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[Crossref]

J. J. Healy and J. T. Sheridan, “Sampling and discretization of the linear canonical transform,” Signal Process. 89, 641-648 (2009).

[Crossref]

F. Oktem and H. M. Ozaktas, “Exact relation between continuous and discrete linear canonical transforms,” IEEE Signal Process. Lett. 16, 727-730 (2009).

[Crossref]

A. Cortes, I. Velez, and J. F. Sevillano, “Radix rk FFTs: matricial representation and SDC/SDF pipeline implementation,” IEEE Trans. Signal Process. 57, 2824-2839 (2009).

[Crossref]

A. Koç, H. M. Ozaktas, C. Candan, and M. A. Kutay, “Digital computation of linear canonical transforms,” IEEE Trans. Signal Process. 56, 2383-2394 (2008).

[Crossref]

J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “An additional sampling criterion for the linear canonical transform,” Opt. Lett. 33, 2599-2601 (2008).

[Crossref]
[PubMed]

U. Gopinathan, G. Situ, T. J. Naughton, and J. T. Sheridan, “Noninterferometric phase retrieval using a fractional Fourier system,” J. Opt. Soc. Am. A 25, 108-115 (2008).

[Crossref]

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[Crossref]
[PubMed]

J. J. Healy and J. T. Sheridan, “Cases where the linear canonical transform of a signal has compact support or is band-limited,” Opt. Lett. 33, 228-230 (2008).

[Crossref]
[PubMed]

J. Zhao, R. Tao, and Y. Wang, “Sampling rate conversion for linear canonical transform,” Signal Process. 88, 2825-2832 (2008).

[Crossref]

B.-Z. Li, R. Tao, and Y. Wang, “New sampling formulae related to linear canonical transform,” Signal Process. 87, 983-990 (2007).

[Crossref]

T. Alieva and M. J. Bastiaans, “Properties of the linear canonical integral transformation,” J. Opt. Soc. Am. A 24, 3658-3665 (2007).

[Crossref]

A. Nelleri, J. Joseph, and K. Singh, “Digital Fresnel field encryption for three-dimensional information security,” Opt. Eng. (Bellingham) 46, 045801 (8 pages) (2007).

[Crossref]

S. G. Johnson and M. Frigo, “A modified split-radix FFT with fewer arithmetic operations,” IEEE Trans. Signal Process. 55, 111-119 (2007).

[Crossref]

T. J. Lundy and J. Van Buskirk, “A new matrix approach to real FFTs and convolutions of length 2k,” Computing 80, 23-45 (2007).

[Crossref]

A. Averbuch, R. R. Coifman, D. L. Donoho, M. Elad, and M. Israeli, “Fast and accurate polar Fourier transform,” Appl. Comput. Harmon. Anal. 21, 145-167 (2006).

[Crossref]

B. M. Hennelly, D. P. Kelly, R. F. Patten, J. E. Ward, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Metrology and the linear canonical transform,” J. Mod. Opt. 53, 2167-2186 (2006).

[Crossref]

D. P. Kelly, J. E. Ward, B. M. Hennelly, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Paraxial speckle-based metrology systems with an aperture,” J. Opt. Soc. Am. A 23, 2861-2870 (2006).

[Crossref]

R. F. Patten, B. M. Hennelly, D. P. Kelly, F. T. O'Neill, Y. Liu, and J. T. Sheridan, “Speckle photography: mixed domain fractional Fourier motion detection,” Opt. Lett. 31, 32-34 (2006).

[Crossref]
[PubMed]

A. Stern, “Sampling of linear canonical transformed signals,” Signal Process. 86, 1421-1425 (2006).

[Crossref]

B. Deng, R. Tao, and Y. Wang, “Convolution theorems for the linear canonical transform and their applications,” Sci. China Ser. F, Inf. Sci. 49, 592-603 (2006).

[Crossref]

H. M. Ozaktas, A. Koç. I. Sari, and M. Alper Kutay, “Efficient computation of quadratic-phase integrals in optics,” Appl. Opt. 31, 35-37 (2006).

[Crossref]

M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” Proc. IEEE 93, 216-231 (2005).

[Crossref]

B. M. Hennelly and J. T. Sheridan, “Fast numerical algorithm for the linear canonical transform,” J. Opt. Soc. Am. A 22, 928-937 (2005).

[Crossref]

B. M. Hennelly and J. T. Sheridan, “Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms,” J. Opt. Soc. Am. A 22, 917-927 (2005).

