A simple and effective method for the analytic description of important optical beams, when truncated by finite apertures

In this paper we present a simple and effective method, based on appropriate superpositions of Bessel-Gauss beams, which in the Fresnel regime is able to describe in analytic form the 3D evolution of important waves as Bessel beams, plane waves, gaussian beams, Bessel-Gauss beams, when truncated by finite apertures. One of the byproducts of our mathematical method is that one can get in few seconds, or minutes, high-precision results which normally require quite long times of numerical simulation. The method works in Electromagnetism (Optics, Microwaves,...), as well as in Acoustics. OCIS codes: (999.9999) Non-diffracting waves; (260.1960) Diffraction theory; (070.7545) Wave propagation; (070.0070) Fourier optics and signal processing; (200.0200) Optics in computing; (050.1120) Apertures; (070.1060) Acousto-optical signal processing; (280.0280) Remote sensing and sensors; (050.1755) Computational electromagnetic methods.Comment: Paper of 21 pages with 13 Figures. Source file in LaTe

Arbitrary shape surface Fresnel diffraction

Fresnel diffraction calculation on an arbitrary shape surface is proposed. This method is capable of calculating Fresnel diffraction from a source surface with an arbitrary shape to a planar destination surface. Although such calculation can be readily calculated by the direct integral of a diffraction calculation, the calculation cost is proportional to $O(N^2)$ in one dimensional or $O(N^4)$ in two dimensional cases, where $N$ is the number of sampling points. However, the calculation cost of the proposed method is $O(N \log N)$ in one dimensional or $O(N^2 \log N)$ in two dimensional cases using non-uniform fast Fourier transform

Single-random phase encoding architecture using a focus tunable lens

We propose a new nonlinear optical architecture based on a focus tunable lens and an iterative phase retrieval algorithm. It constitutes a compact encryption system that uses a single-random phase key to simultaneously encrypt (decrypt) amplitude and phase data. Summarily, the information encoded in a transmittance object (phase and amplitude) is randomly modulated by a diffuser when a laser beam illuminates it; once the beam reaches a focus tunable lens, different subjective speckle distributions are registered at some image plane as the focal length is tuned to different values. This set of speckle patterns constitutes a delocalized ciphertext, which is used in an iterative phase retrieval algorithm to reconstruct a complex ciphertext. The original data are decrypted propagating this ciphertext through a virtual optical system. In this system, amplitude data are straightforwardly decrypted while phase data can only be restored if the random modulation produced in the encryption process is compensated. Thus, an encryption-decryption process and authentication protocol can simultaneously be performed. We validate the feasibility of our proposal with simulated and experimental results.Fil: Mosso Solano, Edward Fabian. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Pontificia Universidad Católica de Valparaíso; ChileFil: Bolognini, Nestor Alberto. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Investigaciones Ópticas. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Centro de Investigaciones Ópticas. Universidad Nacional de La Plata. Centro de Investigaciones Ópticas; ArgentinaFil: Pérez, D.G.. Pontificia Universidad Católica de Valparaíso; Chil

Direct Inversion of Digital 3D Fraunhofer Holography Maps

The Differential Fourier Holography (DFH) gives an exact mathematical solution of the inverse problem of diffraction in the Fraunhofer regime. After the first publication [1] the Differential Fourier Holography was successfully applied in many experiments to obtain amplitude and phase information about two-dimensional (2D) images. In this article we demonstrate numerically the possibility to apply the DFH also for investigation of unknown 3D Objects. The first simulation is made for a double-spiral structure plus a line as a reference object

Computing extinction maps of star nulling interferometers

Herein is discussed the performance of spaceborne nulling interferometers searching for extra-solar planets, in terms of their extinction maps projected on-sky. In particular, it is shown that the designs of Spatial Filtering (SF) and Achromatic Phase Shifter (APS) subsystems, both required to achieve planet detection and characterization, can sensibly affect the nulling maps produced by a simple Bracewell interferometer. Analytical relationships involving cross correlation products are provided and numerical simulations are performed, demonstrating marked differences in the aspect of extinction maps and the values of attained fringes contrasts. It is concluded that depending on their basic principles and designs, FS and APS will result in variable capacities for serendipitous discoveries of planets orbiting around their parent star. The mathematical relationships presented in this paper are assumed to be general, i.e. they should apply to other types of multi-apertures nulling interferometers.Comment: 10 pages, 5 figure

Compensation for the setup instability in ptychographic imaging

The high-frequency vibration of the imaging system degrades the quality of the reconstruction of ptychography by acting as a low-pass filter on ideal diffraction patterns. In this study, we demonstrate that by subtracting the deliberately blurred diffraction patterns from the recorded patterns and adding the properly amplified subtraction to the original data, the high-frequency components lost by the vibration of the setup can be recovered, and thus the image quality can be distinctly improved. Because no prior knowledge regarding the vibrating properties of the imaging system is needed, the proposed method is general and simple and has applications in several research fields.Comment: 13pages, 10figure