OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 43, Iss. 19 — Jul. 1, 2004
  • pp: 3838–3847

Frequency response characteristics of a birefringent lens with off-axis aberrations

Sucharita Sanyal, Yoshimasa Kawata, Ajay Ghosh, and Surajit Mandal  »View Author Affiliations

Applied Optics, Vol. 43, Issue 19, pp. 3838-3847 (2004)

View Full Text Article

Enhanced HTML    Acrobat PDF (228 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We report the frequency response characteristics of an optical system consisting of a lens made of a uniaxial birefringent crystal sandwiched between two linear polarizers; the lens has prespecified off-axis aberrations such as primary astigmatism and primary coma. An analytical expression is obtained for the optical transfer function of the proposed system by use of the autocorrelation of the pupil function over the lens aperture. Some specific cases are computed and illustrated graphically. It has been shown that the proposed system has imaging characteristics distinctly different from those of an ordinary glass lens, and these may be advantageous for better balancing of aberrations in conventional imaging systems.

© 2004 Optical Society of America

OCIS Codes
(110.0110) Imaging systems : Imaging systems
(110.3000) Imaging systems : Image quality assessment
(110.4850) Imaging systems : Optical transfer functions
(220.0220) Optical design and fabrication : Optical design and fabrication
(220.1000) Optical design and fabrication : Aberration compensation
(260.5430) Physical optics : Polarization

Original Manuscript: October 30, 2003
Revised Manuscript: April 12, 2004
Published: July 1, 2004

