i»?The problem of phase retrieval, i.e., the recovery of a function given the magnitude of its Fourier transform, arises in various fields of science and engineering, including electron microscopy, crystallography, astronomy, and optical imaging. Exploring phase retrieval in optical settings, specifically when the light originates from a laser, is natural since optical detection devices [e.g., charge-coupled device (CCD) cameras, photosensitive films, and the human eye] cannot measure the phase of a light wave. This is because, generally, optical measurement devices that rely on converting photons to electrons (current) do not allow for direct recording of the phase: the electromagnetic field oscillates at rates of ~1015âHz, which no electronic measurement device can follow. Indeed, optical measurement/detection systems measure the photon flux, which is proportional to the magnitude squared of the field, not the phase. Consequently, measuring the phase of optical waves (electromagnetic fields oscillating at 1015âHz and higher) involves additional complexity, typically by requiring interference with another known field, in the process of holography.

/pdf/phase-retrieval-with-application-to-optical-imaging-a-4h5glyrutw.pdf

Phase Retrieval with Application to Optical Imaging: A contemporary overview

Phase recovery from intensity-only measurements forms the heart of coherent imaging techniques and holography. In this study, we demonstrate that a neural network can learn to perform phase recovery and holographic image reconstruction after appropriate training. This deep learning-based approach provides an entirely new framework to conduct holographic imaging by rapidly eliminating twin-image and self-interference-related spatial artifacts. This neural network-based method is fast to compute and reconstructs phase and amplitude images of the objects using only one hologram, requiring fewer measurements in addition to being computationally faster. We validated this method by reconstructing the phase and amplitude images of various samples, including blood and Pap smears and tissue sections. These results highlight that challenging problems in imaging science can be overcome through machine learning, providing new avenues to design powerful computational imaging systems.

/pdf/phase-recovery-and-holographic-image-reconstruction-using-1ue2w051g5.pdf

Phase recovery and holographic image reconstruction using deep learning in neural networks

Phase recovery from intensity-only measurements forms the heart of coherent imaging techniques and holography. Here we demonstrate that a neural network can learn to perform phase recovery and holographic image reconstruction after appropriate training. This deep learning-based approach provides an entirely new framework to conduct holographic imaging by rapidly eliminating twin-image and self-interference related spatial artifacts. Compared to existing approaches, this neural network based method is significantly faster to compute, and reconstructs improved phase and amplitude images of the objects using only one hologram, i.e., requires less number of measurements in addition to being computationally faster. We validated this method by reconstructing phase and amplitude images of various samples, including blood and Pap smears, and tissue sections. These results are broadly applicable to any phase recovery problem, and highlight that through machine learning challenging problems in imaging science can be overcome, providing new avenues to design powerful computational imaging systems.

/pdf/phase-recovery-and-holographic-image-reconstruction-using-5clpneh94w.pdf

Phase retrieval from series of images obtained by defocus variation

The theory of deconvolving the microdiffraction data-set available in a scanning transmission electron microscope or, equivalently, the set of all bright- and dark-field images available in a conventional transmission electron microscope to obtain super- resolution micrographs (which are not limited by the transfer function of the objective lens) is developed and described with reference to holography and other phase-retrieval schemes. By the use of a Wigner distribution, influences of the instrument function can be entirely separated from the information pertaining to the specimen. The final solution yields an unambiguous estimate of the complex value of the specimen function at a resolution which in theory is only limited by the electron wavelength. The faithfulness of the image processing is shown to be not seriously affected by specimen thickness or partial coherence in the illuminating beam. The inversion procedure is remarkably noise insensitive, implying that it should result in a robust and practicable experimental technique, though one that will require very large computing facilities.

The theory of super-resolution electron microscopy via Wigner-distribution deconvolution

An evaluation is made of an iterative method for determining the amplitude and phase from the image intensity recorded in optical systems. The method, which requires two images recorded at different lens defocus values, is tested with simulated data subject to error arising from the photographic recording of the image. In the case of error-free data, the solution for the phase distribution appears to be indeterminate to within a constant. The results for photographic noise levels of up to 20% of the maximum image intensity reflect the small effect of error on the calculated phase distribution. The calculation of phase distributions for both symmetric and asymmetric amplitude-phase distributions shows that the use of two images, taken at defocus values differing by about 100 nm in electron optics and about 1 mm in optics (depending on the numerical aperture of the objective lens), may be used to determine the complex object wave-function in both dark-field and bright-field optics.

http://iopscience.iop.org/article/10.1088/0022-3727/6/18/305/pdf

An examination of an iterative method for the solution of the phase problem in optics and electron optics: I. Test calculations

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An examination of an iterative method for the solution of the phase problem in optics and electron optics: I. Test calculations