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[CrossRef]

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[CrossRef]

F. S. Oktem, and H. M. Ozaktas, “Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space-bandwidth product,” J. Opt. Soc. Am. A 27, 1885–1895 (2010).

[CrossRef]

U. Gopinathan, G. Pedrini, B. Javidi, and W. Osten, “Lensless 3D digital holographic microscopic imaging at vacuum UV wavelength,” J. Disp. Technol. 6, 479–483 (2010).

[CrossRef]

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

[CrossRef]

Z. Zalevsky, V. Mico, and J. Garcia, “Nanophotonics for optical super resolution from an information theoretical perspective: a review,” J. Nanophoton. 3, 032502 (2009).

[CrossRef]

A. Koc, 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. Healy and J. Sheridan, “Bandwidth, compact support, apertures and the linear canonical transform in ABCD systems,” Proc. SPIE 6994, 69940W (2008).

[CrossRef]

M. Testorf and A. Lohmann, “Holography in phase space,” Appl. Opt. 47, A70–A77 (2008).

[CrossRef]

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[CrossRef]

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

[CrossRef]

J. Maycock, C. McElhinney, B. Hennelly, T. Naughton, J. McDonald, and B. Javidi, “Reconstruction of partially occluded objects encoded in three-dimensional scenes by using digital holograms,” Appl. Opt. 45, 2975–2985 (2006).

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M. J. Bastiaans and T. Alieva, “Synthesis of an arbitrary ABCD system with fixed lens positions,” Opt. Lett. 31, 2414–2416 (2006).

[CrossRef]

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Optical system design for orthosymplectic transformations in phase space,” J. Opt. Soc. Am. A 23, 2494–2500 (2006).

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

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J. Rodrigo, T. Alieva, and M. Calvo, “Gyrator transform: properties and applications,” Opt. Express 15, 2190–2203 (2007).

[CrossRef]

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Optical system design for orthosymplectic transformations in phase space,” J. Opt. Soc. Am. A 23, 2494–2500 (2006).

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M. J. Bastiaans and T. Alieva, “Synthesis of an arbitrary ABCD system with fixed lens positions,” Opt. Lett. 31, 2414–2416 (2006).

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T. Alieva and M. J. Bastiaans, “Alternative representation of the linear canonical integral transform,” Opt. Lett. 30, 3302–3304 (2005).

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H. Ozaktas, S. Ark, and T. Coşkun, “Fundamental structure of Fresnel diffraction: longitudinal uniformity with respect to fractional Fourier order,” Opt. Lett. 37, 103–105 (2012).

[CrossRef]

H. Ozaktas, S. Ark, and T. Coşkun, “Fundamental structure of fresnel diffraction: natural sampling grid and the fractional Fourier transform,” Opt. Lett. 36, 2524–2526 (2011).

[CrossRef]

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

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

[CrossRef]

H. M. Ozaktas, B. Barshan, D. Mendlovic, and 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).

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[CrossRef]

H. Ozaktas, S. Ark, and T. Coşkun, “Fundamental structure of fresnel diffraction: natural sampling grid and the fractional Fourier transform,” Opt. Lett. 36, 2524–2526 (2011).

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[CrossRef]

U. Gopinathan, G. Pedrini, B. Javidi, and W. Osten, “Lensless 3D digital holographic microscopic imaging at vacuum UV wavelength,” J. Disp. Technol. 6, 479–483 (2010).

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[CrossRef]

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[CrossRef]

F. Gori and G. Guattari, “Effects of coherence on the degrees of freedom of an image,” J. Opt. Soc. Am. 61, 36–39 (1971).

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J. Healy and J. Sheridan, “Bandwidth, compact support, apertures and the linear canonical transform in ABCD systems,” Proc. SPIE 6994, 69940W (2008).

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J. Maycock, C. McElhinney, B. Hennelly, T. Naughton, J. McDonald, and B. Javidi, “Reconstruction of partially occluded objects encoded in three-dimensional scenes by using digital holograms,” Appl. Opt. 45, 2975–2985 (2006).

[CrossRef]

B. Hennelly and J. Sheridan, “Optical encryption and the space bandwidth product,” Opt. Commun. 247, 291–305 (2005).

[CrossRef]

U. Gopinathan, G. Pedrini, B. Javidi, and W. Osten, “Lensless 3D digital holographic microscopic imaging at vacuum UV wavelength,” J. Disp. Technol. 6, 479–483 (2010).

[CrossRef]

J. Maycock, C. McElhinney, B. Hennelly, T. Naughton, J. McDonald, and B. Javidi, “Reconstruction of partially occluded objects encoded in three-dimensional scenes by using digital holograms,” Appl. Opt. 45, 2975–2985 (2006).

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

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

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

[CrossRef]

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[CrossRef]

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[CrossRef]

H. M. Ozaktas, B. Barshan, D. Mendlovic, and 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]

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F. S. Oktem, and H. M. Ozaktas, “Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space-bandwidth product,” J. Opt. Soc. Am. A 27, 1885–1895 (2010).

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[CrossRef]

H. Ozaktas, S. Ark, and T. Coşkun, “Fundamental structure of Fresnel diffraction: longitudinal uniformity with respect to fractional Fourier order,” Opt. Lett. 37, 103–105 (2012).

[CrossRef]

H. Ozaktas, S. Ark, and T. Coşkun, “Fundamental structure of fresnel diffraction: natural sampling grid and the fractional Fourier transform,” Opt. Lett. 36, 2524–2526 (2011).

[CrossRef]

G. Forbes, V. Manko, H. Ozaktas, R. Simon, and K. Wolf, “Wigner distributions and phase space in optics,” J. Opt. Soc. Am. A 17, 2274 (2000).

[CrossRef]

F. S. Oktem, and H. M. Ozaktas, “Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space-bandwidth product,” J. Opt. Soc. Am. A 27, 1885–1895 (2010).

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

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

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

[CrossRef]

H. M. Ozaktas and M. F. Erden, “Relationships among ray optical, Gaussian beam, and fractional Fourier transform descriptions of first-order optical systems,” Opt. Commun. 143, 75–86 (1997).

[CrossRef]

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

[CrossRef]

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

[CrossRef]

H. M. Ozaktas, B. Barshan, D. Mendlovic, and 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]

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U. Gopinathan, G. Pedrini, B. Javidi, and W. Osten, “Lensless 3D digital holographic microscopic imaging at vacuum UV wavelength,” J. Disp. Technol. 6, 479–483 (2010).

[CrossRef]

Z. Zalevsky, N. Shamir, and D. Mendlovic, “Geometrical superresolution in infrared sensor: experimental verification,” Opt. Eng. 43, 1401–1406 (2004).

[CrossRef]

J. Healy and J. Sheridan, “Bandwidth, compact support, apertures and the linear canonical transform in ABCD systems,” Proc. SPIE 6994, 69940W (2008).

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G. Forbes, V. Manko, H. Ozaktas, R. Simon, and K. Wolf, “Wigner distributions and phase space in optics,” J. Opt. Soc. Am. A 17, 2274 (2000).

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[CrossRef]

Z. Zalevsky, N. Shamir, and D. Mendlovic, “Geometrical superresolution in infrared sensor: experimental verification,” Opt. Eng. 43, 1401–1406 (2004).

[CrossRef]

Z. Zalevsky, D. Mendlovic, and A. Lohmann, “Understanding superresolution in wigner space,” J. Opt. Soc. Am. A 17, 2422–2430 (2000).

[CrossRef]

K. Wolf, D. Mendlovic, and Z. Zalevsky, “Generalized Wigner function for the analysis of superresolution systems,” Appl. Opt. 37, 4374–4379 (1998).

[CrossRef]

D. Mendlovic, A. Lohmann, and Z. Zalevsky, “Space-bandwidth product adaptation and its application to superresolution: examples,” J. Opt. Soc. Am. A 14, 563–567 (1997).

[CrossRef]

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[CrossRef]

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

K. Wolf, D. Mendlovic, and Z. Zalevsky, “Generalized Wigner function for the analysis of superresolution systems,” Appl. Opt. 37, 4374–4379 (1998).

[CrossRef]

J. Maycock, C. McElhinney, B. Hennelly, T. Naughton, J. McDonald, and B. Javidi, “Reconstruction of partially occluded objects encoded in three-dimensional scenes by using digital holograms,” Appl. Opt. 45, 2975–2985 (2006).

[CrossRef]

M. Testorf and A. Lohmann, “Holography in phase space,” Appl. Opt. 47, A70–A77 (2008).

[CrossRef]

D. Claus, D. Iliescu, and P. Bryanston-Cross, “Quantitative space-bandwidth product analysis in digital holography,” Appl. Opt. 50, H116–H127 (2011).

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

[CrossRef]

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

[CrossRef]

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Z. Zalevsky, V. Mico, and J. Garcia, “Nanophotonics for optical super resolution from an information theoretical perspective: a review,” J. Nanophoton. 3, 032502 (2009).

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[CrossRef]

H. M. Ozaktas, B. Barshan, D. Mendlovic, and 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, and A. Lohmann, “Space-bandwidth product adaptation and its application to superresolution: fundamentals,” J. Opt. Soc. Am. A 14, 558–562 (1997).

[CrossRef]

D. Mendlovic, A. Lohmann, and Z. Zalevsky, “Space-bandwidth product adaptation and its application to superresolution: examples,” J. Opt. Soc. Am. A 14, 563–567 (1997).

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[CrossRef]

A. Stern, “Uncertainty principles in linear canonical transform domains and some of their implications in optics,” J. Opt. Soc. Am. A 25, 647–652 (2008).

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F. S. Oktem, and H. M. Ozaktas, “Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space-bandwidth product,” J. Opt. Soc. Am. A 27, 1885–1895 (2010).

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