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Volumn 22, Issue 5, 2005, Pages 917-927

Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; FOURIER TRANSFORMS; INTEGRAL EQUATIONS; MATRIX ALGEBRA; OPTIMIZATION; PROBABILITY DISTRIBUTIONS; VECTORS;

EID: 19944379483     PISSN: 10847529     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAA.22.000917     Document Type: Article
Times cited : (178)

References (29)
  • 3
    • 0000216419 scopus 로고    scopus 로고
    • "Fractional Fourier transform calculation through the fast Fourier transform algorithm"
    • J. Garcia, D. Mas, and R. G. Dorsch, "Fractional Fourier transform calculation through the fast Fourier transform algorithm," Appl. Opt. 35, 7013-7018 (1996).
    • (1996) Appl. Opt. , vol.35 , pp. 7013-7018
    • Garcia, J.1    Mas, D.2    Dorsch, R.G.3
  • 4
    • 0000578198 scopus 로고    scopus 로고
    • "Numerical calculation of fractional Fourier transforms with a single fast Fourier transform algorithm"
    • F. J. Marinho and L. M. Bernardo, "Numerical calculation of fractional Fourier transforms with a single fast Fourier transform algorithm," J. Opt. Soc. Am. A 15, 2111-2116 (1998).
    • (1998) J. Opt. Soc. Am. A , vol.15 , pp. 2111-2116
    • Marinho, F.J.1    Bernardo, L.M.2
  • 5
    • 0032648792 scopus 로고    scopus 로고
    • "Fast algorithms for free-space diffraction patterns calculation"
    • 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).
    • (1999) Opt. Commun. , vol.164 , pp. 233-245
    • Mas, D.1    Garcia, J.2    Ferreira, C.3    Bernardo, L.M.4    Marinho, F.5
  • 6
    • 0029291375 scopus 로고
    • "Light propagation in the Fresnel region. New numerical approach"
    • M. Sypek, "Light propagation in the Fresnel region. New numerical approach," Opt. Commun. 116, 43-48 (1995).
    • (1995) Opt. Commun. , vol.116 , pp. 43-48
    • Sypek, M.1
  • 7
    • 0242303028 scopus 로고    scopus 로고
    • "Fast numerical calculation of Fresnel patterns in convergent systems"
    • D. Mas, J. Perez, C. Hernandez, C. Vazquez, J. J. Miret, and C. Illueca, "Fast numerical calculation of Fresnel patterns in convergent systems," Opt. Commun. 227, 245-258 (2003).
    • (2003) Opt. Commun. , vol.227 , pp. 245-258
    • Mas, D.1    Perez, J.2    Hernandez, C.3    Vazquez, C.4    Miret, J.J.5    Illueca, C.6
  • 8
    • 0000170077 scopus 로고    scopus 로고
    • "Computation considerations and fast algorithms for calculating the diffraction integral"
    • D. Mendlovic, Z. Zalevsky, and N. Konforti, "Computation considerations and fast algorithms for calculating the diffraction integral," J. Mod. Opt. 44, 407-414 (1997).
    • (1997) J. Mod. Opt. , vol.44 , pp. 407-414
    • Mendlovic, D.1    Zalevsky, Z.2    Konforti, N.3
  • 9
    • 14944341033 scopus 로고    scopus 로고
    • "Light tubes, Wigner diagrams and optical signal propagation simulation"
    • H. J. Caulfield, ed. (SPIE Press, Bellingham, Wash.)
    • W. T. Rhodes, "Light tubes, Wigner diagrams and optical signal propagation simulation," in Optical Information Processing: A Tribute to Adolf Lohmann, H. J. Caulfield, ed. (SPIE Press, Bellingham, Wash., 2002), pp. 343-356.
    • (2002) Optical Information Processing: A Tribute to Adolf Lohmann , pp. 343-356
    • Rhodes, W.T.1
  • 10
    • 0035759783 scopus 로고    scopus 로고
    • "Numerical simulation of Fresnel-regime wave propagation: The light tube model"
    • F. Wyrowski, ed., Proc. SPIE
    • W. T. Rhodes, "Numerical simulation of Fresnel-regime wave propagation: the light tube model," in Wave-Optical Systems Engineering, F. Wyrowski, ed., Proc. SPIE 4436, 21-26 (2001).
    • (2001) Wave-Optical Systems Engineering , vol.4436 , pp. 21-26
    • Rhodes, W.T.1
  • 11
    • 0034167502 scopus 로고    scopus 로고
    • "Fast algorithm for chirp transforms with zooming-in ability and its applications"
    • X. Deng, B. Bihari, J. Gang, F. Zhao, and R. T. Chen, "Fast algorithm for chirp transforms with zooming-in ability and its applications," J. Opt. Soc. Am. A 17, 762-771 (2000).
    • (2000) J. Opt. Soc. Am. A , vol.17 , pp. 762-771
    • Deng, X.1    Bihari, B.2    Gang, J.3    Zhao, F.4    Chen, R.T.5
  • 12
    • 33745014742 scopus 로고
    • "On the quantum correction for thermodynamic equilibrium"
    • E. Wigner, "On the quantum correction for thermodynamic equilibrium," Phys. Rev. 40, 749-759 (1932).
    • (1932) Phys. Rev. , vol.40 , pp. 749-759
    • Wigner, E.1
  • 13
    • 0003562442 scopus 로고    scopus 로고
    • "Application of the Wigner distribution function in optics"
    • W. Mecklenbrauker and F. Hlawatsch, eds. (Elsevier Science, Amsterdam)
