Related papers: Kernel Phase and Kernel Amplitude in Fizeau Imagin…
Calibration of radio interferometric observations becomes increasingly difficult towards lower frequencies. Below ~300 MHz, spatially variant refractions and propagation delays of radio waves traveling through the ionosphere cause phase…
While characterization of coherent wavefields is essential to laser, x-ray and electron imaging, sensors measure the squared magnitude of the field, rather than the field itself. Holography or phase retrieval must be used to characterize…
A new type of an optical interferometer is discussed the phase difference between the interfering beams in which is substantially wavelength dependent. It is shown that the function measured with this device is an integral transform of the…
We generalize the technique of fringe-rate filtering, whereby visibilities measured by a radio interferometer are re-weighted according to their temporal variation. As the Earth rotates, radio sources traverse through an interferometer's…
We have designed a plenoptic sensor to retrieve phase and amplitude changes resulting from a laser beam's propagation through atmospheric turbulence. Compared with the commonly restricted domain of (-pi, pi) in phase reconstruction by…
This is the third article in a series of three dealing with the exploitation of speckle for imaging purposes. In complex media, a fundamental limit is the multiple scattering phenomenon that completely blurs the imaging process in depth.…
Achromatic combinations of a diffractive Phase Fresnel Lens and a refractive correcting element have been proposed for X-ray and gamma-ray astronomy and for microlithography, but considerations of absorption often dictate that the…
Quantum interferometry methods exploit quantum resources, such as photonic entanglement, to enhance phase estimation beyond classical limits. Nonlinear optics has served as a workhorse for the generation of entangled photon pairs, ensuring…
Quantitative phase microscopy (QPM), a technique combining phase imaging and microscopy, enables visualization of the 3D topography in reflective samples, as well as the inner structure or refractive index distribution of transparent and…
Optical imaging with microarcsecond resolution will reveal details across and outside stellar surfaces but requires kilometer-scale interferometers, challenging to realize either on the ground or in space. Intensity interferometry,…
Long baseline optical interferometry and aperture synthesis using ground-based telescopes can enable unprecedented angular resolution astronomy in the optical domain. However, atmospheric turbulence leads to large, dynamic phase errors…
Context: Ground-based telescopes are susceptible to seeing, an atmospheric phenomenon that reduces the resolving power of large observatories to that of a home telescope. Compensating these effects is therefore critical to realizing the…
Spherical radial-basis-based kernel interpolation abounds in image sciences including geophysical image reconstruction, climate trends description and image rendering due to its excellent spatial localization property and perfect…
Random feature approximation is arguably one of the most popular techniques to speed up kernel methods in large scale algorithms and provides a theoretical approach to the analysis of deep neural networks. We analyze generalization…
We propose and demonstrate a new phase retrieval method for imaging through random media. Although methods to recover the Fourier amplitude through random distortions are well established, recovery of the Fourier phase has been a more…
We present an application of a quadrature phase interferometer to the measurement of the angular position of a parallel laser beam with interferometric precision. In our experimental realization we reach a resolution of 6.8e-10 rad (1.4e-4…
The search for the optimal shape parameter for Radial Basis Function (RBF) kernel approximation has been an outstanding research problem for decades. In this work, we establish a theoretical framework for this problem by leveraging a…
Panel-based, kernel-split quadrature is currently one of the most efficient methods available for accurate evaluation of singular and nearly singular layer potentials in two dimensions. However, it can fail completely for the layer…
Quantum entanglement and squeezing have significantly improved phase estimation and imaging in interferometric settings beyond the classical limits. However, for a wide class of non-interferometric phase imaging/retrieval methods vastly…
Kernel interpolation is a fundamental technique for approximating functions from scattered data, with a well-understood convergence theory when interpolating elements of a reproducing kernel Hilbert space. Beyond this classical setting,…