[Crossref]

L. Onural, “Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulations,” Opt. Eng. (Bellingham) 43, 2557-2563 (2004).

[Crossref]

B. M. Hennelly and J. T. Sheridan, “Image encryption and the fractional Fourier transform,” Optik (Stuttgart) 114, 251-265 (2003).

S.-C. Pei and J.-J. Ding, “Closed-form discrete fractional and affine Fourier transforms,” IEEE Trans. Signal Process. 48, 1338-1353 (2000).

[Crossref]

B. Barshan, M. Alper Kutay, and H. M. Ozaktas, “Optimal filtering with linear canonical transformations,” Opt. Commun. 135, 32-36 (1997).

[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

J. W. Cooley and J. W. Tukey, “An algorithm for the machine computation of complex Fourier series,” Math. Comput. 19, 297-301 (1965).

[Crossref]

H. M. Ozaktas, A. Koç. I. Sari, and M. Alper Kutay, “Efficient computation of quadratic-phase integrals in optics,” Appl. Opt. 31, 35-37 (2006).

[Crossref]

B. Barshan, M. Alper Kutay, and H. M. Ozaktas, “Optimal filtering with linear canonical transformations,” Opt. Commun. 135, 32-36 (1997).

[Crossref]

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

[Crossref]

A. Averbuch, R. R. Coifman, D. L. Donoho, M. Elad, and M. Israeli, “Fast and accurate polar Fourier transform,” Appl. Comput. Harmon. Anal. 21, 145-167 (2006).

[Crossref]

B. Barshan, M. Alper Kutay, and H. M. Ozaktas, “Optimal filtering with linear canonical transformations,” Opt. Commun. 135, 32-36 (1997).

[Crossref]

H. O. Bartelt, K.-H. Brenner, and A. W. Lohmann, “The Wigner distribution function and its optical production,” Opt. Commun. 32, 32-38 (1980).

[Crossref]

T. Alieva and M. J. Bastiaans, “Properties of the linear canonical integral transformation,” J. Opt. Soc. Am. A 24, 3658-3665 (2007).

[Crossref]

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[Crossref]

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

[Crossref]

A. Koç, H. M. Ozaktas, C. Candan, and M. A. Kutay, “Digital computation of linear canonical transforms,” IEEE Trans. Signal Process. 56, 2383-2394 (2008).

[Crossref]

A. Averbuch, R. R. Coifman, D. L. Donoho, M. Elad, and M. Israeli, “Fast and accurate polar Fourier transform,” Appl. Comput. Harmon. Anal. 21, 145-167 (2006).

[Crossref]

J. W. Cooley and J. W. Tukey, “An algorithm for the machine computation of complex Fourier series,” Math. Comput. 19, 297-301 (1965).

[Crossref]

A. Cortes, I. Velez, and J. F. Sevillano, “Radix rk FFTs: matricial representation and SDC/SDF pipeline implementation,” IEEE Trans. Signal Process. 57, 2824-2839 (2009).

[Crossref]

B. Deng, R. Tao, and Y. Wang, “Convolution theorems for the linear canonical transform and their applications,” Sci. China Ser. F, Inf. Sci. 49, 592-603 (2006).

[Crossref]

S.-C. Pei and J.-J. Ding, “Closed-form discrete fractional and affine Fourier transforms,” IEEE Trans. Signal Process. 48, 1338-1353 (2000).

[Crossref]

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A. Averbuch, R. R. Coifman, D. L. Donoho, M. Elad, and M. Israeli, “Fast and accurate polar Fourier transform,” Appl. Comput. Harmon. Anal. 21, 145-167 (2006).

[Crossref]

A. Averbuch, R. R. Coifman, D. L. Donoho, M. Elad, and M. Israeli, “Fast and accurate polar Fourier transform,” Appl. Comput. Harmon. Anal. 21, 145-167 (2006).

[Crossref]

S. G. Johnson and M. Frigo, “A modified split-radix FFT with fewer arithmetic operations,” IEEE Trans. Signal Process. 55, 111-119 (2007).

[Crossref]

M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” Proc. IEEE 93, 216-231 (2005).

[Crossref]

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U. Gopinathan, G. Situ, T. J. Naughton, and J. T. Sheridan, “Noninterferometric phase retrieval using a fractional Fourier system,” J. Opt. Soc. Am. A 25, 108-115 (2008).

