Abstract

Recent progress in coherent and incoherent optical inverse-scattering problems is reviewed with emphasis on the construction of grating-groove profiles from known or desired diffraction efficiencies and the detection of phase gratings hidden by diffusers using optical correlation techniques. Retrieval and synthesis problems and the role of coherence are described. The coherent grating-profile reconstruction is revisited in terms of the full mathematical description of our previous procedure. The crucial role of prior phase information for uniqueness of the reconstruction is elucidated. The theoretical prediction and experimental verification of a provoking coherence effect are presented: The signature of a hidden phase grating can be seen in the far-zone coherence function but not in the far-zone intensity for a certain range of ratios of the diffuser correlation length to the grating period.

© 1986 Optical Society of America

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  6. H. P. Baltes, A. M. J. Huiser, “Synthesis and detection of electromagnetic authenticity features,” in Inverse Methods in Electromagnetic Imaging, W. M. Boerner, H. Brand, M. Vogel, eds. (Reidel, Dordrecht, The Netherlands, 1985), pp. 1235–1244.
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  8. J. R. Fienup, “Phase retrieval from a single intensity distribution,” in Optics in Modern Science and Technology (Organizing Committee of ICO-13, Sapporo, Japan, 1984), pp. 606–609.
  9. M. Bertero, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis. I. The case of coherent illumination,” Opt. Acta 29, 727–746 (1982).
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  23. A. Roger, M. Breidne, “Grating profile reconstruction by inverse scattering method,” Opt. Commun. 35, 298–302 (1980).
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  24. K. H. Rieder, N. Garcia, V. Celli, “An effective procedure to determine corrugation functions from atomic beam-diffraction intensities,” Surf. Sci. 108, 169–180 (1981).
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  25. T. Asakura, H. Fujii, “Multiple slit interference with partially coherent light,” Optik (Stuttgart) 40, 217–224 (1974).
  26. H. Fujii, T. Asakura, “Partially coherent multiple-beam interference,” Appl. Phys. 3, 121–129 (1974).
    [CrossRef]
  27. M. Francon, Optical Interferometry (Academic, New York, 1966), pp. 178–180.
  28. H. P. Baltes, H. A. Ferwerda, A. S. Glass, B. Steinle, “Retrieval of structural information from far-zone intensity and coherence of scattered radiation,” Opt. Acta 28, 11–28 (1981).
    [CrossRef]
  29. H. P. Baltes, H. A. Ferwerda, “Inverse problems and coherence,” IEEE Trans. Antennas Propag. AP-29, 405–406 (1981).
    [CrossRef]
  30. H. A. Ferwerda, H. P. Baltes, A. S. Glass, B. Steinle, “The importance of coherence in inverse problems in optics,” Radio Sci. 16, 1047–1051 (1981).
    [CrossRef]
  31. H. P. Baltes, A. S. Glass, K. M. Jauch, “Multiplexing of coherence by beamsplitters,” Opt. Acta 28, 873–874 (1981).
    [CrossRef]
  32. H. P. Baltes, K. M. Jauch, “Multiplex version of the van Cittert-Zernike theorem,” J. Opt. Soc. Am. 71, 1434–1439 (1981).
    [CrossRef]
  33. A. S. Glass, H. P. Baltes, “The significance of far-zone coherence for sources or scatterers with hidden periodicity,” Opt. Acta 29, 169–185 (1982).
    [CrossRef]
  34. A. S. Glass, H. P. Baltes, K. M. Jauch, “The detection of hidden diffractors by coherence measurements,” Proc. Soc. Photo-Opt. Instrum. Eng. 369, 681–686 (1982).
  35. K. M. Jauch, H. P. Baltes, “Coherence of radiation scattered by gratings covered by a diffuser: experimental evidence,” Opt. Acta 28, 1013–1015 (1981).
    [CrossRef]
  36. A. S. Glass, “The significance of image reversal in the detection of hidden diffractors by interferometry,” Opt. Acta 19, 575–583 (1982).
    [CrossRef]
  37. 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]
  38. K. M. Jauch, H. P. Baltes, A. S. Glass, “Measurement of coherence of radiation from diffusely illuminated beam splitters,” Proc. Soc. Photo-Opt. Instrum. Eng. 369, 687–690 (1982).
  39. J. C. Dainty, D. Newman, “Detection of gratings hidden by diffusers using photon-correlation techniques,” Opt. Lett. 8, 608–610 (1983).
    [CrossRef] [PubMed]
  40. D. Newman, J. C. Dainty, “Detection of gratings by diffusers using intensity interferometry,” J. Opt. Soc. Am. A 1, 403–411 (1984).
    [CrossRef]
  41. A. S. Glass, K. M. Jauch, E. R. Pike, J. Rarity, “Unmasking hidden diffractors by photon correlation,” in Optics in Modern Science and Technology (Organizing Committee of ICO-13, Sapporo, Japan, 1984), pp. 650–653.
  42. A. S. Glass, K. M. Jauch, E. R. Pike, J. Rarity, “Revealing hidden diffractors by correlation measurements,” Proc. Soc. Photo-Opt. Instrum. Eng.492 (to be published).
  43. J. N. Zemel, University of Pennsylvania, Philadelphia, Pa. 19104 (personal communication).

