Abstract

A method is described for efficiently obtaining the comprehensive information of a polychromatic radiator. Under certain conditions both the spatial and spectral details of the radiative object can be recovered simultaneously from the three-dimensional spatial coherence function in the diffraction region. The recovery of object information is based on a Fourier-transform relationship derived from the basic formula [ E. Wolf and W. H. Carter, J. Opt. Soc. Am. 68, 953– 964 ( 1978)] describing the field correlation function in terms of the source correlation function. A new type of interferometer is proposed for the efficient collection of the spatial coherence data. Experimental results of the spectral-image recovery are also presented.

© 1986 Optical Society of America

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  1. M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, London, 1970), Chap. 10.
  2. M. J. Beran, G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964), Chaps. 2 and 3.
  3. J. Perina, Coherence of Light (Van Nostrand-Reinhold, London, 1972), Chaps. 2 and 3.
  4. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chaps. 3 and 5.
  5. L. Mertz, Transformations in Optics (Wiley, New York, 1965), Chaps. 1 and 2.
  6. G. A. Vanasse, H. Sakai, “Fourier spectroscopy,” in Progress in Optics, E. Wolf, ed. (North-Holland, New York, 1967), Vol. 6, pp. 261–327.
    [CrossRef]
  7. L. Mertz, Transformations in Optics (Wiley, New York, 1965), Chap. 4.
  8. T. D. Beard, “Imaging by correlation of intensity fluctuations,” Appl. Phys. Lett. 15, 227–229 (1969).
    [CrossRef]
  9. D. Kohler, L. Mandel, “Source reconstruction from the modulus of the correlation function: practical approach to the phase problem of optical coherence theory,”J. Opt. Soc. Am. 63, 126–134 (1973).
    [CrossRef]
  10. W. T. Rhodes, J. W. Goodman, “Interferometric technique for recording and restoring images degraded by unknown aberrations,”J. Opt. Soc. Am. 63, 647–656 (1973).
    [CrossRef]
  11. J. J. Burk, J. B. Breckinridge, “Passive imaging through the turbulent atomosphere: fundamental limit on the spatial frequency resolution of a rotational shearing interferometer,”J. Opt. Soc. Am. 68, 67–77 (1978).
    [CrossRef]
  12. A. H. Greenaway, J. C. Dainty, “On long-base line amplitude interferometers in astronomical applications,” Opt. Acta 25, 181–189 (1978).
    [CrossRef]
  13. C. Roddier, F. Roddier, “Imaging with a coherence interferometer in optical astronomy,” in Image Formation from Coherence Functions in Astronomy, C. van Schooneveld, ed. (Reidel, Dordrecht, The Netherlands, 1979), pp. 175–178.
    [CrossRef]
  14. K. Itoh, Y. Ohtsuka, “Interferometric image reconstruction through the turbulent atmosphere,” Appl. Opt. 20, 4239–4244 (1981).
    [CrossRef] [PubMed]
  15. See, for example, R. E. Loughhead, R. J. Bray, N. Brown, “Instrument profile of a triple Fabry–Perot interferometer for use in solar spectroscopy,” Appl. Opt. 17, 415–419 (1978).
    [CrossRef] [PubMed]
  16. See, for example, J. M. Hill, J. R. P. Angel, J. S. Scott, D. Lindley, P. Hintzen, “Multiple object spectroscopy: the Medusa spectrograph,” Astrophys. J. 242, L69–L72 (1980).
    [CrossRef]
  17. See, for example, J. B. Breckinridge, N. A. Page, R. R. Shannon, J. M. Rodgers, “Reflecting Schmidt imaging spectrometers,” Appl. Opt. 22, 1175–1180 (1983).
    [CrossRef] [PubMed]
  18. M. Harwit, N. J. A. Sloane, Hadamard Transform Optics (Academic, New York, 1979), Chaps. 3–5.
  19. H. Sakai, “Doubly multiplex Fourier spectroscopy,”J. Opt. Soc. Am. 73, 1947 (1983).
  20. G. Weigelt, “Speckle interferometry, speckle holography, speckle spectroscopy, and reconstruction of high-resolution images from space telescope,” in Proceedings, ESO Conference on Scientific Importance of High Angular Resolution at IR and Optical Wavelengths, M. H. Ulrich, K. Kjar, eds. (European Space Organization, Garching, 1981), pp. 95–113.