Sucharita Sanyal, Yoshimasa Kawata, Ajay Ghosh, and Surajit Mandal, "Frequency response characteristics of a birefringent lens with off-axis aberrations," Appl. Opt. 43, 3838-3847 (2004)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. Tsujiuchi, “A density filter improving aberrant optical image,” J. Phys. Soc. Jpn. 12, 744–000 (1957). [CrossRef]
  2. M. Mino, Y. Okano, “Improvement in the OTF of a defocused optical system through the use of shaded apertures,” Appl. Opt. 10, 2219–2225 (1971). [CrossRef] [PubMed]
  3. S. C. Biswas, A. Boivin, “Influence of primary astigmatism on the performance of optimum apodizers,” J. Opt. (Paris) 4, 1–00 (1975).
  4. S. C. Biswas, A. Boivin, “Influence of spherical aberration on the performance of optimum apodizers,” Opt. Acta 23, 569–588 (1976). [CrossRef]
  5. S. C. Biswas, A. Boivin, “Performance of optimum apodizers in the presence of primary coma,” Can. J. Phys. 57, 1388 (1979). [CrossRef]
  6. M. J. Yzuel, F. Calvo, “A study of the possibility of image optimization by apodization filters in optical systems with residual aberrations,” Opt. Acta. 26, 1397–1406 (1979). [CrossRef]
  7. M. J. Yzuel, F. Calvo, “Point-spread function calculation for optical systems with residual aberrations and a non-uniform transmission pupil,” Opt. Acta 30, 233–242 (1983). [CrossRef]
  8. J. Ojeda-Castaneda, P. Andres, A. Diaz, “Annular apodizers for low sensitivity to defocus and to spherical aberration,” Opt. Lett. 11, 487–489 (1986). [CrossRef] [PubMed]
  9. J. Ojeda-Castaneda, L. R. Berriel-Valdos, E. Montes, “Bessel annular apodizers: imaging characteristics,” Appl. Opt. 26, 2770–2772 (1987). [CrossRef] [PubMed]
  10. J. Tsujiuchi, “Correction of optical images by compensation of aberrations and by spatial frequency filtering,” in Progress in Optics, Vol. II, E. Wolf, ed. (North Holland, Amsterdam, 1963), pp. 131–180. [CrossRef]
  11. S. Mezouari, A. R. Harvey, “Phase pupil functions for reduction of defocus and spherical aberrations,” Opt. Lett. 28, 771–773 (2003). [CrossRef] [PubMed]
  12. A. K. Chakraborty, S. Das, D. K. Basu, A. Ghosh, “Imaging characteristics of a birefringent lens,” Polarization Considerations for Optical Systems II, R. A. Chipman, ed., Proc. SPIE1166, 130–134 (1990). [CrossRef]
  13. S. Sanyal, P. Bandyopadhyay, A. Ghosh, “Vector wave imagery using a birefringent lens,” Opt. Eng. 37, 592–599 (1998). [CrossRef]
  14. S. Sanyal, A. Ghosh, “Imaging characteristics of birefringent lenses under focused and defocused condition,” Optik 110, 513–520 (1999).
  15. S. Sanyal, A. Ghosh, “High focal depth with a quasi-bifocus birefringent lens,” Appl. Opt. 39, 2321–2325 (2000). [CrossRef]
  16. S. Sanyal, A. Ghosh, “Frequency response characteristics of a birefringent lens,” Opt. Eng. 41, 592–597 (2002). [CrossRef]
  17. S. Sanyal, A. Ghosh, “Image assessment of a birefringent lens based on the factor of encircled energy,” Opt. Eng. 42, 1058–1064 (2003). [CrossRef]
  18. S. Sanyal, A. Ghosh, “High tolerance to spherical aberrations and defects of focus using a birefringent lens,” Appl. Opt. 41, 4611–4619 (2002). [CrossRef] [PubMed]
  19. S. Sanyal, A. Ghosh, “Light throughput of a birefringent lens—a comparative study,” J. Opt. (India) 30(2), 85–93 (2001).
  20. S. Sanyal, A. Ghosh, “Imaging behaviour of a birefringent lens suffering from primary coma,” J. Opt. (India) 29(1), 15–23 (2000).
  21. S. Sanyal, Y. Kawata, S. Mandal, A. Ghosh, “High tolerance to off-axis aberrations with a birefringent lens,” Opt. Eng. (to be published).
  22. H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London A 231, 91–103 (1955). [CrossRef]
  23. M. De, “The influence of astigmatism on the response function of an optical system,” Proc. R. Soc. London A 233, 91–104 (1956).
  24. M. De, B. K. Nath, “Response of optical systems suffering from primary coma,” Optik 15, 739–750 (1958).
  25. F. Ratajczyk, “A method of calculation of permissible birefringence in lenses of the optical instruments,” Optik (Stuttgart) 68, 61–68 (1984).
  26. R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).
  27. R. A. Chipman, “Polarization aberration diagrams,” Opt. Eng. 28, 100–106 (1989). [CrossRef]
  28. J. P. Mcguire, R. A. Chipman, “Diffraction image formation in optical systems with polarization aberrations. I. Formulation and examples,” J. Opt. Soc. Am. A 7, 1614–1626 (1990). [CrossRef]
  29. J. P. Mcguire, R. A. Chipman, “Polarization aberrations. I. Rotationally symmetric systems,” Appl. Opt. 33, 5080–5100 (1994). [CrossRef] [PubMed]
  30. H. Kikuta, K. Iwata, H. Shimomura, “First-order aberration of a double-focus lens made of a uniaxial crystal,” J. Opt. Soc. Am. A 9, 814–819 (1992). [CrossRef]
  31. Y. Unno, “Distorted wave front produced by a high-resolution projection optical system having rotationally symmetric birefringence,” Appl. Opt. 37, 7241–7247 (1998). [CrossRef]
  32. J. Lesso, A. Duncan, W. Sibbett, M. Padgett, “Aberrations introduced by a lens made from a birefringent material,” Appl. Opt. 39, 592–598 (2000). [CrossRef]
  33. Y. Unno, “Influence of birefringence on the image formation of high-resolution projection optics,” Appl. Opt. 39, 3243–3252 (2000). [CrossRef]
  34. Y. Unno, A. Suzuki, “Analyses of imaging performance degradation caused by birefringence residual in lens materials,” in Optical Microlithography XIV, C. J. Progler, ed., Proc. SPIE4346, 1306–1317 (2001). [CrossRef]
  35. I. Abdulhalim, C. N. Pannell, D. N. Payne, “Fiber compatible fast acousto-optic modulator using a gradient index lens as the interaction medium,” Appl. Phys. Lett. 62, 3402–3404 (1993). [CrossRef]
  36. I. Abdulhalim, C. N. Pannell, “Photoelastically induced light modulation in gradient-index lenses,” Opt. Lett. 18, 1274–1276 (1993). [CrossRef] [PubMed]
  37. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1985).
  38. H. H. Hopkins, Wave Theory of Aberration (Clarendon, Oxford, 1950).
  39. V. N. Mahajan, Aberration Theory Made Simple (SPIE, Bellingham, Wash., 1991). [CrossRef]
  40. G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed. (Cambridge U. Press, London, 1966).
  41. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited