Propagation based phase retrieval of simulated intensity measurements using artificial neural networks (original) (raw)
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Propagation based phase retrieval using artificial neural networks
arXiv: Image and Video Processing, 2017
Determining the phase of a wave from intensity measurements has many applications in fields such as electron microscopy, visible light optics, and medical imaging. Propagation based phase retrieval, where the phase is obtained from defocused images, has shown significant promise. There are, however, limitations in the accuracy of the retrieved phase arising from such methods. Sources of error include shot noise, image misalignment, and diffraction artifacts. We explore the use of artificial neural networks (ANNs) to improve the accuracy of propagation based phase retrieval algorithms. We employ a phase retrieval algorithm based on the transport-of-intensity equation to obtain the phase from simulated micrographs of procedurally generated specimens. We then train an ANN with pairs of retrieved and exact phases, and use the trained ANN to process a test set of retrieved maps. The total error in the phase is significantly reduced using this method. We also discuss a variety of potentia...
Sensors
Quantitative phase imaging has been of interest to the science and engineering community and has been applied in multiple research fields and applications. Recently, the data-driven approach of artificial intelligence has been utilized in several optical applications, including phase retrieval. However, phase images recovered from artificial intelligence are questionable in their correctness and reliability. Here, we propose a theoretical framework to analyze and quantify the performance of a deep learning-based phase retrieval algorithm for quantitative phase imaging microscopy by comparing recovered phase images to their theoretical phase profile in terms of their correctness. This study has employed both lossless and lossy samples, including uniform plasmonic gold sensors and dielectric layer samples; the plasmonic samples are lossy, whereas the dielectric layers are lossless. The uniform samples enable us to quantify the theoretical phase since they are established and well unde...
Phase imaging with an untrained neural network
Light: Science & Applications, 2020
Most of the neural networks proposed so far for computational imaging (CI) in optics employ a supervised training strategy, and thus need a large training set to optimize their weights and biases. Setting aside the requirements of environmental and system stability during many hours of data acquisition, in many practical applications, it is unlikely to be possible to obtain sufficient numbers of ground-truth images for training. Here, we propose to overcome this limitation by incorporating into a conventional deep neural network a complete physical model that represents the process of image formation. The most significant advantage of the resulting physics-enhanced deep neural network (PhysenNet) is that it can be used without training beforehand, thus eliminating the need for tens of thousands of labeled data. We take single-beam phase imaging as an example for demonstration. We experimentally show that one needs only to feed PhysenNet a single diffraction pattern of a phase object...
Deep learning-based quantitative phase microscopy
Frontiers in Physics, 2023
Quantitative phase microscopy (QPM) is a powerful tool for label-free and noninvasive imaging of transparent specimens. In this paper, we propose a novel QPM approach that utilizes deep learning to reconstruct accurately the phase image of transparent specimens from a defocus bright-field image. A U-net based model is used to learn the mapping relation from the defocus intensity image to the phase distribution of a sample. Both the off-axis hologram and defocused bright-field image are recorded in pair for thousands of virtual samples generated by using a spatial light modulator. After the network is trained with the above data set, the network can fast and accurately reconstruct the phase information through a defocus bright-field intensity image. We envisage that this method will be widely applied in life science and industrial detection.
Optical convolution for quantitative phase retrieval using the transport of intensity equation
Applied Optics, 2017
Propagation-based phase imaging using the transport of intensity equation (TIE) allows rapid, deterministic phase retrieval from defocused images. However, computational solutions to the TIE suffer from significant low-frequency noise artifacts and are unique up to the application of boundary conditions on the phase. We demonstrate that quantitative phase can be imaged directly at the detector for a class of pure-phase samples by appropriately patterning the illumination to solve the TIE through an optical convolution with the source. This can reduce noise artifacts, obviates the need for user-supplied boundary conditions and is demonstrated via simulation and experiment.