  21. E. Wolf, W. H. Carter, “Coherence and radiant intensity in scalar wave fields generated by fluctuating primary planar sources,”J. Opt. Soc. Am. 68, 953–964 (1978).
    [CrossRef]
  22. E. Wolf, A. J. Devaney, “On a relationship between spectral properties and spatial coherence properties of light,” Opt. Lett. 6, 168–170 (1981).
    [CrossRef] [PubMed]
  23. A. W. Lohmann, J. Ojeda-Castaneda, “Spatial periodicities in partially coherent fields,” Opt. Acta 30, 475–479 (1983).
    [CrossRef]
  24. E. Wolf, A. J. Devaney, F. Gori, “Relationship between spectral properties and spatial properties in one-dimensional free fields,” Opt. Commun. 46, 4–8 (1983).
    [CrossRef]
  25. G. Indebetouw, “Spatially periodic wave fields: an experimental demonstration of the relationship between the lateral and the longitudinal spatial frequencies,” Opt. Commun. 49, 86–90 (1984).
    [CrossRef]
  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. H. P. Baltes, H. A. Ferwerda, A. S. Glass, B. Steinle, “Retrieval of structural information from the far-zone intensity and coherence of scattered radiation,” Opt. Acta 28, 11–28 (1981).
    [CrossRef]
  28. H. P. Baltes, A. S. Glass, K. M. Jauch, “Multiplexing of coherence by beam-splitters,” Opt. Acta 28, 873–876 (1981).
    [CrossRef]
  29. H. P. Baltes, K. M. Jauch, “Multiplex version of the Van Cittert–Zernike theorem,”J. Opt. Soc. Am. 71, 1434–1439 (1981).
    [CrossRef]
  30. A. S. Glass, H. P. Baltes, “The significance of far-zone coherence for sources or scatters with hidden periodicity,” Opt. Acta 29, 169–185 (1982).
    [CrossRef]
  31. K. M. Jauch, H. P. Baltes, “Coherence of radiation scattered by grating covered by a diffuser,” Opt. Acta 28, 1013–1015 (1981).
    [CrossRef]
  32. K. M. Jauch, H. P. Baltes, “Reversing-wave-front interferometry of radiation from a diffusely illuminated phase grating,” Opt. Lett. 7, 127–129 (1982).
    [CrossRef] [PubMed]
  33. D. Newman, J. C. Dainty, “Detection of gratings hidden by diffusers using intensity interferometry,” J. Opt. Soc. Am. A 1, 403–411 (1984).
    [CrossRef]
  34. E. B. Fomalont, “Earth-rotation aperture synthesis,” Proc. IEEE 61, 1211–1218 (1973).
    [CrossRef]
  35. R. N. Bracewell, “Computer image processing,” Ann. Rev. Astron. Astrophys. 17, 113–134 (1979).
    [CrossRef]
  36. P. J. Napier, A. R. Thompson, R. D. Eckers, “The very large array: design and performance of a modern synthesis radio telescope,” Proc. IEEE 71, 1295–1320 (1983).
    [CrossRef]
  37. O. Bryngdahl, A. W. Lohmann, “Variable magnification in incoherent holography,” Appl. Opt. 9, 231–232 (1970).
    [CrossRef] [PubMed]
  38. J. C. Dainty, R. J. Scaddan, “A coherence interferometer for direct measurement of the atmospheric transfer function,” Mon. Not. R. Astron. Soc. 167, 69–73 (1974).
  39. J. B. Breckinridge, “Measurement of the amplitude of phase excursions in the earth’s atmosphere,”J. Opt. Soc. Am. 66, 143–144 (1976).
    [CrossRef]
  40. J. W. O’Byrne, School of Physics, University of Sydney, Sydney, Australia (personal communication).
  41. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 2.
  42. J. F. Walkup, J. W. Goodman, “Limitations of fringe parameter estimation at low light levels,”J. Opt. Soc. Am. 63, 399–407 (1973).
    [CrossRef]
  43. A. V. Oppenheim, R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), p. 125.
  44. A. D. Code, “Stellar energy distribution,” in Stellar Atmosphere, J. L. Greenstein, ed. (U. Chicago Press, Chicago, Ill., 1960). p. 85.
  45. J. C. Dainty, “Stellar speckle interferometry,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 286–306.
  46. K. Itoh, Y. Ohtsuka, “Phase estimation based on the maximum likelihood criterion,” Appl. Opt. 22, 3054–3057 (1983).
    [CrossRef] [PubMed]

