A number of methods have recently been proposed in the literature for the encryption of two-dimensional information by use of optical systems based on the fractional Fourier transform. Typically, these methods require random phase screen keys for decrypting the data, which must be stored at the receiver and must be carefully aligned with the received encrypted data. A new technique based on a random shifting, or jigsaw, algorithm is proposed. This method does not require the use of phase keys. The image is encrypted by juxtaposition of sections of the image in fractional Fourier domains. The new method has been compared with existing methods and shows comparable or superior robustness to blind decryption. Optical implementation is discussed, and the sensitivity of the various encryption keys to blind decryption is examined.

/pdf/optical-image-encryption-by-random-shifting-in-fractional-7mdzyi0wkp.pdf

Optical image encryption by random shifting in fractional Fourier domains

Fractional Fourier transform as a signal processing tool: An overview of recent developments

In this paper we review a number of optical image encryption techniques proposed in the literature inspired by the architecture of the classic optical Double Random Phase Encoding (DRPE) system. The optical DRPE method and its numerical simulation algorithm are first investigated in relation to the sampling considerations at various stages of the system according to the spreading of the input signal in both the space and spatial frequency domains. Then the several well-known optically inspired encryption techniques are examined and categorized into all optical techniques and image scrambling techniques. Each method is numerically implemented and compared with the optical DRPE scheme, in which random phase diffusers (masks) are applied after different transformations. The optical system used for each method is first illustrated and the corresponding unitary numerical algorithm implementation is then investigated in order to retain the properties of the optical counterpart. The simulation results for the sensitivities of the various encryption keys are presented and the robustness of each method is examined. This overview allows the numerical simulations of the corresponding optical encryption systems, and the extra degree of freedom (keys) provided by different techniques that enhance the optical encryption security, to be generally appreciated and briefly compared and contrasted.

A review of optical image encryption techniques

https://www.uv.es/~gpoei/articulos/(1999)_OC_164_fast_algor_for_Fresnel_y_FRT.pdf

Fast algorithms for free-space diffraction patterns calculation

Compressive sensing is a relatively new measurement paradigm which seeks to capture the “essential” aspects of a high-dimensional object using as few measurements as possible. In this work we demonstrate successful application of compressive sensing framework to digital Fresnel holography. It is shown that when applying compressive sensing approach to Fresnel fields a special sampling scheme should be adopted for improved results.

Compressive Fresnel Holography

A numerical algorithm based on a single fast Fourier transform is proposed. Its precision and calculation efficiency show better performance than those of previously published algorithms. It is also shown that if specific conditions are met, the numerical calculations of two successive fractional Fourier transforms produce results that are similar to the analytical solution.

Numerical calculation of fractional Fourier transforms with a single fast-Fourier-transform algorithm

We propose an electro-optic time-lens (EOTL) model based on the coupled-mode theory. The model describes the
propagation of a femtosecond pulse in an electro-optical crystal with parabolic refractive index modulation by a
microwave. The proposed model integrates the second order dispersion approximation ( β 2 ≠ 0) and takes into
consideration the possible mismatch between the microwave phase velocity and the pulse group velocity. The coupled-mode
theory uses the Hermite-Gaussian functions which are the modes of an ideal electro-optic time-lens. The model
characterizes completely the performances of EOTL, including the aberrations, and it establishes the maximum velocity
mismatch for which the pulse profile propagates through the crystal without significant distortion. The theoretical model
is numerically implement considering the propagation of a short pulse in a Litium Niobate time-lens.

Francisco J. Marinho

Papers

Fast algorithms for free-space diffraction patterns calculation

Numerical calculation of fractional Fourier transforms with a single fast-Fourier-transform algorithm

Electro-optic time lens model for femtosecond pulses