Now showing 1 - 10 of 15
  • Publication
    2D Non-separable Linear Canonical Transform (2D-NS-LCT) based cryptography
    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.
      546
  • Publication
    Automated Filter Selection for Suppression of Gibbs Ringing Artefacts in MRI
    (Elsevier, 2022-11) ;
    Gibbs ringing creates artefacts in magnetic resonance images that can mislead clinicians. Reconstruction algorithms attempt to suppress Gibbs ringing, or an additional ringing suppression algorithm may be applied post reconstruction. Novel reconstruction algorithms are often compared with filtered Fourier reconstruction, but the choices of filters and filter parameters can be arbitrary and sub-optimal. Evaluation of different reconstruction and post-processing algorithms is difficult to automate or subjective: many metrics have been used in the literature. In this paper, we evaluate twelve of those metrics and demonstrate that none of them are fit for purpose. We propose a novel metric and demonstrate its efficacy in 1D and 2D simulations. We use our new metric to optimise and compare 17 smoothing filters for suppression of Gibbs artefacts. We examine the transfer functions of the optimised filters, with counter-intuitive results regarding the highest-performing filters. Our results will simplify and improve the comparison of novel MRI reconstruction and post-processing algorithms, and lead to the automation of ringing suppression in MRI. They also apply more generally to other applications in which data is captured in the Fourier domain.
      89
  • Publication
    Constraints to solve parallelogram grid problems in 2D non separable linear canonical transform
    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.
      399
  • Publication
    Wigner cross-terms in sampled and other periodic signals
    (Optical Society of America, 2009-10-11) ; ;
    If we sample a scalar wave field, it becomes periodic in frequency. We examine the cross-terms which occur between these periodic replicas in the Wigner-Ville distribution function of such a signal. We present analytic results for Gaussian signals. The results also have implications for physical systems which contain periodic gratings.
      349
  • Publication
    Cross terms of the Wigner distribution function and aliasing in numerical simulations of paraxial optical systems
    (Optical Society of America, 2010-04-15) ; ;
    Sampling a function periodically replicates its spectrum. As a bilinear function of the signal, the associated Wigner distribution function contains cross terms between the replicas. Often neglected, these cross terms affect numerical simulations of paraxial optical systems. We develop expressions for these cross terms and show their effect on an example calculation
      542Scopus© Citations 12
  • Publication
    Unitary Algorithm for Nonseparable Linear Canonical Transforms Applied to Iterative Phase Retrieval
    Abstract: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.
      850Scopus© Citations 27
  • Publication
    The choice of optical system is critical for the security of double random phase encryption systems
    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.
      617Scopus© Citations 2
  • Publication
    Cases where the linear canonical transform of a signal has compact support or is band-limited
    (Optical Society of America, 2008-02-01) ;
    A signal may have compact support, be band-limited (i.e., its Fourier transform has compact support), or neither (“unbounded”). We determine conditions for the linear canonical transform of a signal having these properties. We examine the significance of these conditions for special cases of the linear canonical transform and consider the physical significance of our results
      443Scopus© Citations 54
  • Publication
    Fast linear canonical transforms
    (Optical Society of America, 2010-01-01) ;
    The linear canonical transform provides a mathematical model of paraxial propagation though quadratic phase systems. We review the literature on numerical approximation of this transform, including discretization, sampling, and fast algorithms, and identify key results. We then propose a frequency-division fast linear canonical transform algorithm comparable to the Sande–Tukey fast Fourier transform. Results calculated with an implementation of this algorithm are presented and compared with the corresponding analytic functions.
      1137Scopus© Citations 81
  • Publication
    Inclusive Teaching & Learning Case Studies in Engineering, Architecture & Affiliated Disciplines
    Diversity and inclusion are core to UCD values. We seek to attract students from a wide range of social and economic backgrounds and students who reflect the true diversity of the country. And as a global university, UCD attracts international students from over 100 countries. This diversity enriches our campus, and the experience of our students. The University's strategy 2020-2024 'Rising to the Future' also recognises the importance of inclusion and diversity, in seeking to "provide an inclusive educational experience that defines international best practice and prepares our graduates to thrive in present and future societies." However, an inclusive educational experience will not be achieved by simply creating diversity in the student body. It requires that we adjust our approach in everything we do to support and encourage our students’ success. We have clearly articulated in our strategy, and further emphasised in our Education and Student Success strategy, that our goal is to "equip all our educators with the tools and resources required to embed Universal Design for Learning on an institution-wide basis".
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