M. Nieto-Vesperinas, “A study on the performance of least
square optimization methods in the problem of phase
retrieval,” Opt. Acta 33, 713–722
(1986).

[CrossRef]

J. R. Fienup, C. C. Wackerman, “Phase-retrieval stagnation problems and
solutions,” J. Opt. Soc. Am. A 3, 1897–1907
(1986).

[CrossRef]

M. Nieto-Vesperinas, J. A. Méndez, “Phase retrieval by Monte Carlo
methods,” Opt. Commun. 59, 249–254
(1986).

[CrossRef]

H. V. Deighton, M. S. Scivier, M. A. Fiddy, “Solution of the two-dimensional phase
problem,” Opt. Lett. 10, 250–251
(1985).

[CrossRef]
[PubMed]

H. H. Barrett, W. E. Smith, R. G. Paxman, “Monte Carlo methods in
optics,” Acta Polytech. Scand. Appl. Phys.
Ser. 149, 3 (1985).

P. L. Van Hove, M. H. Hayes, J. S. Lim, A. V. Oppenheim, “Signal reconstruction from Fourier
transform magnitude,” IEEE Trans. Acoust.
Speech Signal Process. ASSP-31, 1286–1293
(1983).

[CrossRef]

H. H. Arsenault, K. Chalasinska-Macukov, “The solution to the phase retrieval
problem using the sampling theorem,” Opt.
Commun. 47, 380–386
(1983);K. Chalasinska-Macukov, H. Arsenault, “Fast iterative solution to exact
equations for the two-dimensional phase problem,”
J. Opt. Soc. Am. A 2, 46–50
(1985).

[CrossRef]

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated
annealing,” Science 220, 671–680
(1983).

[CrossRef]
[PubMed]

W. E. Smith, H. H. Barrett, R. G. Paxman, “Reconstruction of objects from coded
images by simulated annealing,” Opt.
Lett. 8, 199–201
(1983);W. E. Smith, R. G. Paxman, H. H. Barrett, “Image reconstruction from coded data:
I. Reconstruction algorithms and experimental
results,” J. Opt Soc. Am. A 2, 491–500
(1985).

[CrossRef]
[PubMed]

R. H. T. Bates, “Fourier phase problems are uniquely
solvable in more than one dimension. I: Underlying
theory,” Optik 61, 247–262
(1982);K. L. Garden, R. H. T. Bates, “Fourier phase problems are uniquely
solvable in more than one dimension. II: One-dimensional
considerations,” Optik 62, 131–142
(1982);W. R. Fright, R. M. T. Bates, “Fourier phase problems are uniquely
solvable in more than one dimension. III: Computational examples for two
dimensions,” Optik 62, 219–230
(1982).

M. H. Hayes, J. H. McClellan, “Reducible polynomials in more than one
variable,” Proc. IEEE 70, 197–198
(1982).

[CrossRef]

J. R. Fienup, “Phase retrieval algorithms: a
comparison,” Appl. Opt. 21, 2758–2769
(1982).

[CrossRef]
[PubMed]

Y. M. Bruck, L. G. Sodin, “On the ambiguity of the image
reconstruction problem,” Opt.
Commun. 30, 304–308
(1979).

[CrossRef]

J. R. Fienup, “Space object imaging through the
turbulent atmosphere,” Opt. Eng. 18, 529–534
(1979).

[CrossRef]

J. R. Fienup, “Reconstruction of an object from the
modulus of its Fourier transform,” Opt.
Lett. 3, 27–29
(1978).

[CrossRef]
[PubMed]

B. R. Frieden, D. G. Currie, “On unfolding the autocorrelation
function,” J. Opt. Soc. Am. 66, 1111 (A)
(1976).

P. J. Napier, R. H. T. Bates, “Inferring phase information from
modulus information in two-dimensional aperture
synthesis,” Astron. Astrophys. Suppl. 15, 427–430
(1974).

C. Y. C. Liu, A. W. Lohmann, “High resolution image formation through
the turbulent atmosphere,” Opt.
Commun. 8, 372–377
(1973).

