메뉴 건너뛰기




Volumn 2005, Issue 10, 2005, Pages 1498-1519

Fractional transforms in optical information processing

Author keywords

Fractional convolution; Fractional cyclic transforms; Fractional Fourier transform; Fractional optics

Indexed keywords

FRACTIONAL CONVOLUTION; FRACTIONAL CYCLIC TRANSFORMS; FRACTIONAL FOURIER TRANSFORM; FRACTIONAL OPTICS;

EID: 27844559156     PISSN: 11108657     EISSN: None     Source Type: Journal    
DOI: 10.1155/ASP.2005.1498     Document Type: Review
Times cited : (65)

References (158)
  • 1
    • 0031999127 scopus 로고    scopus 로고
    • Perspectives in optical computing
    • H. J. Caulfield, "Perspectives in optical computing," IEEE Computer, vol. 31, no. 2, pp. 22-25, 1998.
    • (1998) IEEE Computer , vol.31 , Issue.2 , pp. 22-25
    • Caulfield, H.J.1
  • 2
    • 0024753990 scopus 로고
    • Fourier optical signal processors
    • D. L. Flannery and J. L. Horner, "Fourier optical signal processors," Proc. IEEE, vol. 77, no. 10, pp. 1511-1527, 1989.
    • (1989) Proc. IEEE , vol.77 , Issue.10 , pp. 1511-1527
    • Flannery, D.L.1    Horner, J.L.2
  • 4
    • 27844515269 scopus 로고    scopus 로고
    • Mathematical models of optical methods in data processing
    • A. V. Pavlov, "Mathematical models of optical methods in data processing," Journal of Computer and Systems Sciences International, vol. 39, no. 3, pp. 441-447, 2000.
    • (2000) Journal of Computer and Systems Sciences International , vol.39 , Issue.3 , pp. 441-447
    • Pavlov, A.V.1
  • 5
    • 0003727094 scopus 로고
    • Wiley Series in Pure and Applied Optics, John Wiley, New York, NY, USA
    • A. Van der Lugt, Ed., Optical Signal Processing, Wiley Series in Pure and Applied Optics, John Wiley, New York, NY, USA, 1992.
    • (1992) Optical Signal Processing
    • Van Der Lugt, A.1
  • 7
    • 0030150127 scopus 로고    scopus 로고
    • Wavelet processing and optics
    • Y. Li, H. H. Szu, Y. Sheng, and H. J. Caulfield, "Wavelet processing and optics," Proc. IEEE, vol. 84, no. 5, pp. 720-732, 1996.
    • (1996) Proc. IEEE , vol.84 , Issue.5 , pp. 720-732
    • Li, Y.1    Szu, H.H.2    Sheng, Y.3    Caulfield, H.J.4
  • 9
    • 0018040035 scopus 로고
    • Propagation of the generalized radiance through lenses
    • A. Walther, "Propagation of the generalized radiance through lenses," Journal of the Optical Society of America, vol. 68, no. 11, pp. 1606-1610, 1978.
    • (1978) Journal of the Optical Society of America , vol.68 , Issue.11 , pp. 1606-1610
    • Walther, A.1
  • 10
    • 0016073256 scopus 로고
    • Ambiguity function in Fourier optics
    • A. Papoulis, "Ambiguity function in Fourier optics," Journal of the Optical Society of America, vol. 64, no. 6, pp. 779-788, 1974.
    • (1974) Journal of the Optical Society of America , vol.64 , Issue.6 , pp. 779-788
    • Papoulis, A.1
  • 11
    • 0017957904 scopus 로고
    • The Wigner distribution function applied to optical signals and systems
    • M. J. Bastiaans, "The Wigner distribution function applied to optical signals and systems," Optics Communication, vol. 25, no. 1, pp. 26-30, 1978.
    • (1978) Optics Communication , vol.25 , Issue.1 , pp. 26-30
    • Bastiaans, M.J.1
  • 12
    • 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," Journal of the Optical Society of America, vol. 69, no. 12, pp. 1710-1716, 1979.
    • (1979) Journal of the Optical Society of America , vol.69 , Issue.12 , pp. 1710-1716
    • Bastiaans, M.J.1
  • 13
    • 84867571153 scopus 로고
    • Application of the Wigner distribution function to partially coherent light
    • M. J. Bastiaans, "Application of the Wigner distribution function to partially coherent light," Journal of the Optical Society of America A, vol. 3, no. 8, pp. 1227-1238, 1986.
    • (1986) Journal of the Optical Society of America A , vol.3 , Issue.8 , pp. 1227-1238
    • Bastiaans, M.J.1
  • 15
    • 0027652515 scopus 로고
    • Fractional Fourier transforms and their optical implementation: I
    • D. Mendlovic and H. M. Ozaktas, "Fractional Fourier transforms and their optical implementation: I," Journal of the Optical Society of America A, vol. 10, no. 9, pp. 1875-1881, 1993.
    • (1993) Journal of the Optical Society of America A , vol.10 , Issue.9 , pp. 1875-1881
    • Mendlovic, D.1    Ozaktas, H.M.2
  • 16
    • 0027740848 scopus 로고
    • Fractional Fourier transforms and their optical implementation. II
    • H. M. Ozaktas and D. Mendlovic, "Fractional Fourier transforms and their optical implementation. II," Journal of the Optical Society of America A, vol. 10, no. 12, pp. 2522-2531, 1993.
    • (1993) Journal of the Optical Society of America A , vol.10 , Issue.12 , pp. 2522-2531
    • Ozaktas, H.M.1    Mendlovic, D.2
  • 17
    • 0027641018 scopus 로고
    • Fourier transforms of fractional order and their optical interpretation
    • H. M. Ozaktas and D. Mendlovic, "Fourier transforms of fractional order and their optical interpretation," Optics Communications, vol. 101, no. 3-4, pp. 163-169, 1993.
    • (1993) Optics Communications , vol.101 , Issue.3-4 , pp. 163-169
    • Ozaktas, H.M.1    Mendlovic, D.2
  • 18
    • 84946282862 scopus 로고
    • The fractional Fourier transform in optical propagation problems
    • T. Alieva, V. Lopez, F. Agullo-Lopez, and L. B. Almeida, "The fractional Fourier transform in optical propagation problems," Journal of Modern Optics, vol. 41, no. 5, pp. 1037-1044, 1994.
    • (1994) Journal of Modern Optics , vol.41 , Issue.5 , pp. 1037-1044
    • Alieva, T.1    Lopez, V.2    Agullo-Lopez, F.3    Almeida, L.B.4
  • 19
    • 0008857739 scopus 로고
    • Wurzeln aus der Hankel-, Fourier- und aus anderen stetigen Transformationen
    • H. Kober, "Wurzeln aus der Hankel-, Fourier- und aus anderen stetigen Transformationen," Quart. J. Math. Oxford. Ser., vol. 10, pp. 45-59, 1939.
    • (1939) Quart. J. Math. Oxford. Ser. , vol.10 , pp. 45-59
    • Kober, H.1
  • 20
    • 77958407025 scopus 로고
    • The fractional order Fourier transform and its applications to quantum mechanics
    • V. Namias, "The fractional order Fourier transform and its applications to quantum mechanics," Journal of the Institute of Mathematics and Its Applications, vol. 25, pp. 241-265, 1980.
