OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 19, Iss. 4 — Apr. 1, 2002
  • pp: 781–791

Point-spread function for a rotationally symmetric birefringent lens

Yasuyuki Unno  »View Author Affiliations

JOSA A, Vol. 19, Issue 4, pp. 781-791 (2002)

View Full Text Article

Enhanced HTML    Acrobat PDF (782 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Imaging properties of a birefringent lens, in which the fast (or the slow) axis is distributed in the radial direction whereas magnitude of birefringence varies as a quadratic function of the pupil radius, are investigated by calculating a point-spread function. It is found that the point image is analytically described by using the Lommel function as well as the zero-order Bessel function, and a localized intensity null surrounded by bright regions in all directions can be realized at a geometrical focus under certain conditions. The magnitude of birefringence that is tolerable in image formations is also discussed, assuming that the lens is applied to microlithography.

© 2002 Optical Society of America

OCIS Codes
(110.2990) Imaging systems : Image formation theory
(110.3000) Imaging systems : Image quality assessment
(110.3960) Imaging systems : Microlithography
(260.1440) Physical optics : Birefringence
(260.5430) Physical optics : Polarization

Original Manuscript: May 22, 2001
Revised Manuscript: September 25, 2001
Manuscript Accepted: September 27, 2001
Published: April 1, 2002

Yasuyuki Unno, "Point-spread function for a rotationally symmetric birefringent lens," J. Opt. Soc. Am. A 19, 781-791 (2002)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. F. Ratajczyk, “A method of calculation of permissible birefringence in lenses of the optical instruments,” Optik (Stuttgart) 68, 61–68 (1984).
  2. 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]
  3. J. P. Lesso, A. J. Duncan, W. Sibbett, M. J. Padgett, “Aberrations introduced by a lens made from a birefringent material,” Appl. Opt. 39, 592–598 (2000). [CrossRef]
  4. Y. Unno, “Influence of birefringence on the image formation of high-resolution projection optics,” Appl. Opt. 39, 3243–3252 (2000). [CrossRef]
  5. 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]
  6. L. Dayson, “Common-path interferometer for testing purposes,” J. Opt. Soc. Am. 47, 386–390 (1957). [CrossRef]
  7. X. Yang, C. Xiang, G. Zhang, “Birefringent common-path interferometer for testing large convex spherical surfaces,” Opt. Eng. 32, 1080–1083 (1993). [CrossRef]
  8. K. Kinnstatter, M. Ojima, S. Yonezawa, “Amplitude detection for the focus error in optical disks using a birefringent lens,” Appl. Opt. 29, 4408–4413 (1990). [CrossRef] [PubMed]
  9. S. Sanyal, P. Bandyopadhyay, A. Ghosh, “Vector wave imagery using a birefringent lens,” Opt. Eng. 37, 592–599 (1998). [CrossRef]
  10. S. Sanyal, A. Ghosh, “High focal depth with a quasi-bifocus birefringent lens,” Appl. Opt. 39, 2321–2325 (2000). [CrossRef]
  11. H. Fukuda, A. Imai, T. Terasawa, S. Okazaki, “New approach to resolution limit and advanced image formation techniques in optical lithography,” IEEE Trans. Electron Devices 38, 67–75 (1991). [CrossRef]
  12. M. Maenhoudt, S. Verhaegen, K. Ronse, P. Zandbergen, E. Muzio, “Limits of optical lithography,” in Optical Microlithography XIII, C. J. Progler, ed., Proc. SPIE4000, 373–387 (2000). [CrossRef]
  13. R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).
  14. R. A. Chipman, L. J. Chipman, “Polarization aberration diagrams,” Opt. Eng. 28, 100–106 (1989). [CrossRef]
  15. J. P. McGuire, R. A. Chipman, “Diffraction image formation in optical systems with polarization aberrations. I: Formulation and example,” J. Opt. Soc. Am. A 7, 1614–1626 (1990). [CrossRef]
  16. C. Jones, “A new calculus for the treatment of optical systems. I. Description and discussion of the calculus,” J. Opt. Soc. Am. 31, 488–493 (1941). [CrossRef]
  17. Y. Unno, “Distorted wave front produced by a high-resolution projection optical system having rotationally symmetric birefringence,” Appl. Opt. 37, 7241–7247 (1998). [CrossRef]
  18. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 3.
  19. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 8.
  20. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 9.
  21. A. Yariv, Optical Electronics, 4th ed. (Saunders, Fort Worth, Texas, 1991), Chap. 1.
  22. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 4.
  23. L. C. Andrews, Special Functions of Mathematics for Engineers, 2nd ed. (Oxford U. Press, Oxford, UK, 1998), Chap. 6.
  24. W. J. Condell, “Fraunhofer diffraction from a circular annular aperture with helical phase factor,” J. Opt. Soc. Am. A 2, 206–208 (1985). [CrossRef]
  25. M. Harris, C. A. Hill, J. M. Vaughan, “Optical helices and spiral interference fringes,” Opt. Commun. 106, 161–166 (1994). [CrossRef]
  26. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986). [CrossRef] [PubMed]
  27. K. T. Gahagan, G. A. Swartzlander, “Trapping of low-index microparticles in an optical vortex,” J. Opt. Soc. Am. B 15, 524–534 (1998). [CrossRef]
  28. J. Arlt, M. J. Padgett, “Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam,” Opt. Lett. 25, 191–193 (2000). [CrossRef]

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