On the transport of intensity technique for phase retrieval
Ultramicroscopy, 2004
The Transport of Intensity technique is becoming a viable alternative to electron holography for phase retrieval in Transmission Electron Microscopy. However, several issues are still to be clarified in order to ascertain the applicability of the technique; among them, the controversy regarding its geometrical or wave-optical nature, as related to the phase detection limit. We show here that the Transport of Intensity is a wave-optical technique that works in a special regime of small defocus where the image intensity is linear with the defocus parameter. By a simple analytical example we show that the Transport of Intensity correctly reconstructs the electron optical phase shift even when the phase is smaller than p; a value defining the boundary between the geometrical and wave approaches. Another example is given, the reconstruction of a phase jump, accompanied with experimental support showing that phase retrieval by Electron Holography and Transport of Intensity techniques yields results in good agreement. r
QUANTITATIVE EVALUATION OF PHASE RETRIEVAL ALGORITHMS IN PROPAGATION BASED PHASE TOMOGRAPHY
Phase contrast provides new possibilities in X-ray imaging, offering up to 1000 times higher sensitivity than standard absorption contrast. In propagation based phase contrast imaging, a quantitative relationship exists between intensity in the image plane and the phase shift induced by the object. Inversion of this relationship is called phase retrieval. Used as input to a 3D tomographic reconstruction algorithm this gives a reconstruction of the refractive index. Several methods for phase retrieval have been described, but few quantitative studies have been performed. In this paper we describe three phase retrieval methods, respectively based on the Transport of Intensity Equation (TIE), Contrast Transfer Function (CTF) and a Mixed approach recently developed at the ESRF. The methods are evaluated using simulated and experimental data in the case of mixed absorption and phase objects. Using the TIE on simulated data we obtain a reconstruction with a mean error of 10 %, but fail to achieve a qualitatively acceptable reconstruction of experimental data. The CTF approach yields qualitative reconstructions both using simulated and experimental data. Using the Mixed approach, we obtain reconstructions with close correspondence to expected values with an average errors of 3.8 % for the simulated and 5.9 % for the experimental data.
2014 IEEE International Conference on Image Processing (ICIP), 2014
We present a variational reconstruction algorithm for the phaseretrieval problem by using the differential interference contrast microscopy. Principally, we rely on the transport-of-intensity equation that specifies the sought phase as the solution of a partial differential equation. Our approach is based on an iterative reconstruction algorithm involving the total variation regularisation which is efficiently solved via the alternating direction method of multipliers. We illustrate the applicability of the method via real data experiments. To the best of our knowledge, this work demonstrates the performance of such an iterative algorithm on real data for the first time.
Recursive method for phase retrieval using transport of intensity and its applications
Propagation of optical fields is governed by the Helmholtz equation or the paraxial wave equation. Transport of intensity is a noninterferometric method to find the phase of an object by recording optical intensities at different distances of propagation. The transport of intensity equation results from the imaginary part of the complex paraxial wave equation and is equivalent to the principle of conservation of energy. The real part of the paraxial wave equation yields the Eikonal equation in the presence of diffraction. The amplitude and phase of the optical field must therefore simultaneously satisfy both the real and imaginary parts of the paraxial wave equation during propagation. In this paper, we demonstrate, with illustrative examples, how to exploit this to retrieve the phase through recursive calculations of the phase and intensity. This is achieved using the transport of intensity equation, which is solved using standard techniques, and the real part of the paraxial wave equation, or the transport of phase equation, which is solved using a Gauss–Seidel iterative method. Examples include calculation of the imaged phase induced through self-phase modulation of a focused laser beam in a liquid and the imaged phase of light reflected from a surface, which yields the 3D surface profile.
Lensless Three-Dimensional Quantitative Phase Imaging Using Phase Retrieval Algorithm
Journal of Imaging, 2020
Quantitative phase imaging (QPI) techniques are widely used for the label-free examining of transparent biological samples. QPI techniques can be broadly classified into interference-based and interferenceless methods. The interferometric methods which record the complex amplitude are usually bulky with many optical components and use coherent illumination. The interferenceless approaches which need only the intensity distribution and works using phase retrieval algorithms have gained attention as they require lesser resources, cost, space and can work with incoherent illumination. With rapid developments in computational optical techniques and deep learning, QPI has reached new levels of applications. In this tutorial, we discuss one of the basic optical configurations of a lensless QPI technique based on the phase-retrieval algorithm. Simulative studies on QPI of thin, thick, and greyscale phase objects with assistive pseudo-codes and computational codes in Octave is provided. Bin...