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Image distortion due to weak gravitational lensing is examined using a non-perturbative method of integrating the geodesic deviation and optical scalar equations along the null geodesics connecting the observer to a distant source. The…
Microwave imaging is commonly based on the solution of linearized inverse scattering problems by matched filtering algorithms, i.e., by applying the adjoint of the forward scattering operator to the observation data. A more rigorous…
In some super-resolution techniques, adjacent points are illuminated at different times. Thereby, their locations and light intensities can be detected even if the images are very blurred due to diffraction. According to conventional…
Coherent diffraction imaging is a high-resolution imaging technique whose potential can be greatly enhanced by applying the extrapolation method presented here. We demonstrate enhancement in resolution of a non-periodical object…
Off-axis parabolic mirrors (OAPs) are occasionally desirable for specialized applications, but are known to introduce field-dependent astigmatic aberrations. In an experiment where optical tweezers are formed by OAPs, another OAP is added…
The Calder\'on problem consists in recovering an unknown coefficient of a partial differential equation from boundary measurements of its solution. These measurements give rise to a highly nonlinear forward operator. As a consequence, the…
Fundamental wave features of light play an important role in the realization of superresolution for two spatially separated point sources. It has been shown that (partial) coherence, which is an inevitable feature in practical light…
We present a physical-optics based theory of the physical mechanism for aberration of starlight. We apply non-relativistic and relativistic theories for wavefront image formation and include the effects of optically transmitting media…
Fourier imaging is an indirect imaging method which records the diffraction pattern of the object scene coherently in the focal plane of the imaging system and reconstructs the image using computational resources. The spatial resolution,…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
Ptychography has become prominent at synchrotron facilities worldwide for characterizing biological and material specimens' topological structures and properties at the nanometer or atomic scale, due to its lens - less, highly quantitative…
We consider the problem of direction finding using partly calibrated arrays, a distributed subarray with position errors between subarrays. The key challenge is to enhance angular resolution in the presence of position errors. To achieve…
Matrix sensing problems exhibit pervasive non-convexity, plaguing optimization with a proliferation of suboptimal spurious solutions. Avoiding convergence to these critical points poses a major challenge. This work provides new theoretical…
Quantum imaging with spatially entangled photons offers advantages such as enhanced spatial resolution, robustness against noise, and counter-intuitive phenomena, while a biphoton spatial aberration generally degrades its performance.…
We obtain existence and convergence theorems on two variants of the proximal point algorithm for proper lower semicontinuous convex functions in complete geodesic spaces with curvature bounded above.
Optical resolution photoacoustic microscopy (OR-PAM) leverages optical focusing and acoustic detection for microscopic optical absorption imaging. Intrinsically it owns high optical lateral resolution and poor acoustic axial resolution.…
We consider a large class of optical cavities and gain media with an off-axis external feedback which introduces a two-point nonlocality. This nonlocality moves the lasing threshold and opens large windows of control parameters where weak…
We study an inverse problem for the wave equation where localized wave sources in random scattering media are to be determined from time resolved measurements of the waves at an array of receivers. The sources are far from the array, so the…
We investigate the techniques and ideas used in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM…
The nonlinear curvature wavefront sensor (nlCWFS) uses multiple (typically four) out-of-focus images to reconstruct the phase and amplitude of a propagating light beam. Because these images are located between the pupil and focal planes,…