K. K. Sharma and S. D. Joshi, "On scaling properties of the fractional Fourier transform and its relation with other transforms," Opt. Commun. 257, 27-38 (2006).

[CrossRef]

I. Moreno, M. M. Sánchez-López, C. Ferreira, J. A. Davis, and F. Mateos, "Teaching Fourier optics through ray matrices," Eur. J. Phys. 26, 261-271 (2005).

[CrossRef]

K. B. Wolf, "Construction of optical systems," Geometric Optics in Phase Space (Springer-Verlag, 2004), Chap. 10.

L. Z. Cai and Y. Q. Wang, "Optical implementation of scale invariant fractional Fourier transform of continuously variable orders with a two-lens system," Opt. Laser Technol. 24, 249-252 (2002).

A. Torre, "The fractional Fourier transform and some of its applications to optics," Prog. Opt. 43, 531-596 (2002).

[CrossRef]

C. Sheppard and K. G. Larkin, "Similarity theorems for fractional Fourier transforms and fractional Hankel transforms," Opt. Commun. 154, 173-178 (1998).

[CrossRef]

S. Liu, H. Ren, J. Zhang, and X. Zhang, "Image-scaling problem in the optical fractional Fourier transform," Appl. Opt. 36, 5671-5674 (1997).

[CrossRef]
[PubMed]

Z. Zalevsky, D. Mendlovic, and J. C. Caulfield, "Fractional correlator with real-time control of space-invariance property," Appl. Opt. 36, 2370-2375 (1997).

[CrossRef]
[PubMed]

D. Mendlovic, R. G. Dorsch, A. W. Lohmann, Z. Zalevsky, and C. Ferreira, "Optical illustration of a varied fractional Fourier transform order and the Radon-Wigner display," Appl. Opt. 35, 3925-3929 (1996).

[CrossRef]
[PubMed]

L. M. Bernardo, "ABCD matrix formalism of fractional Fourier optics," Opt. Eng. (Bellingham) 35, 742-740 (1996).

[CrossRef]

A. Gerrard and J. M. Burch, Introduction to Matrix Methods in Optics (Dover, 1975).

M. Moshinski and C. Quesne, "Linear canonical transformations and their unitary representations," J. Math. Phys. 12, 1772-1780 (1971).

[CrossRef]

E. U. Condon, "Immersion of the Fourier transform in a continuous group of functional transformations," Proc. Natl. Acad. Sci. U.S.A. 23, 158-164 (1937).

[CrossRef]
[PubMed]

A. Gerrard and J. M. Burch, Introduction to Matrix Methods in Optics (Dover, 1975).

L. Z. Cai and Y. Q. Wang, "Optical implementation of scale invariant fractional Fourier transform of continuously variable orders with a two-lens system," Opt. Laser Technol. 24, 249-252 (2002).

E. U. Condon, "Immersion of the Fourier transform in a continuous group of functional transformations," Proc. Natl. Acad. Sci. U.S.A. 23, 158-164 (1937).

[CrossRef]
[PubMed]

I. Moreno, M. M. Sánchez-López, C. Ferreira, J. A. Davis, and F. Mateos, "Teaching Fourier optics through ray matrices," Eur. J. Phys. 26, 261-271 (2005).

[CrossRef]

I. Moreno, J. A. Davis, and K. Crabtree, "Fractional Fourier transform optical system with programmable diffractive lenses," Appl. Opt. 42, 6544-6548 (2003).

[CrossRef]
[PubMed]

I. Moreno, M. M. Sánchez-López, C. Ferreira, J. A. Davis, and F. Mateos, "Teaching Fourier optics through ray matrices," Eur. J. Phys. 26, 261-271 (2005).

[CrossRef]

D. Mendlovic, R. G. Dorsch, A. W. Lohmann, Z. Zalevsky, and C. Ferreira, "Optical illustration of a varied fractional Fourier transform order and the Radon-Wigner display," Appl. Opt. 35, 3925-3929 (1996).

