.51% and 99.27% intensity regeneration at measurement planes with optimized initial phase estimates for the low- and high-power beams, respectively.

Single-shot imaging through scattering medium with a deterministic phase-retrieval algorithm

In this paper, we introduce atmospheric adaptive optics (AO) system architectures that utilize scintillation-resistant wavefront sensors based on iterative phase retrieval (IPR) techniques (described in detail in Part I) for closed-loop mitigation of atmospheric turbulence-induced wavefront aberrations in strong intensity scintillation conditions. The objective is to provide a framework (mathematical and numerical models, performance metrics, control algorithms, and wave-optics modeling and simulation results) for the potential integration of IPR-based wavefront sensing techniques into the following major atmospheric optics system types: directed energy laser beam projection, remote laser power delivery (remote power beaming), and free-space optical communications. Theoretical analysis and numerical simulation results demonstrate that the proposed closed-loop AO system architectures and control algorithms can be uniquely applicable for addressing one of the most challenging AO problems of turbulence effects mitigation in the presence of strong-intensity scintillations.

Phase contrast x-ray imaging techniques have shown the ability to overcome the weakness of the low sensitivity of conventional x-ray imaging. Among them, in-line phase contrast imaging, blessed with simplicity of arrangement, is deemed to be a promising technique in clinical application. To obtain quantitative information from in-line phase contrast images, numerous phase-retrieval techniques have been developed. The theories of these phase-retrieval techniques are mostly proposed on the basis of the ideal detector and the noise-free environment. However, in practice, both detector resolution and system noise would have impacts on the performance of these phase-retrieval methods. To assess the impacts of above-mentioned factors, we include the effects of Gaussian shaped detectors varying in the full width at half maximum (FWHM) and system noise at different levels into numerical simulations. The performance of the phase-retrieval methods under such conditions is evaluated by the root mean square error. The results demonstrate that an increase in the detector FWHM or noise level degrades the effect of phase retrieval, especially for objects in small size.

The holographic twin image problem: a deterministic phase solution