    • (1980) Journal of the Institute of Mathematics and Its Applications , vol.25 , pp. 241-265
    • Namias, V.1
  • 21
    • 77957689582 scopus 로고
    • On Namias' fractional Fourier transforms
    • A. C. McBride and F. H. Kerr, "On Namias' fractional Fourier transforms," IMA Journal of Applied Mathematics, vol. 39, no. 2, pp. 159-175, 1987.
    • (1987) IMA Journal of Applied Mathematics , vol.39 , Issue.2 , pp. 159-175
    • McBride, A.C.1    Kerr, F.H.2
  • 22
    • 0027682286 scopus 로고
    • Image rotation, Wigner rotation, and the fractional Fourier transform
    • A. W. Lohmann, "Image rotation, Wigner rotation, and the fractional Fourier transform," Journal of the Optical Society of America A, vol. 10, no. 10, pp. 2181-2186, 1993.
    • (1993) Journal of the Optical Society of America A , vol.10 , Issue.10 , pp. 2181-2186
    • Lohmann, A.W.1
  • 23
    • 0028546458 scopus 로고
    • The fractional Fourier transform and time-frequency representations
    • L. B. Almeida, "The fractional Fourier transform and time-frequency representations," IEEE Trans. Signal Processing, vol. 42, no. 11, pp. 3084-3091, 1994.
    • (1994) IEEE Trans. Signal Processing , vol.42 , Issue.11 , pp. 3084-3091
    • Almeida, L.B.1
  • 24
    • 77957719167 scopus 로고    scopus 로고
    • Introduction to the fractional Fourier transform and its applications
    • P. W. Hawkes, Ed., Academic Press, London, UK
    • H. M. Ozaktas, M. A. Kutay, and D. Mendlovic, "Introduction to the fractional Fourier transform and its applications," in Advances in Imaging and Electron Physics, P. W. Hawkes, Ed., vol. 106, pp. 239-291, Academic Press, London, UK, 1999.
    • (1999) Advances in Imaging and Electron Physics , vol.106 , pp. 239-291
    • Ozaktas, H.M.1    Kutay, M.A.2    Mendlovic, D.3
  • 25
    • 77956711851 scopus 로고    scopus 로고
    • Fractional transformation in optics
    • E. Wolf, Ed., Elsevier, Amsterdam, The Netherlands
    • A. W. Lohmann, D. Mendlovic, and Z. Zalevsky, "Fractional transformation in optics," in Progress in Optics, E. Wolf, Ed., vol. 38, pp. 263-342, Elsevier, Amsterdam, The Netherlands, 1998.
    • (1998) Progress in Optics , vol.38 , pp. 263-342
    • Lohmann, A.W.1    Mendlovic, D.2    Zalevsky, Z.3
  • 26
    • 0030129614 scopus 로고    scopus 로고
    • Some important fractional transformations for signal processing
    • A. W. Lohmann, D. Mendlovic, Z. Zalevsky, and R. G. Dorsch, "Some important fractional transformations for signal processing," Optics Communications, vol. 125, no. 1-3, pp. 18-20, 1996.
    • (1996) Optics Communications , vol.125 , Issue.1-3 , pp. 18-20
    • Lohmann, A.W.1    Mendlovic, D.2    Zalevsky, Z.3    Dorsch, R.G.4
  • 27
    • 0037765521 scopus 로고    scopus 로고
    • Fractionalization of the linear cyclic transforms
    • T. Alieva and M. L. Calvo, "Fractionalization of the linear cyclic transforms," Journal of the Optical Society of America A, vol. 17, no. 12, pp. 2330-2338, 2000.
    • (2000) Journal of the Optical Society of America A , vol.17 , Issue.12 , pp. 2330-2338
    • Alieva, T.1    Calvo, M.L.2
  • 28
    • 0442299916 scopus 로고    scopus 로고
    • Fractional cyclic transforms in optics: Theory and applications
    • S. G. Pandalai, Ed., Research Signpost, Trivandrum, India
    • T. Alieva, M. J. Bastiaans, and M. L. Calvo, "Fractional cyclic transforms in optics: theory and applications," in Recent Research and Developments in Optics, S. G. Pandalai, Ed., vol. 1, pp. 105-122, Research Signpost, Trivandrum, India, 2001.
    • (2001) Recent Research and Developments in Optics , vol.1 , pp. 105-122
    • Alieva, T.1    Bastiaans, M.J.2    Calvo, M.L.3
  • 31
    • 77956712784 scopus 로고    scopus 로고
    • The fractional Fourier transform and some of its applications to optics
    • E. Wolf, Ed., North-Holland, Amsterdam, The Netherlands
    • A. Torre, "The fractional Fourier transform and some of its applications to optics," in Progress in Optics, E. Wolf, Ed., vol. 43, pp. 531-596, North-Holland, Amsterdam, The Netherlands, 2002.
    • (2002) Progress in Optics , vol.43 , pp. 531-596
    • Torre, A.1
  • 32
    • 12044254133 scopus 로고
    • Complex wave-field reconstruction using phase-space tomography
    • M. G. Raymer, M. Beck, and D. F. McAlister, "Complex wave-field reconstruction using phase-space tomography," Physical Review Letters, vol. 72, no. 8, pp. 1137-1140, 1994.
    • (1994) Physical Review Letters , vol.72 , Issue.8 , pp. 1137-1140
    • Raymer, M.G.1    Beck, M.2    McAlister, D.F.3
  • 33
    • 0034319868 scopus 로고    scopus 로고
    • On fractional Fourier transform moments
    • T. Alieva and M. J. Bastiaans, "On fractional Fourier transform moments," IEEE Signal Processing Lett., vol. 7, no. 11, pp. 320-323, 2000.
    • (2000) IEEE Signal Processing Lett. , vol.7 , Issue.11 , pp. 320-323
    • Alieva, T.1    Bastiaans, M.J.2
  • 34
    • 0038780107 scopus 로고    scopus 로고
    • Phase-space distributions in quasi-polar coordinates and the fractional Fourier transform
    • T. Alieva and M. J. Bastiaans, "Phase-space distributions in quasi-polar coordinates and the fractional Fourier transform," Journal of the Optical Society of America A, vol. 17, no. 12, pp. 2324-2329, 2000.
    • (2000) Journal of the Optical Society of America A , vol.17 , Issue.12 , pp. 2324-2329
    • Alieva, T.1    Bastiaans, M.J.2
  • 35
    • 0037235246 scopus 로고    scopus 로고
    • Signal reconstruction from two close fractional Fourier power spectra
    • T. Alieva, M. J. Bastiaans, and L. Stanković, "Signal reconstruction from two close fractional Fourier power spectra," IEEE Trans. Signal Processing, vol. 51, no. 1, pp. 112-123, 2003.
    • (2003) IEEE Trans. Signal Processing , vol.51 , Issue.1 , pp. 112-123
    • Alieva, T.1    Bastiaans, M.J.2    Stanković, L.3
  • 36
    • 0042575525 scopus 로고    scopus 로고
    • Phase reconstruction from intensity measurements in linear systems
    • M. J. Bastiaans and K. B. Wolf, "Phase reconstruction from intensity measurements in linear systems," Journal of the Optical Society of America A, vol. 20, no. 6, pp. 1046-1049, 2003.
    • (2003) Journal of the Optical Society of America A , vol.20 , Issue.6 , pp. 1046-1049
    • Bastiaans, M.J.1    Wolf, K.B.2
  • 37
    • 0020849487 scopus 로고
    • Deterministic phase retrieval: A Green's function solution
    • R. M. Teague, "Deterministic phase retrieval: a Green's function solution," Journal of the Optical Society of America, vol. 73, no. 11, pp. 1434-1441, 1983.
    • (1983) Journal of the Optical Society of America , vol.73 , Issue.11 , pp. 1434-1441
    • Teague, R.M.1
  • 38
    • 0000418977 scopus 로고    scopus 로고
    • Gerchberg-Saxton algorithm applied in the fractional Fourier or the Fresnel domain
    • Z. Zalevsky, D. Mendlovic, and R. G. Dorsch, "Gerchberg-Saxton algorithm applied in the fractional Fourier or the Fresnel domain," Optics Letters, vol. 21, no. 12, pp. 842-844, 1996.
    • (1996) Optics Letters , vol.21 , Issue.12 , pp. 842-844
    • Zalevsky, Z.1    Mendlovic, D.2    Dorsch, R.G.3
  • 39
    • 0005830780 scopus 로고    scopus 로고
    • Numerical investigation of phase retrieval in a fractional Fourier transform
    • B.-Z. Dong, Y. Zhang, B.-Y. Gu, and G.-Z. Yang, "Numerical investigation of phase retrieval in a fractional Fourier transform," Journal of the Optical Society of America A, vol. 14, no. 10, pp. 2709-2714, 1997.
    • (1997) Journal of the Optical Society of America A , vol.14 , Issue.10 , pp. 2709-2714
    • Dong, B.-Z.1    Zhang, Y.2    Gu, B.-Y.3    Yang, G.-Z.4
  • 40
    • 0000276248 scopus 로고    scopus 로고
    • Recursive algorithm for phase retrieval in the fractional Fourier transform domain
    • W.-X. Cong, N.-X. Chen, and B.-Y. Gu, "Recursive algorithm for phase retrieval in the fractional Fourier transform domain," Applied Optics, vol. 37, no. 29, pp. 6906-6910, 1998.
    • (1998) Applied Optics , vol.37 , Issue.29 , pp. 6906-6910
    • Cong, W.-X.1    Chen, N.-X.2    Gu, B.-Y.3
  • 41
    • 0042154224 scopus 로고    scopus 로고
    • Finite-mode analysis by means of intensity information in fractional optical systems
    • T. Alieva and M. J. Bastiaans, "Finite-mode analysis by means of intensity information in fractional optical systems," Journal of the Optical Society of America A, vol. 19, no. 3, pp. 481-484, 2002.
    • (2002) Journal of the Optical Society of America A , vol.19 , Issue.3 , pp. 481-484
    • Alieva, T.1    Bastiaans, M.J.2
  • 43
    • 0043074610 scopus 로고    scopus 로고
    • Wigner distribution moments in fractional Fourier transform systems
    • M. J. Bastiaans and T. Alieva, "Wigner distribution moments in fractional Fourier transform systems," Journal of the Optical Society of America A, vol. 19, no. 9, pp. 1763-1773, 2002.
    • (2002) Journal of the Optical Society of America A , vol.19 , Issue.9 , pp. 1763-1773
    • Bastiaans, M.J.1    Alieva, T.2
  • 44
    • 27844590711 scopus 로고    scopus 로고
    • Wigner distribution moments measured as intensity moments in separable first-order optical systems
    • M. J. Bastiaans and T. Alieva, "Wigner distribution moments measured as intensity moments in separable first-order optical systems," EURASIP Journal on Applied Signal Processing, vol. 2005, no. 10, pp. 1535-1540, 2005.
    • (2005) EURASIP Journal on Applied Signal Processing , vol.2005 , Issue.10 , pp. 1535-1540
    • Bastiaans, M.J.1    Alieva, T.2
  • 45
    • 0141996361 scopus 로고    scopus 로고
    • Time-frequency signal analysis based on the windowed fractional Fourier transform
    • L. Stanković, T. Alieva, and M. J. Bastiaans, "Time-frequency signal analysis based on the windowed fractional Fourier transform," Signal Processing, vol. 83, no. 11, pp. 2459-2468, 2003.
    • (2003) Signal Processing , vol.83 , Issue.11 , pp. 2459-2468
    • Stanković, L.1    Alieva, T.2    Bastiaans, M.J.3
  • 47
    • 3142676383 scopus 로고    scopus 로고
    • Evolution of the vortex and the asymmetrical parts of orbital angular momentum in separable first-order optical systems
    • T. Alieva and M. J. Bastiaans, "Evolution of the vortex and the asymmetrical parts of orbital angular momentum in separable first-order optical systems," Optics Letters, vol. 29, no. 14, pp. 1587-1589, 2004.
    • (2004) Optics Letters , vol.29 , Issue.14 , pp. 1587-1589
    • Alieva, T.1    Bastiaans, M.J.2
  • 48
    • 0028485528 scopus 로고
    • Tomographic time-frequency analysis and its application toward time-varying filtering and adaptive kernel design for multicomponent linear-FM signals
    • J. C. Wood and D. T. Barry, "Tomographic time-frequency analysis and its application toward time-varying filtering and adaptive kernel design for multicomponent linear-FM signals," IEEE Trans. Signal Processing, vol. 42, no. 8, pp.2094-2104, 1994.
    • (1994) IEEE Trans. Signal Processing , vol.42 , Issue.8 , pp. 2094-2104
    • Wood, J.C.1    Barry, D.T.2
  • 49
    • 0028483876 scopus 로고
    • Linear signal synthesis using the Radon-Wigner transform
    • J. C. Wood and D. T. Barry, "Linear signal synthesis using the Radon-Wigner transform," IEEE Trans. Signal Processing, vol. 42, no. 8, pp. 2105-2111, 1994.
    • (1994) IEEE Trans. Signal Processing , vol.42 , Issue.8 , pp. 2105-2111
    • Wood, J.C.1    Barry, D.T.2
  • 50
    • 0003422788 scopus 로고    scopus 로고
    • Fractional Fourier transform as a tool for investigation of fractal objects
    • T. Alieva, "Fractional Fourier transform as a tool for investigation of fractal objects," Journal of the Optical Society of America A, vol. 13, no. 6, pp. 1189-1192, 1996.
    • (1996) Journal of the Optical Society of America A , vol.13 , Issue.6 , pp. 1189-1192
    • Alieva, T.1
  • 51
    • 0030127112 scopus 로고    scopus 로고
    • Optical wave propagation of fractal fields
    • T. Alieva and F. Agullo-Lopez, "Optical wave propagation of fractal fields," Optics Communications, vol. 125, no. 4-6, pp. 267-274, 1996.
    • (1996) Optics Communications , vol.125 , Issue.4-6 , pp. 267-274
    • Alieva, T.1    Agullo-Lopez, F.2
  • 53
    • 9344228386 scopus 로고    scopus 로고
    • Fractional Fourier analysis of objects with scaling symmetry
    • J. L. Vehel, E. Lutton, and C. Tricot, Eds., Springer-Verlag, London, UK
    • T. Alieva and A. Barbé, "Fractional Fourier analysis of objects with scaling symmetry," in Fractals in Engineering, J. L. Vehel, E. Lutton, and C. Tricot, Eds., pp. 252-265, Springer-Verlag, London, UK, 1997.