1984 (1)

1983 (2)

1982 (10)

A. M. J. Huiser, A. Quattropani, H. P. Baltes, “Construction of grating profiles yielding prescribed diffraction efficiencies,” Opt. Commun. 41, 149–153 (1982).
[CrossRef]

M. Bertero, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis. I. The case of coherent illumination,” Opt. Acta 29, 727–746 (1982).
[CrossRef]

M. Bertero, P. Boccacci, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis. II. The case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
[CrossRef]

W. B. Ramsay, H. P. Baltes, H. G. Schmidt-Weinmar, “Anomalies in band-limited asymptotic fields,” J. Opt. Soc. Am. 72, 1618–1629 (1982).
[CrossRef]

H. G. Schmidt-Weinmar, W. B. Ramsay, H. P. Baltes, “Verification of the common plane-wave model by band-limiting the far field of a highly localized source,” Opt. Acta 29, 1081–1090 (1982).
[CrossRef]

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

A. S. Glass, H. P. Baltes, K. M. Jauch, “The detection of hidden diffractors by coherence measurements,” Proc. Soc. Photo-Opt. Instrum. Eng. 369, 681–686 (1982).

A. S. Glass, “The significance of image reversal in the detection of hidden diffractors by interferometry,” Opt. Acta 19, 575–583 (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, A. S. Glass, “Measurement of coherence of radiation from diffusely illuminated beam splitters,” Proc. Soc. Photo-Opt. Instrum. Eng. 369, 687–690 (1982).

1981 (8)

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

K. H. Rieder, N. Garcia, V. Celli, “An effective procedure to determine corrugation functions from atomic beam-diffraction intensities,” Surf. Sci. 108, 169–180 (1981).
[CrossRef]

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

H. P. Baltes, H. A. Ferwerda, “Inverse problems and coherence,” IEEE Trans. Antennas Propag. AP-29, 405–406 (1981).
[CrossRef]

H. A. Ferwerda, H. P. Baltes, A. S. Glass, B. Steinle, “The importance of coherence in inverse problems in optics,” Radio Sci. 16, 1047–1051 (1981).
[CrossRef]

H. P. Baltes, A. S. Glass, K. M. Jauch, “Multiplexing of coherence by beamsplitters,” Opt. Acta 28, 873–874 (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]

Special Issue on Inverse Methods in Electromagnetics, IEEE Trans. Antennas Propag. AP-29(2) (1981).