1984

G. Indebetouw, “Spatially periodic wave fields: an experimental demonstration of the relationship between the lateral and the longitudinal spatial frequencies,” Opt. Commun. 49, 86–90 (1984).
[CrossRef]

D. Newman, J. C. Dainty, “Detection of gratings hidden by diffusers using intensity interferometry,” J. Opt. Soc. Am. A 1, 403–411 (1984).
[CrossRef]

1983

P. J. Napier, A. R. Thompson, R. D. Eckers, “The very large array: design and performance of a modern synthesis radio telescope,” Proc. IEEE 71, 1295–1320 (1983).
[CrossRef]

K. Itoh, Y. Ohtsuka, “Phase estimation based on the maximum likelihood criterion,” Appl. Opt. 22, 3054–3057 (1983).
[CrossRef] [PubMed]

See, for example, J. B. Breckinridge, N. A. Page, R. R. Shannon, J. M. Rodgers, “Reflecting Schmidt imaging spectrometers,” Appl. Opt. 22, 1175–1180 (1983).
[CrossRef] [PubMed]

H. Sakai, “Doubly multiplex Fourier spectroscopy,”J. Opt. Soc. Am. 73, 1947 (1983).

A. W. Lohmann, J. Ojeda-Castaneda, “Spatial periodicities in partially coherent fields,” Opt. Acta 30, 475–479 (1983).
[CrossRef]

E. Wolf, A. J. Devaney, F. Gori, “Relationship between spectral properties and spatial properties in one-dimensional free fields,” Opt. Commun. 46, 4–8 (1983).
[CrossRef]

1982

A. S. Glass, H. P. Baltes, “The significance of far-zone coherence for sources or scatters with hidden periodicity,” Opt. Acta 29, 169–185 (1982).
[CrossRef]

K. M. Jauch, H. P. Baltes, “Reversing-wave-front interferometry of radiation from a diffusely illuminated phase grating,” Opt. Lett. 7, 127–129 (1982).
[CrossRef] [PubMed]

1981

E. Wolf, A. J. Devaney, “On a relationship between spectral properties and spatial coherence properties of light,” Opt. Lett. 6, 168–170 (1981).
[CrossRef] [PubMed]

K. M. Jauch, H. P. Baltes, “Coherence of radiation scattered by grating covered by a diffuser,” Opt. Acta 28, 1013–1015 (1981).
[CrossRef]

H. P. Baltes, H. A. Ferwerda, A. S. Glass, B. Steinle, “Retrieval of structural information from the far-zone intensity and coherence of scattered radiation,” Opt. Acta 28, 11–28 (1981).
[CrossRef]

H. P. Baltes, A. S. Glass, K. M. Jauch, “Multiplexing of coherence by beam-splitters,” Opt. Acta 28, 873–876 (1981).
[CrossRef]

H. P. Baltes, K. M. Jauch, “Multiplex version of the Van Cittert–Zernike theorem,”J. Opt. Soc. Am. 71, 1434–1439 (1981).
[CrossRef]

