M. G. Ertosun, H. Atli, H. M. Ozaktas, B. Barshan, “Complex signal recovery from two fractional Fourier transform intensities: order and noise dependence,” Opt. Commun. 244, 61–70 (2005).

[CrossRef]

M. Testorf, “Comment on ‘Redundancy of phase-space distribution functions in complex field recovery problems’,” Appl. Opt. 44, 55–57 (2005).

[CrossRef]

D. Dragoman, “Reply to comment on ‘Redundancy of phase-space distribution functions in complex field recovery problems’,” Appl. Opt. 44, 58–59 (2005).

[CrossRef]

L. J. Allen, W. McBride, M. P. Oxley, “Exit wave reconstruction using soft x-rays,” Opt. Commun. 233, 77–82 (2004).

[CrossRef]

T. E. Gureyev, A. Pogany, D. M. Paganin, S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231, 53–70 (2004).

[CrossRef]

T. E. Gureyev, “Composite techniques for phase retrieval in the Fresnel region,” Opt. Commun. 220, 49–58 (2003).

[CrossRef]

T. Alieva, M. J. Bastiaans, L. Stankovic, “Signal reconstruction from two close fractional Fourier power spectra,” IEEE Trans. Signal Process. 51, 112–123 (2003).

[CrossRef]

B. Hennelly, J. T. Sheridan, “Fractional Fourier transform-based image encryption: phase retrieval algorithm,” Opt. Commun. 226, 61–80 (2003).

[CrossRef]

X. Liu, K.-H. Brenner, “Reconstruction of two-dimensional complex amplitudes from intensity measurements,” Opt. Commun. 225, 19–30 (2003).

[CrossRef]

D. Dragoman, “Redundancy of phase-space distribution functions in complex field recovery problems,” Appl. Opt. 42, 1932–1937 (2003).

[CrossRef]
[PubMed]

M. Bastiaans, K. Wolf, “Phase reconstruction from intensity measurements in linear systems,” J. Opt. Soc. Am. A 20, 1046–1049 (2003).

[CrossRef]

L. J. Allen, M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199, 65–75 (2001).

[CrossRef]

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev E 63, 037602-1–037602-4 (2001).

[CrossRef]

C. Candan, M. Alper Kutay, H. M. Ozaktas, “The discrete fractional Fourier transform,” IEEE Trans. Signal Process. 48, 1329–1337 (2000).

[CrossRef]

T. Alieva, M. J. Bastiaans, “On fractional Fourier transform moments,” IEEE Signal Process. Lett. 7, 321–323 (2000).

[CrossRef]

M. A. Kutay, H. Özaktaş, H. M. Ozaktas, O. Arikan, “The fractional Fourier domain decomposition,” Signal Process. 77, 105–109 (1999).

[CrossRef]

W.-X. Cong, N.-X. Chen, B.-Y. Gu, “Phase retrieval in the Fresnel transform system: a recursive algorithm,” J. Opt. Soc. Am. A 16, 1827–1830 (1999).

[CrossRef]

Y. Zhang, B. Dong, B. Gu, G. Yang, “Beam shaping in the fractional Fourier transform domain,” J. Opt. Soc. Am. A 15, 1114–1120 (1998).

[CrossRef]

J. Miao, D. Sayre, H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998).

[CrossRef]

W.-X. Cong, N.-X. Chen, B.-Y. Gu, “A new method for phase retrieval in the optical system,” Chin. Phys. Lett. 15, 24–26 (1998).

[CrossRef]

W.-X. Cong, N.-X. Chen, B.-Y. Gu, “A recursive method for phase retrieval in Fourier transform domain,” Chin. Sci. Bull. 43, 40–44 (1998).

[CrossRef]

W.-X. Cong, N.-X. Chen, B.-Y. Gu, “Recursive algorithm for phase retrieval in the fractional Fourier transform domain,” Appl. Opt. 37, 6906–6910 (1998).

[CrossRef]

K. A. Nugent, T. E. Gureyev, D. Cookson, D. Paganin, Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).

[CrossRef]
[PubMed]

H. M. Ozaktas, O. Arikan, M. A. Kutay, G. Bozdağı, “Digital computation of the fractional Fourier transform,” IEEE Trans. Signal Process. 44, 2141–2150 (1996).

[CrossRef]

Z. Zalevsky, D. Mendlovic, R. G. Dorsch, “Gerchberg–Saxton algorithm applied in the fractional Fourier or the Fresnel domain,” Opt. Lett. 21, 842–844 (1996).

[CrossRef]
[PubMed]

H. M. Ozaktas, D. Mendlovic, “Fractional Fourier optics,” J. Opt. Soc. Am. A 12, 743–751 (1995).

[CrossRef]

D. F. McAlister, M. Beck, L. Clarke, A. Mayer, M. G. Raymer, “Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms,” Opt. Lett. 20, 1181–1183 (1995).

