Related papers: Gabor-Type Holography Solved Analytically for Comp…
Explicit solutions of differential equations of complex fractional orders with respect to functions and with continuous variable coefficients are established. The representations of solutions are given in terms of some convergent infinite…
In this work we study arbitrary-order hybrid discretizations of Friedrichs systems. Friedrichs systems provide a framework that goes beyond the standard classification of partial differential equations into hyperbolic or elliptic, and are…
The enhanced-NA Fresnel hologram reconstructs a holographic image at a viewing angle larger than the diffraction angle of a hologram pixel. The image space is limited by the bandwidth of a digital hologram. In this study, we investigate the…
Diffraction limit is manifested in the loss of high spatial frequency information that results from decay of evanescent waves. As a result, conventional far-field optics yields no information about an object's subwavelength features. Here…
Zernike polynomials are widely used to describe the wavefront phase as they are well suited to the circular geometry of various optical apertures. Non-conventional optical systems, such as future large optical telescopes with highly…
The expansion of viewing angle is a crucial factor in holographic displays implemented with a spatial light modulator having a finite space-bandwidth. The enhanced-NA Fresnel hologram reconstructs a holographic image at an angle larger than…
We propose differential holography as a method to overcome the long-standing forward-scattering problem in photoelectron holography and related techniques for the three-dimensional imaging of atoms. Atomic images reconstructed from…
In recent work [P. Grohs and M. Rathmair. Stable Gabor Phase Retrieval and Spectral Clustering. Communications on Pure and Applied Mathematics (2018)] the instabilities of the Gabor phase retrieval problem, i.e., the problem of…
We present an original heterodyne holography method for digital holography that relies on two-dimensional heterodyne detection to record the phase and the amplitude of a f ield. The technique has been tested on objects as much as 13 mm in…
The survey is devoted to numerical solution of the fractional equation $A^\alpha u=f$, $0 < \alpha <1$, where $A$ is a symmetric positive definite operator corresponding to a second order elliptic boundary value problem in a bounded domain…
The viewing-angle enlargement of a holographic image is a crucial factor for realizing the holographic display. The numerical aperture (NA) of digital hologram other than a pixel specification has been known to determine the angular field…
Solving Algebra Problems with Geometry Diagrams (APGDs) is still a challenging problem because diagram processing is not studied as intensively as language processing. To work against this challenge, this paper proposes a hologram reasoning…
In this paper, we study quantitative spatial analytic bounds and unique continuation inequalities of solutions for fractional heat equations with an analytic lower order term on the whole space. At first, we show that the solution has a…
This paper presents a "reinvention" of Gabor Holography that does not suffer optically from the inherent twin-image problem originating back to Gabor's original Nobel Prize awarded invention. In-line or on-axis holography was ironically…
In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary…
We present a novel algorithm for generating high quality holograms for Computer Generated Holography - Holographic Predictive Search. This approach is presented as an alternative to traditional Holographic Search Algorithms such as Direct…
We analyze the inverse problem to reconstruct the shape of a three dimensional homogeneous dielectric obstacle from the knowledge of noisy far field data. The forward problem is solved by a system of second kind boundary integral equations.…
Ultrathin flat meta-optics have shown great promise for holography in recent years. However, most of the reported meta-optical holograms rely on only phase modulation and neglect the amplitude information. Modulation of both amplitude and…
This paper is devoted to the efficient numerical solution of the Helmholtz equation in a two- or three-dimensional rectangular domain with an absorbing boundary condition (ABC). The Helmholtz problem is discretized by standard bilinear and…
We performed an extensive numerical analysis of the Holstein model. Combining variational Lanczos diagonalisation, density matrix renormalisation group, kernel polynomial expansion, and cluster perturbation theory techniques we solved for…