Advertisement

Applied Physics B

, 124:229 | Cite as

Apodization for improving the two-point resolution of coherent optical systems with defect of focus

  • Andra Naresh Kumar Reddy
  • Svetlana Nikolaevna Khonina
Article
  • 58 Downloads

Abstract

An amplitude apodization influenced defocused optical system used to form a coherent light illuminated two-point sources with an improved resolution is analyzed. The composite coherent image intensity distributions in the defocused and the Gaussian (Yd = 0) planes have been calculated and compared. It has shown the resolution of the apodized optical system is significantly increased for an excessive amount of defocusing effect. As is clearly evidenced by the presence of irradiance dip in the resulting intensity profiles can describe the super-two-point resolution phenomena in a maximum defocused plane (Yd = 2π).

Notes

Acknowledgements

The Corresponding author is indebted to Asher A. Friesem and Nir Davidson, Department of Physics of Complex systems, Weizmann Institute of Science, Israel for useful discussions, which indeed improved the paper. This work was supported by the Israel Science Foundation (ISF) in part of optimizing the calculations and by the Ministry of Science and Education, Russia within the state assignment FSRC “Crystallography and Photonics” RAS in part of simulation results.

References

  1. 1.
    F. Aieta, P. Genevet, M. Kats, F. Capasso, Aberrations of flat lenses and aplanatic metasurfaces. Opt. Exp. 21, 31530–31539 (2013)ADSCrossRefGoogle Scholar
  2. 2.
    P.J. Sands, Inhomogeneous lenses, III. Paraxial optics. J. Opt. Soc. Am. 61, 1436–1443 (1971)CrossRefGoogle Scholar
  3. 3.
    P.J. Sands, Third order aberrations of inhomogeneous lenses. J. Opt. Soc. Am. 60, 1436–1443 (1970)ADSCrossRefGoogle Scholar
  4. 4.
    A. Naresh Kumar Reddy, M. Hashemi, S.N. Khonina, Apodzation of two-dimensional pupils with aberrations. Pramana J. Phys. 90(6), 77 (2018)ADSCrossRefGoogle Scholar
  5. 5.
    A. Naresh Kumar Reddy, D. Karuna Sagar, Spherical aberration of the point spread function with asymmetric pupil mask. Adv. Opt. Technol. 2016, 1608342 (2016)Google Scholar
  6. 6.
    L.N. Hazra, P.K. Purkait, M. De, Apodization of aberrated pupils. Can. J. Phys. 57, 1340–1346 (1979)ADSCrossRefGoogle Scholar
  7. 7.
    D. Karuna Sagar, G. Bikshamaiah, M. Keshavulu Goud, S. Lacha, Goud, Defect of focus in two-line resolution with Hanning amplitude filters. J. Mod. Opt. 53(14), 2011–2019 (2006)ADSCrossRefGoogle Scholar
  8. 8.
    A. Naresh Kumar Reddy, D. Karuna Sagar, S.N. Khonina, Complex pupil masks for aberrated imaging of closely spaced objects. Opt. Spectrosc. 123(6), 940–949 (2017)ADSCrossRefGoogle Scholar
  9. 9.
    J.P. Mills, B.J. Thompson, Selected Papers on Apodization: Coherent Optical Systems, SPIE Milestone Series, vol. MS 119 (SPIE Optical Engineering Press, Ellingham, 1996)Google Scholar
  10. 10.
    M. Martinez-Corral, M.T. Caballero, E.H.K. Stelzer, J. Swoger, Tailoring the axial shape of the point spread function using Toraldo concept. Opt. Exp. 10(1), 98–103 (2002)ADSCrossRefGoogle Scholar
  11. 11.
    N. Reza, L.N. Hazra, Toraldo filters with concentric unequal annuli of fixed phase by evolutionary programming. J. Opt. Soc. Am. A .30(2), 189–195 (2012)ADSCrossRefGoogle Scholar