[CrossRef]
[PubMed]

O. Aytür, H. M. Ozaktas, “Non-orthogonal domains in phase space of quantum optics and their relation to fractional Fourier transforms,” Opt. Commun. 120, 166–170 (1995).

[CrossRef]

H. M. Ozaktas, O. Aytür, “Fractional Fourier domains,” Signal Process. 46, 119–124 (1995).

[CrossRef]

L. B. Almeida, “The fractional Fourier transform and time-frequency representations,” IEEE Trans. Signal Process. 42, 3084–3091 (1994).

[CrossRef]

H. M. Ozaktas, B. Barshan, D. Mendlovic, “Convolution and filtering in fractional Fourier domains,” Opt. Rev. 1, 15–16 (1994).

[CrossRef]

M. G. Raymer, M. Beck, D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).

[CrossRef]
[PubMed]

H. M. Ozaktas, B. Barshan, D. Mendlovic, L. Onural, “Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms,” J. Opt. Soc. Am. A 11, 547–559 (1994).

[CrossRef]

G. Yang, B. Dong, B. Gu, J. Zhuang, O. K. Ersoy, “Gerchberg–Saxton and Yang–Gu algorithms for phase retrieval in a nonunitary transform system: a comparison,” Appl. Opt. 33, 209–218 (1994).

[CrossRef]
[PubMed]

D. Mendlovic, H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation: I,” J. Opt. Soc. Am. A 10, 1875–1881 (1993).

[CrossRef]

A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional order Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993).

[CrossRef]

H. M. Ozaktas, D. Mendlovic, “Fractional Fourier transforms and their optical implementation: II,” J. Opt. Soc. Am. A 10, 2522–2531 (1993).

[CrossRef]

V. Yu. Ivanov, V. P. Sivokon, M. A. Vorontsov, “Phase retrieval from a set of intensity measurements: theory and experiment,” J. Opt. Soc. Am. A 9, 1515–1524 (1992).

[CrossRef]

W. Coene, G. Janssen, M. Op. de Beeck, D. Van Dyck, “Phase retrieval through focus variation for ultra-resolution in field-emission transmission electron microscopy,” Phys. Rev. Lett. 69, 3743–3746 (1992).

[CrossRef]
[PubMed]

G. Yang, B. Gu, “On the amplitude-phase retrieval problem in the optical system,” Acta Phys. Sin. 30, 410–413 (1981).

B. Gu, G. Yang, “On the phase retrieval problem in optical and electronic microscopy,” Acta Opt. Sin. 1, 517–522 (1981).

D. L. Misell, “A method for the solution of the phase problem in electron microscopy,” J. Phys. D 6, L6–L9 (1973).

[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics: I. Test calculations,” J. Phys. D 6, 2200–2216 (1973).

[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics: II. Sources of error,” J. Phys. D 6, 2217–2224 (1973).

[CrossRef]

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

T. Alieva, M. J. Bastiaans, L. Stankovic, “Signal reconstruction from two close fractional Fourier power spectra,” IEEE Trans. Signal Process. 51, 112–123 (2003).

[CrossRef]

T. Alieva, M. J. Bastiaans, “On fractional Fourier transform moments,” IEEE Signal Process. Lett. 7, 321–323 (2000).

[CrossRef]

L. J. Allen, W. McBride, M. P. Oxley, “Exit wave reconstruction using soft x-rays,” Opt. Commun. 233, 77–82 (2004).

[CrossRef]

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev E 63, 037602-1–037602-4 (2001).

[CrossRef]

L. J. Allen, M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199, 65–75 (2001).

[CrossRef]

L. B. Almeida, “The fractional Fourier transform and time-frequency representations,” IEEE Trans. Signal Process. 42, 3084–3091 (1994).

[CrossRef]

C. Candan, M. Alper Kutay, H. M. Ozaktas, “The discrete fractional Fourier transform,” IEEE Trans. Signal Process. 48, 1329–1337 (2000).

[CrossRef]

M. A. Kutay, H. Özaktaş, H. M. Ozaktas, O. Arikan, “The fractional Fourier domain decomposition,” Signal Process. 77, 105–109 (1999).

[CrossRef]

H. M. Ozaktas, O. Arikan, M. A. Kutay, G. Bozdağı, “Digital computation of the fractional Fourier transform,” IEEE Trans. Signal Process. 44, 2141–2150 (1996).

[CrossRef]

M. G. Ertosun, H. Atli, H. M. Ozaktas, B. Barshan, “Complex signal recovery from two fractional Fourier transform intensities: order and noise dependence,” Opt. Commun. 244, 61–70 (2005).