K. Itoh, Y. Ohtsuka, “Interferometric image reconstruction through the turbulent atmosphere,” Appl. Opt. 20, 4239–4244 (1981).
[CrossRef] [PubMed]

1980

See, for example, J. M. Hill, J. R. P. Angel, J. S. Scott, D. Lindley, P. Hintzen, “Multiple object spectroscopy: the Medusa spectrograph,” Astrophys. J. 242, L69–L72 (1980).
[CrossRef]

1979

R. N. Bracewell, “Computer image processing,” Ann. Rev. Astron. Astrophys. 17, 113–134 (1979).
[CrossRef]

1978

1976

1974

J. C. Dainty, R. J. Scaddan, “A coherence interferometer for direct measurement of the atmospheric transfer function,” Mon. Not. R. Astron. Soc. 167, 69–73 (1974).

1973

1970

1969

T. D. Beard, “Imaging by correlation of intensity fluctuations,” Appl. Phys. Lett. 15, 227–229 (1969).
[CrossRef]

1964

Angel, J. R. P.

See, for example, J. M. Hill, J. R. P. Angel, J. S. Scott, D. Lindley, P. Hintzen, “Multiple object spectroscopy: the Medusa spectrograph,” Astrophys. J. 242, L69–L72 (1980).
[CrossRef]

Baltes, H. P.

A. S. Glass, H. P. Baltes, “The significance of far-zone coherence for sources or scatters with hidden periodicity,” Opt. Acta 29, 169–185 (1982).
[CrossRef]

K. M. Jauch, H. P. Baltes, “Reversing-wave-front interferometry of radiation from a diffusely illuminated phase grating,” Opt. Lett. 7, 127–129 (1982).
[CrossRef] [PubMed]

K. M. Jauch, H. P. Baltes, “Coherence of radiation scattered by grating covered by a diffuser,” Opt. Acta 28, 1013–1015 (1981).
[CrossRef]

H. P. Baltes, A. S. Glass, K. M. Jauch, “Multiplexing of coherence by beam-splitters,” Opt. Acta 28, 873–876 (1981).
[CrossRef]

H. P. Baltes, K. M. Jauch, “Multiplex version of the Van Cittert–Zernike theorem,”J. Opt. Soc. Am. 71, 1434–1439 (1981).
[CrossRef]

H. P. Baltes, H. A. Ferwerda, A. S. Glass, B. Steinle, “Retrieval of structural information from the far-zone intensity and coherence of scattered radiation,” Opt. Acta 28, 11–28 (1981).
[CrossRef]

Beard, T. D.

T. D. Beard, “Imaging by correlation of intensity fluctuations,” Appl. Phys. Lett. 15, 227–229 (1969).
[CrossRef]

Beran, M. J.

M. J. Beran, G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964), Chaps. 2 and 3.

Born, M.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, London, 1970), Chap. 10.

Bracewell, R. N.

R. N. Bracewell, “Computer image processing,” Ann. Rev. Astron. Astrophys. 17, 113–134 (1979).
[CrossRef]

Bray, R. J.

Breckinridge, J. B.

Brown, N.

Bryngdahl, O.

Burk, J. J.

Carter, W. H.

Code, A. D.

A. D. Code, “Stellar energy distribution,” in Stellar Atmosphere, J. L. Greenstein, ed. (U. Chicago Press, Chicago, Ill., 1960). p. 85.

Dainty, J. C.

D. Newman, J. C. Dainty, “Detection of gratings hidden by diffusers using intensity interferometry,” J. Opt. Soc. Am. A 1, 403–411 (1984).
[CrossRef]

A. H. Greenaway, J. C. Dainty, “On long-base line amplitude interferometers in astronomical applications,” Opt. Acta 25, 181–189 (1978).
[CrossRef]

J. C. Dainty, R. J. Scaddan, “A coherence interferometer for direct measurement of the atmospheric transfer function,” Mon. Not. R. Astron. Soc. 167, 69–73 (1974).