1980 (5)

D. L. Greenaway, “Cards and card readers for voucher and access control systems,” Landis & Gyr Rev. 27(1), 20–25 (1980).

P. Wiblé, “PHONOCARD—a pay phone operated by prepaid cards,” Landis & Gyr Rev. 27 (1), 39–45 (1980).

B. J. Hoenders, H. P. Baltes, “On the existence of nonradiating frequencies in the radiation from stochastic current distributions,” J. Phys. A 13, 995–1006 (1980).
[CrossRef]

A. Roger, M. Breidne, “Grating profile reconstruction by inverse scattering method,” Opt. Commun. 35, 298–302 (1980).
[CrossRef]

A. Roger, D. Maystre, “Inverse scattering method in electromagnetic optics: application to diffraction gratings,” J. Opt. Soc. Am. 70, 1483–1495 (1980).
[CrossRef]

1974 (2)

T. Asakura, H. Fujii, “Multiple slit interference with partially coherent light,” Optik (Stuttgart) 40, 217–224 (1974).

H. Fujii, T. Asakura, “Partially coherent multiple-beam interference,” Appl. Phys. 3, 121–129 (1974).
[CrossRef]

Asakura, T.

T. Asakura, H. Fujii, “Multiple slit interference with partially coherent light,” Optik (Stuttgart) 40, 217–224 (1974).

H. Fujii, T. Asakura, “Partially coherent multiple-beam interference,” Appl. Phys. 3, 121–129 (1974).
[CrossRef]

Baltes, H. P.

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

A. S. Glass, H. P. Baltes, K. M. Jauch, “The detection of hidden diffractors by coherence measurements,” Proc. Soc. Photo-Opt. Instrum. Eng. 369, 681–686 (1982).

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, A. S. Glass, “Measurement of coherence of radiation from diffusely illuminated beam splitters,” Proc. Soc. Photo-Opt. Instrum. Eng. 369, 687–690 (1982).

A. M. J. Huiser, A. Quattropani, H. P. Baltes, “Construction of grating profiles yielding prescribed diffraction efficiencies,” Opt. Commun. 41, 149–153 (1982).
[CrossRef]

W. B. Ramsay, H. P. Baltes, H. G. Schmidt-Weinmar, “Anomalies in band-limited asymptotic fields,” J. Opt. Soc. Am. 72, 1618–1629 (1982).
[CrossRef]

H. G. Schmidt-Weinmar, W. B. Ramsay, H. P. Baltes, “Verification of the common plane-wave model by band-limiting the far field of a highly localized source,” Opt. Acta 29, 1081–1090 (1982).
[CrossRef]

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

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

H. P. Baltes, H. A. Ferwerda, “Inverse problems and coherence,” IEEE Trans. Antennas Propag. AP-29, 405–406 (1981).
[CrossRef]

H. A. Ferwerda, H. P. Baltes, A. S. Glass, B. Steinle, “The importance of coherence in inverse problems in optics,” Radio Sci. 16, 1047–1051 (1981).
[CrossRef]

H. P. Baltes, A. S. Glass, K. M. Jauch, “Multiplexing of coherence by beamsplitters,” Opt. Acta 28, 873–874 (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]

B. J. Hoenders, H. P. Baltes, “On the existence of nonradiating frequencies in the radiation from stochastic current distributions,” J. Phys. A 13, 995–1006 (1980).
[CrossRef]

A. M. J. Huiser, H. P. Baltes, “A new perturbation expansion for electromagnetic scattering by stochastic surfaces,” in Proceedings of the URSI Commission F Symposium (URSI, Louvain, 1983), pp. 309–313.

H. P. Baltes, A. M. J. Huiser, “Synthesis and detection of electromagnetic authenticity features,” in Inverse Methods in Electromagnetic Imaging, W. M. Boerner, H. Brand, M. Vogel, eds. (Reidel, Dordrecht, The Netherlands, 1985), pp. 1235–1244.
[CrossRef]

Bertero, M.