[CrossRef]

O. Aytür, H. M. Ozaktas, “Non-orthogonal domains in phase space of quantum optics and their relation to fractional Fourier transforms,” Opt. Commun. 120, 166–170 (1995).

[CrossRef]

H. M. Ozaktas, O. Aytür, “Fractional Fourier domains,” Signal Process. 46, 119–124 (1995).

[CrossRef]

K. A. Nugent, T. E. Gureyev, D. Cookson, D. Paganin, Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).

[CrossRef]
[PubMed]

M. G. Ertosun, H. Atli, H. M. Ozaktas, B. Barshan, “Complex signal recovery from two fractional Fourier transform intensities: order and noise dependence,” Opt. Commun. 244, 61–70 (2005).

[CrossRef]

H. M. Ozaktas, B. Barshan, D. Mendlovic, “Convolution and filtering in fractional Fourier domains,” Opt. Rev. 1, 15–16 (1994).

[CrossRef]

H. M. Ozaktas, B. Barshan, D. Mendlovic, L. Onural, “Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms,” J. Opt. Soc. Am. A 11, 547–559 (1994).

[CrossRef]

T. Alieva, M. J. Bastiaans, L. Stankovic, “Signal reconstruction from two close fractional Fourier power spectra,” IEEE Trans. Signal Process. 51, 112–123 (2003).

[CrossRef]

T. Alieva, M. J. Bastiaans, “On fractional Fourier transform moments,” IEEE Signal Process. Lett. 7, 321–323 (2000).

[CrossRef]

D. F. McAlister, M. Beck, L. Clarke, A. Mayer, M. G. Raymer, “Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms,” Opt. Lett. 20, 1181–1183 (1995).

[CrossRef]
[PubMed]

M. G. Raymer, M. Beck, D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).

[CrossRef]
[PubMed]

H. M. Ozaktas, O. Arikan, M. A. Kutay, G. Bozdağı, “Digital computation of the fractional Fourier transform,” IEEE Trans. Signal Process. 44, 2141–2150 (1996).

[CrossRef]

X. Liu, K.-H. Brenner, “Reconstruction of two-dimensional complex amplitudes from intensity measurements,” Opt. Commun. 225, 19–30 (2003).

[CrossRef]

C. Candan, M. Alper Kutay, H. M. Ozaktas, “The discrete fractional Fourier transform,” IEEE Trans. Signal Process. 48, 1329–1337 (2000).

[CrossRef]

W.-X. Cong, N.-X. Chen, B.-Y. Gu, “Phase retrieval in the Fresnel transform system: a recursive algorithm,” J. Opt. Soc. Am. A 16, 1827–1830 (1999).

[CrossRef]

W.-X. Cong, N.-X. Chen, B.-Y. Gu, “Recursive algorithm for phase retrieval in the fractional Fourier transform domain,” Appl. Opt. 37, 6906–6910 (1998).

[CrossRef]

W.-X. Cong, N.-X. Chen, B.-Y. Gu, “A new method for phase retrieval in the optical system,” Chin. Phys. Lett. 15, 24–26 (1998).

[CrossRef]

W.-X. Cong, N.-X. Chen, B.-Y. Gu, “A recursive method for phase retrieval in Fourier transform domain,” Chin. Sci. Bull. 43, 40–44 (1998).

[CrossRef]

W. Coene, G. Janssen, M. Op. de Beeck, D. Van Dyck, “Phase retrieval through focus variation for ultra-resolution in field-emission transmission electron microscopy,” Phys. Rev. Lett. 69, 3743–3746 (1992).

[CrossRef]
[PubMed]

W.-X. Cong, N.-X. Chen, B.-Y. Gu, “Phase retrieval in the Fresnel transform system: a recursive algorithm,” J. Opt. Soc. Am. A 16, 1827–1830 (1999).

[CrossRef]

W.-X. Cong, N.-X. Chen, B.-Y. Gu, “Recursive algorithm for phase retrieval in the fractional Fourier transform domain,” Appl. Opt. 37, 6906–6910 (1998).

[CrossRef]

W.-X. Cong, N.-X. Chen, B.-Y. Gu, “A recursive method for phase retrieval in Fourier transform domain,” Chin. Sci. Bull. 43, 40–44 (1998).

[CrossRef]

W.-X. Cong, N.-X. Chen, B.-Y. Gu, “A new method for phase retrieval in the optical system,” Chin. Phys. Lett. 15, 24–26 (1998).

[CrossRef]

K. A. Nugent, T. E. Gureyev, D. Cookson, D. Paganin, Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).

[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, 1987), pp. 231–275.

W. Coene, G. Janssen, M. Op. de Beeck, D. Van Dyck, “Phase retrieval through focus variation for ultra-resolution in field-emission transmission electron microscopy,” Phys. Rev. Lett. 69, 3743–3746 (1992).