    • (1997) Fractals in Engineering , pp. 252-265
    • Alieva, T.1    Barbé, A.2
  • 54
    • 16644388302 scopus 로고    scopus 로고
    • Fresnel diffraction by deterministic fractal gratings: An experimental study
    • D. Rodriguez Merlo, J. A. Rodrigo Martín-Romo, T. Alieva, and M. L. Calvo, "Fresnel diffraction by deterministic fractal gratings: an experimental study," Optics and Spectroscopy, vol. 95, no. 1, pp. 131-133, 2003.
    • (2003) Optics and Spectroscopy , vol.95 , Issue.1 , pp. 131-133
    • Merlo, D.R.1    Martín-Romo, J.A.R.2    Alieva, T.3    Calvo, M.L.4
  • 55
    • 0002764938 scopus 로고
    • Fractal optics
    • J. C. Dainty, Ed., Academic Press, London, UK
    • J. Uozumi and T. Asakura, "Fractal optics," in Current Trends in Optics, J. C. Dainty, Ed., pp. 83-94, Academic Press, London, UK, 1994.
    • (1994) Current Trends in Optics , pp. 83-94
    • Uozumi, J.1    Asakura, T.2
  • 56
    • 0141534358 scopus 로고    scopus 로고
    • Paraxial diffraction on structures generated by multiplicative iterative procedures
    • T. Alieva and M. L. Calvo, "Paraxial diffraction on structures generated by multiplicative iterative procedures," Journal of Optics A: Pure and Applied Optics, vol. 5, no. 5, pp. S324-S328, 2003.
    • (2003) Journal of Optics A: Pure and Applied Optics , vol.5 , Issue.5
    • Alieva, T.1    Calvo, M.L.2
  • 57
    • 0028382656 scopus 로고
    • Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms
    • 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," Journal of the Optical Society of America A, vol. 11, no. 2, pp. 547-559, 1994.
    • (1994) Journal of the Optical Society of America A , vol.11 , Issue.2 , pp. 547-559
    • Ozaktas, H.M.1    Barshan, B.2    Mendlovic, D.3    Onural, L.4
  • 58
    • 0030826059 scopus 로고    scopus 로고
    • Product and convolution theorems for the fractional Fourier transform
    • L. B. Almeida, "Product and convolution theorems for the fractional Fourier transform," IEEE Signal Processing Lett., vol. 4, no. 1, pp. 15-17, 1997.
    • (1997) IEEE Signal Processing Lett. , vol.4 , Issue.1 , pp. 15-17
    • Almeida, L.B.1
  • 61
    • 0000773494 scopus 로고    scopus 로고
    • Fractional Wiener filter
    • Z. Zalevsky and D. Mendlovic, "Fractional Wiener filter" Applied Optics, vol. 35, no. 20, pp. 3930-3936, 1996.
    • (1996) Applied Optics , vol.35 , Issue.20 , pp. 3930-3936
    • Zalevsky, Z.1    Mendlovic, D.2
  • 63
    • 0011778811 scopus 로고    scopus 로고
    • Fractional Fourier transform description with use of differential operators
    • B. Ruiz and H. Rabal, "Fractional Fourier transform description with use of differential operators," Journal of the Optical Society of America A, vol. 14, no. 11, pp. 2905-2913, 1997.
    • (1997) Journal of the Optical Society of America A , vol.14 , Issue.11 , pp. 2905-2913
    • Ruiz, B.1    Rabal, H.2
  • 64
    • 0032047886 scopus 로고    scopus 로고
    • A convolution and product theorem for the fractional Fourier transform
    • A. I. Zayed, "A convolution and product theorem for the fractional Fourier transform," IEEE Signal Processing Lett., vol. 5, no. 4, pp. 101-103, 1998.
    • (1998) IEEE Signal Processing Lett. , vol.5 , Issue.4 , pp. 101-103
    • Zayed, A.I.1
  • 65
    • 0032652552 scopus 로고    scopus 로고
    • New properties of the Radon transform of the cross Wigner/ambiguity distribution function
    • I. Raveh and D. Mendlovic, "New properties of the Radon transform of the cross Wigner/ambiguity distribution function," IEEE Trans. Signal Processing, vol. 47, no. 7, pp. 2077-2080, 1999.
    • (1999) IEEE Trans. Signal Processing , vol.47 , Issue.7 , pp. 2077-2080
    • Raveh, I.1    Mendlovic, D.2
  • 66
    • 0030189141 scopus 로고    scopus 로고
    • Synthesis of pattern recognition filters for fractional Fourier processing
    • A. W. Lohmann, Z. Zalevsky, and D. Mendlovic, "Synthesis of pattern recognition filters for fractional Fourier processing," Optics Communications, vol. 128, no. 4-6, pp. 199-204, 1996.
    • (1996) Optics Communications , vol.128 , Issue.4-6 , pp. 199-204
    • Lohmann, A.W.1    Zalevsky, Z.2    Mendlovic, D.3
  • 67
    • 0000094831 scopus 로고    scopus 로고
    • Optical correlation based on the fractional Fourier transform
    • S. Granieri, R. Arizaga, and E. E. Sicre, "Optical correlation based on the fractional Fourier transform," Applied Optics, vol. 36, no. 26, pp. 6636-6645, 1997.
    • (1997) Applied Optics , vol.36 , Issue.26 , pp. 6636-6645
    • Granieri, S.1    Arizaga, R.2    Sicre, E.E.3
  • 68
    • 0038576936 scopus 로고    scopus 로고
    • Fractional correlations based on the modified fractional order Fourier transform
    • A. M. Almanasreh and M. A. G. Abushagur, "Fractional correlations based on the modified fractional order Fourier transform," Optical Engineering, vol. 37, no. 1, pp. 175-184, 1998.
    • (1998) Optical Engineering , vol.37 , Issue.1 , pp. 175-184
    • Almanasreh, A.M.1    Abushagur, M.A.G.2
  • 69
    • 27844450686 scopus 로고    scopus 로고
    • Generalized fractional convolution
    • J. Joseph, A. Sharma, and V. K. Rastogi, Eds., Anita Publications, New Delhi, India
    • T. Alieva and M. L. Calvo, "Generalized fractional convolution," in Perspectives in Modern Optics and Optical Instrumentation, J. Joseph, A. Sharma, and V. K. Rastogi, Eds., pp. 163-173, Anita Publications, New Delhi, India, 2002.
    • (2002) Perspectives in Modern Optics and Optical Instrumentation , pp. 163-173
    • Alieva, T.1    Calvo, M.L.2
  • 70
    • 0035340022 scopus 로고    scopus 로고
    • Fractional convolution and correlation via operator methods and an application to detection of linear FM signals
    • O. Akay and G. F. Boudreaux-Bartels, "Fractional convolution and correlation via operator methods and an application to detection of linear FM signals," IEEE Trans. Signal Processing, vol. 49, no. 5, pp. 979-993, 2001.
    • (2001) IEEE Trans. Signal Processing , vol.49 , Issue.5 , pp. 979-993
    • Akay, O.1    Boudreaux-Bartels, G.F.2
  • 71
    • 84975605198 scopus 로고
    • Space-variant Fresnel transform optical correlator
    • J. A. Davis, D. M. Cottrell, N. Nestorovic, and S. M. Highnote, "Space-variant Fresnel transform optical correlator" Applied Optics, vol. 31, no. 32, pp. 6889-6893, 1992.
