Reduction of the stagnation effect by combined iterative and deterministic single beam phase retrieval techniques

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 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.

Coherent x-ray scattering in a grazing-incidence geometry was used to image SiGe nanoislands grown by liquid phase epitaxy on Si(001). Due to their narrow size distribution, identical shape, and orientation, the total scattered intensity obtained in this geometry represents a coherent diffraction pattern from an average island. Iterative phase retrieval techniques were used for the reconstruction of the projected electron density of hundred nanometer size islands. So far other x-ray imaging methods do not achieve the obtained spatial resolution of 10--15 nm for islands of this size.

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.

The holographic twin image problem: a deterministic phase solution

Phase retrieval by amplitude modulation using digital micromirror device

The imaging quality of in-line digital holography is challenged by the twin-image and aliasing effects because sensors only respond to intensity and pixels are of finite size. As a result, phase retrieval and pixel superresolution techniques serve as the two essential ingredients for high-fidelity holographic imaging. In this work, we combine the two within a unified algorithmic framework. Pixel super-resolution phase retrieval is recast as an optimization problem and is solved via gradient descent-based algorithms. Regularization techniques and Nesterov’s momentum are introduced to further speed up data acquisition and iterative reconstruction. The proposed algorithms are verified through a proof-of-concept lensless on-chip microscope. We demonstrate experimentally the capability of pixel super-resolution phase retrieval techniques in revealing the subpixel and quantitative phase information of complex biological samples.

Deterministic phase retrieval is reinterpreted in terms of phase-space optics. A novel derivation of the transport-of-intensity equation is presented based on the Wigner distribution function and the ambiguity function. The phase retrieval problem is formulated as estimating the local first-order moment of the Wigner function from intensity information. A comparison with phase-space tomography suggests a generalization of deterministic phase retrieval that provides larger flexibility for signal recovery. In addition, one particular numerical implementation of generalized deterministic phase retrieval is presented. Simulated intensity data are used to validate the method.

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.

In this paper, the problem of the joint estimation of the range and azimuth of multiple targets in a multiple-input multiple-output stepped-frequency continuous wave radar system is investigated. Three deterministic algorithms solving it through an iterative beam cancellation procedure are described; moreover, an iterative technique, based on the expectation-maximization algorithm, is developed with the aim of refining their estimates. The accuracy achieved by all the considered algorithms is assessed on the basis of the raw data acquired from a low power wideband radar device. Our results evidence that these algorithms achieve similar accuracies, but at the price of different computational efforts.

Large field of view multispectral imaging through scattering medium is a fundamental quest in optics community. It has gained special attention from researchers in recent years for its wide range of potential applications. However, the main bottlenecks of the current imaging systems are the requirements on specific illumination, poor image quality and limited field of view. In this work, we demonstrated a single-shot high-resolution colour-imaging through scattering media using a monochromatic camera. This novel imaging technique is enabled by the spatial, spectral decorrelation property and the optical memory effect of the scattering media. Moreover the use of deconvolution image processing further annihilate above-mentioned drawbacks arise due iterative refocusing, scanning or phase retrieval procedures.

A more general technique termed frequency-shifting (FS) is proposed, based on which the behavior of periodicity is eliminated and absolute phase can be retrieved pixel-wisely without any phase unwrapping.

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.

Broadband phase retrieval needed when: a) Narrow spectral filters are unavailable. b) Dim sources. c) Low throughput due to misalignment. d) Short exposures times. i.e., Pointing instability (space); and Atmospheric instability (ground based AO). Traditional approach is computationally burdensome for extreme bandwidths. Approximate approach: a) Substitute monochromatic model. b) Blur model and data. Test case performance: a) approx.270x reduction in computational cost for FGS-like test case. b) Good accuracy for monolithic system. c) Acceptable accuracy for segmented systems. i.e., Reduced by diffraction and Reduced by higher order segment model.

Phase-space tomography and related deterministic phase retrieval methods are investigated in the context of coherent self-imaging. The periodicity of the complex signal is used to establish relationships for accurate and unique signal recovery.