Robust phase-unwrapping method for phase images with high noise content

Automated phase unwrapping in digital holography with deep learning

Digital holography can provide quantitative phase images related to the morphology and content of biological samples. After the numerical image reconstruction, the phase values are limited between -π and π; thus, discontinuity may occur due to the modulo 2π operation. We propose a new deep learning model that can automatically reconstruct unwrapped focused-phase images by combining digital holography and a Pix2Pix generative adversarial network (GAN) for image-to-image translation. Compared with numerical phase unwrapping methods, the proposed GAN model overcomes the difficulty of accurate phase unwrapping due to abrupt phase changes and can perform phase unwrapping at a twice faster rate. We show that the proposed model can generalize well to different types of cell images and has high performance compared to recent U-net models. The proposed method can be useful in observing the morphology and movement of biological cells in real-time applications.

Two-dimensional phase unwrapping to help characterize an electromagnetic beam for quasi-optical mode converter design

An improved two-dimensional phase unwrapping procedure is discussed that uses a weighted least-squares algorithm, a congruence operation, and a filter to unwrap the phase distribution of an electromagnetic beam. These improvements make possible several advances for mirror designs used in gyrotron quasi-optical mode converters. The improved phase unwrapping procedure is demonstrated by applying it to a measured beam and a simulated beam that are used to design mirrors. The unwrapping procedure produces a smooth unwrapped phase that does not change the characteristics of the beam. The smooth unwrapped phase distribution is also used to find an estimate for the wavenumber vector distribution that is needed to design the mirrors.

Phase-unwrapping algorithm for images with high noise content based on a local histogram

We present a robust algorithm of phase unwrapping that was designed for use on phase images with high noise content. We proceed with the algorithm by first identifying regions with continuous phase values placed between fringe boundaries in an image and then phase shifting the regions with respect to one another by multiples of 2pi to unwrap the phase. Image pixels are segmented between interfringe and fringe boundary areas by use of a local histogram of a wrapped phase. The algorithm has been used successfully to unwrap phase images generated in a three-dimensional shape measurement for noninvasive quantification of human skin structure in dermatology, cosmetology, and plastic surgery.

Bayesian neural-networks-based evaluation of binary speckle data

We present a new method using Bayesian probability theory and neural networks for the evaluation of speckle interference patterns for an automated analysis of deformation and erosion measurements. The method is applied to the fringe pattern reconstruction of speckle measurements with a Twyman-Green interferometer. Given a binary speckle image, the method returns the fringe pattern without noise, thus removing the need for smoothing and allowing a straightforward unwrapping procedure and determination of the surface shape. Because no parameters have to be adjusted, the method is especially suited for continuous and automated monitoring of surface changes.

Robust, fast, and effective two-dimensional automatic phase unwrapping algorithm based on image decomposition

We describe what is to our knowledge a novel approach to phase unwrapping. Using the principle of unwrapping following areas with similar phase values (homogenous areas), the algorithm reacts satisfactorily to random noise and breaks in the wrap distributions. Execution times for a 512 x 512 pixel phase distribution are in the order of a half second on a desktop computer. The precise value depends upon the particular image under analysis. Two inherent parameters allow tuning of the algorithm to images of different quality and nature.

Fast two-dimensional phase-unwrapping algorithm based on sorting by reliability following a noncontinuous path

We describe what is to our knowledge a novel technique for phase unwrapping. Several algorithms based on unwrapping the most-reliable pixels first have been proposed. These were restricted to continuous paths and were subject to difficulties in defining a starting pixel. The technique described here uses a different type of reliability function and does not follow a continuous path to perform the unwrapping operation. The technique is explained in detail and illustrated with a number of examples.

Noise-residue filtering of interferometric phase images

The effect of noise-induced phase inconsistency on interferometric phase information content is studied. Phase inconsistencies, or residues, hinder a correct unwrapping of the phase signal. The probability of noise-induced phase inconsistencies is obtained as a function of the signal-to-noise ratio. Moreover, a two-dimensional noise-residue filter, intended to be applied as a preprocessing step before phase unwrapping, is proposed. The method is based on the observation that the noise creates adjacent phase inconsistencies mainly in interferometric phase images. A local analysis leads to a set of rules to be applied to reduce noise-induced phase inconsistencies. The filter performances are tested on noisy synthetic and real phase data.

Unwrapping of Digital Speckle-Pattern Interferometry Phase Maps by use of a Minimum L(0)-Norm Algorithm

The performance of a minimum L(0)-norm unwrapping algorithm is investigated by use of synthetic digital speckle-pattern interferometry (DSPI) wrapped phase maps that simulate experimentally obtained data. This algorithm estimates its own weights to mask inconsistent pixels. Particular features usually included in DSPI wrapped phase distributions, such as shears, speckle noise, fringe cuts, object physical limits, and superimposed phase maps, are analyzed. Some adequate approaches to solving these features are discussed. Finally, it is shown that a complex case in which shears and fringe cuts coexist in the wrapped phase cannot be solved satisfactorily with the minimum L(0)-norm algorithm by itself. To cope with this problem, we propose a new scheme.

Large deformation mechanical testing of biological membranes using speckle interferometry in transmission. I: Experimental apparatus

This paper describes an apparatus designed to study large mechanical deformations in biological membranes. The task of mechanically characterizing biological membranes is challenging because of the anisotropic and nonlinear nature of their material properties. The apparatus described here is well suited to the task because it uses speckle interferometry to measure in-plane displacements in a distributed fashion and has multiple degrees of freedom in the applied stress mechanism. In this way few a priori assumptions or restrictions are imposed on the applied stress and strain fields. The interferometer operates in transmission mode to increase the light efficiency of the system since the sample biological membranes are translucent and reflect little light. The experimental results confirm that the strain fields in the biological membranes that are generated in the experiments are highly nonuniform and cannot be properly estimated from a small number of point measurements.

Large deformation mechanical testing of biological membranes using speckle interferometry in transmission. II: Finite element modeling

In holography and speckle interferometry the measurement range is generally limited by the greatest number of fringes that can be resolved in a single image. As a result these techniques have been generally confined to small displacement measurement applications. In the case of out-of-plane measurements one can overcome this limitation by simply adding incremental measurements at individual detector pixels. In the case of in-plane measurements, however, summing incremental measurements is not a straightforward procedure since the interference pattern moves laterally across the detector as the material deforms. We describe a modeling technique based on finite elements which solves this problem. In combination with a full field method such as holography or speckle interferometry, it provides a very sensitive measurement technique with dense spatial sampling and large dynamic range. Experimental results of speckle interferometry operating in transmission to measure in-plane displacements of biological membranes are presented, where total material displacements are of the order of millimeters. The results also demonstrate how the finite strain tensor is calculated analytically from the data at any point on the material.