Abstract

Questions are raised concerning the uniqueness of solutions to the phase-retrieval problem for functions with disconnected support. A counterexample is presented showing the importance of considering the flipping of infinite proper subsets of nonreal zeros.

© 1981 Optical Society of America

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References

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  1. A. H. Greenaway, "Proposal for phase recovery from a single intensity distribution," Opt. Lett. 1, 10–12 (1977).
  2. R. H. T. Bates, "Fringe visibility intensities may uniquely define brightness distributions," Astron. Astrophys. 70, L27–L29 (1978).
  3. E. M. Hofstetter, "Construction of time-limited functions with specified autocorrelation functions," IEEE Trans. Inf. Theory IT-10, 119–126 (1964).
  4. A. Walther, "The question of phase retrieval in optics," Opt. Acta 10, 41–49 (1963).
  5. R. H. T. Bates et al., "Self-consistent deconvolution. I: Theory," Optik (Stuttgart) 44, 183–201 (1976).
  6. T. R. Crimmins and J. R. Fienup, "Phase retrieval for functions with disconnected support," in Appendix B of J. R. Fienup, "High resolution imaging of space objects," interim scientific report to Air Force Office of Scientific Research, ERIM Report No. 145400-7-P (Environmental Research Institute of Michigan, Ann Arbor, Mich., March 1981).
  7. Yu. M. Bruck and L. G. Sodin, "On the ambiguity of the image reconstruction problem," Opt. Commun. 30, 304–308 (1979).

1979 (1)

Yu. M. Bruck and L. G. Sodin, "On the ambiguity of the image reconstruction problem," Opt. Commun. 30, 304–308 (1979).

1978 (1)

R. H. T. Bates, "Fringe visibility intensities may uniquely define brightness distributions," Astron. Astrophys. 70, L27–L29 (1978).

1977 (1)

1976 (1)

R. H. T. Bates et al., "Self-consistent deconvolution. I: Theory," Optik (Stuttgart) 44, 183–201 (1976).

1964 (1)

E. M. Hofstetter, "Construction of time-limited functions with specified autocorrelation functions," IEEE Trans. Inf. Theory IT-10, 119–126 (1964).

1963 (1)

A. Walther, "The question of phase retrieval in optics," Opt. Acta 10, 41–49 (1963).

Bates, R. H. T.

R. H. T. Bates, "Fringe visibility intensities may uniquely define brightness distributions," Astron. Astrophys. 70, L27–L29 (1978).

R. H. T. Bates et al., "Self-consistent deconvolution. I: Theory," Optik (Stuttgart) 44, 183–201 (1976).

Bruck, Yu. M.

Yu. M. Bruck and L. G. Sodin, "On the ambiguity of the image reconstruction problem," Opt. Commun. 30, 304–308 (1979).

Crimmins, T. R.

T. R. Crimmins and J. R. Fienup, "Phase retrieval for functions with disconnected support," in Appendix B of J. R. Fienup, "High resolution imaging of space objects," interim scientific report to Air Force Office of Scientific Research, ERIM Report No. 145400-7-P (Environmental Research Institute of Michigan, Ann Arbor, Mich., March 1981).

Fienup, J. R.

T. R. Crimmins and J. R. Fienup, "Phase retrieval for functions with disconnected support," in Appendix B of J. R. Fienup, "High resolution imaging of space objects," interim scientific report to Air Force Office of Scientific Research, ERIM Report No. 145400-7-P (Environmental Research Institute of Michigan, Ann Arbor, Mich., March 1981).

Greenaway, A. H.

Hofstetter, E. M.

E. M. Hofstetter, "Construction of time-limited functions with specified autocorrelation functions," IEEE Trans. Inf. Theory IT-10, 119–126 (1964).

Sodin, L. G.

Yu. M. Bruck and L. G. Sodin, "On the ambiguity of the image reconstruction problem," Opt. Commun. 30, 304–308 (1979).

Walther, A.

A. Walther, "The question of phase retrieval in optics," Opt. Acta 10, 41–49 (1963).

Astron. Astrophys. (1)

R. H. T. Bates, "Fringe visibility intensities may uniquely define brightness distributions," Astron. Astrophys. 70, L27–L29 (1978).

IEEE Trans. Inf. Theory (1)

E. M. Hofstetter, "Construction of time-limited functions with specified autocorrelation functions," IEEE Trans. Inf. Theory IT-10, 119–126 (1964).

Opt. Acta (1)

A. Walther, "The question of phase retrieval in optics," Opt. Acta 10, 41–49 (1963).

Opt. Commun. (1)

Yu. M. Bruck and L. G. Sodin, "On the ambiguity of the image reconstruction problem," Opt. Commun. 30, 304–308 (1979).

Opt. Lett. (1)

Optik (1)

R. H. T. Bates et al., "Self-consistent deconvolution. I: Theory," Optik (Stuttgart) 44, 183–201 (1976).

Other (1)

T. R. Crimmins and J. R. Fienup, "Phase retrieval for functions with disconnected support," in Appendix B of J. R. Fienup, "High resolution imaging of space objects," interim scientific report to Air Force Office of Scientific Research, ERIM Report No. 145400-7-P (Environmental Research Institute of Michigan, Ann Arbor, Mich., March 1981).

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