[CrossRef]
[PubMed]

A. Gerrard and J. M. Burch, Introduction to Matrix Methods in Optics (Dover, 1975).

K. K. Sharma and S. D. Joshi, "On scaling properties of the fractional Fourier transform and its relation with other transforms," Opt. Commun. 257, 27-38 (2006).

[CrossRef]

C. Sheppard and K. G. Larkin, "Similarity theorems for fractional Fourier transforms and fractional Hankel transforms," Opt. Commun. 154, 173-178 (1998).

[CrossRef]

D. Mendlovic, R. G. Dorsch, A. W. Lohmann, Z. Zalevsky, and C. Ferreira, "Optical illustration of a varied fractional Fourier transform order and the Radon-Wigner display," Appl. Opt. 35, 3925-3929 (1996).

[CrossRef]
[PubMed]

A. W. Lohmann, "A fake zoom lens for fractional Fourier experiments," Opt. Commun. 115, 437-443 (1995).

[CrossRef]

I. Moreno, M. M. Sánchez-López, C. Ferreira, J. A. Davis, and F. Mateos, "Teaching Fourier optics through ray matrices," Eur. J. Phys. 26, 261-271 (2005).

[CrossRef]

Z. Zalevsky, D. Mendlovic, and J. C. Caulfield, "Fractional correlator with real-time control of space-invariance property," Appl. Opt. 36, 2370-2375 (1997).

[CrossRef]
[PubMed]

D. Mendlovic, R. G. Dorsch, A. W. Lohmann, Z. Zalevsky, and C. Ferreira, "Optical illustration of a varied fractional Fourier transform order and the Radon-Wigner display," Appl. Opt. 35, 3925-3929 (1996).

[CrossRef]
[PubMed]

D. Mendlovic and H. M. Ozaktas, "Fractional Fourier transforms and their optical implementation," J. Opt. Soc. Am. A 10, 1875-1881 (1993).

[CrossRef]

I. Moreno, M. M. Sánchez-López, C. Ferreira, J. A. Davis, and F. Mateos, "Teaching Fourier optics through ray matrices," Eur. J. Phys. 26, 261-271 (2005).

[CrossRef]

I. Moreno, J. A. Davis, and K. Crabtree, "Fractional Fourier transform optical system with programmable diffractive lenses," Appl. Opt. 42, 6544-6548 (2003).

[CrossRef]
[PubMed]

M. Moshinski and C. Quesne, "Linear canonical transformations and their unitary representations," J. Math. Phys. 12, 1772-1780 (1971).

[CrossRef]

M. Moshinski and C. Quesne, "Linear canonical transformations and their unitary representations," J. Math. Phys. 12, 1772-1780 (1971).

[CrossRef]

I. Moreno, M. M. Sánchez-López, C. Ferreira, J. A. Davis, and F. Mateos, "Teaching Fourier optics through ray matrices," Eur. J. Phys. 26, 261-271 (2005).

[CrossRef]

K. K. Sharma and S. D. Joshi, "On scaling properties of the fractional Fourier transform and its relation with other transforms," Opt. Commun. 257, 27-38 (2006).

[CrossRef]

C. Sheppard and K. G. Larkin, "Similarity theorems for fractional Fourier transforms and fractional Hankel transforms," Opt. Commun. 154, 173-178 (1998).

[CrossRef]

A. Torre, "The fractional Fourier transform and some of its applications to optics," Prog. Opt. 43, 531-596 (2002).

[CrossRef]

L. Z. Cai and Y. Q. Wang, "Optical implementation of scale invariant fractional Fourier transform of continuously variable orders with a two-lens system," Opt. Laser Technol. 24, 249-252 (2002).

K. B. Wolf, "Construction of optical systems," Geometric Optics in Phase Space (Springer-Verlag, 2004), Chap. 10.

Z. Zalevsky, D. Mendlovic, and J. C. Caulfield, "Fractional correlator with real-time control of space-invariance property," Appl. Opt. 36, 2370-2375 (1997).

