OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 17, Iss. 12 — Dec. 1, 2000
  • pp: 2223–2228

Aberrations of diffracted wave fields. II. Diffraction gratings

Virendra N. Mahajan  »View Author Affiliations

JOSA A, Vol. 17, Issue 12, pp. 2223-2228 (2000)

View Full Text Article

Enhanced HTML    Acrobat PDF (244 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The Rayleigh–Sommerfeld theory is applied to diffraction of a spherical wave by a grating. The grating equation is obtained from the aberration-free diffraction pattern, and its aberrations are shown to be the same as the conventional aberrations obtained by using Fermat’s principle. These aberrations are shown to be not associated with the diffraction process. Moreover, it is shown that the irradiance distribution of a certain diffraction order is the Fraunhofer diffraction pattern of the grating aperture as a whole aberrated by the aberration of that order.

© 2000 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(080.1010) Geometric optics : Aberrations (global)
(110.2990) Imaging systems : Image formation theory
(230.1950) Optical devices : Diffraction gratings
(260.1960) Physical optics : Diffraction theory

Original Manuscript: April 24, 2000
Revised Manuscript: July 3, 2000
Manuscript Accepted: July 14, 2000
Published: December 1, 2000

Virendra N. Mahajan, "Aberrations of diffracted wave fields. II. Diffraction gratings," J. Opt. Soc. Am. A 17, 2223-2228 (2000)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. J. E. Harvey, R. V. Shack, “Aberrations of diffracted wave fields,” Appl. Opt. 17, 3003–3009 (1978);also, J. E. Harvey, “Fourier treatment of near-field scalar theory,” Am. J. Phys. 47, 974–980 (1979). [CrossRef] [PubMed]
  2. V. N. Mahajan, “Aberrations of diffracted wave fields. I. Optical imaging,” J. Opt. Soc. Am. A 17, 2216–2222 (2000). [CrossRef]
  3. D. J. Schroeder, Astronomical Optics (Academic, New York, 1987), Chap. 14.A comprehensive treatment of gratings is given in this book. However, the aberration function given by Eq. (14.2.1) is for a reflection grating, although Figure 14.1 is for a transmission grating. The correct expression for a transmission grating is obtained if the sign of the first term in each square bracket is made minus [D. J. Schroeder, Professor Emeritus, Department of Physics and Astronomy, Beloit College, Beloit, Wisconsin 53511 (personal communication, 2000)].
  4. W. T. Welford, “Aberration theory of gratings and grating mountings,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1965), Vol. IV, Chap. 6.
  5. A. Sommerfeld, Optics (Academic, New York, 1972), Vol. 4, pp. 199–201; substitute Eq. (8) on p. 201 into Eq. (6) on p. 199.
  6. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 43–44; substitute Eq. (3-23) on p. 44 into Eq. (3-15) on p. 43.
  7. H. Osterberg, L. W. Smith, “Closed solutions of Rayleigh’s diffraction integrals for axial points,” J. Opt. Soc. Am. A 51, 1050–1054 (1961). [CrossRef]
  8. V. N. Mahajan, “Axial irradiance and optimum focusing of laser beams,” Appl. Opt. 22, 3042–3053 (1983). [CrossRef] [PubMed]
  9. V. N. Mahajan, Optical Imaging and Aberrations. Part I: Ray Geometrical Optics (SPIE, Bellingham, Wash., 1998), Sec. 5.2.
  10. V. N. Mahajan, Optical Imaging and Aberrations. Part I: Ray Geometrical Optics (SPIE, Bellingham, Wash., 1998), Sec. 3.2.
  11. V. N. Mahajan, “Comparison of geometrical and diffraction point-spread functions,” in International Conference on Optics and Optoelectronics ’98, K. Singh, O. P. Nijhawan, A. K. Gupta, A. K. Musla, eds., Proc. SPIE3729, 434–445 (1998). [CrossRef]
  12. M. V. R. K. Murty, “Use of convergent and divergent illumination with plane gratings,” J. Opt. Soc. Am. 52, 768–773 (1962). [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.


Fig. 1

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited