[1] [1] L M Bernardo. Talbot self-imaging in fractional Fourier planes of real and complex orders [J]. Opt Commun, 1997, 140(4-6): 195-198.

[2] [2] R S Romaniuk, S Simrock, V M Lutkovski. Photonics applications in industry and research IV [C]. SPIE, 2005, 5948: 59482Q.

[3] [3] M V Shovgenyuk, Y M Kozlovskii. Self-image of periodic phase elements in the fractional Fourier transform domain [C]. SPIE, 2006, 6027: 60270E.

[4] [4] Hua Wenqiang, Bian Fenggang, Song Li, et al.. Fractional Talbot effect of phase gratings illuminated by partially coherent synchrotron radiation [J]. Acta Optica Sinica, 2013, 33(1): 0134001.

[5] [5] Hua Jianwen, Liu Liren. Fractional Talbot effect under fractional Fourier transform [J]. Chinese J Lasers, 1997, 24(2): 163-168.

[6] [6] Qu Weijuan, Yan Aimin, Liu Liren, et al.. Fractional Talbot effect of 2D skewed periodic array [J]. Chinese J Lasers, 2006, 33(3): 356-360.

[7] [7] T Alieva, M Bastiaans. Alternative representation of the linear canonical integral transform [J]. Opt Lett, 2005, 30(24): 3302-3304.

[8] [8] M J Bastiaans. The wigner distribution function applied to optical signals and systems [J]. Opt Commun, 1978, 25(1): 26-30.

[9] [9] D F V James, G S Agarwal. The generalized Fresnel transform and its applications to optics [J]. Opt Commun, 1996, 126(4-6): 207-212.

[10] [10] C Palma, V Bagini. Extension of the Fresnel transform to ABCD systems [J]. J Opt Soc Am A, 1997, 14(8): 1774-1779.

[11] [11] S Abe, J T Sheridan. Generalization of the fractional Fourier transformation to an arbitrary linear lossless transformation: an operator approach [J]. J Phys A Math Gen, 1994, 27(12): 4179-4187.

[12] [12] H M Ozaktas, Z Zalevsky, M A Kutay. The Fractional Fourier Transform with Applications in Optics and Signal Processing [M]. New York: Wiley, 2001. 63-183.

[13] [13] H M Ozaktas, O Arikan, M A Kutay, et al.. Digital computation of the fractional Fourier transform [J]. IEEE Trans Signal Process, 1996, 44(9): 2141-2150.

[14] [14] J Garcia, D Mas, R G Dorsch. Fractional Fourier transform calculation through the fast Fourier transform algorithm [J]. Appl Opt, 1996 35(35): 7013-7018.

[15] [15] S C Pei, M H Yeh. Improved discrete fractional Fourier transform [J]. Opt Lett, 1997, 22(14): 1047-1049.

[16] [16] X G Deng, Y P Li, D Y Fan. A fast algorithm for fractional Fourier transform [J]. Opt Commun, 1997, 138(4-6): 270-274.

[17] [17] F J Marinho, L M Bernardo. Numerical calculation of fractional Fourier transforms with a single fast Fourier transform algorithm [J]. J Opt Soc Am A, 1998, 15(8): 2111-2116.

[18] [18] M H Yeh, S C Pei. A method for the discrete fractional Fourier transform computation [J]. IEEE Trans Signal Processing, 2003, 51(3): 889-891.

[19] [19] X Yang, Q Tan, X Wei, et al.. Improved fast fractional-Fourier-transform algorithm [J]. J Opt Soc Am A, 2004, 21(9): 1677-1681.

[20] [20] D Mas, J Garcia, C Ferreira, et al.. Fast algorithms for free-space diffraction patterns calculation [J]. Opt Commun, 1999, 164(4-6): 233-245.

[21] [21] M Sypek. Light propagation in the Fresnel region. New numerical approach [J]. Opt Commun, 1995, 116(1-3): 43-48.

[22] [22] D Mas, J Perez, C Hernandez, et al.. Fast numerical calculation of Fresnel patterns in convergent systems [J]. Opt Commun, 2003, 227(4-6): 245-258.

[23] [23] D Mendlovic, Z Zalevsky, N Konforti. Computation considerations and fast algorithms for calculating the diffraction integral [J]. J Mod Opt, 1997, 44(22): 407-414.