Now showing 1 - 8 of 8
  • 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.
  • 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.
  • Publication
    Concussion is associated with altered preparatory postural adjustments during gait initiation
    Gait initiation is a useful surrogate measure of supraspinal motor control mechanisms but has never been evaluated in a cohort following concussion. The aim of this study was to quantify the preparatory postural adjustments (PPAs) of gait initiation (GI) in fifteen concussion patients (4 females, 11 males) in comparison to a group of fifteen age- and sex- matched controls. All participants completed variants of the GI task where their dominant and non-dominant limbs as the stepping and support limbs. Task performance was quantified using the centre of pressure (COP) trajectory of each foot (computed from a force plate) and the centre of mass (COM) trajectory (estimated from an inertial measurement unit placed on the sacrum). Concussed patients exhibited decreased COP excursion on their dominant foot, both when it was the stepping limb (sagittal plane: 9.71mm [95% CI: 8.14 to 11.27mm] vs 14.9mm [95%CI: 12.31 to 17.49mm]; frontal plane: 36.95mm [95% CI: 30.87 to 43.03mm] vs 54.24mm [95%CI: 46.99 to 61.50mm]) and when it was the support limb (sagittal plane: 10.43mm [95% CI: 8.73 to 12.13mm] vs 18.13mm [95%CI: 14.92 to 21.35mm]; frontal plane: 66.51mm [95% CI: 60.45 to 72.57mm] vs 88.43mm [95%CI: 78.53 to 98.32mm]). This was reflected in the trajectory of the COM, wherein concussion patients exhibited lower posterior displacement (19.67mm [95%CI: 19.65mm to 19.7mm]) compared with controls (23.62mm [95%CI: 23.6 to 23.64]). On this basis, we conclude that individuals with concussion display deficits during a GI task which are potentially indicative of supraspinal impairments in motor control.
      390Scopus© 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.
      658Scopus© Citations 23
  • Publication
    Sparsity based Terahertz reflective off-axis digital holography
    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.
      378Scopus© Citations 5
  • Publication
    Measuring optical phase digitally in coherent metrology systems
    (Society of Photo-optical Instrumentation Engineers (SPIE), 2017-04-09) ; ; ;
    The accurate measurement of optical phase has many applications in metrology. For biological samples, which appear transparent, the phase data provides information about the refractive index of the sample. In speckle metrology, the phase can be used to estimate stress and strains of a rough surface with high sensitivity. In this theoretical manuscript we compare and contrast the properties of two techniques for estimating the phase distribution of a wave field under the paraxial approximation: (I) A digital holographic system, and (II) An idealized phase retrieval system. Both systems use a CCD or CMOS array to measure the intensities of the wave fields that are reflected from or transmitted through the sample of interest. This introduces a numerical aspect to the problem. For the two systems above we examine how numerical calculations can limit the performance of these systems leading to a near-infinite number of possible solutions.
  • Publication
    Quantification of postural control deficits in patients with recent concussion: An inertial-sensor based approach
    Background: The aim of this study was to quantify postural control ability in a group with concussion compared with a healthy control group. Method: Fifteen concussion patients (4 females, 11 males) and a group of fifteen age- and sex-matched controls were recruited. Participants were tested during the performance of the three stance variants (bilateral, tandem and unilateral) of the balance error scoring system standing on a force place, while wearing an inertial measurement unit placed at the posterior aspect of the sacrum. Findings: The area of postural sway was computed using the force-plate and the '95% ellipsoid volume of sway' was computed from the accelerometer data. Concussed patients exhibited increased sway area (1513 mm2 [95% CI: 935 to 2091 mm2] vs 646 mm2 [95% CI: 519 to 772 mm2]; p = 0.02) and sway volume (9.46 m3 s− 6 [95% CI: 8.02 to 19.94 m3 s− 6] vs 2.68 m3 s− 6 [95% CI: 1.81 to 3.55 m3 s− 6]; p = 0.01) in the bilateral stance position of the balance error scoring system. The sway volume metric also had excellent accuracy in identifying task 'errors' (tandem stance: 91% accuracy [95% CI: 85–96%], p < 0.001; unilateral stance: 91% accuracy [95% CI: 86–96%], p < 0.001). Interpretation: Individuals with concussion display increased postural sway during bilateral stance. The sway volume that was calculated from the accelerometer data not only differentiated a group with concussion from a healthy control group, but successfully identified when task errors had occurred. This may be of value in the development of a pitch-side assessment system for concussion.
      544Scopus© Citations 29
  • 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.
      478Scopus© Citations 2