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Register a new userDesigning and using prior knowledge for phase retrieval
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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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Coherent diffraction imaging (CDI) is high-resolution lensless microscopy that has been applied to image a wide range of specimens using synchrotron radiation, X-ray free electron lasers, high harmonic generation, soft X-ray laser and electrons. Despite these rapid advances, it remains a challenge to reconstruct fine features in weakly scattering objects such as biological specimens from noisy data. Here we present an effective iterative algorithm, termed oversampling smoothness (OSS), for phase retrieval of noisy diffraction intensities. OSS exploits the correlation information among the pixels or voxels in the region outside of a support in real space. By properly applying spatial frequency filters to the pixels or voxels outside the support at different stage of the iterative process (i.e. a smoothness constraint), OSS finds a balance between the hybrid input-output (HIO) and error reduction (ER) algorithms to search for a global minimum in solution space, while reducing the oscillations in the reconstruction. Both our numerical simulations with Poisson noise and experimental data from a biological cell indicate that OSS consistently outperforms the HIO, ER-HIO and noise robust (NR)-HIO algorithms at all noise levels in terms of accuracy and consistency of the reconstructions. We expect OSS to find application in the rapidly growing CDI field as well as other disciplines where phase retrieval from noisy Fourier magnitudes is needed.
We present a novel method for Ankylography: three-dimensional structure reconstruction from a single shot diffraction intensity pattern. Our approach allows reconstruction of objects containing many more details than was ever demonstrated, in a faster and more accurate fashion
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 both light optics and electron optics, the amplitude of a wave scattered by an object is an observable that is usually recorded in the form of an intensity distribution in a real space image or a diffraction image. In contrast, retrieval of the phase of a scattered wave is a well-known challenge, which is usually approached by interferometric or numerical methods. In electron microscopy, as a result of constraints in the lens setup, it is particularly difficult to retrieve the phase of a diffraction image. Here, we use a defocused beam generated by a nanofabricated hologram to form a reference wave that can be interfered with a diffracted beam. This setup provides an extended interference region with the sample wavefunction in the Fraunhofer plane. As a case study, we retrieve the phase of an electron vortex beam. Beyond this specific example, the approach can be used to retrieve the wavefronts of diffracted beams from a wide range of samples.
Metasurfaces offer the potential to control light propagation at the nanoscale for applications in both free-space and surface-confined geometries. Existing metasurfaces frequently utilize metallic polaritonic elements with high absorption losses, and/or fixed geometrical designs that serve a single function. Here we overcome these limitations by demonstrating a reconfigurable hyperbolic metasurface comprising of a heterostructure of isotopically enriched hexagonal boron nitride (hBN) in direct contact with the phase-change material (PCM) vanadium dioxide (VO2). Spatially localized metallic and dielectric domains in VO2 change the wavelength of the hyperbolic phonon polaritons (HPhPs) supported in hBN by a factor 1.6 at 1450cm-1. This induces in-plane launching, refraction and reflection of HPhPs in the hBN, proving reconfigurable control of in-plane HPhP propagation at the nanoscale15. These results exemplify a generalizable framework based on combining hyperbolic media and PCMs in order to design optical functionalities such as resonant cavities, beam steering, waveguiding and focusing with nanometric control.
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