Submit Article
Asian Journal of Physics Vol 32, Nos 5 – 8 (2023) 243-252

A review of the contributions by John T Sheridan to the theory of linear canonical transforms

John J Healy1, Bryan M Hennelly2, and Liang Zhao3
School of Electrical and Electronic Engineering, University College Dublin, Belfield, Dublin 4, Ireland.
School of Computer Science and School of Electronic Engineering, Maynooth University, Maynooth, Co. Kildare, Ireland.
National Engineering Laboratory for Educational Big Data, Central China Normal University, Wuhan 430079, China.

Dedicated in memory of Prof John Sheridan

The linear canonical transforms are a three-parameter li group of integral transforms that can be used as an optical propagation model. This was a popular and productive topic for the late John Sheridan. In this article, we review and celebrate his contributions to the advancement of that field.. © Anita Publications. All rights reserved.
Keywords: Linear canonical transforms, Fourier optics, Paraxial propagation, Quadratic phase systems.

Peer Review Information
Method: Single- anonymous; Screened for Plagiarism? Yes
Buy this Article in Print © Anita Publications. All rights reserve

References

  1. Healy J J,  Kutay MA, Ozaktas H M and Sheridan JT, eds, Linear canonical transforms: Theory and applications, (Vol 198), Springer, 2015.
  2. Rhodes W T, Brenner K H, Sheridan J T, Why teach Wigner Optics?. In Education and Training in Optics and Photonics, (p ETuB3), (Optica Publishing Group), 2003.
  3. Sheridan J T, Hennelly B, Kelly D, Wigner optics and wave optics: fundamentals and practical applications. In Wave-Optical Systems Engineering II (SPIE), Vol 5182, 2003, pp 34–45.
  4. Mendlovic D, Ozaktas H M, Fourier transformation and their optical interpretation: Part I. J Opt Soc Am, (1993): 1875-1881.
  5. Namias Victor, The fractional order Fourier transform and its application to quantum mechanics, IMA Journal of Applied Mathematics, 25(1980)241–265.
  6. Fan X, Healy J J, O’Dwyer K, Winnik J, Hennelly B M, Adaptation of the Standard Off-Axis Digital Holographic Microscope to Achieve Variable Magnification, Photonics, 8(2021)264; doi.org/10.3390/photonics8070264.
  7. Zheng Y, Healy J J, On the independent significance of generalizations of the Wigner distribution function, J Opt Soc Am A, 40(2023)326–336.
  8. Abe S, Sheridan J T, Optical operations on wave functions as the Abelian subgroups of the special affine Fourier transformation, Opt Lett, 19(1994)1801–1803.
  9. Abe S, Sheridan J T, Generalization of the fractional Fourier transformation to an arbitrary linear lossless transformation an operator approach, J Phys A: Math Theor, 27(1994)4179; doi. 10.1088/0305-4470/27/12/023.
  10. Abe S, Sheridan J T, Almost-Fourier and almost-Fresnel transformations, Opt Commun, 113(1995)385–388.
  11. Abe S, Sheridan J T, Random fractional Fourier transform: stochastic perturbations along the axis of propagation, J Opt Soc Am A, 16(1999)1986–1991.
  12. Hennelly B, Sheridan J T, Optical image encryption by random shifting in fractional Fourier domains, Opt Lett, 28(2003)269–271.
  13. Hennelly B M, Sheridan J T, Image encryption and the fractional Fourier transform, Optik, 114(2003)251–265.
  14. Gopinathan U, Monaghan D S, Naughton T J, Sheridan J T, A known-plaintext heuristic attack on the Fourier plane encryption algorithm, Opt Express, 14(2006)3181–3186.
  15. Liu S, Guo C, Sheridan J T, A review of optical image encryption techniques, Opt Laser Technol, 57(2014)327–342.
  16. Guo C, Liu S, Sheridan J T, Iterative phase retrieval algorithms. I: optimization, Appl Opt, 54(2015)4698–4708.
  17. Guo C, Liu S, Sheridan J T, Iterative phase retrieval algorithms. Part II: Attacking optical encryption systems, Appl Opt, 54(2015)4709–4719.
  18. Javidi B, Carnicer A, Yamaguchi M, Nomura T, Pérez-Cabré E, Millán M S, Nishchal N K, Torroba R, Barrera J F, He W, Peng X, Stern A, Rivenson Y, Alfalou A, Brosseau C, Guo C, Sheridan J T, Situ G, Naruse M, Matsumoto T, Ignasi Juvells, Tajahuerce E, Lancis J, Chen W, Chen X, Pinkse P W H, Mosk A P, Markman A, Roadmap on optical security, J Opt, 18(2016)083001; doi. 10.1088/2040-8978/18/8/083001.
  19. Kelly D P, Hennelly B M, Sheridan J T, Magnitude and direction of motion with speckle correlation and the optical fractional Fourier transform, Appl Opt, 44(2005)2720–2727.
