J. J. Healy and J. T. Sheridan, “Fast linear canonical transforms,” J. Opt. Soc. Am. A 27, 21–30 (2010).

[CrossRef]

I. Moreno, J. A. Davis, D. M. Cottrell, N. Zhang, and X.-C. Yuan, “Encoding generalized phase functions on Dammann gratings,” Opt. Lett. 35, 1536–1538 (2010).

[CrossRef]

J. A. Davis, B. M. L. Pascoquin, C. S. Tuvey, and D. M. Cottrell, “Fourier transform pupil functions for modifying the depth of focus of optical imaging systems,” Appl. Opt. 48, 4893–4898 (2009).

[CrossRef]

J. A. Davis, M. J. Mitry, M. A. Bandres, I. Ruiz, K. P. McAuley, and D. M. Cottrell, “Generation of accelerating Airy and accelerating parabolic beams using phase-only patterns,” Appl. Opt. 48, 3171–3177 (2009).

J. A. Davis, B. A. Slovick, C. S. Tuvey, and Don M. Cottrell, “High diffraction efficiency from one- and two-dimensional Nyquist frequency binary phase gratings,” Appl. Opt. 47, 2828–2834 (2008).

J. A. Davis, M. J. Mitry, M. A. Bandres, and D. M. Cottrell, “Observation of accelerating parabolic beams,” Opt. Express 16, 12866–12871 (2008).

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]

D. P. Kelly, B. M. Hennelly, W. T. Rhodes, and J. T. Sheridan, “Analytical and numerical analysis of linear optical systems,” Opt. Eng. 45, 088201 (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).

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]

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).

[CrossRef]

D. Mendlovic, A. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407–414 (1997).

[CrossRef]

M. Sypek, “Light propagation in the Fresnel region. New numerical approach,” Opt. Commun. 116, 43–48 (1995).

[CrossRef]

D. Psaltis, E. G. Paek, and AS. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).

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. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).

J. A. Davis, M. J. Mitry, M. A. Bandres, I. Ruiz, K. P. McAuley, and D. M. Cottrell, “Generation of accelerating Airy and accelerating parabolic beams using phase-only patterns,” Appl. Opt. 48, 3171–3177 (2009).

J. A. Davis, M. J. Mitry, M. A. Bandres, and D. M. Cottrell, “Observation of accelerating parabolic beams,” Opt. Express 16, 12866–12871 (2008).

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).

[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]

I. Moreno, J. A. Davis, D. M. Cottrell, N. Zhang, and X.-C. Yuan, “Encoding generalized phase functions on Dammann gratings,” Opt. Lett. 35, 1536–1538 (2010).

[CrossRef]

J. A. Davis, M. J. Mitry, M. A. Bandres, I. Ruiz, K. P. McAuley, and D. M. Cottrell, “Generation of accelerating Airy and accelerating parabolic beams using phase-only patterns,” Appl. Opt. 48, 3171–3177 (2009).

J. A. Davis, B. M. L. Pascoquin, C. S. Tuvey, and D. M. Cottrell, “Fourier transform pupil functions for modifying the depth of focus of optical imaging systems,” Appl. Opt. 48, 4893–4898 (2009).

[CrossRef]

J. A. Davis, M. J. Mitry, M. A. Bandres, and D. M. Cottrell, “Observation of accelerating parabolic beams,” Opt. Express 16, 12866–12871 (2008).

D. M. Cottrell, J. A. Davis, T. R. Hedman, and R. A. Lilly, “Multiple imaging phase-encoded optical elements written on programmable spatial light modulators,” Appl. Opt. 29, 2505–2509 (1990).

[CrossRef]

J. A. Davis, M. A. Waring, G. W. Bach, R. A. Lilly, and D. M. Cottrell, “Compact optical correlator design,” Appl. Opt. 28, 10–11 (1989).

[CrossRef]

J. A. Davis, B. A. Slovick, C. S. Tuvey, and Don M. Cottrell, “High diffraction efficiency from one- and two-dimensional Nyquist frequency binary phase gratings,” Appl. Opt. 47, 2828–2834 (2008).

I. Moreno, J. A. Davis, D. M. Cottrell, N. Zhang, and X.-C. Yuan, “Encoding generalized phase functions on Dammann gratings,” Opt. Lett. 35, 1536–1538 (2010).

[CrossRef]

J. A. Davis, M. J. Mitry, M. A. Bandres, I. Ruiz, K. P. McAuley, and D. M. Cottrell, “Generation of accelerating Airy and accelerating parabolic beams using phase-only patterns,” Appl. Opt. 48, 3171–3177 (2009).

J. A. Davis, B. M. L. Pascoquin, C. S. Tuvey, and D. M. Cottrell, “Fourier transform pupil functions for modifying the depth of focus of optical imaging systems,” Appl. Opt. 48, 4893–4898 (2009).

[CrossRef]

J. A. Davis, B. A. Slovick, C. S. Tuvey, and Don M. Cottrell, “High diffraction efficiency from one- and two-dimensional Nyquist frequency binary phase gratings,” Appl. Opt. 47, 2828–2834 (2008).

J. A. Davis, M. J. Mitry, M. A. Bandres, and D. M. Cottrell, “Observation of accelerating parabolic beams,” Opt. Express 16, 12866–12871 (2008).

J. A. Davis, C. S. Tuvey, O. López-Coronado, J. Campos, M. J. Yzuel, and C. Iemmi, “Tailoring the depth of focus for optical imaging systems using a Fourier transform approach,” Opt. Lett. 32, 844–846 (2007).

[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).

J. A. Davis and R. A. Lilly, “Ray-matrix approach for diffractive optics,” Appl. Opt. 32, 155–159 (1993).

[CrossRef]

D. M. Cottrell, J. A. Davis, T. R. Hedman, and R. A. Lilly, “Multiple imaging phase-encoded optical elements written on programmable spatial light modulators,” Appl. Opt. 29, 2505–2509 (1990).

[CrossRef]

J. A. Davis, M. A. Waring, G. W. Bach, R. A. Lilly, and D. M. Cottrell, “Compact optical correlator design,” Appl. Opt. 28, 10–11 (1989).

[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).

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).

[CrossRef]

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).

[CrossRef]

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978), Chap. 8.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1988).

F. Gori, “Why is the Fresnel transform so little known?,” in Current Trends in Optics, J. C. Dainty, ed. (Academic, 1994).

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]

D. P. Kelly, B. M. Hennelly, W. T. Rhodes, and J. T. Sheridan, “Analytical and numerical analysis of linear optical systems,” Opt. Eng. 45, 088201 (2006).

[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]

D. P. Kelly, B. M. Hennelly, W. T. Rhodes, and J. T. Sheridan, “Analytical and numerical analysis of linear optical systems,” Opt. Eng. 45, 088201 (2006).

[CrossRef]

D. Mendlovic, A. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407–414 (1997).

[CrossRef]

J. A. Davis and R. A. Lilly, “Ray-matrix approach for diffractive optics,” Appl. Opt. 32, 155–159 (1993).

[CrossRef]

D. M. Cottrell, J. A. Davis, T. R. Hedman, and R. A. Lilly, “Multiple imaging phase-encoded optical elements written on programmable spatial light modulators,” Appl. Opt. 29, 2505–2509 (1990).

[CrossRef]

J. A. Davis, M. A. Waring, G. W. Bach, R. A. Lilly, and D. M. Cottrell, “Compact optical correlator design,” Appl. Opt. 28, 10–11 (1989).

[CrossRef]

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).

[CrossRef]

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).

[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).

J. A. Davis, M. J. Mitry, M. A. Bandres, I. Ruiz, K. P. McAuley, and D. M. Cottrell, “Generation of accelerating Airy and accelerating parabolic beams using phase-only patterns,” Appl. Opt. 48, 3171–3177 (2009).

D. Mendlovic, A. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407–414 (1997).

[CrossRef]

J. A. Davis, M. J. Mitry, M. A. Bandres, I. Ruiz, K. P. McAuley, and D. M. Cottrell, “Generation of accelerating Airy and accelerating parabolic beams using phase-only patterns,” Appl. Opt. 48, 3171–3177 (2009).

J. A. Davis, M. J. Mitry, M. A. Bandres, and D. M. Cottrell, “Observation of accelerating parabolic beams,” Opt. Express 16, 12866–12871 (2008).

I. Moreno, J. A. Davis, D. M. Cottrell, N. Zhang, and X.-C. Yuan, “Encoding generalized phase functions on Dammann gratings,” Opt. Lett. 35, 1536–1538 (2010).

[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).

D. Psaltis, E. G. Paek, and AS. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).

D. Psaltis, E. G. Paek, and AS. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).

D. P. Kelly, B. M. Hennelly, W. T. Rhodes, and J. T. Sheridan, “Analytical and numerical analysis of linear optical systems,” Opt. Eng. 45, 088201 (2006).

[CrossRef]

J. A. Davis, M. J. Mitry, M. A. Bandres, I. Ruiz, K. P. McAuley, and D. M. Cottrell, “Generation of accelerating Airy and accelerating parabolic beams using phase-only patterns,” Appl. Opt. 48, 3171–3177 (2009).

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).

J. J. Healy and J. T. Sheridan, “Fast linear canonical transforms,” J. Opt. Soc. Am. A 27, 21–30 (2010).

[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]

D. P. Kelly, B. M. Hennelly, W. T. Rhodes, and J. T. Sheridan, “Analytical and numerical analysis of linear optical systems,” Opt. Eng. 45, 088201 (2006).

[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]

J. A. Davis, B. A. Slovick, C. S. Tuvey, and Don M. Cottrell, “High diffraction efficiency from one- and two-dimensional Nyquist frequency binary phase gratings,” Appl. Opt. 47, 2828–2834 (2008).

A. Stern, “Why is the linear canonical transform so little known?,” in Proceedings of 5th International Workshop on Information Optics, G. Cristóbal, B. Javidi, and S. Vallmitjana, eds (Springer, 2006), pp. 225–234.

M. Sypek, “Light propagation in the Fresnel region. New numerical approach,” Opt. Commun. 116, 43–48 (1995).

[CrossRef]

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).

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

[CrossRef]

J. A. Davis, B. M. L. Pascoquin, C. S. Tuvey, and D. M. Cottrell, “Fourier transform pupil functions for modifying the depth of focus of optical imaging systems,” Appl. Opt. 48, 4893–4898 (2009).

[CrossRef]

J. A. Davis, B. A. Slovick, C. S. Tuvey, and Don M. Cottrell, “High diffraction efficiency from one- and two-dimensional Nyquist frequency binary phase gratings,” Appl. Opt. 47, 2828–2834 (2008).

J. A. Davis, C. S. Tuvey, O. López-Coronado, J. Campos, M. J. Yzuel, and C. Iemmi, “Tailoring the depth of focus for optical imaging systems using a Fourier transform approach,” Opt. Lett. 32, 844–846 (2007).

[CrossRef]

D. Psaltis, E. G. Paek, and AS. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford University Press, 1997), Chap. 2.

D. Mendlovic, A. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407–414 (1997).

[CrossRef]

J. A. Davis, M. J. Mitry, M. A. Bandres, I. Ruiz, K. P. McAuley, and D. M. Cottrell, “Generation of accelerating Airy and accelerating parabolic beams using phase-only patterns,” Appl. Opt. 48, 3171–3177 (2009).

J. A. Davis, B. A. Slovick, C. S. Tuvey, and Don M. Cottrell, “High diffraction efficiency from one- and two-dimensional Nyquist frequency binary phase gratings,” Appl. Opt. 47, 2828–2834 (2008).

J. A. Davis, M. A. Waring, G. W. Bach, R. A. Lilly, and D. M. Cottrell, “Compact optical correlator design,” Appl. Opt. 28, 10–11 (1989).

[CrossRef]

D. M. Cottrell, J. A. Davis, T. R. Hedman, and R. A. Lilly, “Multiple imaging phase-encoded optical elements written on programmable spatial light modulators,” Appl. Opt. 29, 2505–2509 (1990).

[CrossRef]

J. A. Davis and R. A. Lilly, “Ray-matrix approach for diffractive optics,” Appl. Opt. 32, 155–159 (1993).

[CrossRef]

J. A. Davis, B. M. L. Pascoquin, C. S. Tuvey, and D. M. Cottrell, “Fourier transform pupil functions for modifying the depth of focus of optical imaging systems,” Appl. Opt. 48, 4893–4898 (2009).

[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).

D. Mendlovic, A. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407–414 (1997).

[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]

J. J. Healy and J. T. Sheridan, “Fast linear canonical transforms,” J. Opt. Soc. Am. A 27, 21–30 (2010).

[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]

M. Sypek, “Light propagation in the Fresnel region. New numerical approach,” Opt. Commun. 116, 43–48 (1995).

[CrossRef]

D. Mas, J. Garcia, C. Ferreira, L. M. Bernardo, and F. Marinho, “Fast algorithms for free-space diffraction patterns calculation,” Opt. Commun. 164, 233–245 (1999).

[CrossRef]

D. P. Kelly, B. M. Hennelly, W. T. Rhodes, and J. T. Sheridan, “Analytical and numerical analysis of linear optical systems,” Opt. Eng. 45, 088201 (2006).

[CrossRef]

D. Psaltis, E. G. Paek, and AS. S. Venkatesh, “Optical image correlation with a binary spatial light modulator,” Opt. Eng. 23, 698–704 (1984).

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]

I. Moreno, J. A. Davis, D. M. Cottrell, N. Zhang, and X.-C. Yuan, “Encoding generalized phase functions on Dammann gratings,” Opt. Lett. 35, 1536–1538 (2010).

[CrossRef]

J. R. Leger and G. J. Swanson, “Efficient array illuminator using binary-optics phase plates at fractional-Talbot planes,” Opt. Lett. 15, 288–290 (1990).

[CrossRef]

J. A. Davis, C. S. Tuvey, O. López-Coronado, J. Campos, M. J. Yzuel, and C. Iemmi, “Tailoring the depth of focus for optical imaging systems using a Fourier transform approach,” Opt. Lett. 32, 844–846 (2007).

[CrossRef]

H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1988).

A. Yariv, Optical Electronics in Modern Communications, 5th ed. (Oxford University Press, 1997), Chap. 2.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, 1978), Chap. 8.

A. Stern, “Why is the linear canonical transform so little known?,” in Proceedings of 5th International Workshop on Information Optics, G. Cristóbal, B. Javidi, and S. Vallmitjana, eds (Springer, 2006), pp. 225–234.

F. Gori, “Why is the Fresnel transform so little known?,” in Current Trends in Optics, J. C. Dainty, ed. (Academic, 1994).