[CrossRef]
[PubMed]

Y. Zhang, B. Dong, B. Gu, G. Yang, “Beam shaping in the fractional Fourier transform domain,” J. Opt. Soc. Am. A 15, 1114–1120 (1998).

[CrossRef]

B. Dong, Y. Zhang, B. Gu, G. Yang, “Numerical investigation of phase retrieval in a fractional Fourier transform,” J. Opt. Soc. Am. A 14, 2709–2714 (1997).

[CrossRef]

G. Yang, B. Dong, B. Gu, J. Zhuang, O. K. Ersoy, “Gerchberg–Saxton and Yang–Gu algorithms for phase retrieval in a nonunitary transform system: a comparison,” Appl. Opt. 33, 209–218 (1994).

[CrossRef]
[PubMed]

M. G. Ertosun, H. Atli, H. M. Ozaktas, B. Barshan, “Complex signal recovery from two fractional Fourier transform intensities: order and noise dependence,” Opt. Commun. 244, 61–70 (2005).

[CrossRef]

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev E 63, 037602-1–037602-4 (2001).

[CrossRef]

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

[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, 1987), pp. 231–275.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Y. Zhang, B. Dong, B. Gu, G. Yang, “Beam shaping in the fractional Fourier transform domain,” J. Opt. Soc. Am. A 15, 1114–1120 (1998).

[CrossRef]

B. Dong, Y. Zhang, B. Gu, G. Yang, “Numerical investigation of phase retrieval in a fractional Fourier transform,” J. Opt. Soc. Am. A 14, 2709–2714 (1997).

[CrossRef]

G. Yang, B. Dong, B. Gu, J. Zhuang, O. K. Ersoy, “Gerchberg–Saxton and Yang–Gu algorithms for phase retrieval in a nonunitary transform system: a comparison,” Appl. Opt. 33, 209–218 (1994).

[CrossRef]
[PubMed]

G. Yang, B. Gu, “On the amplitude-phase retrieval problem in the optical system,” Acta Phys. Sin. 30, 410–413 (1981).

B. Gu, G. Yang, “On the phase retrieval problem in optical and electronic microscopy,” Acta Opt. Sin. 1, 517–522 (1981).

W.-X. Cong, N.-X. Chen, B.-Y. Gu, “Phase retrieval in the Fresnel transform system: a recursive algorithm,” J. Opt. Soc. Am. A 16, 1827–1830 (1999).

[CrossRef]

W.-X. Cong, N.-X. Chen, B.-Y. Gu, “Recursive algorithm for phase retrieval in the fractional Fourier transform domain,” Appl. Opt. 37, 6906–6910 (1998).

[CrossRef]

W.-X. Cong, N.-X. Chen, B.-Y. Gu, “A recursive method for phase retrieval in Fourier transform domain,” Chin. Sci. Bull. 43, 40–44 (1998).

[CrossRef]

W.-X. Cong, N.-X. Chen, B.-Y. Gu, “A new method for phase retrieval in the optical system,” Chin. Phys. Lett. 15, 24–26 (1998).

[CrossRef]

T. E. Gureyev, A. Pogany, D. M. Paganin, S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231, 53–70 (2004).

[CrossRef]

T. E. Gureyev, “Composite techniques for phase retrieval in the Fresnel region,” Opt. Commun. 220, 49–58 (2003).

[CrossRef]

K. A. Nugent, T. E. Gureyev, D. Cookson, D. Paganin, Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).

[CrossRef]
[PubMed]

B. Hennelly, J. T. Sheridan, “Fractional Fourier transform-based image encryption: phase retrieval algorithm,” Opt. Commun. 226, 61–80 (2003).

[CrossRef]

W. Coene, G. Janssen, M. Op. de Beeck, D. Van Dyck, “Phase retrieval through focus variation for ultra-resolution in field-emission transmission electron microscopy,” Phys. Rev. Lett. 69, 3743–3746 (1992).

[CrossRef]
[PubMed]

M. A. Kutay, H. Özaktaş, H. M. Ozaktas, O. Arikan, “The fractional Fourier domain decomposition,” Signal Process. 77, 105–109 (1999).

[CrossRef]

H. M. Ozaktas, O. Arikan, M. A. Kutay, G. Bozdağı, “Digital computation of the fractional Fourier transform,” IEEE Trans. Signal Process. 44, 2141–2150 (1996).

[CrossRef]

İ. Ş. Yetik, M. A. Kutay, H. Özaktaş, H. M. Ozaktas, “Continuous and discrete fractional Fourier domain decomposition,” in Proceedings of the 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing, (Institute of Electrical and Electronics Engineers, 2000), pp. I:93–96.