M. Bertero, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis. I. The case of coherent illumination,” Opt. Acta 29, 727–746 (1982).
[CrossRef]

M. Bertero, P. Boccacci, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis. II. The case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
[CrossRef]

Boccacci, P.

M. Bertero, P. Boccacci, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis. II. The case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
[CrossRef]

Breidne, M.

A. Roger, M. Breidne, “Grating profile reconstruction by inverse scattering method,” Opt. Commun. 35, 298–302 (1980).
[CrossRef]

Celli, V.

K. H. Rieder, N. Garcia, V. Celli, “An effective procedure to determine corrugation functions from atomic beam-diffraction intensities,” Surf. Sci. 108, 169–180 (1981).
[CrossRef]

Dainty, J. C.

Ferwerda, H. A.

H. P. Baltes, H. A. Ferwerda, “Inverse problems and coherence,” IEEE Trans. Antennas Propag. AP-29, 405–406 (1981).
[CrossRef]

H. A. Ferwerda, H. P. Baltes, A. S. Glass, B. Steinle, “The importance of coherence in inverse problems in optics,” Radio Sci. 16, 1047–1051 (1981).
[CrossRef]

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

H. A. Ferwerda, “Phase problem in object reconstruction and Interferometry,” in Technical Digest of the Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints (Optical Society of America, Washington, D.C., 1983), pp. THA1-1–THA1-4.

Fienup, J. R.

J. R. Fienup, “Phase retrieval from a single intensity distribution,” in Optics in Modern Science and Technology (Organizing Committee of ICO-13, Sapporo, Japan, 1984), pp. 606–609.

Francon, M.

M. Francon, Optical Interferometry (Academic, New York, 1966), pp. 178–180.

Fujii, H.

T. Asakura, H. Fujii, “Multiple slit interference with partially coherent light,” Optik (Stuttgart) 40, 217–224 (1974).

H. Fujii, T. Asakura, “Partially coherent multiple-beam interference,” Appl. Phys. 3, 121–129 (1974).
[CrossRef]

Garcia, N.

K. H. Rieder, N. Garcia, V. Celli, “An effective procedure to determine corrugation functions from atomic beam-diffraction intensities,” Surf. Sci. 108, 169–180 (1981).
[CrossRef]

Glass, A. S.

K. M. Jauch, H. P. Baltes, A. S. Glass, “Measurement of coherence of radiation from diffusely illuminated beam splitters,” Proc. Soc. Photo-Opt. Instrum. Eng. 369, 687–690 (1982).

A. S. Glass, “The significance of image reversal in the detection of hidden diffractors by interferometry,” Opt. Acta 19, 575–583 (1982).
[CrossRef]

A. S. Glass, H. P. Baltes, K. M. Jauch, “The detection of hidden diffractors by coherence measurements,” Proc. Soc. Photo-Opt. Instrum. Eng. 369, 681–686 (1982).

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

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

H. A. Ferwerda, H. P. Baltes, A. S. Glass, B. Steinle, “The importance of coherence in inverse problems in optics,” Radio Sci. 16, 1047–1051 (1981).
[CrossRef]

H. P. Baltes, A. S. Glass, K. M. Jauch, “Multiplexing of coherence by beamsplitters,” Opt. Acta 28, 873–874 (1981).
[CrossRef]

A. S. Glass, K. M. Jauch, E. R. Pike, J. Rarity, “Unmasking hidden diffractors by photon correlation,” in Optics in Modern Science and Technology (Organizing Committee of ICO-13, Sapporo, Japan, 1984), pp. 650–653.

A. S. Glass, K. M. Jauch, E. R. Pike, J. Rarity, “Revealing hidden diffractors by correlation measurements,” Proc. Soc. Photo-Opt. Instrum. Eng.492 (to be published).

Greenaway, D. L.

D. L. Greenaway, “Cards and card readers for voucher and access control systems,” Landis & Gyr Rev. 27(1), 20–25 (1980).

Hoenders, B. J.