[CrossRef]

M. Pincus, “A closed form solution of certain
programming problems,” Oper. Res. 16, 690–694
(1968);“A Monte Carlo
method for the approximate solution of certain types of constrained
optimization problems,” Oper. Res. 18, 1225–1228
(1970).

[CrossRef]

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, “Equation of state calculations by fast
computing machines,” J. Chem. Phys. 21, 1087–1092
(1953).

[CrossRef]

H. H. Arsenault, K. Chalasinska-Macukov, “The solution to the phase retrieval
problem using the sampling theorem,” Opt.
Commun. 47, 380–386
(1983);K. Chalasinska-Macukov, H. Arsenault, “Fast iterative solution to exact
equations for the two-dimensional phase problem,”
J. Opt. Soc. Am. A 2, 46–50
(1985).

[CrossRef]

H. H. Barrett, W. E. Smith, R. G. Paxman, “Monte Carlo methods in
optics,” Acta Polytech. Scand. Appl. Phys.
Ser. 149, 3 (1985).

W. E. Smith, H. H. Barrett, R. G. Paxman, “Reconstruction of objects from coded
images by simulated annealing,” Opt.
Lett. 8, 199–201
(1983);W. E. Smith, R. G. Paxman, H. H. Barrett, “Image reconstruction from coded data:
I. Reconstruction algorithms and experimental
results,” J. Opt Soc. Am. A 2, 491–500
(1985).

[CrossRef]
[PubMed]

R. H. T. Bates, “Fourier phase problems are uniquely
solvable in more than one dimension. I: Underlying
theory,” Optik 61, 247–262
(1982);K. L. Garden, R. H. T. Bates, “Fourier phase problems are uniquely
solvable in more than one dimension. II: One-dimensional
considerations,” Optik 62, 131–142
(1982);W. R. Fright, R. M. T. Bates, “Fourier phase problems are uniquely
solvable in more than one dimension. III: Computational examples for two
dimensions,” Optik 62, 219–230
(1982).

P. J. Napier, R. H. T. Bates, “Inferring phase information from
modulus information in two-dimensional aperture
synthesis,” Astron. Astrophys. Suppl. 15, 427–430
(1974).

Y. M. Bruck, L. G. Sodin, “On the ambiguity of the image
reconstruction problem,” Opt.
Commun. 30, 304–308
(1979).

[CrossRef]

H. H. Arsenault, K. Chalasinska-Macukov, “The solution to the phase retrieval
problem using the sampling theorem,” Opt.
Commun. 47, 380–386
(1983);K. Chalasinska-Macukov, H. Arsenault, “Fast iterative solution to exact
equations for the two-dimensional phase problem,”
J. Opt. Soc. Am. A 2, 46–50
(1985).

[CrossRef]

A. H. Greenaway, J. G. Walker, J. A. G. Coombs, “Ambiguities in speckle reconstructions.
Some ways of avoiding them,” in Indirect
Imaging, J. A. Roberts, ed. (Cambridge U. Press,
Cambridge, 1984), pp.
111–117.

B. R. Frieden, D. G. Currie, “On unfolding the autocorrelation
function,” J. Opt. Soc. Am. 66, 1111 (A)
(1976).

J. C. Dainty, J. R. Fienup, “Phase retrieval and image
reconstruction for astronomy,” in Image
Recovery: Theory and Application, H. Stark, ed. (Academic,
New York, 1987), pp.
231–275.

J. R. Fienup, C. C. Wackerman, “Phase-retrieval stagnation problems and
solutions,” J. Opt. Soc. Am. A 3, 1897–1907
(1986).

[CrossRef]

J. R. Fienup, “Phase retrieval algorithms: a
comparison,” Appl. Opt. 21, 2758–2769
(1982).

[CrossRef]
[PubMed]

J. R. Fienup, “Space object imaging through the
turbulent atmosphere,” Opt. Eng. 18, 529–534
(1979).

[CrossRef]

J. R. Fienup, “Reconstruction of an object from the
modulus of its Fourier transform,” Opt.
Lett. 3, 27–29
(1978).

[CrossRef]
[PubMed]

J. C. Dainty, J. R. Fienup, “Phase retrieval and image
reconstruction for astronomy,” in Image
Recovery: Theory and Application, H. Stark, ed. (Academic,
New York, 1987), pp.
231–275.

