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Reconstructing an object solely from its scattered intensity distribution is a common problem that occurs in many applications. Currently, there are no efficient direct methods to reconstruct the object, though in many cases, with some prior knowledge, iterative algorithms result in reasonable reconstructions. Unfortunately, even with advanced computational resources, these algorithms are highly time consuming. Here we present a novel rapid all-optical method based on a digital degenerate cavity laser, whose most probable lasing mode well approximates the object. We present experimental results showing the high speed (<100 ns) and efficiency of our method in agreement with our numerical simulations and analysis. The method is scalable, and can be applicable to any two dimensional object with known compact support, including complex-valued objects.
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Any object on earth has two fundamental properties: it is finite, and it is made of atoms. Structural information about an object can be obtained from diffraction amplitude measurements that account for either one of these traits. Nyquist-sampling of the Fourier amplitudes is sufficient to image single particles of finite size at any resolution. Atomic resolution data is routinely used to image molecules replicated in a crystal structure. Here we report an algorithm that requires neither information, but uses the fact that an image of a natural object is compressible. Intended applications include tomographic diffractive imaging, crystallography, powder diffraction, small angle x-ray scattering and random Fourier amplitude measurements.
In this work we consider the problem of reconstruction of a signal from the magnitude of its Fourier transform, also known as phase retrieval. The problem arises in many areas of astronomy, crystallography, optics, and coherent diffraction imaging (CDI). Our main goal is to develop an efficient reconstruction method based on continuous optimization techniques. Unlike current reconstruction methods, which are based on alternating projections, our approach leads to a much faster and more robust method. However, all previous attempts to employ continuous optimization methods, such as Newton-type algorithms, to the phase retrieval problem failed. In this work we provide an explanation for this failure, and based on this explanation we devise a sufficient condition that allows development of new reconstruction methods---approximately known Fourier phase. We demonstrate that a rough (up to $pi/2$ radians) Fourier phase estimate practically guarantees successful reconstruction by any reasonable method. We also present a new reconstruction method whose reconstruction time is orders of magnitude faster than that of the current method-of-choice in phase retrieval---Hybrid Input-Output (HIO). Moreover, our method is capable of successful reconstruction even in the situations where HIO is known to fail. We also extended our method to other applications: Fourier domain holography, and interferometry. Additionally we developed a new sparsity-based method for sub-wavelength CDI. Using this method we demonstrated experimental resolution exceeding several times the physical limit imposed by the diffraction light properties (so called diffraction limit).
In this work, the SLM-based phase retrieval system will be used to inspect carbon reinforced plastics samples (CFRP) under applying a thermal load. For this purpose, the system is used to capture a sequence of 8 spatially separated recording planes, where the distance between subsequent planes equals 2 mm. For detecting the hidden failures two sets of intensity observations are recorded. The first set for the initial state and the second set is captured after applying the load. To recover the phase information associated with the two states, the captured intensities have been subjected to an iterative algorithm based on the method of generalized projection.
We present a new method for real- and complex-valued image reconstruction from two intensity measurements made in the Fourier plane: the Fourier magnitude of the unknown image, and the intensity of the interference pattern arising from superimposition of the original signal with a reference beam. This approach can provide significant advantages in digital holography since it poses less stringent requirements on the reference beam. In particular, it does not require spatial separation between the sought signal and the reference beam. Moreover, the reference beam need not be known precisely, and in fact, may contain severe errors, without leading to a deterioration in the reconstruction quality. Numerical simulations are presented to demonstrate the speed and quality of reconstruction.
In this work we develop an algorithm for signal reconstruction from the magnitude of its Fourier transform in a situation where some (non-zero) parts of the sought signal are known. Although our method does not assume that the known part comprises the boundary of the sought signal, this is often the case in microscopy: a specimen is placed inside a known mask, which can be thought of as a known light source that surrounds the unknown signal. Therefore, in the past, several algorithms were suggested that solve the phase retrieval problem assuming known boundary values. Unlike our method, these methods do rely on the fact that the known part is on the boundary. Besides the reconstruction method we give an explanation of the phenomena observed in previous work: the reconstruction is much faster when there is more energy concentrated in the known part. Quite surprisingly, this can be explained using our previous results on phase retrieval with approximately known Fourier phase.
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