[CrossRef]

H. M. Ozaktas, Z. Zalevsky, M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

X. Liu, K.-H. Brenner, “Reconstruction of two-dimensional complex amplitudes from intensity measurements,” Opt. Commun. 225, 19–30 (2003).

[CrossRef]

D. F. McAlister, M. Beck, L. Clarke, A. Mayer, M. G. Raymer, “Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms,” Opt. Lett. 20, 1181–1183 (1995).

[CrossRef]
[PubMed]

M. G. Raymer, M. Beck, D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).

[CrossRef]
[PubMed]

L. J. Allen, W. McBride, M. P. Oxley, “Exit wave reconstruction using soft x-rays,” Opt. Commun. 233, 77–82 (2004).

[CrossRef]

Z. Zalevsky, D. Mendlovic, R. G. Dorsch, “Gerchberg–Saxton algorithm applied in the fractional Fourier or the Fresnel domain,” Opt. Lett. 21, 842–844 (1996).

[CrossRef]
[PubMed]

H. M. Ozaktas, D. Mendlovic, “Fractional Fourier optics,” J. Opt. Soc. Am. A 12, 743–751 (1995).

[CrossRef]

H. M. Ozaktas, B. Barshan, D. Mendlovic, L. Onural, “Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms,” J. Opt. Soc. Am. A 11, 547–559 (1994).

[CrossRef]

H. M. Ozaktas, B. Barshan, D. Mendlovic, “Convolution and filtering in fractional Fourier domains,” Opt. Rev. 1, 15–16 (1994).

[CrossRef]

D. Mendlovic, H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation: I,” J. Opt. Soc. Am. A 10, 1875–1881 (1993).

[CrossRef]

H. M. Ozaktas, D. Mendlovic, “Fractional Fourier transforms and their optical implementation: II,” J. Opt. Soc. Am. A 10, 2522–2531 (1993).

[CrossRef]

D. L. Misell, “A method for the solution of the phase problem in electron microscopy,” J. Phys. D 6, L6–L9 (1973).

[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics: I. Test calculations,” J. Phys. D 6, 2200–2216 (1973).

[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics: II. Sources of error,” J. Phys. D 6, 2217–2224 (1973).

[CrossRef]

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev E 63, 037602-1–037602-4 (2001).

[CrossRef]

K. A. Nugent, T. E. Gureyev, D. Cookson, D. Paganin, Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).

[CrossRef]
[PubMed]

L. J. Allen, W. McBride, M. P. Oxley, “Exit wave reconstruction using soft x-rays,” Opt. Commun. 233, 77–82 (2004).

[CrossRef]

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev E 63, 037602-1–037602-4 (2001).

[CrossRef]

L. J. Allen, M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199, 65–75 (2001).

[CrossRef]

M. G. Ertosun, H. Atli, H. M. Ozaktas, B. Barshan, “Complex signal recovery from two fractional Fourier transform intensities: order and noise dependence,” Opt. Commun. 244, 61–70 (2005).

[CrossRef]

C. Candan, M. Alper Kutay, H. M. Ozaktas, “The discrete fractional Fourier transform,” IEEE Trans. Signal Process. 48, 1329–1337 (2000).

[CrossRef]

M. A. Kutay, H. Özaktaş, H. M. Ozaktas, O. Arikan, “The fractional Fourier domain decomposition,” Signal Process. 77, 105–109 (1999).

[CrossRef]

H. M. Ozaktas, O. Arikan, M. A. Kutay, G. Bozdağı, “Digital computation of the fractional Fourier transform,” IEEE Trans. Signal Process. 44, 2141–2150 (1996).

[CrossRef]

O. Aytür, H. M. Ozaktas, “Non-orthogonal domains in phase space of quantum optics and their relation to fractional Fourier transforms,” Opt. Commun. 120, 166–170 (1995).

[CrossRef]

H. M. Ozaktas, O. Aytür, “Fractional Fourier domains,” Signal Process. 46, 119–124 (1995).

[CrossRef]

H. M. Ozaktas, D. Mendlovic, “Fractional Fourier optics,” J. Opt. Soc. Am. A 12, 743–751 (1995).

[CrossRef]

H. M. Ozaktas, B. Barshan, D. Mendlovic, L. Onural, “Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms,” J. Opt. Soc. Am. A 11, 547–559 (1994).

[CrossRef]

H. M. Ozaktas, B. Barshan, D. Mendlovic, “Convolution and filtering in fractional Fourier domains,” Opt. Rev. 1, 15–16 (1994).

[CrossRef]

D. Mendlovic, H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation: I,” J. Opt. Soc. Am. A 10, 1875–1881 (1993).

[CrossRef]

H. M. Ozaktas, D. Mendlovic, “Fractional Fourier transforms and their optical implementation: II,” J. Opt. Soc. Am. A 10, 2522–2531 (1993).