    • (1992) Applied Optics , vol.31 , Issue.32 , pp. 6889-6893
    • Davis, J.A.1    Cottrell, D.M.2    Nestorovic, N.3    Highnote, S.M.4
  • 72
    • 84975542033 scopus 로고
    • Anamorphic fractional Fourier transform: Optical implementation and applications
    • D. Mendlovic, Y. Bitran, R. G. Dorsch, C. Ferreira, J. García, and H. M. Ozaktas, "Anamorphic fractional Fourier transform: optical implementation and applications," Applied Optics, vol. 34, no. 32, pp. 7451-7456, 1995.
    • (1995) Applied Optics , vol.34 , Issue.32 , pp. 7451-7456
    • Mendlovic, D.1    Bitran, Y.2    Dorsch, R.G.3    Ferreira, C.4    García, J.5    Ozaktas, H.M.6
  • 73
    • 0000531118 scopus 로고    scopus 로고
    • Space-variant simultaneous detection of several objects by the use of multiple anamorphic fractional-Fourier-transform filters
    • J. García, D. Mendlovic, Z. Zalevsky, and A. W. Lohmann, "Space-variant simultaneous detection of several objects by the use of multiple anamorphic fractional-Fourier-transform filters," Applied Optics, vol. 35, no. 20, pp. 3945-3952, 1996.
    • (1996) Applied Optics , vol.35 , Issue.20 , pp. 3945-3952
    • García, J.1    Mendlovic, D.2    Zalevsky, Z.3    Lohmann, A.W.4
  • 74
    • 0030735844 scopus 로고    scopus 로고
    • Flexible optical implementation of fractional Fourier transform processors. Applications to correlation and filtering
    • J. García, R. G. Dorsch, A. W. Lohmann, C. Ferreira, and Z. Zalevsky, "Flexible optical implementation of fractional Fourier transform processors. Applications to correlation and filtering," Optics Communications, vol. 133, no. 1-6, pp. 393-400, 1997.
    • (1997) Optics Communications , vol.133 , Issue.1-6 , pp. 393-400
    • García, J.1    Dorsch, R.G.2    Lohmann, A.W.3    Ferreira, C.4    Zalevsky, Z.5
  • 75
    • 0037758718 scopus 로고    scopus 로고
    • Fractional correlation operation: Performance analysis
    • Y. Bitran, Z. Zalevsky, D. Mendlovic, and R. G. Dorsch, "Fractional correlation operation: performance analysis," Applied Optics, vol. 35, no. 2, pp. 297-303, 1996.
    • (1996) Applied Optics , vol.35 , Issue.2 , pp. 297-303
    • Bitran, Y.1    Zalevsky, Z.2    Mendlovic, D.3    Dorsch, R.G.4
  • 76
    • 0042074135 scopus 로고    scopus 로고
    • Importance of the phase and amplitude in the fractional Fourier domain
    • T. Alieva and M. L. Calvo, "Importance of the phase and amplitude in the fractional Fourier domain," Journal of the Optical Society of America A, vol. 20, no. 3, pp. 533-541, 2003.
    • (2003) Journal of the Optical Society of America A , vol.20 , Issue.3 , pp. 533-541
    • Alieva, T.1    Calvo, M.L.2
  • 77
    • 0000118219 scopus 로고
    • Non-conventional joint-transform correlator
    • F. T. S. Yu, C. Zhang, Y. Jin, and D. A. Gregory, "Non-conventional joint-transform correlator," Optics Letters, vol. 14, no. 17, pp. 922-924, 1989.
    • (1989) Optics Letters , vol.14 , Issue.17 , pp. 922-924
    • Yu, F.T.S.1    Zhang, C.2    Jin, Y.3    Gregory, D.A.4
  • 78
    • 0035875927 scopus 로고    scopus 로고
    • Optical encryption using quadratic phase systems
    • G. Unnikrishnan and K. Singh, "Optical encryption using quadratic phase systems," Optics Communications, vol. 193, no. 1-6, pp. 51-67, 2001.
    • (2001) Optics Communications , vol.193 , Issue.1-6 , pp. 51-67
    • Unnikrishnan, G.1    Singh, K.2
  • 79
    • 0035881760 scopus 로고    scopus 로고
    • Optical image encryption based on the generalized fractional convolution operation
    • B. Zhu and S. Liu, "Optical image encryption based on the generalized fractional convolution operation," Optics Communications, vol. 195, no. 5-6, pp. 371-381, 2001.
    • (2001) Optics Communications , vol.195 , Issue.5-6 , pp. 371-381
    • Zhu, B.1    Liu, S.2
  • 80
    • 0001248217 scopus 로고    scopus 로고
    • Optical image encryption based on multifractional Fourier transforms
    • B. Zhu, S. Liu, and Q. Ran, "Optical image encryption based on multifractional Fourier transforms," Optics Letters, vol. 25, no. 16, pp. 1159-1161, 2000.
    • (2000) Optics Letters , vol.25 , Issue.16 , pp. 1159-1161
    • Zhu, B.1    Liu, S.2    Ran, Q.3
  • 81
    • 1642356690 scopus 로고    scopus 로고
    • Optical encryption using a localized fractional Fourier transform
    • N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, "Optical encryption using a localized fractional Fourier transform," Optical Engineering, vol. 42, no. 12, pp. 3566-3571, 2003.
    • (2003) Optical Engineering , vol.42 , Issue.12 , pp. 3566-3571
    • Nishchal, N.K.1    Unnikrishnan, G.2    Joseph, J.3    Singh, K.4
  • 82
    • 0037443119 scopus 로고    scopus 로고
    • Optical image encryption by random shifting in fractional Fourier domains
    • B. Hennelly and J. T. Sheridan, "Optical image encryption by random shifting in fractional Fourier domains," Optics Letters, vol. 28, no. 4, pp. 269-271, 2003.
    • (2003) Optics Letters , vol.28 , Issue.4 , pp. 269-271
    • Hennelly, B.1    Sheridan, J.T.2
  • 83
    • 0141998034 scopus 로고    scopus 로고
    • Fractional Fourier transform-based image encryption: Phase retrieval algorithm
    • B. Hennelly and J. T. Sheridan, "Fractional Fourier transform-based image encryption: phase retrieval algorithm," Optics Communications, vol. 226, no. 1-6, pp. 61-80, 2003.
    • (2003) Optics Communications , vol.226 , Issue.1-6 , pp. 61-80
    • Hennelly, B.1    Sheridan, J.T.2
  • 84
    • 0141973669 scopus 로고    scopus 로고
    • Image encryption and the fractional Fourier transform
    • B. M. Hennelly and J. T. Sheridan, "Image encryption and the fractional Fourier transform," Optik, vol. 114, no. 6, pp. 251-265, 2003.
    • (2003) Optik , vol.114 , Issue.6 , pp. 251-265
    • Hennelly, B.M.1    Sheridan, J.T.2
  • 85
    • 0042699896 scopus 로고    scopus 로고
    • Fully phase encryption using fractional Fourier transform
    • N. K. Nishchal, J. Joseph, and K. Singh, "Fully phase encryption using fractional Fourier transform," Optical Engineering, vol. 42, no. 6, pp. 1583-1588, 2003.
    • (2003) Optical Engineering , vol.42 , Issue.6 , pp. 1583-1588
    • Nishchal, N.K.1    Joseph, J.2    Singh, K.3
  • 86
    • 0035308124 scopus 로고    scopus 로고
    • Watermarking in the space/spatial-frequency domain using two-dimensional Radon-Wigner distribution
    • S. Stankovic, I. Djurovic, and I. Pitas, "Watermarking in the space/spatial-frequency domain using two-dimensional Radon-Wigner distribution," IEEE Trans. Image Processing, vol. 10, no. 4, pp. 650-658, 2001.