    • M. J. Bastiaans, "Application of the Wigner distribution function in optics," in The Wigner Distribution - Theory and Applications in Signal Processing, W. Mecklenbrauker and F. Hlawatsch, eds. (Elsevier Science, Amsterdam, 1997).
    • (1997) The Wigner Distribution - Theory and Applications in Signal Processing
    • Bastiaans, M.J.1
  • 15
    • 0027682286 scopus 로고
    • "Image rotation, Wigner rotation and the fractional Fourier transform"
    • A. W. Lohmann, "Image rotation, Wigner rotation and the fractional Fourier transform," J. Opt. Soc. Am. A 10, 2181-2186 (1993).
    • (1993) J. Opt. Soc. Am. A , vol.10 , pp. 2181-2186
    • Lohmann, A.W.1
  • 18
    • 0000010577 scopus 로고
    • "Wigner distribution function and its application to first-order optics"
    • M. J. Bastiaans, "Wigner distribution function and its application to first-order optics," J. Opt. Soc. Am. 69, 1710-1716 (1979).
    • (1979) J. Opt. Soc. Am. , vol.69 , pp. 1710-1716
    • Bastiaans, M.J.1
  • 19
    • 21344493264 scopus 로고
    • "Generalization of the fractional Fourier transformation to an arbitrary linear lossless transformation: An operator approach"
    • Corrigenda, 7937-7938, 1994
    • S. Abe and J. T. Sheridan, "Generalization of the fractional Fourier transformation to an arbitrary linear lossless transformation: an operator approach," J. Phys. A 27, 4179-4187 (1994); Corrigenda, 7937-7938 (1994).
    • (1994) J. Phys. A , vol.27 , pp. 4179-4187
    • Abe, S.1    Sheridan, J.T.2
  • 20
    • 0028546432 scopus 로고
    • "Optical operations on wave functions as the Abelian subgroups of the special affine Fourier transformation"
    • S. Abe and J. T. Sheridan, "Optical operations on wave functions as the Abelian subgroups of the special affine Fourier transformation," Opt. Lett. 19, 1801-1803 (1994).
    • (1994) Opt. Lett. , vol.19 , pp. 1801-1803
    • Abe, S.1    Sheridan, J.T.2
  • 21
    • 84968470212 scopus 로고
    • "An algorithm for the machine calculation of complex Fourier series"
    • J. W. Cooley and J. W. Tukey, "An algorithm for the machine calculation of complex Fourier series," Math. Comput. 19, 297-301 (1965).
    • (1965) Math. Comput. , vol.19 , pp. 297-301
    • Cooley, J.W.1    Tukey, J.W.2
  • 22
    • 0019543409 scopus 로고
    • "Interpolation and decimation of digital signals - A tutorial review"
    • R. E. Crochiere and L. R. Rabiner, "Interpolation and decimation of digital signals - A tutorial review," Proc. IEEE 69, 300-331 (1981).
    • (1981) Proc. IEEE , vol.69 , pp. 300-331
    • Crochiere, R.E.1    Rabiner, L.R.2
  • 23
    • 0020102107 scopus 로고
    • "First-order optics - A canonical operator representation: Lossless systems"
    • M. Nazarathy and J. Shamir, "First-order optics - a canonical operator representation: lossless systems," J. Opt. Soc. Am. 72, 356-364 (1982).
    • (1982) J. Opt. Soc. Am. , vol.72 , pp. 356-364
    • Nazarathy, M.1    Shamir, J.2
  • 24
    • 0016073256 scopus 로고
    • "Ambiguity function in Fourier optics"
    • A. Papoulis, "Ambiguity function in Fourier optics," J. Opt. Soc. Am. 64, 779-788 (1974).
    • (1974) J. Opt. Soc. Am. , vol.64 , pp. 779-788
    • Papoulis, A.1
  • 26
    • 0037765510 scopus 로고    scopus 로고
    • "Understanding superresolution in Wigner space"
    • Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, "Understanding superresolution in Wigner space," J. Opt. Soc. Am. A 17, 2422-2429 (2000).
    • (2000) J. Opt. Soc. Am. A , vol.17 , pp. 2422-2429
    • Zalevsky, Z.1    Mendlovic, D.2    Lohmann, A.W.3
  • 27
    • 0001264301 scopus 로고    scopus 로고
    • "Space - Bandwidth product adaptation and its application to superresolution: Fundamentals"
    • D. Mendlovic and A. W. Lohmann, "Space - bandwidth product adaptation and its application to superresolution: fundamentals," J. Opt. Soc. Am. A 14, 558-562 (1997).
    • (1997) J. Opt. Soc. Am. A , vol.14 , pp. 558-562
    • Mendlovic, D.1    Lohmann, A.W.2
  • 28
    • 0001264302 scopus 로고    scopus 로고
    • "Space-bandwidth product adaptation and its application to superresolution: Examples"
    • D. Mendlovic, A. W. Lohmann, and Z. Zalevsky, "Space-bandwidth product adaptation and its application to superresolution: examples," J. Opt. Soc. Am. A 14, 536-567 (1997).
    • (1997) J. Opt. Soc. Am. A , vol.14 , pp. 536-567
    • Mendlovic, D.1    Lohmann, A.W.2    Zalevsky, Z.3
  • 29
    • 19944406134 scopus 로고    scopus 로고
    • "Fast numerical algorithm for the linear canonical transform"
    • B. M. Hennelly and J. T. Sheridan, "Fast numerical algorithm for the linear canonical transform," J. Opt. Soc. Am. A 22, 928-937 (2005).
    • (2005) J. Opt. Soc. Am. A , vol.22 , pp. 928-937
    • Hennelly, B.M.1    Sheridan, J.T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.