OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 30, Iss. 10 — Oct. 1, 2013
  • pp: 2150–2161

Balanced diffraction aberrations, independent of the observation point: application to a tilted dielectric plate

Colin J. R. Sheppard  »View Author Affiliations


JOSA A, Vol. 30, Issue 10, pp. 2150-2161 (2013)
http://dx.doi.org/10.1364/JOSAA.30.002150


View Full Text Article

Enhanced HTML    Acrobat PDF (508 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Balancing of Zernike aberrations breaks down if the defocus term is large enough that the condition (z/λ)2/[π(NA)4] is not satisfied. A modified Zernike aberration expansion, based on the Zernike aberrations, is developed that accurately includes axial displacement as a low-order term, even for large displacements. This expansion can be used to analyze aberrations for on-axis illumination of a high numerical aperture system. But more importantly, for systems of moderate numerical aperture it allows balanced aberration coefficients to be determined independent of the assumption of a particular reference point. The approach is applied to the case of a tilted dielectric plate. An exact expression is given for the wave front aberration, valid for both large angles of tilt and high beam convergence angles, that is independent of observation distance. Analytical expressions for the third- and fifth-order aberration coefficients are derived. Expressions are given for expansion of multiple-angle power series terms into Zernike polynomials.

© 2013 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(260.1960) Physical optics : Diffraction theory

ToC Category:
Physical Optics

History
Original Manuscript: June 13, 2013
Revised Manuscript: August 30, 2013
Manuscript Accepted: August 30, 2013
Published: September 30, 2013

Citation
Colin J. R. Sheppard, "Balanced diffraction aberrations, independent of the observation point: application to a tilted dielectric plate," J. Opt. Soc. Am. A 30, 2150-2161 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-10-2150


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. C. J. R. Sheppard, “Limitations of the paraxial Debye approximation,” Opt. Lett. 38, 1074–1076 (2013). [CrossRef]
  2. H. H. Hopkins, “The Airy disc formula for systems of high relative aperture,” Proc. Phys. Soc. 55, 116–128 (1943). [CrossRef]
  3. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959). [CrossRef]
  4. P. Török, P. Varga, Z. Laczik, and G. R. Booker, “Electromagnetic diffraction of light focused through a planar interface between materials of mismatched refractive indices: an integral representation,” J. Opt. Soc. Am. A 12, 325–332 (1995). [CrossRef]
  5. L. E. Helseth, “Electromagnetic focusing through a tilted dielectric surface,” Opt. Commun. 215, 247–250 (2003). [CrossRef]
  6. M. Born and E. Wolf, Principles of Optics, 1st ed. (Pergamon, 1959).
  7. E. H. Linfoot and E. Wolf, “Phase distribution near focus in an aberration-free diffraction image,” Proc. Phys. Soc. London Sect. B 69, 823–832 (1956). [CrossRef]
  8. J. C. Dainty, “The image of a point for an aberration free lens with a circular pupil,” Opt. Commun. 1, 176–178 (1969). [CrossRef]
  9. C. J. R. Sheppard, “Orthogonal aberration functions for high-aperture optical systems,” J. Opt. Soc. Am. A 21, 832–838 (2004). [CrossRef]
  10. C. J. R. Sheppard, “Orthogonal aberration functions for high-aperture optical systems: erratum,” J. Opt. Soc. Am. A 21, 2468–2469 (2004). [CrossRef]
  11. C. J. R. Sheppard, S. Campbell, and M. D. Hirschhorn, “Zernike expansion of separable function of Cartesian coordinates,” Appl. Opt. 43, 3963–3966 (2004). [CrossRef]
  12. C. J. R. Sheppard and H. J. Matthews, “Imaging in high aperture optical systems,” J. Opt. Soc. Am. A 4, 1354–1360 (1987). [CrossRef]
  13. C. J. R. Sheppard, “Aberrations in high aperture conventional and confocal imaging systems,” Appl. Opt. 27, 4782–4786 (1988). [CrossRef]
  14. C. J. R. Sheppard, “Aberrations in high aperture optical systems,” Optik 105, 29–33 (1997).
  15. R. Kant, “An analytical solution of vector diffraction for focusing optical systems with Seidel aberrations. I. Spherical aberration, curvature of field, and distortion,” J. Mod. Opt. 40, 2293–2310 (1993). [CrossRef]
  16. G. Conforti, “Zernike aberration coefficients from Seidel and higher-order power-series coefficients,” Opt. Lett. 8, 407–408 (1983). [CrossRef]
  17. R. K. Tyson, “Conversion of Zernike aberration coefficients to Seidel and higher-order power-series aberration coefficients,” Opt. Lett. 7, 262–264 (1982). [CrossRef]
  18. G. N. Lawrence and R. D. Day, “Interferometric characterization of full spheres: data reduction techniques,” Appl. Opt. 26, 4875–4882 (1987). [CrossRef]
  19. B. Cuny, “Correction des aberrations introduites par une lame inclinée en lumière convergente,” Rev. Opt. 34, 460–464 (1955).
  20. H. de Lang, “Compensation of aberrations caused by oblique plane parallel plates,” Philips Res. Rep. 12, 181–189 (1957).
  21. M. Herzberger, Modern Geometrical Optics (Interscience, 1958).
  22. W. J. Smith, Modern Optical Engineering (McGraw-Hill, 1966).
  23. R. Kingslake, Lens Design Fundamentals (Academic, 1978).
  24. W. T. Welford, Aberrations of Optical Systems (Hilger, 1986).
  25. H. A. Buchdahl, An Introduction to Hamiltonian Optics (Dover, 1993).
  26. R. E. Gerber and M. Mansuripur, “Tilt correction in an optical disk system,” Appl. Opt. 35, 7000–7007 (1996). [CrossRef]
  27. J. Braat, “Analytical expressions for the wave-front aberration coefficients of a tilted plane-parallel plate,” Appl. Opt. 36, 8459–8467 (1997). [CrossRef]
  28. A. Miks and P. Pokorny, “Analytical expressions for the circle of confusion induced by plane-parallel plate,” Opt. Lasers Eng. 50, 1517–1521 (2012). [CrossRef]
  29. K. Thompson, “Description of the third-order optical aberrations of near-circular pupil optical systems without symmetry,” J. Opt. Soc. Am. A 22, 1389–1401 (2005). [CrossRef]
  30. R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).
  31. J. P. McGuire and R. A. Chipman, “Polarization aberrations. 1. Rotationally symmetric optical systems,” Appl. Opt. 33, 5080–5100 (1994). [CrossRef]
  32. M. Shribak, S. Inoue, and R. Oldenbourg, “Polarization aberrations caused by differential transmission and phase shift in high numerical- aperture lenses: theory, measurement, and rectification,” Opt. Eng. 41, 943–954 (2002). [CrossRef]
  33. M. Totzeck, P. Gräupner, T. Heil, A. Göhnermeier, O. Dittmann, D. Krähmer, V. Kamenov, J. Ruoff, and D. Flagello, “Polarization influence on imaging,” J. Microlith. Microfab. Microsyst. 4, 031108 (2005). [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

OSA is a member of CrossRef.

CrossCheck Deposited