    • (2001) IEEE Trans. Image Processing , vol.10 , Issue.4 , pp. 650-658
    • Stankovic, S.1    Djurovic, I.2    Pitas, I.3
  • 87
    • 0035323514 scopus 로고    scopus 로고
    • Digital watermarking in the fractional Fourier transformation domain
    • I. Djurovic, S. Stankovic, and I. Pitas, "Digital watermarking in the fractional Fourier transformation domain," Journal of Network and Computer Applications, vol. 24, no. 2, pp. 167-173, 2001.
    • (2001) Journal of Network and Computer Applications , vol.24 , Issue.2 , pp. 167-173
    • Djurovic, I.1    Stankovic, S.2    Pitas, I.3
  • 88
    • 0028478769 scopus 로고
    • Fractional Fourier transforms, wavelet transforms, and adaptive neural networks
    • S.-Y. Lee and H. H. Szu, "Fractional Fourier transforms, wavelet transforms, and adaptive neural networks," Optical Engineering, vol. 33, no. 7, pp. 2326-2330, 1994.
    • (1994) Optical Engineering , vol.33 , Issue.7 , pp. 2326-2330
    • Lee, S.-Y.1    Szu, H.H.2
  • 89
    • 0032141137 scopus 로고    scopus 로고
    • Optical neural network using fractional Fourier transform, log-likelihood, and parallelism
    • S.-G. Shin, S.-I. Jin, S.-Y. Shin, and S.-Y. Lee, "Optical neural network using fractional Fourier transform, log-likelihood, and parallelism," Optics Communications, vol. 153, no. 4-6, pp. 218-222, 1998.
    • (1998) Optics Communications , vol.153 , Issue.4-6 , pp. 218-222
    • Shin, S.-G.1    Jin, S.-I.2    Shin, S.-Y.3    Lee, S.-Y.4
  • 90
    • 0037092909 scopus 로고    scopus 로고
    • Generalized Vander Lugt correlator as an optical pattern classifier and its optimal learning rate
    • S.-I. Jin, Y.-S. Bae, and S.-Y. Lee, "Generalized Vander Lugt correlator as an optical pattern classifier and its optimal learning rate," Optics Communications, vol. 206, no. 1-3, pp. 19-25, 2002.
    • (2002) Optics Communications , vol.206 , Issue.1-3 , pp. 19-25
    • Jin, S.-I.1    Bae, Y.-S.2    Lee, S.-Y.3
  • 91
    • 0036128617 scopus 로고    scopus 로고
    • Fractional Fourier transform pre-processing for neural networks and its application to object recognition
    • B. Barshan and B. Ayrulu, "Fractional Fourier transform pre-processing for neural networks and its application to object recognition," Neural Networks, vol. 15, no. 1, pp. 131-140, 2002.
    • (2002) Neural Networks , vol.15 , Issue.1 , pp. 131-140
    • Barshan, B.1    Ayrulu, B.2
  • 92
    • 0037404263 scopus 로고    scopus 로고
    • Comparative analysis of different approaches to target differentiation and localization with sonar
    • B. Barshan and B. Ayrulu, "Comparative analysis of different approaches to target differentiation and localization with sonar," Pattern Recognition, vol. 36, no. 5, pp. 1213-1231, 2003.
    • (2003) Pattern Recognition , vol.36 , Issue.5 , pp. 1213-1231
    • Barshan, B.1    Ayrulu, B.2
  • 93
    • 0036121784 scopus 로고    scopus 로고
    • Fractional correlation filter for fuzzy associative memories
    • S. Q. Zhang and M. A. Karim, "Fractional correlation filter for fuzzy associative memories," Optical Engineering, vol. 41, no. 1, pp. 126-129, 2002.
    • (2002) Optical Engineering , vol.41 , Issue.1 , pp. 126-129
    • Zhang, S.Q.1    Karim, M.A.2
  • 94
  • 95
    • 0010024813 scopus 로고    scopus 로고
    • Optical implementation of the fractional Hilbert transform for two-dimensional objects
    • A. W. Lohmann, E. Tepichin, and J. G. Ramirez, "Optical implementation of the fractional Hilbert transform for two-dimensional objects," Applied Optics, vol. 36, no. 26, pp. 6620-6626, 1997.
    • (1997) Applied Optics , vol.36 , Issue.26 , pp. 6620-6626
    • Lohmann, A.W.1    Tepichin, E.2    Ramirez, J.G.3
  • 96
    • 0000461102 scopus 로고    scopus 로고
    • Analysis of the fractional Hilbert transform
    • J. A. Davis, D. E. McNamara, and D. M. Cottrell, "Analysis of the fractional Hilbert transform," Applied Optics, vol. 37, no. 29, pp. 6911-6913, 1998.
    • (1998) Applied Optics , vol.37 , Issue.29 , pp. 6911-6913
    • Davis, J.A.1    McNamara, D.E.2    Cottrell, D.M.3
  • 98
    • 85180047409 scopus 로고
    • University of California Press, Berkeley and Los Angeles, Calif, USA
    • R. K. Luneburg, Mathematical Theory of Optics, University of California Press, Berkeley and Los Angeles, Calif, USA, 1966.
    • (1966) Mathematical Theory of Optics
    • Luneburg, R.K.1
  • 99
    • 0030145797 scopus 로고    scopus 로고
    • The generalized Fresnel transform and its applications to optics
    • D. F. V. James and G. S. Agarwal, "The generalized Fresnel transform and its applications to optics," Optics Communications, vol. 126, no. 4-6, pp. 207-212, 1996.
    • (1996) Optics Communications , vol.126 , Issue.4-6 , pp. 207-212
    • James, D.F.V.1    Agarwal, G.S.2
  • 100
    • 0029226887 scopus 로고
    • Almost-Fourier and almost-Fresnel transformations
    • S. Abe and J. T. Sheridan, "Almost-Fourier and almost-Fresnel transformations," Optics Communications, vol. 113, no. 4-6, pp. 385-388, 1995.
    • (1995) Optics Communications , vol.113 , Issue.4-6 , pp. 385-388
    • Abe, S.1    Sheridan, J.T.2
  • 105
    • 0032166986 scopus 로고    scopus 로고
    • Similarity theorems for fractional Fourier transforms and fractional Hankel transforms
    • C. J. R. Sheppard and K. G. Larkin, "Similarity theorems for fractional Fourier transforms and fractional Hankel transforms," Optics Communications, vol. 154, no. 4, pp. 173-178, 1998.
    • (1998) Optics Communications , vol.154 , Issue.4 , pp. 173-178
    • Sheppard, C.J.R.1    Larkin, K.G.2
  • 106
    • 0036173698 scopus 로고    scopus 로고
    • Eigenfunctions of linear canonical transform
    • S.-C. Pei and J.-J. Ding, "Eigenfunctions of linear canonical transform," IEEE Trans. Signal Processing, vol. 50, no. 1, pp. 11-26, 2002.
    • (2002) IEEE Trans. Signal Processing , vol.50 , Issue.1 , pp. 11-26
    • Pei, S.-C.1    Ding, J.-J.2
  • 107
    • 0028199265 scopus 로고
    • Self Fourier functions and fractional Fourier transforms
    • D. Mendlovic, H. M. Ozaktas, and A. W. Lohmann, "Self Fourier functions and fractional Fourier transforms," Optics Communications, vol. 105, no. 1-2, pp. 36-38, 1994.
