Related papers: Implementing non-scalar diffraction in Fourier opt…
Extending super-resolution imaging techniques to objects hidden in strongly scattering media potentially revolutionize the technical analysis for much broader categories of samples, such as biological tissues. The main challenge is the…
Control of light through a microscope objective with a high numerical aperture is a common requirement in applications such as optogenetics, adaptive optics, or laser processing. Light propagation, including polarization effects, can be…
In this paper, we study the mathematical imaging problem of optical diffraction tomography (ODT) for the scenario of a microscopic rigid particle rotating in a trap created, for instance, by acoustic or optical forces. Under the influence…
Fluorescence recovery after photobleaching (FRAP) measurements offer an important tool for analyzing diffusion and binding processes. Confocal scanning laser microscopes that are used in FRAP experiments bleach regions with a radially…
In order to efficiently image a non-absorbing sample (a phase object), dedicated phase contrast optics are required. Typically, these optics are designed with the assumption that the sample is weakly scattering, implying a linear relation…
While scattered light conveys most of the information we perceive, scattering may also distort that information before it reaches our detectors. The problem is acute in many applications, such as in high-resolution microscopy of biological…
We revisit the Fourier transform of a Hankel function, of considerable importance in the theory of knife edge diffraction. Our approach is based directly upon the underlying Bessel equation, which admits manipulation into an alternate…
The purpose of this paper is to investigate the scattering by a nonlinear crystal whose depth is about the wavelength of the impinging field. More precisely, an infinite nonlinear slab is illuminated by an incident field which is the sum of…
On-invasive optical imaging techniques are essential diagnostic tools in many fields. Although various recent methods have been proposed to utilize and control light in multiple scattering media, non-invasive optical imaging through and…
Fourier-based optical computing operations, such as spatial differentiation, have recently been realized in compact form factors using flat optics. Experimental demonstrations, however, have been limited to coherent light requiring laser…
The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data…
A two-dimensional (2D) mathematical model of quadratically distorted (QD) grating is established with the principles of Fraunhofer diffraction and Fourier optics. Discrete sampling and bisection algorithm are applied for finding numerical…
Nonlinear computation is essential for various information processing tasks. Optical implementations are attractive because passive light propagation can manipulate high-dimensional signals with extreme throughput and parallelism; yet…
Spectral methods for solving partial differential equations (PDEs) and stochastic partial differential equations (SPDEs) often use Fourier or polynomial spectral expansions on either uniform and non-uniform grids. However, while very widely…
X-ray Bragg coherent diffraction imaging has been demonstrated as a powerful three-dimensional (3D) microscopy approach for the investigation of sub-micrometer-scale crystalline particles. It is based on the measurement of a series of…
Accurately estimating the point spread function (PSF) of an optical system requires solving free-space wave propagation, which entails evaluating a diffraction integral. This integral is traditionally computed numerically using Fast Fourier…
I propose a superoscillation measurement method for subdiffraction incoherent optical sources, with potential applications in astronomy, remote sensing, fluorescence microscopy, and spectroscopy. The proposal, based on coherent optical…
A simple method for presenting a dynamic transition between Fresnel and Fraunhofer diffraction zones is considered. Experiments are conducted on different apertures and diffraction patterns are photographed at various distances between the…
A nonlinear algebraic equation system of 5 variables is numerically solved, which is derived from the application of the Fourier transform to a differential equation system that allows modeling the behavior of the temperatures and the…
In conventional diffraction theory, a subwavelength period is considered a prerequisite to achieve interesting resonance-assisted physical phenomena, such as bound states in the continuum and diverse zero-order spectral responses with…