J. C. Dainty, “Stellar speckle interferometry,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 286–306.

Devaney, A. J.

E. Wolf, A. J. Devaney, F. Gori, “Relationship between spectral properties and spatial properties in one-dimensional free fields,” Opt. Commun. 46, 4–8 (1983).
[CrossRef]

E. Wolf, A. J. Devaney, “On a relationship between spectral properties and spatial coherence properties of light,” Opt. Lett. 6, 168–170 (1981).
[CrossRef] [PubMed]

Eckers, R. D.

P. J. Napier, A. R. Thompson, R. D. Eckers, “The very large array: design and performance of a modern synthesis radio telescope,” Proc. IEEE 71, 1295–1320 (1983).
[CrossRef]

Ferwerda, H. A.

H. P. Baltes, H. A. Ferwerda, A. S. Glass, B. Steinle, “Retrieval of structural information from the far-zone intensity and coherence of scattered radiation,” Opt. Acta 28, 11–28 (1981).
[CrossRef]

Fomalont, E. B.

E. B. Fomalont, “Earth-rotation aperture synthesis,” Proc. IEEE 61, 1211–1218 (1973).
[CrossRef]

Glass, A. S.

A. S. Glass, H. P. Baltes, “The significance of far-zone coherence for sources or scatters with hidden periodicity,” Opt. Acta 29, 169–185 (1982).
[CrossRef]

H. P. Baltes, A. S. Glass, K. M. Jauch, “Multiplexing of coherence by beam-splitters,” Opt. Acta 28, 873–876 (1981).
[CrossRef]

H. P. Baltes, H. A. Ferwerda, A. S. Glass, B. Steinle, “Retrieval of structural information from the far-zone intensity and coherence of scattered radiation,” Opt. Acta 28, 11–28 (1981).
[CrossRef]

Goodman, J. W.

Gori, F.

E. Wolf, A. J. Devaney, F. Gori, “Relationship between spectral properties and spatial properties in one-dimensional free fields,” Opt. Commun. 46, 4–8 (1983).
[CrossRef]

Greenaway, A. H.

A. H. Greenaway, J. C. Dainty, “On long-base line amplitude interferometers in astronomical applications,” Opt. Acta 25, 181–189 (1978).
[CrossRef]

Harwit, M.

M. Harwit, N. J. A. Sloane, Hadamard Transform Optics (Academic, New York, 1979), Chaps. 3–5.

Hill, J. M.

See, for example, J. M. Hill, J. R. P. Angel, J. S. Scott, D. Lindley, P. Hintzen, “Multiple object spectroscopy: the Medusa spectrograph,” Astrophys. J. 242, L69–L72 (1980).
[CrossRef]

Hintzen, P.

See, for example, J. M. Hill, J. R. P. Angel, J. S. Scott, D. Lindley, P. Hintzen, “Multiple object spectroscopy: the Medusa spectrograph,” Astrophys. J. 242, L69–L72 (1980).
[CrossRef]

Indebetouw, G.

G. Indebetouw, “Spatially periodic wave fields: an experimental demonstration of the relationship between the lateral and the longitudinal spatial frequencies,” Opt. Commun. 49, 86–90 (1984).
[CrossRef]

Itoh, K.

Jauch, K. M.

K. M. Jauch, H. P. Baltes, “Reversing-wave-front interferometry of radiation from a diffusely illuminated phase grating,” Opt. Lett. 7, 127–129 (1982).
[CrossRef] [PubMed]

K. M. Jauch, H. P. Baltes, “Coherence of radiation scattered by grating covered by a diffuser,” Opt. Acta 28, 1013–1015 (1981).
[CrossRef]

H. P. Baltes, A. S. Glass, K. M. Jauch, “Multiplexing of coherence by beam-splitters,” Opt. Acta 28, 873–876 (1981).
[CrossRef]

H. P. Baltes, K. M. Jauch, “Multiplex version of the Van Cittert–Zernike theorem,”J. Opt. Soc. Am. 71, 1434–1439 (1981).
[CrossRef]

Kohler, D.

