Related papers: Analytical decomposition of Zernike and hexagonal …
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…
We consider the differential equation that Zernike proposed to classify aberrations of wavefronts in a circular pupil, as if it were a classical Hamiltonian with a non-standard potential. The trajectories turn out to be closed ellipses. We…
Orthogonal moment-based image representations are fundamental in computer vision, but classical methods suffer from high computational complexity and numerical instability at large orders. Zernike and pseudo-Zernike moments, for instance,…
In the recent years a significant progress was achieved in the field of design and fabrication of optical systems based on freeform optical surfaces. They provide a possibility to build fast, wide-angle and high-resolution systems, which…
We report an extensive numerical study and supporting experimental results on the spectral characterization of optical aberrations in macroscopic fluidic lenses with tunable focal distance and aperture shape. Using a Shack-Hartmann…
The focal field properties of radially/azimuthally polarized Zernike polynomials are studied. A method to design the pupil field in order to shape the focal field of radially or azimuthally polarized phase vortex is introduced. With this…
We present the details of predicting atmospheric turbulence by mining Zernike moment data obtained from simulations as well as experiments. Temporally correlated optical wave-fronts were simulated such that they followed Kolmogorov phase…
High contrast imaging (HCI) is fundamentally limited by wavefront aberrations, and the ability to perform wavefront sensing from focal plane images is key to reach the full potential of ground and space-based instruments. Vortex focal plane…
Wavefront aberrations can reflect the imaging quality of high-performance optical systems better than geometric aberrations. Although laser interferometers have emerged as the main tool for measurement of transmitted wavefronts, their…
The partial derivatives and Laplacians of the Zernike circle polynomials occur in various places in the literature on computational optics. In a number of cases, the expansion of these derivatives and Laplacians in the circle polynomials…
The demand for higher resolution telescopes leads to segmented primary mirrors which need to be phased for operation. A phasing sensor applying a wavelength sweep technique provides a large capture range without modulating the position of…
We present a method using Zernike moments for quantifying rotational and reflectional symmetries in scanning transmission electron microscopy (STEM) images, aimed at improving structural analysis of materials at the atomic scale. This…
Optical imaging quality can be severely degraded by system and sample induced aberrations. Existing adaptive optics systems typically rely on iterative search algorithm to correct for aberrations and improve images. This study demonstrates…
Sets of orthogonal basis functions over two-dimensional circular areas--most often representing pupils in optical applications--are known in the literature for the full circle (Zernike or Jacobi polynomials) and the annulus. This work…
Optical aberrations significantly degrade image quality in microscopy, particularly when imaging deeper into samples. These aberrations arise from distortions in the optical wavefront and can be mathematically represented using Zernike…
We present an enhanced version of the Zernike wavefront sensor, that simultaneously measures phase and amplitude aberrations. The 'vector-Zernike' wavefront sensor consists of a patterned liquid-crystal mask, which imposes $\pm \pi/2$ phase…
Due to the massive increase in astronomical images (such as James Webb and Solar Dynamic Observatory), automatic image description is essential for solar and astronomical. Zernike moments (ZMs) are unique due to the orthogonality and…
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,…
A pupil plane wavefront reconstruction procedure is proposed based on analysis of a sequence of focal plane images corresponding to a sequence of random pupil plane phase probes. The developed method provides the unique nontrivial solution…
We present a promising approach to the extremely fast sensing and correction of small wavefront errors in adaptive optics systems. As our algorithm's computational complexity is roughly proportional to the number of actuators, it is…