B. R. Frieden, D. G. Currie, “On unfolding the autocorrelation
function,” J. Opt. Soc. Am. 66, 1111 (A)
(1976).

F. J. Fuentes, Instituto de Astrofísica de Canarias,
La Laguna Tenerife,
Spain (personal
communication).

F. J. Fuentes, M. Nieto-Vesperinas, R. Navarro, “A fortan program to obtain a
function of two variables from its autocorrelation,”
submitted to Trans. Math. Software.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated
annealing,” Science 220, 671–680
(1983).

[CrossRef]
[PubMed]

A. H. Greenaway, J. G. Walker, J. A. G. Coombs, “Ambiguities in speckle reconstructions.
Some ways of avoiding them,” in Indirect
Imaging, J. A. Roberts, ed. (Cambridge U. Press,
Cambridge, 1984), pp.
111–117.

J. M. Hammersley, D. C. Handscomb, Monte Carlo Methods
(Methuen,
London, 1967), p.
113.

J. M. Hammersley, D. C. Handscomb, Monte Carlo Methods
(Methuen,
London, 1967), p.
113.

P. L. Van Hove, M. H. Hayes, J. S. Lim, A. V. Oppenheim, “Signal reconstruction from Fourier
transform magnitude,” IEEE Trans. Acoust.
Speech Signal Process. ASSP-31, 1286–1293
(1983).

[CrossRef]

M. H. Hayes, J. H. McClellan, “Reducible polynomials in more than one
variable,” Proc. IEEE 70, 197–198
(1982).

[CrossRef]

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated
annealing,” Science 220, 671–680
(1983).

[CrossRef]
[PubMed]

P. L. Van Hove, M. H. Hayes, J. S. Lim, A. V. Oppenheim, “Signal reconstruction from Fourier
transform magnitude,” IEEE Trans. Acoust.
Speech Signal Process. ASSP-31, 1286–1293
(1983).

[CrossRef]

C. Y. C. Liu, A. W. Lohmann, “High resolution image formation through
the turbulent atmosphere,” Opt.
Commun. 8, 372–377
(1973).

[CrossRef]

C. Y. C. Liu, A. W. Lohmann, “High resolution image formation through
the turbulent atmosphere,” Opt.
Commun. 8, 372–377
(1973).

[CrossRef]

M. H. Hayes, J. H. McClellan, “Reducible polynomials in more than one
variable,” Proc. IEEE 70, 197–198
(1982).

[CrossRef]

M. Nieto-Vesperinas, J. A. Méndez, “Phase retrieval by Monte Carlo
methods,” Opt. Commun. 59, 249–254
(1986).

[CrossRef]

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, “Equation of state calculations by fast
computing machines,” J. Chem. Phys. 21, 1087–1092
(1953).

[CrossRef]

P. J. Napier, R. H. T. Bates, “Inferring phase information from
modulus information in two-dimensional aperture
synthesis,” Astron. Astrophys. Suppl. 15, 427–430
(1974).

F. J. Fuentes, M. Nieto-Vesperinas, R. Navarro, “A fortan program to obtain a
function of two variables from its autocorrelation,”
submitted to Trans. Math. Software.

M. Nieto-Vesperinas, “A study on the performance of least
square optimization methods in the problem of phase
retrieval,” Opt. Acta 33, 713–722
(1986).

[CrossRef]

M. Nieto-Vesperinas, J. A. Méndez, “Phase retrieval by Monte Carlo
methods,” Opt. Commun. 59, 249–254
(1986).

[CrossRef]

F. J. Fuentes, M. Nieto-Vesperinas, R. Navarro, “A fortan program to obtain a
function of two variables from its autocorrelation,”
submitted to Trans. Math. Software.

P. L. Van Hove, M. H. Hayes, J. S. Lim, A. V. Oppenheim, “Signal reconstruction from Fourier
transform magnitude,” IEEE Trans. Acoust.
Speech Signal Process. ASSP-31, 1286–1293
(1983).

[CrossRef]

H. H. Barrett, W. E. Smith, R. G. Paxman, “Monte Carlo methods in
optics,” Acta Polytech. Scand. Appl. Phys.
Ser. 149, 3 (1985).

W. E. Smith, H. H. Barrett, R. G. Paxman, “Reconstruction of objects from coded
images by simulated annealing,” Opt.
Lett. 8, 199–201
(1983);W. E. Smith, R. G. Paxman, H. H. Barrett, “Image reconstruction from coded data:
I. Reconstruction algorithms and experimental
results,” J. Opt Soc. Am. A 2, 491–500
(1985).

[CrossRef]
[PubMed]

M. Pincus, “A closed form solution of certain
programming problems,” Oper. Res. 16, 690–694
(1968);“A Monte Carlo
method for the approximate solution of certain types of constrained
optimization problems,” Oper. Res. 18, 1225–1228
(1970).

[CrossRef]

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, “Equation of state calculations by fast
computing machines,” J. Chem. Phys. 21, 1087–1092
(1953).

[CrossRef]

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, “Equation of state calculations by fast
computing machines,” J. Chem. Phys. 21, 1087–1092
(1953).

[CrossRef]

R. Y. Rubinstein, Simulation and the Monte Carlo Methods
(Wiley, New
York, 1981), p.
260.

H. H. Barrett, W. E. Smith, R. G. Paxman, “Monte Carlo methods in
optics,” Acta Polytech. Scand. Appl. Phys.
Ser. 149, 3 (1985).

W. E. Smith, H. H. Barrett, R. G. Paxman, “Reconstruction of objects from coded
images by simulated annealing,” Opt.
Lett. 8, 199–201
(1983);W. E. Smith, R. G. Paxman, H. H. Barrett, “Image reconstruction from coded data:
I. Reconstruction algorithms and experimental
results,” J. Opt Soc. Am. A 2, 491–500
(1985).

[CrossRef]
[PubMed]

Y. M. Bruck, L. G. Sodin, “On the ambiguity of the image
reconstruction problem,” Opt.
Commun. 30, 304–308
(1979).

[CrossRef]

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, “Equation of state calculations by fast
computing machines,” J. Chem. Phys. 21, 1087–1092
(1953).

[CrossRef]

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, “Equation of state calculations by fast
computing machines,” J. Chem. Phys. 21, 1087–1092
(1953).

[CrossRef]

P. L. Van Hove, M. H. Hayes, J. S. Lim, A. V. Oppenheim, “Signal reconstruction from Fourier
transform magnitude,” IEEE Trans. Acoust.
Speech Signal Process. ASSP-31, 1286–1293
(1983).

[CrossRef]

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated
annealing,” Science 220, 671–680
(1983).

[CrossRef]
[PubMed]

A. H. Greenaway, J. G. Walker, J. A. G. Coombs, “Ambiguities in speckle reconstructions.
Some ways of avoiding them,” in Indirect
Imaging, J. A. Roberts, ed. (Cambridge U. Press,
Cambridge, 1984), pp.
111–117.

H. H. Barrett, W. E. Smith, R. G. Paxman, “Monte Carlo methods in
optics,” Acta Polytech. Scand. Appl. Phys.
Ser. 149, 3 (1985).

P. J. Napier, R. H. T. Bates, “Inferring phase information from
modulus information in two-dimensional aperture
synthesis,” Astron. Astrophys. Suppl. 15, 427–430
(1974).

P. L. Van Hove, M. H. Hayes, J. S. Lim, A. V. Oppenheim, “Signal reconstruction from Fourier
transform magnitude,” IEEE Trans. Acoust.
Speech Signal Process. ASSP-31, 1286–1293
(1983).

[CrossRef]

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, “Equation of state calculations by fast
computing machines,” J. Chem. Phys. 21, 1087–1092
(1953).

[CrossRef]

B. R. Frieden, D. G. Currie, “On unfolding the autocorrelation
function,” J. Opt. Soc. Am. 66, 1111 (A)
(1976).

M. Pincus, “A closed form solution of certain
programming problems,” Oper. Res. 16, 690–694
(1968);“A Monte Carlo
method for the approximate solution of certain types of constrained
optimization problems,” Oper. Res. 18, 1225–1228
(1970).

[CrossRef]

H. H. Arsenault, K. Chalasinska-Macukov, “The solution to the phase retrieval
problem using the sampling theorem,” Opt.
Commun. 47, 380–386
(1983);K. Chalasinska-Macukov, H. Arsenault, “Fast iterative solution to exact
equations for the two-dimensional phase problem,”
J. Opt. Soc. Am. A 2, 46–50
(1985).

[CrossRef]

C. Y. C. Liu, A. W. Lohmann, “High resolution image formation through
the turbulent atmosphere,” Opt.
Commun. 8, 372–377
(1973).

[CrossRef]

Y. M. Bruck, L. G. Sodin, “On the ambiguity of the image
reconstruction problem,” Opt.
Commun. 30, 304–308
(1979).

[CrossRef]

J. R. Fienup, “Reconstruction of an object from the
modulus of its Fourier transform,” Opt.
Lett. 3, 27–29
(1978).

[CrossRef]
[PubMed]

W. E. Smith, H. H. Barrett, R. G. Paxman, “Reconstruction of objects from coded
images by simulated annealing,” Opt.
Lett. 8, 199–201
(1983);W. E. Smith, R. G. Paxman, H. H. Barrett, “Image reconstruction from coded data:
I. Reconstruction algorithms and experimental
results,” J. Opt Soc. Am. A 2, 491–500
(1985).

[CrossRef]
[PubMed]

M. Nieto-Vesperinas, “A study on the performance of least
square optimization methods in the problem of phase
retrieval,” Opt. Acta 33, 713–722
(1986).

[CrossRef]

M. Nieto-Vesperinas, J. A. Méndez, “Phase retrieval by Monte Carlo
methods,” Opt. Commun. 59, 249–254
(1986).

[CrossRef]

J. R. Fienup, “Space object imaging through the
turbulent atmosphere,” Opt. Eng. 18, 529–534
(1979).

[CrossRef]

R. H. T. Bates, “Fourier phase problems are uniquely
solvable in more than one dimension. I: Underlying
theory,” Optik 61, 247–262
(1982);K. L. Garden, R. H. T. Bates, “Fourier phase problems are uniquely
solvable in more than one dimension. II: One-dimensional
considerations,” Optik 62, 131–142
(1982);W. R. Fright, R. M. T. Bates, “Fourier phase problems are uniquely
solvable in more than one dimension. III: Computational examples for two
dimensions,” Optik 62, 219–230
(1982).

M. H. Hayes, J. H. McClellan, “Reducible polynomials in more than one
variable,” Proc. IEEE 70, 197–198
(1982).

[CrossRef]

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated
annealing,” Science 220, 671–680
(1983).

[CrossRef]
[PubMed]

J. C. Dainty, J. R. Fienup, “Phase retrieval and image
reconstruction for astronomy,” in Image
Recovery: Theory and Application, H. Stark, ed. (Academic,
New York, 1987), pp.
231–275.

J. M. Hammersley, D. C. Handscomb, Monte Carlo Methods
(Methuen,
London, 1967), p.
113.

R. Y. Rubinstein, Simulation and the Monte Carlo Methods
(Wiley, New
York, 1981), p.
260.

F. J. Fuentes, M. Nieto-Vesperinas, R. Navarro, “A fortan program to obtain a
function of two variables from its autocorrelation,”
submitted to Trans. Math. Software.

A. H. Greenaway, J. G. Walker, J. A. G. Coombs, “Ambiguities in speckle reconstructions.
Some ways of avoiding them,” in Indirect
Imaging, J. A. Roberts, ed. (Cambridge U. Press,
Cambridge, 1984), pp.
111–117.

F. J. Fuentes, Instituto de Astrofísica de Canarias,
La Laguna Tenerife,
Spain (personal
communication).