[Crossref]

B. M. Hennelly, D. P. Kelly, R. F. Patten, J. E. Ward, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Metrology and the linear canonical transform,” J. Mod. Opt. 53, 2167-2186 (2006).

[Crossref]

D. P. Kelly, J. E. Ward, B. M. Hennelly, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Paraxial speckle-based metrology systems with an aperture,” J. Opt. Soc. Am. A 23, 2861-2870 (2006).

[Crossref]

F. Gori, “Fresnel transform and sampling theorem,” Opt. Commun. 39, 293-297 (1981).

[Crossref]

J. J. Healy and J. T. Sheridan, “Sampling and discretization of the linear canonical transform,” Signal Process. 89, 641-648 (2009).

[Crossref]

J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “An additional sampling criterion for the linear canonical transform,” Opt. Lett. 33, 2599-2601 (2008).

[Crossref]
[PubMed]

J. J. Healy and J. T. Sheridan, “Cases where the linear canonical transform of a signal has compact support or is band-limited,” Opt. Lett. 33, 228-230 (2008).

[Crossref]
[PubMed]

J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “An additional sampling criterion for the linear canonical transform,” Opt. Lett. 33, 2599-2601 (2008).

[Crossref]
[PubMed]

R. F. Patten, B. M. Hennelly, D. P. Kelly, F. T. O'Neill, Y. Liu, and J. T. Sheridan, “Speckle photography: mixed domain fractional Fourier motion detection,” Opt. Lett. 31, 32-34 (2006).

[Crossref]
[PubMed]

D. P. Kelly, J. E. Ward, B. M. Hennelly, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Paraxial speckle-based metrology systems with an aperture,” J. Opt. Soc. Am. A 23, 2861-2870 (2006).

[Crossref]

B. M. Hennelly, D. P. Kelly, R. F. Patten, J. E. Ward, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Metrology and the linear canonical transform,” J. Mod. Opt. 53, 2167-2186 (2006).

[Crossref]

B. M. Hennelly and J. T. Sheridan, “Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms,” J. Opt. Soc. Am. A 22, 917-927 (2005).

[Crossref]

B. M. Hennelly and J. T. Sheridan, “Fast numerical algorithm for the linear canonical transform,” J. Opt. Soc. Am. A 22, 928-937 (2005).

[Crossref]

B. M. Hennelly and J. T. Sheridan, “Image encryption and the fractional Fourier transform,” Optik (Stuttgart) 114, 251-265 (2003).

A. Averbuch, R. R. Coifman, D. L. Donoho, M. Elad, and M. Israeli, “Fast and accurate polar Fourier transform,” Appl. Comput. Harmon. Anal. 21, 145-167 (2006).

[Crossref]

S. G. Johnson and M. Frigo, “A modified split-radix FFT with fewer arithmetic operations,” IEEE Trans. Signal Process. 55, 111-119 (2007).

[Crossref]

M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” Proc. IEEE 93, 216-231 (2005).

[Crossref]

A. Nelleri, J. Joseph, and K. Singh, “Digital Fresnel field encryption for three-dimensional information security,” Opt. Eng. (Bellingham) 46, 045801 (8 pages) (2007).

[Crossref]

J. E. Ward, D. P. Kelly, and J. T. Sheridan, “Three-dimensional speckle size in generalized optical systems with limiting apertures,” J. Opt. Soc. Am. A 26, 1858-1867 (2009).

[Crossref]

R. F. Patten, B. M. Hennelly, D. P. Kelly, F. T. O'Neill, Y. Liu, and J. T. Sheridan, “Speckle photography: mixed domain fractional Fourier motion detection,” Opt. Lett. 31, 32-34 (2006).

[Crossref]
[PubMed]

D. P. Kelly, J. E. Ward, B. M. Hennelly, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Paraxial speckle-based metrology systems with an aperture,” J. Opt. Soc. Am. A 23, 2861-2870 (2006).

[Crossref]

B. M. Hennelly, D. P. Kelly, R. F. Patten, J. E. Ward, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Metrology and the linear canonical transform,” J. Mod. Opt. 53, 2167-2186 (2006).

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A. Koç, H. M. Ozaktas, C. Candan, and M. A. Kutay, “Digital computation of linear canonical transforms,” IEEE Trans. Signal Process. 56, 2383-2394 (2008).