[CrossRef]

İ. Ş. Yetik, M. A. Kutay, H. Özaktaş, H. M. Ozaktas, “Continuous and discrete fractional Fourier domain decomposition,” in Proceedings of the 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing, (Institute of Electrical and Electronics Engineers, 2000), pp. I:93–96.

[CrossRef]

H. M. Ozaktas, Z. Zalevsky, M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

M. A. Kutay, H. Özaktaş, H. M. Ozaktas, O. Arikan, “The fractional Fourier domain decomposition,” Signal Process. 77, 105–109 (1999).

[CrossRef]

İ. Ş. Yetik, M. A. Kutay, H. Özaktaş, H. M. Ozaktas, “Continuous and discrete fractional Fourier domain decomposition,” in Proceedings of the 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing, (Institute of Electrical and Electronics Engineers, 2000), pp. I:93–96.

[CrossRef]

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev E 63, 037602-1–037602-4 (2001).

[CrossRef]

K. A. Nugent, T. E. Gureyev, D. Cookson, D. Paganin, Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).

[CrossRef]
[PubMed]

T. E. Gureyev, A. Pogany, D. M. Paganin, S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231, 53–70 (2004).

[CrossRef]

T. E. Gureyev, A. Pogany, D. M. Paganin, S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231, 53–70 (2004).

[CrossRef]

D. F. McAlister, M. Beck, L. Clarke, A. Mayer, M. G. Raymer, “Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms,” Opt. Lett. 20, 1181–1183 (1995).

[CrossRef]
[PubMed]

M. G. Raymer, M. Beck, D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).

[CrossRef]
[PubMed]

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

B. Hennelly, J. T. Sheridan, “Fractional Fourier transform-based image encryption: phase retrieval algorithm,” Opt. Commun. 226, 61–80 (2003).

[CrossRef]

T. Alieva, M. J. Bastiaans, L. Stankovic, “Signal reconstruction from two close fractional Fourier power spectra,” IEEE Trans. Signal Process. 51, 112–123 (2003).

[CrossRef]

W. Coene, G. Janssen, M. Op. de Beeck, D. Van Dyck, “Phase retrieval through focus variation for ultra-resolution in field-emission transmission electron microscopy,” Phys. Rev. Lett. 69, 3743–3746 (1992).

[CrossRef]
[PubMed]

T. E. Gureyev, A. Pogany, D. M. Paganin, S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231, 53–70 (2004).

[CrossRef]

Y. Zhang, B. Dong, B. Gu, G. Yang, “Beam shaping in the fractional Fourier transform domain,” J. Opt. Soc. Am. A 15, 1114–1120 (1998).

[CrossRef]

B. Dong, Y. Zhang, B. Gu, G. Yang, “Numerical investigation of phase retrieval in a fractional Fourier transform,” J. Opt. Soc. Am. A 14, 2709–2714 (1997).

[CrossRef]

G. Yang, B. Dong, B. Gu, J. Zhuang, O. K. Ersoy, “Gerchberg–Saxton and Yang–Gu algorithms for phase retrieval in a nonunitary transform system: a comparison,” Appl. Opt. 33, 209–218 (1994).

[CrossRef]
[PubMed]

B. Gu, G. Yang, “On the phase retrieval problem in optical and electronic microscopy,” Acta Opt. Sin. 1, 517–522 (1981).

G. Yang, B. Gu, “On the amplitude-phase retrieval problem in the optical system,” Acta Phys. Sin. 30, 410–413 (1981).

İ. Ş. Yetik, M. A. Kutay, H. Özaktaş, H. M. Ozaktas, “Continuous and discrete fractional Fourier domain decomposition,” in Proceedings of the 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing, (Institute of Electrical and Electronics Engineers, 2000), pp. I:93–96.

[CrossRef]

Y. Zhang, B. Dong, B. Gu, G. Yang, “Beam shaping in the fractional Fourier transform domain,” J. Opt. Soc. Am. A 15, 1114–1120 (1998).

[CrossRef]

B. Dong, Y. Zhang, B. Gu, G. Yang, “Numerical investigation of phase retrieval in a fractional Fourier transform,” J. Opt. Soc. Am. A 14, 2709–2714 (1997).

[CrossRef]

B. Gu, G. Yang, “On the phase retrieval problem in optical and electronic microscopy,” Acta Opt. Sin. 1, 517–522 (1981).

G. Yang, B. Gu, “On the amplitude-phase retrieval problem in the optical system,” Acta Phys. Sin. 30, 410–413 (1981).

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

[CrossRef]
[PubMed]

R. Rolleston, N. George, “Image reconstruction from partial Fresnel zone information,” Appl. Opt. 25, 178–183 (1986).

[CrossRef]
[PubMed]

G. Yang, B. Dong, B. Gu, J. Zhuang, O. K. Ersoy, “Gerchberg–Saxton and Yang–Gu algorithms for phase retrieval in a nonunitary transform system: a comparison,” Appl. Opt. 33, 209–218 (1994).

