X. Tan, B. Gu, G. Yang, B. Dong, “Diffractive phase elements for beam shaping: a new design method,” Appl. Opt. 34, 1314–1320 (1995).

[CrossRef]
[PubMed]

S. Liu, J. Xu, Y. Zhang, L. Chen, C. Li, “General optical implementations of fractional Fourier transforms,” Opt. Lett. 20, 1053–1055 (1995).

[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]

J. R. Fienup, “Phase-retrieval algorithms for a complicated optical system,” Appl. Opt. 32, 1737–1746 (1993).

[CrossRef]
[PubMed]

J. Cordingley, “Application of a binary diffractive optic for beam shaping in semiconductor processing by lasers,” Appl. Opt. 32, 2538–2549 (1993).

[CrossRef]
[PubMed]

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

[CrossRef]

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

[CrossRef]

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

[CrossRef]

H. M. Ozaktas, D. Mendlovic, “Fourier transforms of fractional order and their optical interpretation,” Opt. Commun. 101, 163–169 (1993).

[CrossRef]

F. S. Roux, “Intensity distribution transformation for rotationally symmetric beam shaping,” Opt. Eng. (Bellingham) 30, 529–536 (1991).

[CrossRef]

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. (Bellingham) 19, 297–305 (1980).

[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,” J. Phys. D 6, 2200–2225 (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, 227–246 (1972).

R. W. Gerchberg, W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik (Stuttgart) 34, 275–284 (1971).

R. H. Boucher, “Convergence of algorithms for phase retrieval from two intensity distributions,” in International Optical Computing Conference, W. T. Rhodes, ed., Proc. SPIE231, 130–141 (1980).

[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]

X. Tan, B. Gu, G. Yang, B. Dong, “Diffractive phase elements for beam shaping: a new design method,” Appl. Opt. 34, 1314–1320 (1995).

[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]

B. Gu, G. Yang, B. Dong, “General theory for performing an optical transform,” Appl. Opt. 25, 3197–3206 (1986).

[CrossRef]
[PubMed]

G. Yang, B. Gu, B. Dong, “Theory of the amplitude-phase retrieval in an any linear transform system and its applications,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE1767, 457–479 (1992).

[CrossRef]

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 227–246 (1972).

R. W. Gerchberg, W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik (Stuttgart) 34, 275–284 (1971).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), Chap. 2, p. 21–25.

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]

X. Tan, B. Gu, G. Yang, B. Dong, “Diffractive phase elements for beam shaping: a new design method,” Appl. Opt. 34, 1314–1320 (1995).

[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]

B. Gu, G. Yang, B. Dong, “General theory for performing an optical transform,” Appl. Opt. 25, 3197–3206 (1986).

[CrossRef]
[PubMed]

G. Yang, B. Gu, B. Dong, “Theory of the amplitude-phase retrieval in an any linear transform system and its applications,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE1767, 457–479 (1992).

[CrossRef]

E. Kreyszig, Introductory Functional Analysis with Applications (Wiley, New York, 1986).

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, 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]

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

[CrossRef]

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

[CrossRef]

H. M. Ozaktas, D. Mendlovic, “Fourier transforms of fractional order and their optical interpretation,” Opt. Commun. 101, 163–169 (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,” J. Phys. D 6, 2200–2225 (1973).

[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]

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

[CrossRef]

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

[CrossRef]

H. M. Ozaktas, D. Mendlovic, “Fourier transforms of fractional order and their optical interpretation,” Opt. Commun. 101, 163–169 (1993).

[CrossRef]

F. S. Roux, “Intensity distribution transformation for rotationally symmetric beam shaping,” Opt. Eng. (Bellingham) 30, 529–536 (1991).

[CrossRef]

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 227–246 (1972).

R. W. Gerchberg, W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik (Stuttgart) 34, 275–284 (1971).

Xiang-Gen Xia, “On bandlimited signals with fractional Fourier transform,” IEEE Signal Process. Lett. 3, 72–74 (1996).

[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]

X. Tan, B. Gu, G. Yang, B. Dong, “Diffractive phase elements for beam shaping: a new design method,” Appl. Opt. 34, 1314–1320 (1995).

[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]

B. Gu, G. Yang, B. Dong, “General theory for performing an optical transform,” Appl. Opt. 25, 3197–3206 (1986).

[CrossRef]
[PubMed]

G. Yang, B. Gu, B. Dong, “Theory of the amplitude-phase retrieval in an any linear transform system and its applications,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE1767, 457–479 (1992).

[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]

S. Liu, J. Xu, Y. Zhang, L. Chen, C. Li, “General optical implementations of fractional Fourier transforms,” Opt. Lett. 20, 1053–1055 (1995).

[CrossRef]
[PubMed]

M. Quintanilla, A. M. de Frutos, “Holographic filter that transforms a Gaussian into a uniform beam,” Appl. Opt. 20, 879–880 (1981).

[CrossRef]
[PubMed]

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[CrossRef]

M. T. Eismann, A. M. Tai, J. N. Cederquist, “Iterative design of a holographic beam former,” Appl. Opt. 28, 2641–2650 (1989).

[CrossRef]
[PubMed]

J. Cordingley, “Application of a binary diffractive optic for beam shaping in semiconductor processing by lasers,” Appl. Opt. 32, 2538–2549 (1993).

[CrossRef]
[PubMed]

J. R. Fienup, “Phase-retrieval algorithms for a complicated optical system,” Appl. Opt. 32, 1737–1746 (1993).

[CrossRef]
[PubMed]

B. Gu, G. Yang, B. Dong, “General theory for performing an optical transform,” Appl. Opt. 25, 3197–3206 (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]

X. Tan, B. Gu, G. Yang, B. Dong, “Diffractive phase elements for beam shaping: a new design method,” Appl. Opt. 34, 1314–1320 (1995).

[CrossRef]
[PubMed]

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

[CrossRef]

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

[CrossRef]
[PubMed]

Xiang-Gen Xia, “On bandlimited signals with fractional Fourier transform,” IEEE Signal Process. Lett. 3, 72–74 (1996).

[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]

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]

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

[CrossRef]

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

[CrossRef]

A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (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,” J. Phys. D 6, 2200–2225 (1973).

[CrossRef]

H. M. Ozaktas, D. Mendlovic, “Fourier transforms of fractional order and their optical interpretation,” Opt. Commun. 101, 163–169 (1993).

[CrossRef]

F. S. Roux, “Intensity distribution transformation for rotationally symmetric beam shaping,” Opt. Eng. (Bellingham) 30, 529–536 (1991).

[CrossRef]

J. R. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. (Bellingham) 19, 297–305 (1980).

[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]

S. Liu, J. Xu, Y. Zhang, L. Chen, C. Li, “General optical implementations of fractional Fourier transforms,” Opt. Lett. 20, 1053–1055 (1995).

[CrossRef]
[PubMed]

R. W. Gerchberg, W. O. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik (Stuttgart) 34, 275–284 (1971).

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 227–246 (1972).

G. Yang, B. Gu, B. Dong, “Theory of the amplitude-phase retrieval in an any linear transform system and its applications,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE1767, 457–479 (1992).

[CrossRef]

R. H. Boucher, “Convergence of algorithms for phase retrieval from two intensity distributions,” in International Optical Computing Conference, W. T. Rhodes, ed., Proc. SPIE231, 130–141 (1980).

[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), Chap. 2, p. 21–25.

E. Kreyszig, Introductory Functional Analysis with Applications (Wiley, New York, 1986).