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

  • Vol. 4, Iss. 10 — Oct. 1, 1987
  • pp: 1861–1868

Noncoherent-object hologram: its reconstruction and optical processing

A. S. Marathay  »View Author Affiliations


JOSA A, Vol. 4, Issue 10, pp. 1861-1868 (1987)
http://dx.doi.org/10.1364/JOSAA.4.001861


View Full Text Article

Enhanced HTML    Acrobat PDF (957 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Encoding a complex-amplitude diffraction pattern on a photographic film by addirtg a suitably chosen coherent reference beam forms a conventional hologram. A hologram of a spatially noncoherent object, referred to as a Γ hologram in this paper, is formed by encoding the complex-valued spatial-coherence function on a square-law detector such as photographic film. This record is made possible by means of a self-refetencing interferometer. Such a record behaves much as a hologram does; it permits reconstruction of the original object by illuminating it with a spatially noncoherent planar source of uniform (constant) intensity. If a conventional coherent-light setup is used with a Γ hologram, the intensity distribution of the reconstruction equals the square of the intensity of the original object. In the research reported in this paper, optical processing of spatially noncoherent objects is accomplished by using and modifying the spatial-coherence function. The Γ hologram is used to gain access to this function. This procedure opens new possibilities of noncoherent-object information processing. Examples of matched filtering, low-pass filtering, and high-pass filtering are discussed. The underlying theory has its roots in the fundamental Van Cittert–Zernike theorem of the theory of partial coherence.

© 1987 Optical Society of America

History
Original Manuscript: January 15, 1987
Manuscript Accepted: June 18, 1987
Published: October 1, 1987

Citation
A. S. Marathay, "Noncoherent-object hologram: its reconstruction and optical processing," J. Opt. Soc. Am. A 4, 1861-1868 (1987)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-4-10-1861


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. L. Mertz, N. O. Young, “Fresnel transformations of images,” in Proceedings of Conference on Optical Instruments and Techniques, K. J. Habell, ed. (Chapman and Hall, London, 1962); see also G. L. Rogers, “Experiments in diffraction microscopy,” Proc. Phys. Soc. Edinburgh A 63(III), 193–221 (1952).
  2. G. L. Rogers, Noncoherent Optical Processing (Wiley, New York, 1977).
  3. L. Mertz, Transformation in Optics (Wiley, New York, 1965).
  4. A. W. Lohmann, “Wavefront reconstruction for incoherent objects,”J. Opt. Soc. Am. 55, 1555–1556 (1965). [CrossRef]
  5. H. R. Worthington, “Production of holograms with incoherent illumination,”J. Opt. Soc. Am. 56, 1397–1398 (1966). [CrossRef]
  6. G. Cochran, “New method of making Fresnel transforms with incoherent light,”J. Opt. Soc. Am. 56, 1513–1517 (1966). [CrossRef]
  7. G. D. Collins, “Achromatic Fourier transform holography,” Appl. Opt. 20, 3109–3119 (1981). [CrossRef] [PubMed]
  8. E. N. Leith, G. J. Swanson, “Achromatic interferometers for white light optical processing and holography,” Appl. Opt. 19, 638–644 (1980). [CrossRef] [PubMed]
  9. G. M. Morris, N. George, “Space and wavelength dependence of a dispersion-compensated matched filter,” Appl. Opt. 19, 3843–3850 (1980). [CrossRef] [PubMed]
  10. N. George, S. Wang, “Cosinusoidal transforms in white light,” Appl. Opt. 23, 787–796 (1984). [CrossRef] [PubMed]
  11. A. M. Tai, C. C. Aleksoff, “Grating-based interferometric processor for realtime optical Fourier transformation,” Appl. Opt. 23, 2282–2291 (1984). [CrossRef] [PubMed]
  12. G. Indebetouw, C. Varamit, “Spatial filtering with complementary source-pupil masks,” J. Opt. Soc. Am. A 2, 794–798 (1985). [CrossRef]
  13. A. W. Lohmann, “Incoherent optical processing of complex data,” Appl. Opt. 16, 261–263 (1977). [CrossRef] [PubMed]
  14. A. W. Lohmann, W. T. Rhodes, “Two-pupil synthesis of optical transfer functions,” Appl. Opt. 17, 1141–1151 (1978). [CrossRef] [PubMed]
  15. W. T. Rhodes, “Bipolar pointspread function synthesis by phase switching,” Appl. Opt. 16, 265–267 (1977). [CrossRef] [PubMed]
  16. W. Stoner, “Edge enhancement with incoherent optics,” Appl. Opt. 16, 1451–1452 (1977). [CrossRef] [PubMed]
  17. W. Stoner, “Incoherent optical processing via spatially offset pupil masks,” Appl. Opt. 17, 2454–2467 (1978). [CrossRef] [PubMed]
  18. D. K. Angell, “Incoherent spatial filtering with grating interferometers,” Appl. Opt. 24, 2903–2906 (1985). [CrossRef] [PubMed]
  19. P. Kellman, S. Leonard, E. Barrett, “Digital hologram reconstruction of radio telescope data,” Appl. Opt. 16, 1113–1114 (1977). [CrossRef] [PubMed]
  20. A. S. Marathay, “Hologram and optical processing of spatially noncoherent objects,” J. Opt. Soc. Am. A 3(13), P50 (1986).
  21. K. Itoh, Y. Ohtsuka, “Holographic spectral imaging,” J. Opt. Soc. Am. A 3, 1239–1242 (1986). [CrossRef]
  22. A. S. Marathay, Elements of Optical Coherence Theory (Wiley, New York, 1982).
  23. M. J. Beran, G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964).
  24. For the present discussion we have omitted the quadratic phase factor that occurs in front of the Fourier transform of the intensity of the noncoherent source (see Ref. 22).
  25. M. V. R. K. Murty, “Lateral shearing interferometer,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), Chap. 4, pp. 105–148.
  26. M. V. R. K. Murty, “Interference between wavefronts rotated or reversed with respect to each other and its relation to spatial coherence,”J. Opt. Soc. Am. 54, 1187–1190 (1964). [CrossRef]
  27. J. D. Armitage, A. Lohmann, “Rotary shearing interferometry,” Opt. Acta 12, 185–192 (1965). [CrossRef]
  28. J. B. Breckinridge, “Coherence interferometer and astronomical applications,” Appl. Opt. 11, 2996–2998 (1972). [CrossRef] [PubMed]
  29. J. J. Burke, J. B. Breckinridge, “Passive imaging through the turbulent atmosphere: fundamental limits on the spatial frequency resolution of a rotational shearing interferometer,”J. Opt. Soc. Am. 68, 67–77 (1978). [CrossRef]
  30. J. C. Dainty, R. J. Scaddan, “A coherence interferometer for the direct measurement of the atmospheric transfer function,” Mon. Not. R. Astron. Soc. 167, 69–73 (1974).
  31. The nomenclature is arbitrary to some extent; as used here, the conjugate reconstruction results from the Fourier transform of the function Γ.

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.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited