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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 2 — Feb. 1, 2001
  • pp: 332–337

Necessary conditions for spatially incoherent illumination of a three-dimensional object

Joseph van der Gracht  »View Author Affiliations

JOSA A, Vol. 18, Issue 2, pp. 332-337 (2001)

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Spatially incoherent imaging systems are characterized by a linear-in-intensity relationship between the object and the image distributions. While strict spatial incoherence is theoretically not achievable, a particular imaging system may be made effectively linear in intensity by a choice of the appropriate illumination source location and size. The requirement for source size for effectively incoherent illumination of a two-dimensional object is well known. I extend the arguments for choosing the source size in a two-dimensional imaging system to develop necessary conditions for the source size for effectively spatially incoherent illumination of a three-dimensional object. While the conditions are necessary, they are not sufficient, since coherence in the direction of the optical axis is not addressed.

© 2001 Optical Society of America

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(110.2990) Imaging systems : Image formation theory
(110.4980) Imaging systems : Partial coherence in imaging
(180.6900) Microscopy : Three-dimensional microscopy

Original Manuscript: August 23, 1999
Revised Manuscript: August 31, 2000
Manuscript Accepted: August 31, 2000
Published: February 1, 2001

Joseph van der Gracht, "Necessary conditions for spatially incoherent illumination of a three-dimensional object," J. Opt. Soc. Am. A 18, 332-337 (2001)

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  1. R. E. Swing, “Conditions for microdensitometer linearity,” J. Opt. Soc. Am. 62, 199–207 (1972). [CrossRef]
  2. N. Brousseau, H. H. Arseneault, “Les effets causes par les dimensions de la source dans les systèmes optiques eclaires en lumière spatialement incoherente,” Opt. Commun. 15, 389–391 (1975). [CrossRef]
  3. J. W. Goodman, Statistical Optics, 1st ed. (Wiley, New York, 1985).
  4. B. E. A. Saleh, W. C. Goeke, “Linear restoration of bilinearly distorted images,” J. Opt. Soc. Am. 70, 506–515 (1980). [CrossRef]
  5. B. E. A. Saleh, M. Rabanni, “Restoration of bilinearly distorted images: II. Bayesian method,” J. Opt. Soc. Am. 73, 71–75 (1983) . [CrossRef]
  6. C. J. R. Sheppard, X. Q. Mao, “Three-dimensional imaging in a microscope,” J. Opt. Soc. Am. A 6, 1260–1269 (1989). [CrossRef]
  7. D. N. Sitter, “Space invariant modeling in three-dimensional image formation,” Ph.D. dissertation (Georgia Institute of Technology, Atlanta, Ga., 1991).
  8. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1991).
  9. D. N. Sitter, W. T. Rhodes, “Three-dimensional imaging: a space invariant model for space variant systems,” Appl. Opt. 29, 3789–3794 (1990). [CrossRef] [PubMed]
  10. N. Streibl, “Depth transfer by an imaging system,” Opt. Acta 31, 1233–1241 (1984). [CrossRef]
  11. B. E. A. Saleh, “Optical bilinear transforms,” Opt. Acta 26, 777–799 (1979). [CrossRef]
  12. D. S. Goodman, “Stationary optical projectors,” Ph.D dissertation (University of Arizona, Tucson, Ariz., 1979).
  13. D. Slepian, “On bandwidth,” Proc. IEEE 64, 292–300 (1976). [CrossRef]
  14. H. H. Hopkins, “On the diffraction theory of optical images,” Proc. R. Soc. London Ser. A 217408–432 (1953). [CrossRef]
  15. D. S. Goodman, A. E. Rosenbluth, “Condenser aberrations in Köhler illumination,” in Optical/Laser Microlithography, B. J. Lin, ed., Proc. SPIE922, 108–134 (1988). [CrossRef]

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