    • (1994) Optics Communications , vol.105 , Issue.1-2 , pp. 36-38
    • Mendlovic, D.1    Ozaktas, H.M.2    Lohmann, A.W.3
  • 109
    • 0032795823 scopus 로고    scopus 로고
    • Self-fractional Fourier images
    • T. Alieva and A. M. Barbé, "Self-fractional Fourier images," Journal of Modern Optics, vol. 46, no. 1, pp. 83-99, 1999.
    • (1999) Journal of Modern Optics , vol.46 , Issue.1 , pp. 83-99
    • Alieva, T.1    Barbé, A.M.2
  • 111
    • 0032613435 scopus 로고    scopus 로고
    • Mode analysis in optics through fractional transforms
    • T. Alieva and M. J. Bastiaans, "Mode analysis in optics through fractional transforms," Optics Letters, vol. 24, no. 17, pp. 1206-1208, 1999.
    • (1999) Optics Letters , vol.24 , Issue.17 , pp. 1206-1208
    • Alieva, T.1    Bastiaans, M.J.2
  • 112
    • 0028496555 scopus 로고
    • Fractional Fourier transforms and optical systems
    • L. M. Bernardo and O. D. D. Scares, "Fractional Fourier transforms and optical systems," Optics Communications, vol. 110, no. 5-6, pp. 517-522, 1994.
    • (1994) Optics Communications , vol.110 , Issue.5-6 , pp. 517-522
    • Bernardo, L.M.1    Scares, O.D.D.2
  • 113
    • 0028515765 scopus 로고
    • Fresnel diffraction and the fractional-order Fourier transform
    • P. Pellat-Finet, "Fresnel diffraction and the fractional-order Fourier transform," Optics Letters, vol. 19, no. 18, pp. 1388-1390, 1994.
    • (1994) Optics Letters , vol.19 , Issue.18 , pp. 1388-1390
    • Pellat-Finet, P.1
  • 114
    • 0028494881 scopus 로고
    • Fractional order Fourier transform and Fourier optics
    • P. Pellat-Finet and G. Bonnet, "Fractional order Fourier transform and Fourier optics," Optics Communications, vol. 111, no. 1-2, pp. 141-154, 1994.
    • (1994) Optics Communications , vol.111 , Issue.1-2 , pp. 141-154
    • Pellat-Finet, P.1    Bonnet, G.2
  • 115
    • 0028546549 scopus 로고
    • Fractional Fourier transform as a tool for analyzing beam propagation and spherical mirror resonators
    • H. M. Ozaktas and D. Mendlovic, "Fractional Fourier transform as a tool for analyzing beam propagation and spherical mirror resonators," Optics Letters, vol. 19, no. 21, pp. 1678-1680, 1994.
    • (1994) Optics Letters , vol.19 , Issue.21 , pp. 1678-1680
    • Ozaktas, H.M.1    Mendlovic, D.2
  • 116
    • 0028459614 scopus 로고
    • Expression of the kernel of a fractional Fourier transform in elementary functions
    • Y. B. Karasik, "Expression of the kernel of a fractional Fourier transform in elementary functions," Optics Letters, vol. 19, no. 11, pp. 769-770, 1994.
    • (1994) Optics Letters , vol.19 , Issue.11 , pp. 769-770
    • Karasik, Y.B.1
  • 117
    • 0029389506 scopus 로고
    • Optical implementation of the two-dimensional fractional Fourier transform with different orders in the two dimensions
    • A. Sahin, H. M. Ozaktas, and D. Mendlovic, "Optical implementation of the two-dimensional fractional Fourier transform with different orders in the two dimensions," Optics Communications, vol. 120, no. 3-4, pp. 134-138, 1995.
    • (1995) Optics Communications , vol.120 , Issue.3-4 , pp. 134-138
    • Sahin, A.1    Ozaktas, H.M.2    Mendlovic, D.3
  • 118
    • 0028459601 scopus 로고
    • Relationships between the Radon-Wigner and fractional Fourier transforms
    • A. W. Lohmann and B. H. Soffer, "Relationships between the Radon-Wigner and fractional Fourier transforms," Journal of the Optical Society of America A, vol. 11, no. 6, pp. 1798-1811, 1994.
    • (1994) Journal of the Optical Society of America A , vol.11 , Issue.6 , pp. 1798-1811
    • Lohmann, A.W.1    Soffer, B.H.2
  • 119
    • 0042932668 scopus 로고    scopus 로고
    • Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams
    • A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, "Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams," Journal of the Optical Society of America A, vol. 20, no. 8, pp. 1635-1643, 2003.
    • (2003) Journal of the Optical Society of America A , vol.20 , Issue.8 , pp. 1635-1643
    • Bekshaev, A.Ya.1    Soskin, M.S.2    Vasnetsov, M.V.3
  • 120
    • 0037097394 scopus 로고    scopus 로고
    • Joint transform correlator with fractional Fourier transform
    • S.-I. Jin and S.-Y. Lee, "Joint transform correlator with fractional Fourier transform," Optics Communications, vol. 207, no. 1-6, pp. 161-168, 2002.
    • (2002) Optics Communications , vol.207 , Issue.1-6 , pp. 161-168
    • Jin, S.-I.1    Lee, S.-Y.2
  • 121
    • 0141961671 scopus 로고    scopus 로고
    • Acoustic wave propagation in a 1-D lattice: Analysis of nonlinear effects by the fractional Fourier transform method
    • G. Gonon, O. Richoux, and C. Depollier, "Acoustic wave propagation in a 1-D lattice: analysis of nonlinear effects by the fractional Fourier transform method," Signal Processing, vol. 83, no. 11, pp. 2469-2480, 2003.
    • (2003) Signal Processing , vol.83 , Issue.11 , pp. 2469-2480
    • Gonon, G.1    Richoux, O.2    Depollier, C.3
  • 122
    • 0037683139 scopus 로고    scopus 로고
    • Enhancement of photolithography resolution by fractional Fourier domain filtering
    • J. Du, Z. Cui, Y. Zhang, C. Du, J. Yang, and Y. Guo, "Enhancement of photolithography resolution by fractional Fourier domain filtering," Microelectronic Engineering, vol. 67-68, pp. 31-38, 2003.
    • (2003) Microelectronic Engineering , vol.67-68 , pp. 31-38
    • Du, J.1    Cui, Z.2    Zhang, Y.3    Du, C.4    Yang, J.5    Guo, Y.6
  • 123
    • 0002781783 scopus 로고    scopus 로고
    • Securing information with optical technologies
    • B. Javidi, "Securing information with optical technologies," Physics Today, vol. 50, no. 3, pp. 27-32, 1997.
    • (1997) Physics Today , vol.50 , Issue.3 , pp. 27-32
    • Javidi, B.1
  • 124
    • 0036504010 scopus 로고    scopus 로고
    • A class of fractional integral transforms: A generalization of the fractional Fourier transform
    • A. I. Zayed, "A class of fractional integral transforms: A generalization of the fractional Fourier transform," IEEE Trans. Signal Processing, vol. 50, no. 3, pp. 619-627, 2002.
    • (2002) IEEE Trans. Signal Processing , vol.50 , Issue.3 , pp. 619-627
    • Zayed, A.I.1
  • 125
    • 0346724322 scopus 로고    scopus 로고
    • Complete way to fractionalize Fourier transform
    • D. S. Yeung, Q. Ran, E. C. C. Tsang, and K. L. Teo, "Complete way to fractionalize Fourier transform," Optics Communications, vol. 230, no. 1-3, pp. 55-57, 2004.