[CrossRef]
[PubMed]

D. Mendlovic, R. G. Dorsch, A. W. Lohmann, Z. Zalevsky, and C. Ferreira, "Optical illustration of a varied fractional Fourier transform order and the Radon-Wigner display," Appl. Opt. 35, 3925-3929 (1996).

[CrossRef]
[PubMed]

S. Liu, H. Ren, J. Zhang, and X. Zhang, "Image-scaling problem in the optical fractional Fourier transform," Appl. Opt. 36, 5671-5674 (1997).

[CrossRef]
[PubMed]

I. Moreno, J. A. Davis, and K. Crabtree, "Fractional Fourier transform optical system with programmable diffractive lenses," Appl. Opt. 42, 6544-6548 (2003).

[CrossRef]
[PubMed]

D. Mendlovic, R. G. Dorsch, A. W. Lohmann, Z. Zalevsky, and C. Ferreira, "Optical illustration of a varied fractional Fourier transform order and the Radon-Wigner display," Appl. Opt. 35, 3925-3929 (1996).

[CrossRef]
[PubMed]

Z. Zalevsky, D. Mendlovic, and J. C. Caulfield, "Fractional correlator with real-time control of space-invariance property," Appl. Opt. 36, 2370-2375 (1997).

[CrossRef]
[PubMed]

I. Moreno, M. M. Sánchez-López, C. Ferreira, J. A. Davis, and F. Mateos, "Teaching Fourier optics through ray matrices," Eur. J. Phys. 26, 261-271 (2005).

[CrossRef]

M. Moshinski and C. Quesne, "Linear canonical transformations and their unitary representations," J. Math. Phys. 12, 1772-1780 (1971).

[CrossRef]

L. M. Bernardo and O. D. D. Soares, "Fractional Fourier transforms and imaging," J. Opt. Soc. Am. A 11, 2622-2626 (1994).

[CrossRef]

A. A. Tovar and L. W. Casperson, "Generalized reverse theorems for multipass applications in matrix optics," J. Opt. Soc. Am. A 11, 2633-2642 (1994).

[CrossRef]

D. Mendlovic and H. M. Ozaktas, "Fractional Fourier transforms and their optical implementation," J. Opt. Soc. Am. A 10, 1875-1881 (1993).

[CrossRef]

A. Lohmann, "Image rotation, Wigner rotation, and the fractional Fourier transform," J. Opt. Soc. Am. A 10, 2181-2186 (1993).

[CrossRef]

A. W. Lohmann, "A fake zoom lens for fractional Fourier experiments," Opt. Commun. 115, 437-443 (1995).

[CrossRef]

C. Sheppard and K. G. Larkin, "Similarity theorems for fractional Fourier transforms and fractional Hankel transforms," Opt. Commun. 154, 173-178 (1998).

[CrossRef]

K. K. Sharma and S. D. Joshi, "On scaling properties of the fractional Fourier transform and its relation with other transforms," Opt. Commun. 257, 27-38 (2006).

[CrossRef]

L. M. Bernardo, "ABCD matrix formalism of fractional Fourier optics," Opt. Eng. (Bellingham) 35, 742-740 (1996).

[CrossRef]

L. Z. Cai and Y. Q. Wang, "Optical implementation of scale invariant fractional Fourier transform of continuously variable orders with a two-lens system," Opt. Laser Technol. 24, 249-252 (2002).

E. U. Condon, "Immersion of the Fourier transform in a continuous group of functional transformations," Proc. Natl. Acad. Sci. U.S.A. 23, 158-164 (1937).

[CrossRef]
[PubMed]

A. Torre, "The fractional Fourier transform and some of its applications to optics," Prog. Opt. 43, 531-596 (2002).

[CrossRef]

K. B. Wolf, "Construction of optical systems," Geometric Optics in Phase Space (Springer-Verlag, 2004), Chap. 10.

A. Gerrard and J. M. Burch, Introduction to Matrix Methods in Optics (Dover, 1975).