B. J. Hoenders, H. P. Baltes, “On the existence of nonradiating frequencies in the radiation from stochastic current distributions,” J. Phys. A 13, 995–1006 (1980).
[CrossRef]

Huiser, A. M. J.

A. M. J. Huiser, A. Quattropani, H. P. Baltes, “Construction of grating profiles yielding prescribed diffraction efficiencies,” Opt. Commun. 41, 149–153 (1982).
[CrossRef]

H. P. Baltes, A. M. J. Huiser, “Synthesis and detection of electromagnetic authenticity features,” in Inverse Methods in Electromagnetic Imaging, W. M. Boerner, H. Brand, M. Vogel, eds. (Reidel, Dordrecht, The Netherlands, 1985), pp. 1235–1244.
[CrossRef]

A. M. J. Huiser, H. P. Baltes, “A new perturbation expansion for electromagnetic scattering by stochastic surfaces,” in Proceedings of the URSI Commission F Symposium (URSI, Louvain, 1983), pp. 309–313.

Jauch, K. M.

A. S. Glass, H. P. Baltes, K. M. Jauch, “The detection of hidden diffractors by coherence measurements,” Proc. Soc. Photo-Opt. Instrum. Eng. 369, 681–686 (1982).

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, A. S. Glass, “Measurement of coherence of radiation from diffusely illuminated beam splitters,” Proc. Soc. Photo-Opt. Instrum. Eng. 369, 687–690 (1982).

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

H. P. Baltes, A. S. Glass, K. M. Jauch, “Multiplexing of coherence by beamsplitters,” Opt. Acta 28, 873–874 (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]

A. S. Glass, K. M. Jauch, E. R. Pike, J. Rarity, “Unmasking hidden diffractors by photon correlation,” in Optics in Modern Science and Technology (Organizing Committee of ICO-13, Sapporo, Japan, 1984), pp. 650–653.

A. S. Glass, K. M. Jauch, E. R. Pike, J. Rarity, “Revealing hidden diffractors by correlation measurements,” Proc. Soc. Photo-Opt. Instrum. Eng.492 (to be published).

Kawata, S.

S. Kawata, K. Minami, S. Minami, “Superresolution of Fourier transform spectra by autoregressive model fitting,” in Optics in Modern Science and Technology (Organizing Committee of ICO-13, Sapporo, Japan, 1984), pp. 548–549.

Maystre, D.

Minami, K.

S. Kawata, K. Minami, S. Minami, “Superresolution of Fourier transform spectra by autoregressive model fitting,” in Optics in Modern Science and Technology (Organizing Committee of ICO-13, Sapporo, Japan, 1984), pp. 548–549.

Minami, S.

S. Kawata, K. Minami, S. Minami, “Superresolution of Fourier transform spectra by autoregressive model fitting,” in Optics in Modern Science and Technology (Organizing Committee of ICO-13, Sapporo, Japan, 1984), pp. 548–549.

Newman, D.

Pike, E. R.

M. Bertero, P. Boccacci, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis. II. The case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
[CrossRef]

M. Bertero, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis. I. The case of coherent illumination,” Opt. Acta 29, 727–746 (1982).
[CrossRef]

A. S. Glass, K. M. Jauch, E. R. Pike, J. Rarity, “Unmasking hidden diffractors by photon correlation,” in Optics in Modern Science and Technology (Organizing Committee of ICO-13, Sapporo, Japan, 1984), pp. 650–653.

A. S. Glass, K. M. Jauch, E. R. Pike, J. Rarity, “Revealing hidden diffractors by correlation measurements,” Proc. Soc. Photo-Opt. Instrum. Eng.492 (to be published).

Quattropani, A.

A. M. J. Huiser, A. Quattropani, H. P. Baltes, “Construction of grating profiles yielding prescribed diffraction efficiencies,” Opt. Commun. 41, 149–153 (1982).
[CrossRef]

Ramsay, W. B.