Lindley, D.

See, for example, J. M. Hill, J. R. P. Angel, J. S. Scott, D. Lindley, P. Hintzen, “Multiple object spectroscopy: the Medusa spectrograph,” Astrophys. J. 242, L69–L72 (1980).
[CrossRef]

Lohmann, A. W.

A. W. Lohmann, J. Ojeda-Castaneda, “Spatial periodicities in partially coherent fields,” Opt. Acta 30, 475–479 (1983).
[CrossRef]

O. Bryngdahl, A. W. Lohmann, “Variable magnification in incoherent holography,” Appl. Opt. 9, 231–232 (1970).
[CrossRef] [PubMed]

Loughhead, R. E.

Mandel, L.

Mertz, L.

L. Mertz, Transformations in Optics (Wiley, New York, 1965), Chaps. 1 and 2.

L. Mertz, Transformations in Optics (Wiley, New York, 1965), Chap. 4.

Murty, M. V. R. K.

Napier, P. J.

P. J. Napier, A. R. Thompson, R. D. Eckers, “The very large array: design and performance of a modern synthesis radio telescope,” Proc. IEEE 71, 1295–1320 (1983).
[CrossRef]

Newman, D.

O’Byrne, J. W.

J. W. O’Byrne, School of Physics, University of Sydney, Sydney, Australia (personal communication).

Ohtsuka, Y.

Ojeda-Castaneda, J.

A. W. Lohmann, J. Ojeda-Castaneda, “Spatial periodicities in partially coherent fields,” Opt. Acta 30, 475–479 (1983).
[CrossRef]

Oppenheim, A. V.

A. V. Oppenheim, R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), p. 125.

Page, N. A.

Parrent, G. B.

M. J. Beran, G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, N.J., 1964), Chaps. 2 and 3.

Perina, J.

J. Perina, Coherence of Light (Van Nostrand-Reinhold, London, 1972), Chaps. 2 and 3.

Rhodes, W. T.

Roddier, C.

C. Roddier, F. Roddier, “Imaging with a coherence interferometer in optical astronomy,” in Image Formation from Coherence Functions in Astronomy, C. van Schooneveld, ed. (Reidel, Dordrecht, The Netherlands, 1979), pp. 175–178.
[CrossRef]

Roddier, F.

C. Roddier, F. Roddier, “Imaging with a coherence interferometer in optical astronomy,” in Image Formation from Coherence Functions in Astronomy, C. van Schooneveld, ed. (Reidel, Dordrecht, The Netherlands, 1979), pp. 175–178.
[CrossRef]

Rodgers, J. M.

Sakai, H.

H. Sakai, “Doubly multiplex Fourier spectroscopy,”J. Opt. Soc. Am. 73, 1947 (1983).

G. A. Vanasse, H. Sakai, “Fourier spectroscopy,” in Progress in Optics, E. Wolf, ed. (North-Holland, New York, 1967), Vol. 6, pp. 261–327.
[CrossRef]

Scaddan, R. J.

J. C. Dainty, R. J. Scaddan, “A coherence interferometer for direct measurement of the atmospheric transfer function,” Mon. Not. R. Astron. Soc. 167, 69–73 (1974).

Schafer, R. W.

A. V. Oppenheim, R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), p. 125.

Scott, J. S.

See, for example, J. M. Hill, J. R. P. Angel, J. S. Scott, D. Lindley, P. Hintzen, “Multiple object spectroscopy: the Medusa spectrograph,” Astrophys. J. 242, L69–L72 (1980).
[CrossRef]

Shannon, R. R.

Sloane, N. J. A.

M. Harwit, N. J. A. Sloane, Hadamard Transform Optics (Academic, New York, 1979), Chaps. 3–5.

Steinle, B.