[Crossref]

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

[Crossref]

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

B.-Z. Li, R. Tao, and Y. Wang, “New sampling formulae related to linear canonical transform,” Signal Process. 87, 983-990 (2007).

[Crossref]

A. W. Lohmann, R. G. Dorsch, D. Mendlovic, Z. Zalevsky, and C. Ferreira, “Space-bandwidth product of optical signals and systems,” J. Opt. Soc. Am. A 13, 470-473 (1996).

[Crossref]

H. O. Bartelt, K.-H. Brenner, and A. W. Lohmann, “The Wigner distribution function and its optical production,” Opt. Commun. 32, 32-38 (1980).

[Crossref]

T. J. Lundy and J. Van Buskirk, “A new matrix approach to real FFTs and convolutions of length 2k,” Computing 80, 23-45 (2007).

[Crossref]

A. Nelleri, J. Joseph, and K. Singh, “Digital Fresnel field encryption for three-dimensional information security,” Opt. Eng. (Bellingham) 46, 045801 (8 pages) (2007).

[Crossref]

F. Oktem and H. M. Ozaktas, “Exact relation between continuous and discrete linear canonical transforms,” IEEE Signal Process. Lett. 16, 727-730 (2009).

[Crossref]

R. F. Patten, B. M. Hennelly, D. P. Kelly, F. T. O'Neill, Y. Liu, and J. T. Sheridan, “Speckle photography: mixed domain fractional Fourier motion detection,” Opt. Lett. 31, 32-34 (2006).

[Crossref]
[PubMed]

D. P. Kelly, J. E. Ward, B. M. Hennelly, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Paraxial speckle-based metrology systems with an aperture,” J. Opt. Soc. Am. A 23, 2861-2870 (2006).

[Crossref]

B. M. Hennelly, D. P. Kelly, R. F. Patten, J. E. Ward, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Metrology and the linear canonical transform,” J. Mod. Opt. 53, 2167-2186 (2006).

[Crossref]

L. Onural, “Some mathematical properties of the uniformly sampled quadratic phase function and associated issues in digital Fresnel diffraction simulations,” Opt. Eng. (Bellingham) 43, 2557-2563 (2004).

[Crossref]

F. Oktem and H. M. Ozaktas, “Exact relation between continuous and discrete linear canonical transforms,” IEEE Signal Process. Lett. 16, 727-730 (2009).

[Crossref]

A. Koç, H. M. Ozaktas, C. Candan, and M. A. Kutay, “Digital computation of linear canonical transforms,” IEEE Trans. Signal Process. 56, 2383-2394 (2008).

[Crossref]

H. M. Ozaktas, A. Koç. I. Sari, and M. Alper Kutay, “Efficient computation of quadratic-phase integrals in optics,” Appl. Opt. 31, 35-37 (2006).

[Crossref]

B. Barshan, M. Alper Kutay, and H. M. Ozaktas, “Optimal filtering with linear canonical transformations,” Opt. Commun. 135, 32-36 (1997).

[Crossref]

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

[Crossref]

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

B. M. Hennelly, D. P. Kelly, R. F. Patten, J. E. Ward, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Metrology and the linear canonical transform,” J. Mod. Opt. 53, 2167-2186 (2006).

[Crossref]

R. F. Patten, B. M. Hennelly, D. P. Kelly, F. T. O'Neill, Y. Liu, and J. T. Sheridan, “Speckle photography: mixed domain fractional Fourier motion detection,” Opt. Lett. 31, 32-34 (2006).

[Crossref]
[PubMed]

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[Crossref]

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W. M. Gentleman and G. Sande, “Fast Fourier transforms--for fun and profit,” in Proceedings of AFIPS Fall Joint Computer Conference, Vol. 29 (ACM, 1966), pp. 563-578.

H. M. Ozaktas, A. Koç. I. Sari, and M. Alper Kutay, “Efficient computation of quadratic-phase integrals in optics,” Appl. Opt. 31, 35-37 (2006).

[Crossref]

A. Cortes, I. Velez, and J. F. Sevillano, “Radix rk FFTs: matricial representation and SDC/SDF pipeline implementation,” IEEE Trans. Signal Process. 57, 2824-2839 (2009).

[Crossref]

J. E. Ward, D. P. Kelly, and J. T. Sheridan, “Three-dimensional speckle size in generalized optical systems with limiting apertures,” J. Opt. Soc. Am. A 26, 1858-1867 (2009).

