- Healy, John J.

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# Healy, John J.

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Healy, John J.

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Healy, John J.

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- Publication2D Non-separable Linear Canonical Transform (2D-NS-LCT) based cryptography(2017-04-27)
; ; ; ; ; The 2D non-separable linear canonical transform (2D-NS-LCT) can describe a variety of paraxial optical systems. Digital algorithms to numerically evaluate the 2D-NS-LCTs are not only important in modeling the light field propagations but also of interest in various signal processing based applications, for instance optical encryption. Therefore, in this paper, for the first time, a 2D-NS-LCT based optical Double-random-Phase-Encryption (DRPE) system is proposed which offers encrypting information in multiple degrees of freedom. Compared with the traditional systems, i.e. (i) Fourier transform (FT); (ii) Fresnel transform (FST); (iii) Fractional Fourier transform (FRT); and (iv) Linear Canonical transform (LCT), based DRPE systems, the proposed system is more secure and robust as it encrypts the data with more degrees of freedom with an augmented key-space.417 - PublicationConstraints to solve parallelogram grid problems in 2D non separable linear canonical transform(2017-04-27)
; ; ; ; ; ; The 2D non-separable linear canonical transform (2D-NS-LCT) can model a range of various paraxial optical systems. Digital algorithms to evaluate the 2D-NS-LCTs are important in modeling the light field propagations and also of interest in many digital signal processing applications. In [Zhao 14] we have reported that a given 2D input image with rectangular shape/boundary, in general, results in a parallelogram output sampling grid (generally in an affine coordinates rather than in a Cartesian coordinates) thus limiting the further calculations, e.g. inverse transform. One possible solution is to use the interpolation techniques; however, it reduces the speed and accuracy of the numerical approximations. To alleviate this problem, in this paper, some constraints are derived under which the output samples are located in the Cartesian coordinates. Therefore, no interpolation operation is required and thus the calculation error can be significantly eliminated.286 - PublicationUnitary Algorithm for Nonseparable Linear Canonical Transforms Applied to Iterative Phase RetrievalAbstract:Phase retrieval is an important tool with broad applications in optics. The GerchbergSaxton algorithm has been a workhorse in this area for many years. The algorithm extracts phase information from intensities captured in two planes related by a Fourier transform. The ability to capture the two intensities in domains other than the image and Fourier plains adds flexibility; various authors have extended the algorithm to extract phase from intensities captured in two planes related by other optical transforms, e.g., by free space propagation or a fractional Fourier transform. These generalizations are relatively simple once a unitary discrete transform is available to propagate back and forth between the two measurement planes. In the absence of such a unitary transform, errors accumulate quickly as the algorithm propagates back and forth between the two planes. Unitary transforms are available for many separable systems, but there has been limited work reported on nonseparable systems other than the gyrator transform. In this letter, we simulate a nonseparable system in a unitary way by choosing an advantageous sampling rate related to the system parameters. We demonstrate a simulation of phase retrieval from intensities in the image domain and a second domain related to the image domain by a nonseparable linear canonical transform. This work may permit the use of nonseparable systems in many design problems.
658ScopusÂ© Citations 23 - PublicationThe choice of optical system is critical for the security of double random phase encryption systems(Society of Photo-optical Instrumentation Engineers (SPIE), 2017-06-14)
; ; ; ; ; ; ; The linear canonical transform (LCT) is used in modeling a coherent light field propagation through first-order optical systems. Recently, a generic optical system, known as the Quadratic Phase Encoding System (QPES), for encrypting a two-dimensional (2D) image has been reported. In such systems, two random phase keys and the individual LCT parameters (, , ) serve as secret keys of the cryptosystem. It is important that such encryption systems also satisfies some dynamic security properties. In this work, we therefore examine such systems using two cryptographic evaluation methods, the avalanche effect and bit independence criterion, which indicate the degree of security of the cryptographic algorithms using QPES. We compared our simulation results with the conventional Fourier and the Fresnel transform based DRPE systems. The results show that the LCT based DRPE has an excellent avalanche and bit independence characteristics compared to the conventional Fourier and Fresnel based encryption systems.Keywords: Quadratic Phase Encoding system, linear canonical transform, Double Random Phase Encryption, Avalanche effect and bit independence criterion.478ScopusÂ© Citations 2 - PublicationSparsity based Terahertz reflective off-axis digital holography(Society of Photo-optical Instrumentation Engineers (SPIE), 2017-04-24)
; ; ; ; ; ; ; ; Terahertz radiation lies between the microwave and infrared regions in the electromagnetic spectrum. Emitted frequencies range from 0.1 to 10 THz with corresponding wavelengths ranging from 30 m to 3 mm. In this paper, a continuous-wave Terahertz off-axis digital holographic system is described. A Gaussian fitting method and image normalisation techniques were employed on the recorded hologram to improve the image resolution. A synthesised contrast enhanced hologram is then digitally constructed. Numerical reconstruction is achieved using the angular spectrum method of the filtered off-axis hologram. A sparsity based compression technique is introduced before numerical data reconstruction in order to reduce the dataset required for hologram reconstruction. Results prove that a tiny amount of sparse dataset is sufficient in order to reconstruct the hologram with good image quality.378ScopusÂ© Citations 5