H. P. Baltes, H. A. Ferwerda, A. S. Glass, B. Steinle, “Retrieval of structural information from the far-zone intensity and coherence of scattered radiation,” Opt. Acta 28, 11–28 (1981).
[CrossRef]

Thompson, A. R.

P. J. Napier, A. R. Thompson, R. D. Eckers, “The very large array: design and performance of a modern synthesis radio telescope,” Proc. IEEE 71, 1295–1320 (1983).
[CrossRef]

Vanasse, G. A.

G. A. Vanasse, H. Sakai, “Fourier spectroscopy,” in Progress in Optics, E. Wolf, ed. (North-Holland, New York, 1967), Vol. 6, pp. 261–327.
[CrossRef]

Walkup, J. F.

Weigelt, G.

G. Weigelt, “Speckle interferometry, speckle holography, speckle spectroscopy, and reconstruction of high-resolution images from space telescope,” in Proceedings, ESO Conference on Scientific Importance of High Angular Resolution at IR and Optical Wavelengths, M. H. Ulrich, K. Kjar, eds. (European Space Organization, Garching, 1981), pp. 95–113.

Wolf, E.

E. Wolf, A. J. Devaney, F. Gori, “Relationship between spectral properties and spatial properties in one-dimensional free fields,” Opt. Commun. 46, 4–8 (1983).
[CrossRef]

E. Wolf, A. J. Devaney, “On a relationship between spectral properties and spatial coherence properties of light,” Opt. Lett. 6, 168–170 (1981).
[CrossRef] [PubMed]

E. Wolf, W. H. Carter, “Coherence and radiant intensity in scalar wave fields generated by fluctuating primary planar sources,”J. Opt. Soc. Am. 68, 953–964 (1978).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, London, 1970), Chap. 10.

Ann. Rev. Astron. Astrophys.

R. N. Bracewell, “Computer image processing,” Ann. Rev. Astron. Astrophys. 17, 113–134 (1979).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

T. D. Beard, “Imaging by correlation of intensity fluctuations,” Appl. Phys. Lett. 15, 227–229 (1969).
[CrossRef]

Astrophys. J.

See, for example, J. M. Hill, J. R. P. Angel, J. S. Scott, D. Lindley, P. Hintzen, “Multiple object spectroscopy: the Medusa spectrograph,” Astrophys. J. 242, L69–L72 (1980).
[CrossRef]

J. Opt. Soc. Am.

H. Sakai, “Doubly multiplex Fourier spectroscopy,”J. Opt. Soc. Am. 73, 1947 (1983).

E. Wolf, W. H. Carter, “Coherence and radiant intensity in scalar wave fields generated by fluctuating primary planar sources,”J. Opt. Soc. Am. 68, 953–964 (1978).
[CrossRef]

D. Kohler, L. Mandel, “Source reconstruction from the modulus of the correlation function: practical approach to the phase problem of optical coherence theory,”J. Opt. Soc. Am. 63, 126–134 (1973).
[CrossRef]

W. T. Rhodes, J. W. Goodman, “Interferometric technique for recording and restoring images degraded by unknown aberrations,”J. Opt. Soc. Am. 63, 647–656 (1973).
[CrossRef]

J. J. Burk, J. B. Breckinridge, “Passive imaging through the turbulent atomosphere: fundamental limit on the spatial frequency resolution of a rotational shearing interferometer,”J. Opt. Soc. Am. 68, 67–77 (1978).
[CrossRef]

J. B. Breckinridge, “Measurement of the amplitude of phase excursions in the earth’s atmosphere,”J. Opt. Soc. Am. 66, 143–144 (1976).
[CrossRef]

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]

H. P. Baltes, K. M. Jauch, “Multiplex version of the Van Cittert–Zernike theorem,”J. Opt. Soc. Am. 71, 1434–1439 (1981).
[CrossRef]

J. F. Walkup, J. W. Goodman, “Limitations of fringe parameter estimation at low light levels,”J. Opt. Soc. Am. 63, 399–407 (1973).
[CrossRef]

J. Opt. Soc. Am. A

Mon. Not. R. Astron. Soc.

