A fast-converging iterative method based on weighted feedback for multi-distance phase retrieval

Adaptive constraints by morphological operations for single-shot digital holography

Digital holography provides access to quantitative measurement of the entire complex field, which is indispensable for the investigation of wave-matter interactions. The emerging iterative phase retrieval approach enables to solve the inverse imaging problem only from the given intensity measurements and physical constraints. However, enforcing imprecise constraints limits the reconstruction accuracy and convergence speed. Here, we propose an advanced iterative phase retrieval framework for single-shot in-line digital holography that incorporates adaptive constraints, which achieves optimized convergence behavior, high-fidelity and twin-image-free reconstruction. In conjunction with morphological operations which can extract the object structure while eliminating the irrelevant part such as artifacts and noise, adaptive constraints allow the support region to be accurately estimated and automatically updated at each iteration. Numerical reconstruction of complex-valued objects and the capability of noise immunity are investigated. The improved reconstruction performance of this approach is experimentally validated. Such flexible and versatile framework has promising applications in biomedicine, X-ray coherent diffractive imaging and wavefront sensing.

Characterization of surface defects using a phase retrieval technique in a high-power laser system

In the framework of high-power lasers, surface defects on optics can generate strong light intensification and induce damage sites on downstream optics. To evaluate this intensification during high-energy laser shots, a three-step method is proposed. First, a dedicated measurement bench is designed to measure the intensification induced by defects on a wide variety of optics, including amplifier slabs, KDP crystals, mirrors, gratings, and vacuum windows, for propagation distances up to 2000 mm. A multi-resolution single-beam multiple-intensity reconstruction phase retrieval algorithm is then used to reconstruct a model of the defect, in both amplitude and phase, from a set of intensification measurements. Finally, the impact of the modeled defect on downstream optics is evaluated with a simulation of the high-power laser system. This method is experimentally validated through a case study of damage identified on one of the Laser Mégajoule (LMJ) beams, characterized with the method presented in this paper. The long-distance impact on the LMJ beam is estimated by simulation and compared to a direct near-field measurement.

Computing 3D Phase-Type Holograms Based on Deep Learning Method

Computer holography is a technology that use a mathematical model of optical holography to generate digital holograms. It has wide and promising applications in various areas, especially holographic display. However, traditional computational algorithms for generation of phase-type holograms based on iterative optimization have a built-in tradeoff between the calculating speed and accuracy, which severely limits the performance of computational holograms in advanced applications. Recently, several deep learning based computational methods for generating holograms have gained more and more attention. In this paper, a convolutional neural network for generation of multi-plane holograms and its training strategy is proposed using a multi-plane iterative angular spectrum algorithm (ASM). The well-trained network indicates an excellent ability to generate phase-only holograms for multi-plane input images and to reconstruct correct images in the corresponding depth plane. Numerical simulations and optical reconstructions show that the accuracy of this method is almost the same with traditional iterative methods but the computational time decreases dramatically. The result images show a high quality through analysis of the image performance indicators, e.g., peak signal-to-noise ratio (PSNR), structural similarity (SSIM) and contrast ratio. Finally, the effectiveness of the proposed method is verified through experimental investigations.

Holography and Coherent Diffraction Imaging with Low-(30-250 eV) and High-(80-300 keV) Energy Electrons: History, Principles, and Recent Trends

In this paper, we present the theoretical background to electron scattering in an atomic potential and the differences between low- and high-energy electrons interacting with matter. We discuss several interferometric techniques that can be realized with low- and high-energy electrons and which can be applied to the imaging of non-crystalline samples and individual macromolecules, including in-line holography, point projection microscopy, off-axis holography, and coherent diffraction imaging. The advantages of using low- and high-energy electrons for particular experiments are examined, and experimental schemes for holography and coherent diffraction imaging are compared.

Accurate angle estimation based on moment for multirotation computation imaging

In a multirotation computation imaging system, the fidelity of the reconstructed result is limited by the accuracy of the estimated rotation angles. Here, an accurate angle detection method using image moment is proposed to estimate angles of diffraction images. The second moment of a digital image is adopted as the rotational inertia in order to estimate angles of diffraction images. Compared with previous versions based on Radon/Hough transform, it has higher accuracy and is simultaneously time-saving, which is verified in both simulation and experiment. The angle error of moment method is narrowed down within 0.1°, or even less, and it also can perform well in sample diversity or when slightly out of focus.

Iterative phase retrieval for digital holography: tutorial

This paper provides a tutorial of iterative phase retrieval algorithms based on the Gerchberg-Saxton (GS) algorithm applied in digital holography. In addition, a novel GS-based algorithm that allows reconstruction of 3D samples is demonstrated. The GS-based algorithms recover a complex-valued wavefront using wavefront back-and-forth propagation between two planes with constraints superimposed in these two planes. Iterative phase retrieval allows quantitatively correct and twin-image-free reconstructions of object amplitude and phase distributions from its in-line hologram. The present work derives the quantitative criteria on how many holograms are required to reconstruct a complex-valued object distribution, be it a 2D or 3D sample. It is shown that for a sample that can be approximated as a 2D sample, a single-shot in-line hologram is sufficient to reconstruct the absorption and phase distributions of the sample. Previously, the GS-based algorithms have been successfully employed to reconstruct samples that are limited to a 2D plane. However, realistic physical objects always have some finite thickness and therefore are 3D rather than 2D objects. This study demonstrates that 3D samples, including 3D phase objects, can be reconstructed from two or more holograms. It is shown that in principle, two holograms are sufficient to recover the entire wavefront diffracted by a 3D sample distribution. In this method, the reconstruction is performed by applying iterative phase retrieval between the planes where intensity was measured. The recovered complex-valued wavefront is then propagated back to the sample planes, thus reconstructing the 3D distribution of the sample. This method can be applied for 3D samples such as 3D distribution of particles, thick biological samples, and other 3D phase objects. Examples of reconstructions of 3D objects, including phase objects, are provided. Resolution enhancement obtained by iterative extrapolation of holograms is also discussed.

Lensfree on-chip microscopy based on dual-plane phase retrieval

In lensfree on-chip microscopy, the iterative phase retrieval with defocused images easily enables a high-resolution and whole field reconstruction. However, on the reconstruction of the dense sample, conventional methods suffer from the stagnation problem and noise affection under two intensity measurements, which gives rise to a remarkable loss of the image contrast and resolution. Here we propose a novel dual-plane phase retrieval algorithm to perform a stable and versatile lensless reconstruction. A weighted feedback constraint was utilized to speed up the convergence. Then, a gradient descent minimization based on total variation metric was proposed to suppress the noise affection. With these two object constraints, a smoothed but resolution-preserving result can be achieved. Numerical simulations of Gaussian and Poisson noise were given to prove the noise-robustness of our method. The experiments of USAF resolution target, H&E stained pathological slide, and label-free microglia cell demonstrated the superior performance of our approach compared to other state-of-the-art methods.

3D Imaging Based on Depth Measurement Technologies

Three-dimensional (3D) imaging has attracted more and more interest because of its widespread applications, especially in information and life science. These techniques can be broadly divided into two types: ray-based and wavefront-based 3D imaging. Issues such as imaging quality and system complexity of these techniques limit the applications significantly, and therefore many investigations have focused on 3D imaging from depth measurements. This paper presents an overview of 3D imaging from depth measurements, and provides a summary of the connection between the ray-based and wavefront-based 3D imaging techniques.