W. B. Ramsay, H. P. Baltes, H. G. Schmidt-Weinmar, “Anomalies in band-limited asymptotic fields,” J. Opt. Soc. Am. 72, 1618–1629 (1982).
[CrossRef]

H. G. Schmidt-Weinmar, W. B. Ramsay, H. P. Baltes, “Verification of the common plane-wave model by band-limiting the far field of a highly localized source,” Opt. Acta 29, 1081–1090 (1982).
[CrossRef]

Rarity, J.

A. S. Glass, K. M. Jauch, E. R. Pike, J. Rarity, “Unmasking hidden diffractors by photon correlation,” in Optics in Modern Science and Technology (Organizing Committee of ICO-13, Sapporo, Japan, 1984), pp. 650–653.

A. S. Glass, K. M. Jauch, E. R. Pike, J. Rarity, “Revealing hidden diffractors by correlation measurements,” Proc. Soc. Photo-Opt. Instrum. Eng.492 (to be published).

Rieder, K. H.

K. H. Rieder, N. Garcia, V. Celli, “An effective procedure to determine corrugation functions from atomic beam-diffraction intensities,” Surf. Sci. 108, 169–180 (1981).
[CrossRef]

Roger, A.

A. Roger, M. Breidne, “Grating profile reconstruction by inverse scattering method,” Opt. Commun. 35, 298–302 (1980).
[CrossRef]

A. Roger, D. Maystre, “Inverse scattering method in electromagnetic optics: application to diffraction gratings,” J. Opt. Soc. Am. 70, 1483–1495 (1980).
[CrossRef]

Schmidt-Weinmar, H. G.

W. B. Ramsay, H. P. Baltes, H. G. Schmidt-Weinmar, “Anomalies in band-limited asymptotic fields,” J. Opt. Soc. Am. 72, 1618–1629 (1982).
[CrossRef]

H. G. Schmidt-Weinmar, W. B. Ramsay, H. P. Baltes, “Verification of the common plane-wave model by band-limiting the far field of a highly localized source,” Opt. Acta 29, 1081–1090 (1982).
[CrossRef]

Steinle, B.

H. A. Ferwerda, H. P. Baltes, A. S. Glass, B. Steinle, “The importance of coherence in inverse problems in optics,” Radio Sci. 16, 1047–1051 (1981).
[CrossRef]

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

Wiblé, P.

P. Wiblé, “PHONOCARD—a pay phone operated by prepaid cards,” Landis & Gyr Rev. 27 (1), 39–45 (1980).

Zemel, J. N.

J. N. Zemel, University of Pennsylvania, Philadelphia, Pa. 19104 (personal communication).

Appl. Phys. (1)

H. Fujii, T. Asakura, “Partially coherent multiple-beam interference,” Appl. Phys. 3, 121–129 (1974).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

H. P. Baltes, H. A. Ferwerda, “Inverse problems and coherence,” IEEE Trans. Antennas Propag. AP-29, 405–406 (1981).
[CrossRef]

Special Issue on Inverse Methods in Electromagnetics, IEEE Trans. Antennas Propag. AP-29(2) (1981).

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (1)

J. Phys. A (1)

B. J. Hoenders, H. P. Baltes, “On the existence of nonradiating frequencies in the radiation from stochastic current distributions,” J. Phys. A 13, 995–1006 (1980).
[CrossRef]

Landis & Gyr Rev. (2)

D. L. Greenaway, “Cards and card readers for voucher and access control systems,” Landis & Gyr Rev. 27(1), 20–25 (1980).

P. Wiblé, “PHONOCARD—a pay phone operated by prepaid cards,” Landis & Gyr Rev. 27 (1), 39–45 (1980).

Opt. Acta (8)

H. G. Schmidt-Weinmar, W. B. Ramsay, H. P. Baltes, “Verification of the common plane-wave model by band-limiting the far field of a highly localized source,” Opt. Acta 29, 1081–1090 (1982).
[CrossRef]

