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The differential equation proposed by Frits Zernike to obtain a basis of polynomial orthogonal solutions on the the unit disk to classify wavefront aberrations in circular pupils, is shown to have a set of new orthonormal solution bases,…
To directly image Earth-like planets, contrast levels of 10^-8 - 10^-10 are required. The next generation of instruments will need wavefront control below the nanometer level to achieve these goals. The Zernike wavefront sensor (ZWFS) is a…
Manipulating underwater pressure waves is crucial for marine exploration, as electromagnetic signals are strongly absorbed in water. However, the multi-path phenomenon complicates the accurate capture of acoustic waves by receivers.…
In this paper we present an error analysis for polarimetric data obtained with dual-beam instruments. After recalling the basic concepts, we introduce the analytical expressions for the uncertainties of polarization degree and angle. These…
We revisit one class of z-invariant WaveFront sensor where the LGS is fired aside of the telescope aperture. In this way there is a spatial dependence on the focal plane with respect to the height where the resonant scattering occurs. We…
The next generation of large ground- and space-based optical telescopes will have segmented primary mirrors. Co-phasing the segments requires a sensitive wavefront sensor capable of measuring phase discontinuities. The Zernike wavefront…
This paper describes a package for analytical ray tracing of relatively simple optical systems. AESOP (An Extensible Symbolic Optics Package) enables analysis of the effects of small optical element misalignments or other perturbations. (It…
Strong turbulence conditions create amplitude aberrations through the effects of near-field diffraction. When integrated over long optical path lengths, amplitude aberrations (seen as scintillation) can nullify local areas in the recorded…
It is shown that an aberrated wavefront incident upon a Fabry-Perot optical cavity excites higher order spatial modes in the cavity, and that the spectral width and distribution of these modes is indicative of the type and magnitude of the…
One of the bottlenecks that limit the transition of transformation-optics devices from concepts to practical use is the non-unit magnetic permeability generally required from a mathematical transformation. Simple renormalization of…
Dark wavefront sensing takes shape following quantum mechanics concepts in which one is able to "see" an object in one path of a two-arm interferometer using an as low as desired amount of light actually "hitting" the occulting object. A…
Context. Adaptive optics (AO) is now a tool commonly deployed in astronomy. The real time correction of the atmospheric turbulence that AO enables allows telescopes to perform close to the diffraction limit at the core of their point spread…
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…
Astronomical adaptive optics systems with open-loop deformable mirror control have recently come on-line. In these systems, the deformable mirror surface is not included in the wavefront sensor paths, and so changes made to the deformable…
We present several nonlinear wavefront sensing techniques for few-mode sensors, all of which are empirically calibrated and agnostic to the choice of wavefront sensor. The first class of techniques involves a straightforward extension of…
Wave-front sensing from focal plane multiple images is a promising technique for high-contrast imaging systems. However, the wave-front error of an optics system can be properly reconstructed only when it is very small. This paper presents…
Statistical modeling of high-dimensional matrix-valued data motivates the use of a low-rank representation that simultaneously summarizes key characteristics of the data and enables dimension reduction. Low-rank representations commonly…
Direct imaging of exoplanets requires very high contrast levels, which are obtained using coronagraphs. But residual quasi-static aberrations create speckles in the focal plane downstream of the coronagraph which mask the planet. This…
The interaction between free electrons and optical near fields is attracting increasing attention as a way to manipulate the electron wave function in space, time, and energy. Relying on currently attainable experimental capabilities, we…
Interferometry is one of the central organizing principles of optics. Key to interferometry is the concept of optical delay, which facilitates spectral analysis in terms of time-harmonics. In contrast, when analyzing a beam in a Hilbert…