  20. Kelly D P, Ward J E, Hennelly B M, Gopinathan U, O’Neill F T, Sheridan J T, Paraxial speckle-based metrology systems with an aperture, J Opt Soc Am A, 23(2006)2861–2870.
  21. Ryle J P, Al-Kalbani M, Collins N, Gopinathan U, Boyle G, Coakley D, Sheridan J T, Compact portable ocular microtremor sensor: design, development and calibration, J Biomed Opt, 14(2009)014021; doi.org/10.1117/1.3083435-014021.
  22. Ryle J P, Vohnsen B, Sheridan J T, Simultaneous drift, microsaccades, and ocular microtremor measurement from a single noncontact far-field optical sensor, J Biomed Opt, 20(2015)027004; doi.org/10.1117/1.JBO.20.2.027004.
  23. Mas D, Ferrer B, Sheridan J T, Espinosa J, Resolution limits to object tracking with subpixel accuracy, Opt Lett, 37(2012)4877–4879.
  24. Wan M, Healy J J, Sheridan J T, Fast, sub-pixel accurate, displacement measurement method: optical and terahertz systems, Opt Lett, 45(2020)6611–6614.
  25. Li D, Kelly D P, Sheridan J T, Three-dimensional static speckle fields. Part I. Theory and numerical investigation, J Opt Soc Am A, 28(2011)1896–1903.
  26. Kelly D P, Healy J J, Hennelly B M, Sheridan J T, Quantifying the 2.5 D imaging performance of digital holographic systems, J Eur Opt Soc, 6(2011)11034; doi.org/10.2971/jeos.2011.11034.
  27. Sheridan J T, Kostuk R K, Gil A F, Wang Y, Lu W, Zhong H, Tomita Y, Neipp C, Francés J, Gallego S, Pascual I, Roadmap on holography, J Opt, 22(2020)123002; doi. 10.1088/2040-8986/abb3a4.
  28. Beléndez A, Sheridan J T, Pascual I, Holography: 50th Anniversary of Dennis Gabor’s Nobel Prize. Part I. A historical perspective. In Education and Training in Optics and Photonics, Optica Publishing Group, 2021, pp F2B-1.
  29. Sheridan J T Beléndez A, Pascual I, Holography: 50th Anniversary of Dennis Gabor’s Nobel Prize. Part II. An Engineering Perspective. In Education and Training in Optics and Photonics (pp. F2B-2). Optica Publishing Group, 2021.
  30. Healy J J, Sheridan J T, . Space–bandwidth ratio as a means of choosing between Fresnel and other linear canonical transform algorithms, J Opt Soc Am A, 28(2011)786–790.
  31. Healy J J, Sheridan J T, Cases where the linear canonical transform of a signal has compact support or is band-limited, Opt Lett, 33(2008)228–230.
  32. Hennelly B M, Sheridan J T, Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms, J Opt Soc Am A, 22(2005)917–927.
  33. Ding J J, Research of fractional Fourier transform and linear canonical transform, Ph D Thesis, Taipei: National Taiwan University, 2001.
  34. Healy J J, Hennelly B M, Sheridan J T, Additional sampling criterion for the linear canonical transform, Opt Lett, 33(2008)2599–2601.
  35. Oktem F S, Ozaktas H M, Exact relation between continuous and discrete linear canonical transforms, IEEE Signal Process Lett, 16(2009)727–730.
  36. Healy J J, Sheridan J T, Reevaluation of the direct method of calculating Fresnel and other linear canonical transforms, Opt Lett, 35(2010)947–949.
  37. Healy J J, Simulating first order optical systems—algorithms for and composition of discrete linear canonical transforms, J Opt, 20(2017)014008; doi.10.1088/2040-8986/aa9e20.
  38. Healy J J, Rhodes W T, Sheridan J T, Cross terms of the Wigner distribution function and aliasing in numerical simulations of paraxial optical systems, Opt Lett, 35(2010)1142–1144.
  39. Sheridan J T, Zhao L, Healy J J, The condition number and first order optical systems. In Imaging Systems and Applications (pp. ITu3C-4). Optica Publishing Group. 2012 June.
  40. Zhao L, Healy J J, Sheridan J T, 2013. Unitary discrete linear canonical transform: analysis and application. Appl Opt, 52(2013)C30-C36.
  41. Zhao L, Healy J J, Sheridan J T, Two-dimensional nonseparable linear canonical transform: sampling theorem and unitary discretization, J Opt Soc Am A, 31(2014)2631–2641.
  42. Zhao L., Healy J J, Sheridan J T, Constraints on additivity of the 1D discrete linear canonical transform. Appl Opt, 54(2015)9960–9965.
  43. Hennelly B M, Sheridan J T, Fast numerical algorithm for the linear canonical transform, J Opt Soc Am A, 22(2005).928-937.
  44. Healy J J, Sheridan J T, Fast linear canonical transforms, J Opt Soc Am A, 27(2010)21–30.

Related Posts