[CrossRef]
[PubMed]

W.-X. Cong, N.-X. Chen, B.-Y. Gu, “Recursive algorithm for phase retrieval in the fractional Fourier transform domain,” Appl. Opt. 37, 6906–6910 (1998).

[CrossRef]

D. Dragoman, “Redundancy of phase-space distribution functions in complex field recovery problems,” Appl. Opt. 42, 1932–1937 (2003).

[CrossRef]
[PubMed]

M. Testorf, “Comment on ‘Redundancy of phase-space distribution functions in complex field recovery problems’,” Appl. Opt. 44, 55–57 (2005).

[CrossRef]

D. Dragoman, “Reply to comment on ‘Redundancy of phase-space distribution functions in complex field recovery problems’,” Appl. Opt. 44, 58–59 (2005).

[CrossRef]

W.-X. Cong, N.-X. Chen, B.-Y. Gu, “A new method for phase retrieval in the optical system,” Chin. Phys. Lett. 15, 24–26 (1998).

[CrossRef]

W.-X. Cong, N.-X. Chen, B.-Y. Gu, “A recursive method for phase retrieval in Fourier transform domain,” Chin. Sci. Bull. 43, 40–44 (1998).

[CrossRef]

T. Alieva, M. J. Bastiaans, “On fractional Fourier transform moments,” IEEE Signal Process. Lett. 7, 321–323 (2000).

[CrossRef]

H. M. Ozaktas, O. Arikan, M. A. Kutay, G. Bozdağı, “Digital computation of the fractional Fourier transform,” IEEE Trans. Signal Process. 44, 2141–2150 (1996).

[CrossRef]

L. B. Almeida, “The fractional Fourier transform and time-frequency representations,” IEEE Trans. Signal Process. 42, 3084–3091 (1994).

[CrossRef]

T. Alieva, M. J. Bastiaans, L. Stankovic, “Signal reconstruction from two close fractional Fourier power spectra,” IEEE Trans. Signal Process. 51, 112–123 (2003).

[CrossRef]

C. Candan, M. Alper Kutay, H. M. Ozaktas, “The discrete fractional Fourier transform,” IEEE Trans. Signal Process. 48, 1329–1337 (2000).

[CrossRef]

H. M. Ozaktas, B. Barshan, D. Mendlovic, L. Onural, “Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms,” J. Opt. Soc. Am. A 11, 547–559 (1994).

[CrossRef]

W.-X. Cong, N.-X. Chen, B.-Y. Gu, “Phase retrieval in the Fresnel transform system: a recursive algorithm,” J. Opt. Soc. Am. A 16, 1827–1830 (1999).

[CrossRef]

Y. Zhang, B. Dong, B. Gu, G. Yang, “Beam shaping in the fractional Fourier transform domain,” J. Opt. Soc. Am. A 15, 1114–1120 (1998).

[CrossRef]

J. Miao, D. Sayre, H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998).

[CrossRef]

B. Dong, Y. Zhang, B. Gu, G. Yang, “Numerical investigation of phase retrieval in a fractional Fourier transform,” J. Opt. Soc. Am. A 14, 2709–2714 (1997).

[CrossRef]

R. Rolleston, N. George, “Stationary phase approximations in Fresnel-zone magnitude-only reconstructions,” J. Opt. Soc. Am. A 4, 148–153 (1987).

[CrossRef]

R. P. Millane, “Phase retrieval in crystallography and optics,” J. Opt. Soc. Am. A 7, 394–411 (1990).

[CrossRef]

V. Yu. Ivanov, V. P. Sivokon, M. A. Vorontsov, “Phase retrieval from a set of intensity measurements: theory and experiment,” J. Opt. Soc. Am. A 9, 1515–1524 (1992).

[CrossRef]

D. Mendlovic, H. M. Ozaktas, “Fractional Fourier transforms and their optical implementation: I,” J. Opt. Soc. Am. A 10, 1875–1881 (1993).

[CrossRef]

A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional order Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993).

[CrossRef]

H. M. Ozaktas, D. Mendlovic, “Fractional Fourier transforms and their optical implementation: II,” J. Opt. Soc. Am. A 10, 2522–2531 (1993).

[CrossRef]

M. Bastiaans, K. Wolf, “Phase reconstruction from intensity measurements in linear systems,” J. Opt. Soc. Am. A 20, 1046–1049 (2003).

