Research Output
1 - 10 of 15
Publication
2D Non-separable Linear Canonical Transform (2D-NS-LCT) based cryptography
2017-04-27, Zhao, Liang, Muniraj, Inbarasan, Healy, John J., Malallah, Ra'ed, Cui, Xiao-Guang, Ryle, James P.
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
Wigner cross-terms in sampled and other periodic signals
2009-10-11, Rhodes, William T., Healy, John J., Sheridan, John T.
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.
Publication
Additional sampling criterion for the linear canonical transform
2008-11-15, Healy, John J., Hennelly, Bryan M., Sheridan, John T.
The linear canonical transform describes the effect of first-order quadratic phase optical systems on a wave field. Several recent papers have developed sampling rules for the numerical approximation of the transform. However, sampling an analog function according to existing rules will not generally permit the reconstruction of the analog linear canonical transform of that function from its samples. To achieve this, an additional sampling criterion has been developed for sampling both the input and the output wave fields.
Publication
Cases where the linear canonical transform of a signal has compact support or is band-limited
2008-02-01, Healy, John J., Sheridan, John T.
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
Publication
Automated Filter Selection for Suppression of Gibbs Ringing Artefacts in MRI
2022-11, Wang, Yue, Healy, John J.
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.
Publication
Inclusive Teaching & Learning Case Studies in Engineering, Architecture & Affiliated Disciplines
2021-10-14, Padden, Lisa, Buggy, Conor J., Ahern, Aoife, Rogers, Mark S., Cotterill, Sarah, Healy, John J., Faria, Tiago, Sudhershan, Daniel, Fitzpatrick, Miriam, McCrum, Daniel, Keenahan, Jennifer, Shotton, Elizabeth
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".
Publication
Space-bandwidth ratio as a means of choosing between Fresnel and other linear canonical transform algorithms
2011-05-01, Healy, John J., Sheridan, John T.
The product of the spatial and spatial frequency extents of a wave field has proven useful in the analysis of the sampling requirements of numerical simulations. We propose that the ratio of these quantities is also illuminating. We have shown that the distance at which the so-called “direct method” becomes more efficient than the so-called “spectral method” for simulations of Fresnel transforms may be written in terms of this space-bandwidth ratio. We have proposed generalizations of these algorithms for numerical simulations of general ABCD systems and derived expressions for the “transition space-bandwidth ratio” above which the generalization of the spectral method is the more efficient algorithm and below which the generalization of the direct method is preferable.
Publication
Constraints to solve parallelogram grid problems in 2D non separable linear canonical transform
2017-04-27, Zhao, Liang, Healy, John J., Muniraj, Inbarasan, Cui, Xiao-Guang, Malallah, Ra'ed, Ryle, James P., Sheridan, John T.
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
Unitary Algorithm for Nonseparable Linear Canonical Transforms Applied to Iterative Phase Retrieval
2017-03-20, Zhao, Liang, Sheridan, John T., Healy, John J.
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.
Publication
Sparsity based Terahertz reflective off-axis digital holography
2017-04-24, Wan, Min, Muniraj, Inbarasan, Malallah, Ra'ed, Zhao, Liang, Ryle, James P., Rong, Lu, Healy, John J., Wang, Dayong, Sheridan, John T.
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.