Defocused point spread function of asymmetrically apodized optical imaging systems with slit apertures

Andra Naresh Kumar Reddy (Login required)
Science and Research Laboratory of Automated Systems of Science Researches, Samara National Research University, Russia
Department of Physics (H&S), CMR Institute of Technology, Telangana, India

Dasari Karuna Sagar
Department of Physics, University College of Science, Osmania University, Hyderabad, India

Paper #3046 received 2016.05.28; revised manuscript received 2016.09.05; accepted for publication 2016.09.29; published online 2016.09.30.

DOI: 10.18287/JBPE16.02.030302


In the presence of defocusing, the PSF of an optical imaging system with asymmetric apodization have been investigated analytically. The asymmetry in the PSF has been observed to increase with edge strip width (b) of the slit aperture and further improved by defect of focus in the image plane, permits to achieve a significant improvement in side-lobe suppression. The proposed analytical model of pupil function considers these effects and formulates a space-variant PSF is obtained by employing asymmetric apodization. The optimum values for asymmetric apodization controlling parameter (b) and defocusing parameter (Y) at which results in smoothing the central peak shape and reducing optical side-lobes intensity on one side of the Asymmetric PSF termed as ‘good’ side at the cost of worsening its counterpart known as ‘bad side’ with which renders the resolution of apodized optical imaging systems. In order to simplify the proposed analytical design an efficient method is derived and evaluated.


Defocusing; diffraction; asymmetric apodization; two-line resolution; Point spread function; complex pupil function

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1. H. H. Hopkins, “The Frequency Response of a Defocused Optical System,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 231(1184), 91–103 (1955). Crossref

2. P. A. Stokseth, “Properties of a Defocused Optical System,” J. Opt. Soc. Am. 59(10), 1314 (1969).

3. J. Li, P. Agathoklis, F. Peet, G. Jensen, and T. Sahota, “Measurement and analysis of defocused point spread functions and optical transfer functions of a microscope,” IEEE Pacific Rim Conference on Communications, Computers, and Signal Processing (1995). Crossref

4. A. R. FitzGerrell, E. R. Dowski, and W. T. Cathey, “Defocus transfer function for circularly symmetric pupils,” Applied Optics 36(23), 5796 (1997). Crossref

5. I. Klapp, and Y. Yitzhaky, “Angular motion point spread function model considering aberrations and defocus effects,” J. Opt. Soc. Am. A 23(8), 1856 (2006). Crossref

6. J. Burge, and W. S. Geisler, “Optimal Image-based Defocus Estimates from Individual Natural Images,” Imaging and Applied Optics (2011).

7. X. Zhu, S. Cohen, S. Schiller, and P. Milanfar, “Estimating Spatially Varying Defocus Blur From A Single Image,” IEEE Transactions on Image Processing 22(12), 4879–4891 (2013). Crossref

8. A. Greengard, Y. Y. Schechner, and R. Piestun, “Depth from diffracted rotation,” Opt. Lett. 31(2), 181 (2006).

9. P. Favaro, and S. Soatto, “A geometric approach to shape from defocus,” IEEE Transactions on Pattern Analysis and Machine Intelligence 27(3), 406–417 (2005). Crossref

10. C.-Y. Wen, and C.-H. Lee, “Point spread functions and their applications to forensic image restoration Introduction,” Forensic Science Journal 1(1), 15-26 (2002).

11. G. O. Reynolds, J. B. Deveils, J. B. Parrent Jr, and B. J. Thompson, “The New Physical optic notebook: Tutorials in Fourier Optics,” SPIE Optical Engineering Press, Bellingham, WA and New York (1989).

12. D. N. Grimes, and B. J. Thompson, “Two-Point Resolution with Partially Coherent Light,” J. Opt. Soc. Am. 57(11), 1330 (1967).

13. F. Rojak, MS Thesis, Lowell Technological Institute, Lowell, MA (1961).

14. B. J. Beran, and J. B. Parrent Jr, The theory of partial coherence, Pentice Hall Englewood Cliff, NJ, 124 (1964).

15. O. Falconi, “Limits to which Double Lines, Double Stars, and Disks can be Resolved and Measured,” J. Opt. Soc. Am. 57(8), 987 (1967).

16. F. Kottler, and F. H. Perrin, “Imagery of One-Dimensional Patterns,” J. Opt. Soc. Am. 56(3), 377 (1966).

17. S. V. Gupta, and D. Sen, “Diffrimoscopic image formation under partial coherent illumination (Slits and Opaque strips),” Optica Acta: J. Opt. 18(10), 779-792 (1971). Crossref

18. R. S. Sirohi, “Limit of resolution of diffraction limited circular aperture for line objects,” Optik 29, 437-439 (1969).

19. D. Karuna Sagar, G. Bikshamaiah, and S. Lacha Goud, “Resolution of two-line objects by Hanning pupil functions of apodized optical systems under coherent illumination,” Atti Fond. Giorgio Ronchi 61, 559 (2006).

20. P. K. Mondal, M. L. Calvo, and M. Chevaliar, “Resolution criterion and contrast factor for resolving two-line images under coherent and incoherent illumination,” Proc. SPIE 1319, Optics in Complex Systems 378 (1990).

21. P. K. Mondal, M. L. Calvo, M. Chevaliar, and V. Lakshminarayanan, “Theoretical approach to hyperacuity tests based on resolution criteria for two-line images,” Proc. SPIE 1429, Holography, Interferometry, and Optical Pattern Recognition in Biomedicine 108 (1991).

22. B. L. Metha, “Effect of non-uniform illumination on critical resolution by a circular aperture using partially coherent light,” Atti Fond. Giorgio Ronchi 30, 17 (1975).

23. T. Asakura, “Resolution of two unequally bright points with partially coherent light,” Nouvelle Revue d’Optique 5(3), 169–177 (1974).

24. H. H. Hopkins, and B. Zalar, “Aberration Tolerances Based on the Line Spread Function,” Journal of Modern Optics 34(3), 371–406 (1987). Crossref

25. A. K. Pandey, G. S. Pant, and A. Malhotra, “Standardization of SPECT Filter Parameters,” Indian Journal of Nuclear Medicine 19, 30-35 (2004).

26. L. Cheng, and G. G. Siu, “Asymmetric apodization,” Measurement Science and Technology 2(3), 198–202 (1991).

27. G. G. Siu, L. Cheng, D. S. Chiu, and K. S. Chan, “Improved side-lobe suppression in asymmetric apodization,” Journal of Physics D: Applied Physics 27(3), 459–463 (1994). Crossref

28. M. Keshavulu Goud, R. Komala, A. Naresh Kumar Reddy, and S. Goud, “Point Spread Function of Asymmetrically Apodized Optical Systems with Complex Pupil Filters: The One-Dimensional Case with Slit Aperture,” Acta Physica Polonica A 122(1), 90–95 (2012). Crossref

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