J. C. Dainty, R. J. Scaddan, “A coherence interferometer for direct measurement of the atmospheric transfer function,” Mon. Not. R. Astron. Soc. 167, 69–73 (1974).

Opt. Acta

A. S. Glass, H. P. Baltes, “The significance of far-zone coherence for sources or scatters with hidden periodicity,” Opt. Acta 29, 169–185 (1982).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Geometry: (a) free-space propagation and (b) propagation through a positive lens. The mutual coherence function propagates from polychromatic incoherent source σ to an observation area, where the mutual coherence function at Q1 and Q2 without the time delay is evaluated.

Fig. 2
Fig. 2

Spectral image of a monochromatic point object. The spatial information is preserved in the angular position of image, while the spectral information is encoded in the distance between the origin and the point of image.

Fig. 3
Fig. 3

Schematic of the volume interferometer. The light beams split by BS (beam splitter) are reflected back by P1 and P2 (right-angle prisms) and combined again at BS. The superposed wave field suffers from lateral shear of 180° rotation. The motion of P2 further introduces longitudinal shear, and thus a 3-D shear displacement is achieved.

Fig. 4
Fig. 4

Reconstructed spectral image of a point object composed of He–Cd (4416-Å) and He–Ne (6328-Å) laser spectra. Two different aspects are shown along with the spurious images. The two spectral components lie on the same radial line, which indicates the angular position of object.

Equations (20)

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Γ ( Q 1 , Q 2 , 0 ) = - - 0 ( R 1 R 2 ) - 1 G ( P , ν ) × exp [ j k ( R 1 - R 2 ) ] d ν d P ,
k ( R 1 - R 2 ) k · r ,
k = k ( Z - P ) / Z - P , Z = ( 0 , 0 , Z ) , r = R 1 - R 2 = Q 1 - Q 2 .
Z π a 2 / λ ,
P = ( Z tan ϕ cos θ , Z tan ϕ sin θ ) .
R 1 R 2 - Z / cos ϕ .
Γ ( r ) = - 0 2 π π / 2 π 0 G ( Z tan ϕ cos θ , Z tan ϕ sin θ , ν ) × exp ( j k · r ) tan ϕ cos θ d ν d ϕ d θ ,
Γ t ( t ) = G c ( s ) exp ( - 2 π t · s ) d s ,
Γ t ( t ) = Γ ( c t ) ,
G c ( s ) = G ( Z u / w , Z v / w , s ) / ( - s ω ) .
Γ ( Q 1 , Q 2 , 0 ) = - 0 K ( Q 1 , P , ν ) × K * ( Q 2 , P , ν ) G ( P , ν ) d ν d P ,
K ( Q m , P , ν ) = R m - 1 exp ( j k R m ) .
K ( Q m , P , ν ) = - Z - 1 exp [ j ( k · R m - k Z / cos ϕ ) ] cos ϕ ,
I ( r ) = { Γ ( 0 ) + [ Γ ( 2 r ) + Γ ( - 2 r ) ] / 2 } / 2 ,
I t ( t ) = I ( c t ) = { Γ t ( 0 ) + [ Γ t ( 2 t ) + Γ t ( - 2 t ) ] / 2 } / 2.
I ˜ t ( s ) = { G 0 δ ( s ) + [ G c ( s / 2 ) / 8 + G c ( - s / 2 ) / 8 ] / 2 } / 2 ,
G 0 = - G c ( s ) d s .
ρ 0 = N 0 / [ 2 ( N b + N 0 ) ] 1 / 2 ,
ρ 0 = N 0 / [ 2 ( N b + N t ) ] 1 / 2 ,
N t = η A B N s T 10 3 - 0.4 m v ,

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