  12. 12.
    L. Cheng, G.G. Siu, Asymmetric apodization. Meas. Sci. Technol. 2(3), 198–202 (1991)ADSCrossRefGoogle Scholar
  13. 13.
    G.G. Siu, L. Cheng, D.S. Chiu, Improved side-lobe suppression in asymmetric apodization. J. Phys. D Appl. Phys. 27(3), 459–463 (1994)ADSCrossRefGoogle Scholar
  14. 14.
    M. Kowalczyk, C.J. Zapata-Rodriguez, M. Martinez-Corral, Asymmetric apodization in confocal scanning systems. Appl. Opt. 37(35), 8206–8214 (1998)ADSCrossRefGoogle Scholar
  15. 15.
    V.P. Nayar, N.K. Sharma, Two-point resolution of Gaussian aperture operating in partially coherent light using various resolution criteria. Appl. Opt. 17(14), 2176–2180 (1978)ADSCrossRefGoogle Scholar
  16. 16.
    K. Yamamoto, Y. Ichioka, T. Suzuki, Performance of an apodized aperture in a defocused optical system under partially coherent illumination. Opt. Acta 23(12), 965–986 (1976)ADSCrossRefGoogle Scholar
  17. 17.
    J.P. McGuire Jr., R.A. Chipman, Diffraction image formation in optical systems with polarization aberrations. II. Amplitude response matrices for rotationally symmetric systems. J. Opt. Soc. Am. A 8(6), 833–841 (1991)ADSCrossRefGoogle Scholar
  18. 18.
    J.P. Mills, B.J. Thompson, Effect of aberrations and apodization on the performance of coherent optical systems I. The amplitude response. J. Opt. Soc. Am. A 3(5), 694–703 (1986)ADSCrossRefGoogle Scholar
  19. 19.
    P. Richter, S. Tisza, The effect of lens aberrations on coherent optical filter. Opt. Acta 23(12), 965–986 (1976)CrossRefGoogle Scholar
  20. 20.
    G. Cesini, G. Guattari, P. De Santis, C. Palma, Two-point resolution with anti-phase coherent Illumination. I. One-dimensional systems. J. Opt. (Paris) 10(2), 79–87 (1979)ADSCrossRefGoogle Scholar
  21. 21.
    S.M. Watson, J.P. Mills, S.K. Rogers, Two-point resolution criterion for multiaperture optical telescopes. J. Opt. Soc. Am. A 5(6), 893–903 (1988)ADSCrossRefGoogle Scholar
  22. 22.
    L. Rayleigh, Collected Papers, vol. 3 (Cambridge University Press, London, 1902), p. 84Google Scholar
  23. 23.
    C.M. Sparrow, On spectroscopic resolving power. Astrophys. J. 44, 76–86 (1916)ADSCrossRefGoogle Scholar
  24. 24.
    A. Naresh Kumar Reddy, D. Karuna, Sagar, Two-point resolution of asymmetrically apodized optical systems. Opt. Pura Apl. 46(3), 215–222 (2013)CrossRefGoogle Scholar
  25. 25.
    A. Naresh Kumar Reddy, S.N. Khonina, Two-point resolution with spherical aberration quadratic amplitude filters. Opt. Appl. 48(4), 550–565 (2018)Google Scholar
  26. 26.
    R. Keshavulu, D. Sayanna, Karuna Sagar, S.L. Goud, Effect of defocusing on the sparrow limits for apodized optical systems. Opt. Commun. 217, 59–67 (2003)ADSCrossRefGoogle Scholar
  27. 27.
    L. Wang, T. Tschudi, T. Haldorsson, P.R. Petursson, Speckle reduction in laser projection systems by diffractive optical elements. Appl. Opt. 37(10), 1770–1775 (1998)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Physics of Complex SystemsWeizmann Institute of ScienceRehovotIsrael
  2. 2.Samara National Research UniversitySamaraRussia
  3. 3.Image Processing Systems Institute-Branch of the Federal Scientific Research Centre “Crystallography and Photonics” of Russian Academy of SciencesSamaraRussia

Personalised recommendations