High Precision Single Beam Phase Retrieval Techniques

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.

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.

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.

Phase retrieval imaging is widely significant in the scientific, optical engineering, and medical fields. The transport of intensity equation (TIE) has been extensively applied to phase retrieval imaging. In this paper, we investigate a technique for phase retrieval based on the TIE and TPE equations employing electro-optic materials such as liquid crystals to create optical path length difference through application of a bias voltage across the cell.

Phase retrieval by amplitude modulation using digital micromirror device

Transport of Intensity equation(TIE) is a non-interferometric method used for quantitative phase imaging. By reformulating the TIE using Contrast Transfer Function, it can be determined that the spatial resolution of the phase retrieved using TIE is limited by the product of imaging system transfer function and a sinc function. In this work, we apply the principles of structured illumination fluorescent microscopy to develop a TIE based super resolved phase imaging technique. The sinusoidal intensity pattern down modulates high frequency spectrum of the phase into the system pass band thereby providing a convenient approach to synthetically enlarge the numerical aperture of the system. Resolution enhancement by two folds is demonstrated using simulations.

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.

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-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.

Computational approaches in 3D quantitative phase Imaging: Current and future trends in cellular imaging.

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.

Gaussian process (GP) regression is a nonparametric regression method that can be used to predict continuous quantities. Here, we show that the same technique can be applied to a class of phase imaging techniques based on measurements of intensity at multiple propagation distances, i.e. the transport of intensity equation (TIE). In this paper, we demonstrate how to apply GP regression to estimate the first intensity derivative along the direction of propagation and incorporate non-uniform propagation distance sampling. The low-frequency artifacts that often occur in phase recovery using traditional methods can be significantly suppressed by the proposed GP TIE method. The method is shown to be stable with moderate amounts of Gaussian noise. We validate the method experimentally by recovering the phase of human cheek cells in a bright field microscope and show better performance as compared to other TIE reconstruction methods.

The transport of intensity equation (TIE) has been widely applied to phase imaging. A variety of methods for solving the TIE have been proposed. One of the most popular methods is an FFT-based method, which is simple and fast. However, this method has a strict restriction that the intensity of the object is assumed to be uniform. Otherwise, the accuracy of phase retrieval results may drop significantly. The transport of phase equation (TPE) is an equation coupled with the TIE, and both are derived from the Helmholtz equation. Few works have studied the role of the TPE in 3D imaging. In this work, a non-iterative FFT-based TIE with TPE correction is proposed. The phases at the object plane and four defocused planes are first calculated by the TIE. Ideally, the object intensity and computed phases are supposed to satisfy both the TIE and TPE. But the non-uniformity of object intensity, as well as the use of finite differences of intensities in the calculation of longitudinal derivatives for the FFT-based TIE method, introduce errors in phase retrieval result. We show that by using the TPE, the local refractive index during propagation can be updated and used as a correction in the TIE. The TIE is solved once again using the updated refractive index, and shows reduction of errors. This proposed technique can be extended to amplitude and phase imaging. It also offers the advantage of yielding the unwrapped phase with good accuracy performance and can be potentially applied to medical high-definition 3D imaging, for cells, micro bubbles, etc.

The goal of phase retrieval is to extract the phase of an optical wave field from intensity measurements. The transport-of-intensity equation (TIE)-based method is a popular deterministic solution and has been applied in various fields such as optical microscopy, electron microscopy, and x-ray imaging. For macro-imaging, a camera is often used to capture the images, and thus the phase modulation of the lens should be considered. A new formulation is proposed to extend TIE for phase retrieval in a lens-based wave propagation model. To obtain the defocus step, a data-collection-reading device is designed by equipping a camera with a micrometer caliper. Simulation and real experiments are conducted to test the proposed method.

The transport of intensity equation (TIE) is a two-dimensional second order elliptic partial differential equation that must be solved under appropriate boundary conditions. However, the boundary conditions are difficult to obtain in practice. The fast Fourier transform (FFT) based TIE solutions are widely adopted for its speed and simplicity. However, it implies periodic boundary conditions, which lead to significant boundary artifacts when the imposed assumption is violated. In this work, TIE phase retrieval is considered as an inhomogeneous Neumann boundary value problem with the boundary values experimentally measurable around a hard-edged aperture, without any assumption or prior knowledge about the test object and the setup. The analytic integral solution via Green's function is given, as well as a fast numerical implementation for a rectangular region using the discrete cosine transform. This approach is applicable for the case of non-uniform intensity distribution with no extra effort to extract the boundary values from the intensity derivative signals. Its efficiency and robustness have been verified by several numerical simulations even when the objects are complex and the intensity measurements are noisy. This method promises to be an effective fast TIE solver for quantitative phase imaging applications.