Asian Journal of Physics Vol. 30 Nos 8 & 9 (2021) 1235-1242

Optimizing sampling and padding at the pupil plane for light propagation simulations based in Fourier transforms for wavefront coding
E Acosta1, E González Amador1 and J Arines2


Wavefront coding technique makes use of a phase plate encoding aberrations at the exit pupil of an optical system to extend its depth of focus. The defocused images are deblurred through a deconvolution process involving the OTF of the optical system. Therefore, for both the design of the phase mask as well as the deconvolution process, accurate OTF matrices have to be evaluated. Nyquist frequency imposes an upper limit to the size of the pixel of the image plane when optical systems are simulated by means of Fourier Transforms, but not limited to the size of the pixel in the pupil. In this work, we propose an additional upper limit to the size of the pixel of the pupil to avoid errors due to undersampling the phase and optimize computation time. The work will be illustrated with numerical simulations for two different phase masks proposed for wavefront coding imaging system. ©Anita Publications. All rights reserved
Keywords: Wavefront Coding, Nyquist Frequency, Fourier Transform, Optimizing sampling.

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Method: Single- anonymous; Screened for Plagiarism? Yes
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  1. Dowski E R, Cathey W T, Extended depth of field through wave-front coding, Appl Opt, 34(1995)1859–1866.
  2. Barwick, D S, Increasing the information acquisition volume in iris recognition systems, Appl Opt, 47(2008)4684–4691.
  3. Muyo G, Singh A, Andersson M, Huckridge D, Wood A, Harvey A R, Infrared imaging with a wavefront-coded singlet lens, Opt Express,17(2009)21118–21123.
  4. Muyo G, Singh A, Andersson M, Huckridge D, Harvey A, Optimized thermal imaging with a singlet and pupil plane encoding: experimental realization, Proc SPIE, 6395(2006)63950M;
  5. Acosta E, Olvera-Angeles M, González-Amador E, Sasian J, Schwiegerling J, Arines J, Wavefront coding with Jacobi–Fourier phase masks for retinal imaging, Appl Opt, 59(2020)G234-G238.
  6. Acosta E, Arines J, Optical-digital System Invariant to eye aberrations for retinal imaging, Invest Ophthalmol Vis Sci, 53(2012)3098-3098.
  7. Arnison M R, Cogswell C J, Sheppard C J, Török P, Wavefront coding fluorescence microscopy using high aperture lenses, Opt Imag Micr: Techniques and Advanced Systems, 87(2007)143–165.
  8. Goodman J W, Introduction to Fourier Optics, (McGraw-Hill), 1968.
  9. Voelz D G, Computational Fourier optics: a MATLAB tutorial, (SPIE Press), 2011.
  10. Scrymgeour D A, Adelsberger K, Boye R, Advanced Imaging Optics Utilizing Wavefront Coding, Tech Rep, (Sandia National Lab. 2015).
  11. Zhou M, Alfadhl Y, Chen X, Optimal spatial sampling criterion in a 2D THz holographic imaging system, IEEE Access, 6(2018)8173–8177.
  12. Prasad S, Torgersen T C, Pauca V P, Plemmons R J, van der Gracht J. Engineering the pupil phase to improve image quality, Proc SPIE, 5108(2003)1–13.
  13. González-Amador E, Padilla-Vivanco A, Toxqui-Quitl C, Arines J, Acosta E, Jacobi–Fourier phase mask for wavefront coding, Opt Lasers Eng, 126(2020)105880;doi. org/10.1016/j.optlaseng.2019.105880.

Hartin J, Belanus K, Data Sampling Techniques for Fourier Analysis. Paper presented at 1997 Annual Conference, Milwaukee, Wisconsin, 2(1997)2.127.1 – 2.127.7;–6487.