[Crossref]

J. J. Healy and J. T. Sheridan, “Sampling and discretization of the linear canonical transform,” Signal Process. 89, 641-648 (2009).

[Crossref]

U. Gopinathan, G. Situ, T. J. Naughton, and J. T. Sheridan, “Noninterferometric phase retrieval using a fractional Fourier system,” J. Opt. Soc. Am. A 25, 108-115 (2008).

[Crossref]

J. J. Healy, B. M. Hennelly, and J. T. Sheridan, “An additional sampling criterion for the linear canonical transform,” Opt. Lett. 33, 2599-2601 (2008).

[Crossref]
[PubMed]

J. J. Healy and J. T. Sheridan, “Cases where the linear canonical transform of a signal has compact support or is band-limited,” Opt. Lett. 33, 228-230 (2008).

[Crossref]
[PubMed]

B. M. Hennelly, D. P. Kelly, R. F. Patten, J. E. Ward, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Metrology and the linear canonical transform,” J. Mod. Opt. 53, 2167-2186 (2006).

[Crossref]

D. P. Kelly, J. E. Ward, B. M. Hennelly, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Paraxial speckle-based metrology systems with an aperture,” J. Opt. Soc. Am. A 23, 2861-2870 (2006).

[Crossref]

R. F. Patten, B. M. Hennelly, D. P. Kelly, F. T. O'Neill, Y. Liu, and J. T. Sheridan, “Speckle photography: mixed domain fractional Fourier motion detection,” Opt. Lett. 31, 32-34 (2006).

[Crossref]
[PubMed]

B. M. Hennelly and J. T. Sheridan, “Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms,” J. Opt. Soc. Am. A 22, 917-927 (2005).

[Crossref]

B. M. Hennelly and J. T. Sheridan, “Fast numerical algorithm for the linear canonical transform,” J. Opt. Soc. Am. A 22, 928-937 (2005).

[Crossref]

B. M. Hennelly and J. T. Sheridan, “Image encryption and the fractional Fourier transform,” Optik (Stuttgart) 114, 251-265 (2003).

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[Crossref]

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[Crossref]
[PubMed]

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[Crossref]

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[Crossref]

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[Crossref]

B.-Z. Li, R. Tao, and Y. Wang, “New sampling formulae related to linear canonical transform,” Signal Process. 87, 983-990 (2007).

[Crossref]

B. Deng, R. Tao, and Y. Wang, “Convolution theorems for the linear canonical transform and their applications,” Sci. China Ser. F, Inf. Sci. 49, 592-603 (2006).

[Crossref]

J. W. Cooley and J. W. Tukey, “An algorithm for the machine computation of complex Fourier series,” Math. Comput. 19, 297-301 (1965).

[Crossref]

T. J. Lundy and J. Van Buskirk, “A new matrix approach to real FFTs and convolutions of length 2k,” Computing 80, 23-45 (2007).

[Crossref]

A. Cortes, I. Velez, and J. F. Sevillano, “Radix rk FFTs: matricial representation and SDC/SDF pipeline implementation,” IEEE Trans. Signal Process. 57, 2824-2839 (2009).

[Crossref]

J. Zhao, R. Tao, and Y. Wang, “Sampling rate conversion for linear canonical transform,” Signal Process. 88, 2825-2832 (2008).

[Crossref]

B.-Z. Li, R. Tao, and Y. Wang, “New sampling formulae related to linear canonical transform,” Signal Process. 87, 983-990 (2007).

[Crossref]

B. Deng, R. Tao, and Y. Wang, “Convolution theorems for the linear canonical transform and their applications,” Sci. China Ser. F, Inf. Sci. 49, 592-603 (2006).

[Crossref]

J. E. Ward, D. P. Kelly, and J. T. Sheridan, “Three-dimensional speckle size in generalized optical systems with limiting apertures,” J. Opt. Soc. Am. A 26, 1858-1867 (2009).

[Crossref]

B. M. Hennelly, D. P. Kelly, R. F. Patten, J. E. Ward, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Metrology and the linear canonical transform,” J. Mod. Opt. 53, 2167-2186 (2006).

[Crossref]

D. P. Kelly, J. E. Ward, B. M. Hennelly, U. Gopinathan, F. T. O'Neill, and J. T. Sheridan, “Paraxial speckle-based metrology systems with an aperture,” J. Opt. Soc. Am. A 23, 2861-2870 (2006).

[Crossref]

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