M. Bertero, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis. I. The case of coherent illumination,” Opt. Acta 29, 727–746 (1982).
[CrossRef]

M. Bertero, P. Boccacci, E. R. Pike, “Resolution in diffraction-limited imaging, a singular value analysis. II. The case of incoherent illumination,” Opt. Acta 29, 1599–1611 (1982).
[CrossRef]

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

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

H. P. Baltes, A. S. Glass, K. M. Jauch, “Multiplexing of coherence by beamsplitters,” Opt. Acta 28, 873–874 (1981).
[CrossRef]

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

A. S. Glass, “The significance of image reversal in the detection of hidden diffractors by interferometry,” Opt. Acta 19, 575–583 (1982).
[CrossRef]

Opt. Commun. (2)

A. Roger, M. Breidne, “Grating profile reconstruction by inverse scattering method,” Opt. Commun. 35, 298–302 (1980).
[CrossRef]

A. M. J. Huiser, A. Quattropani, H. P. Baltes, “Construction of grating profiles yielding prescribed diffraction efficiencies,” Opt. Commun. 41, 149–153 (1982).
[CrossRef]

Opt. Lett. (2)

Optik (Stuttgart) (1)

T. Asakura, H. Fujii, “Multiple slit interference with partially coherent light,” Optik (Stuttgart) 40, 217–224 (1974).

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

A. S. Glass, H. P. Baltes, K. M. Jauch, “The detection of hidden diffractors by coherence measurements,” Proc. Soc. Photo-Opt. Instrum. Eng. 369, 681–686 (1982).

K. M. Jauch, H. P. Baltes, A. S. Glass, “Measurement of coherence of radiation from diffusely illuminated beam splitters,” Proc. Soc. Photo-Opt. Instrum. Eng. 369, 687–690 (1982).

Radio Sci. (1)

H. A. Ferwerda, H. P. Baltes, A. S. Glass, B. Steinle, “The importance of coherence in inverse problems in optics,” Radio Sci. 16, 1047–1051 (1981).
[CrossRef]

Surf. Sci. (1)

K. H. Rieder, N. Garcia, V. Celli, “An effective procedure to determine corrugation functions from atomic beam-diffraction intensities,” Surf. Sci. 108, 169–180 (1981).
[CrossRef]

Other (15)

M. Francon, Optical Interferometry (Academic, New York, 1966), pp. 178–180.

H. P. Baltes, A. M. J. Huiser, “Synthesis and detection of electromagnetic authenticity features,” in Inverse Methods in Electromagnetic Imaging, W. M. Boerner, H. Brand, M. Vogel, eds. (Reidel, Dordrecht, The Netherlands, 1985), pp. 1235–1244.
[CrossRef]

H. A. Ferwerda, “Phase problem in object reconstruction and Interferometry,” in Technical Digest of the Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints (Optical Society of America, Washington, D.C., 1983), pp. THA1-1–THA1-4.

J. R. Fienup, “Phase retrieval from a single intensity distribution,” in Optics in Modern Science and Technology (Organizing Committee of ICO-13, Sapporo, Japan, 1984), pp. 606–609.

H. P. Baltes, ed., Inverse Source Problems in Optics (Springer-Verlag, Heidelberg, 1978).
[CrossRef]

H. P. Baltes, ed., Inverse Scattering Problems in Optics (Springer-Verlag, Heidelberg, 1980).
[CrossRef]

R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Heidelberg, 1980).
[CrossRef]

S. Kawata, K. Minami, S. Minami, “Superresolution of Fourier transform spectra by autoregressive model fitting,” in Optics in Modern Science and Technology (Organizing Committee of ICO-13, Sapporo, Japan, 1984), pp. 548–549.