[CrossRef]

H. H. Bauschke, P. L. Combettes, D. R. Luke, “Phase retrieval, error reduction algorithm, and Fienup variants: a view from convex optimization,” J. Opt. Soc. Am. A 19, 1334–1345 (2002).

[CrossRef]

H. M. Ozaktas, D. Mendlovic, “Fractional Fourier optics,” J. Opt. Soc. Am. A 12, 743–751 (1995).

[CrossRef]

D. L. Misell, “A method for the solution of the phase problem in electron microscopy,” J. Phys. D 6, L6–L9 (1973).

[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics: I. Test calculations,” J. Phys. D 6, 2200–2216 (1973).

[CrossRef]

D. L. Misell, “An examination of an iterative method for the solution of the phase problem in optics and electron optics: II. Sources of error,” J. Phys. D 6, 2217–2224 (1973).

[CrossRef]

T. E. Gureyev, A. Pogany, D. M. Paganin, S. W. Wilkins, “Linear algorithms for phase retrieval in the Fresnel region,” Opt. Commun. 231, 53–70 (2004).

[CrossRef]

T. E. Gureyev, “Composite techniques for phase retrieval in the Fresnel region,” Opt. Commun. 220, 49–58 (2003).

[CrossRef]

M. G. Ertosun, H. Atli, H. M. Ozaktas, B. Barshan, “Complex signal recovery from two fractional Fourier transform intensities: order and noise dependence,” Opt. Commun. 244, 61–70 (2005).

[CrossRef]

O. Aytür, H. M. Ozaktas, “Non-orthogonal domains in phase space of quantum optics and their relation to fractional Fourier transforms,” Opt. Commun. 120, 166–170 (1995).

[CrossRef]

B. Hennelly, J. T. Sheridan, “Fractional Fourier transform-based image encryption: phase retrieval algorithm,” Opt. Commun. 226, 61–80 (2003).

[CrossRef]

L. J. Allen, W. McBride, M. P. Oxley, “Exit wave reconstruction using soft x-rays,” Opt. Commun. 233, 77–82 (2004).

[CrossRef]

L. J. Allen, M. P. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199, 65–75 (2001).

[CrossRef]

X. Liu, K.-H. Brenner, “Reconstruction of two-dimensional complex amplitudes from intensity measurements,” Opt. Commun. 225, 19–30 (2003).

[CrossRef]

Z. Zalevsky, D. Mendlovic, R. G. Dorsch, “Gerchberg–Saxton algorithm applied in the fractional Fourier or the Fresnel domain,” Opt. Lett. 21, 842–844 (1996).

[CrossRef]
[PubMed]

D. F. McAlister, M. Beck, L. Clarke, A. Mayer, M. G. Raymer, “Optical phase retrieval by phase-space tomography and fractional-order Fourier transforms,” Opt. Lett. 20, 1181–1183 (1995).

[CrossRef]
[PubMed]

H. M. Ozaktas, B. Barshan, D. Mendlovic, “Convolution and filtering in fractional Fourier domains,” Opt. Rev. 1, 15–16 (1994).

[CrossRef]

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev E 63, 037602-1–037602-4 (2001).

[CrossRef]

M. G. Raymer, M. Beck, D. F. McAlister, “Complex wave-field reconstruction using phase-space tomography,” Phys. Rev. Lett. 72, 1137–1140 (1994).

[CrossRef]
[PubMed]

W. Coene, G. Janssen, M. Op. de Beeck, D. Van Dyck, “Phase retrieval through focus variation for ultra-resolution in field-emission transmission electron microscopy,” Phys. Rev. Lett. 69, 3743–3746 (1992).

[CrossRef]
[PubMed]

K. A. Nugent, T. E. Gureyev, D. Cookson, D. Paganin, Z. Barnea, “Quantitative phase imaging using hard x rays,” Phys. Rev. Lett. 77, 2961–2964 (1996).

[CrossRef]
[PubMed]

H. M. Ozaktas, O. Aytür, “Fractional Fourier domains,” Signal Process. 46, 119–124 (1995).

[CrossRef]

M. A. Kutay, H. Özaktaş, H. M. Ozaktas, O. Arikan, “The fractional Fourier domain decomposition,” Signal Process. 77, 105–109 (1999).

[CrossRef]

İ. Ş. Yetik, M. A. Kutay, H. Özaktaş, H. M. Ozaktas, “Continuous and discrete fractional Fourier domain decomposition,” in Proceedings of the 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing, (Institute of Electrical and Electronics Engineers, 2000), pp. I:93–96.

[CrossRef]

H. M. Ozaktas, Z. Zalevsky, M. A. Kutay, The Fractional Fourier Transform with Applications in Optics and Signal Processing (Wiley, 2001).

H. Stark, ed., Image Recovery: Theory and Application (Academic, 1987).

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