Technical Digest of Topical Meeting on Signal Recovery and Synthesis with Incomplete Information and Partial Constraints (Optical Society of America, Washington, D.C, 1983).

W. M. Boerner, H. Brand, M. Vogel, eds., Inverse Methods in Electromagnetic Imaging (Riedel, Dordrecht, The Netherlands, 1985).
[CrossRef]

S. M. Sze, ed., VLSI Technology (McGraw-Hill, New York, 1983).

A. M. J. Huiser, H. P. Baltes, “A new perturbation expansion for electromagnetic scattering by stochastic surfaces,” in Proceedings of the URSI Commission F Symposium (URSI, Louvain, 1983), pp. 309–313.

A. S. Glass, K. M. Jauch, E. R. Pike, J. Rarity, “Unmasking hidden diffractors by photon correlation,” in Optics in Modern Science and Technology (Organizing Committee of ICO-13, Sapporo, Japan, 1984), pp. 650–653.

A. S. Glass, K. M. Jauch, E. R. Pike, J. Rarity, “Revealing hidden diffractors by correlation measurements,” Proc. Soc. Photo-Opt. Instrum. Eng.492 (to be published).

J. N. Zemel, University of Pennsylvania, Philadelphia, Pa. 19104 (personal communication).

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Figures (5)

Fig. 1
Fig. 1

Scattering geometry.

Fig. 2
Fig. 2

Beam-splitter grating profiles (example 1). Grating period d = 2 λ (profile 1A); d = 2 2 λ (profile 1B); d = 3 2 λ (profiles 1C and 1D).

Fig. 3
Fig. 3

Illustration of nonunique reconstruction. Left side, function G0(x, z); right side, reconstructions A and B of original profile.5

Fig. 4
Fig. 4

Angular distribution of far-zone intensity I(θ) and degree of coherence |μ(θ, −θ)| of radiation from a lamellar phase grating (d = 5λ) hidden by a diffuser. Top, l = d; bottom, l = d/8 (adapted from Ref. 33).

Fig. 5
Fig. 5

Peak values of intensity cross correlation measured at angles (−θ0, θ0), sin θ0 = λ/d, as a function of l/d; Pluses, experiments; solid line, theory [adapted from J. C. Dainty and D. Neumann, Opt. Lett. 8, 608 (1983)].

Tables (2)

Tables Icon

Table 1 Example 1, Diffraction Coefficients cn and Efficiencies en

Tables Icon

Table 2 Example 2, Diffraction Coefficients cn

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

E in ( x , z ) = E in ( x , z ) y ˆ = exp ( i k x x i k z z ) y ˆ ,
E st ( x , z ) = E st ( x , z ) y ˆ .
[ E in ( x , z ) + E st ( x , z ) ] z = h ( x ) = 0.
E st ( x , z ) = Σ n c n exp ( i α n x + i β n z )
E st ( x , z ) Σ n c n exp ( i α n x + i β n z ) + Σ n a n exp ( i α n x | β n | z ) ,
E ( x , z ) = E in ( x , z ) + E st ( x , z ) .
E st ( x , z ) E 0 st ( x , z ) = Σ n c n exp ( i α n x + i β n z ) ,
F = d s | E in [ x , h 0 ( x ) ] + E 0 st [ x , h 0 ( x ) ] | 2
F = d s | E in [ x , h 0 ( x ) ] + E 1 st [ x , h 0 ( x ) ] | 2
E 1 st ( x , z ) = E 0 st ( x , z ) + Σ n a n exp ( i α n | β n | z ) ,
R ( x ) = Σ n c n exp ( 2 π i n x / d ) ,
μ ( x 1 , x 2 ) = exp [ ( x 1 x 2 ) 2 / 2 l 2 ] .
I ( x ) = exp ( x 2 / 2 a 2 )
W ( x 1 , x 2 ) = R ( x 1 ) R * ( x 2 ) I ( x 1 ) I ( x 2 ) μ ( x 1 , x 2 ) ,

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