    • (2004) Optics Communications , vol.230 , Issue.1-3 , pp. 55-57
    • Yeung, D.S.1    Ran, Q.2    Tsang, E.C.C.3    Teo, K.L.4
  • 126
    • 0008319946 scopus 로고    scopus 로고
    • Powers of transfer matrices determined by means of eigenfunctions
    • T. Alieva and M. J. Bastiaans, "Powers of transfer matrices determined by means of eigenfunctions," Journal of the Optical Society of America A, vol. 16, no. 10, pp. 2413-2418, 1999.
    • (1999) Journal of the Optical Society of America A , vol.16 , Issue.10 , pp. 2413-2418
    • Alieva, T.1    Bastiaans, M.J.2
  • 127
    • 0029358647 scopus 로고
    • Fractionalization of Fourier transform
    • C.-C. Shih, "Fractionalization of Fourier transform," Optics Communications, vol. 118, no. 5-6, pp. 495-498, 1995.
    • (1995) Optics Communications , vol.118 , Issue.5-6 , pp. 495-498
    • Shih, C.-C.1
  • 129
    • 84939700451 scopus 로고
    • A discussion of sampling theorems
    • D. A. Linden, "A discussion of sampling theorems," Proc. IRE, vol. 47, no. 7, pp. 1219-1226, 1959.
    • (1959) Proc. IRE , vol.47 , Issue.7 , pp. 1219-1226
    • Linden, D.A.1
  • 130
    • 0011144536 scopus 로고    scopus 로고
    • Deriving the integral representation of a fractional Hankel transform froma fractional Fourier transform
    • L. Yu, Y. Lu, X. Zeng, et al., "Deriving the integral representation of a fractional Hankel transform froma fractional Fourier transform," Optics Letters, vol. 23, no. 15, pp. 1158-1160, 1998.
    • (1998) Optics Letters , vol.23 , Issue.15 , pp. 1158-1160
    • Yu, L.1    Lu, Y.2    Zeng, X.3
  • 131
    • 0032553273 scopus 로고    scopus 로고
    • The Laguerre-Gaussian series representation of two-dimensional fractional Fourier transform
    • L. Yu, W. Huang, M. Huang, Z. Zhu, X. Zeng, and W. Ji, "The Laguerre-Gaussian series representation of two-dimensional fractional Fourier transform," Journal of Physics A: Mathematical and General, vol. 31, no. 46, pp. 9353-9357, 1998.
    • (1998) Journal of Physics A: Mathematical and General , vol.31 , Issue.46 , pp. 9353-9357
    • Yu, L.1    Huang, W.2    Huang, M.3    Zhu, Z.4    Zeng, X.5    Ji, W.6
  • 133
    • 84888896282 scopus 로고    scopus 로고
    • Fractional cosine and sine transforms
    • T. Alieva and M. J. Bastiaans, "Fractional cosine and sine transforms," Asian Journal of Physics, vol. 12, no. 1, pp. 25-32, 2003.
    • (2003) Asian Journal of Physics , vol.12 , Issue.1 , pp. 25-32
    • Alieva, T.1    Bastiaans, M.J.2
  • 134
    • 0242303030 scopus 로고    scopus 로고
    • Effect of spherically aberrated lens on the fractional Fourier transformation systems
    • D. Zhao, H. Mao, H. Liu, X. Wei, F. Jing, and Q. Zhu, "Effect of spherically aberrated lens on the fractional Fourier transformation systems," Optics Communications, vol. 227, no. 4-6, pp. 213-220, 2003.
    • (2003) Optics Communications , vol.227 , Issue.4-6 , pp. 213-220
    • Zhao, D.1    Mao, H.2    Liu, H.3    Wei, X.4    Jing, F.5    Zhu, Q.6
  • 135
    • 0345446574 scopus 로고    scopus 로고
    • Fractional Fourier transform optical system with programmable diffractive lenses
    • I. Moreno, J. A. Davis, and K. Crabtree, "Fractional Fourier transform optical system with programmable diffractive lenses," Applied Optics, vol. 42, no. 32, pp. 6544-6548, 2003.
    • (2003) Applied Optics , vol.42 , Issue.32 , pp. 6544-6548
    • Moreno, I.1    Davis, J.A.2    Crabtree, K.3
  • 136
    • 0344584394 scopus 로고    scopus 로고
    • Reconfigurable electrooptical waveguide for optical processing
    • D. Dragoman and M. Dragoman, "Reconfigurable electrooptical waveguide for optical processing," Applied Optics, vol. 42, no. 32, pp. 6439-6444, 2003.
    • (2003) Applied Optics , vol.42 , Issue.32 , pp. 6439-6444
    • Dragoman, D.1    Dragoman, M.2
  • 137
    • 0037241158 scopus 로고    scopus 로고
    • Engineering functional quantum algorithms
    • art. no. 010302
    • A. Klappenecker and M. Rötteler, "Engineering functional quantum algorithms," Physical Review A, vol. 67, no. 1, 2003, art. no. 010302.
    • (2003) Physical Review A , vol.67 , Issue.1
    • Klappenecker, A.1    Rötteler, M.2
  • 138
    • 0037565213 scopus 로고    scopus 로고
    • Properties of a flattened Gaussian beam in the fractional Fourier transform plane
    • Y. Cai and Q. Lin, "Properties of a flattened Gaussian beam in the fractional Fourier transform plane," Journal of Optics A: Pure and Applied Optics, vol. 5, no. 3, pp. 272-275, 2003.
    • (2003) Journal of Optics A: Pure and Applied Optics , vol.5 , Issue.3 , pp. 272-275
    • Cai, Y.1    Lin, Q.2
  • 139
    • 0942278554 scopus 로고    scopus 로고
    • Propagation of flattened Gaussian beams in apertured fractional Fourier transforming systems
    • D. Zhao, H. Mao, M. Shen, et al., "Propagation of flattened Gaussian beams in apertured fractional Fourier transforming systems," Journal of Optics A: Pure and Applied Optics, vol. 6, no. 1, pp. 148-154, 2004.
    • (2004) Journal of Optics A: Pure and Applied Optics , vol.6 , Issue.1 , pp. 148-154
    • Zhao, D.1    Mao, H.2    Shen, M.3
  • 140
    • 0037373516 scopus 로고    scopus 로고
    • Fractional Fourier transform for elliptical Gaussian beams
    • Y. Cai and Q. Lin, "Fractional Fourier transform for elliptical Gaussian beams," Optics Communications, vol. 217, no. 1-6, pp. 7-13, 2003.
    • (2003) Optics Communications , vol.217 , Issue.1-6 , pp. 7-13
    • Cai, Y.1    Lin, Q.2
  • 141
    • 0141645548 scopus 로고    scopus 로고
    • Fractional Fourier transform for partially coherent and partially polarized Gaussian-Schell model beams
    • Y. Cai, D. Ge, and Q. Lin, "Fractional Fourier transform for partially coherent and partially polarized Gaussian-Schell model beams," Journal of Optics A: Pure and Applied Optics, vol. 5, no. 5, pp. 453-459, 2003.
    • (2003) Journal of Optics A: Pure and Applied Optics , vol.5 , Issue.5 , pp. 453-459
    • Cai, Y.1    Ge, D.2    Lin, Q.3
  • 142
    • 0042932708 scopus 로고    scopus 로고
    • Transformation and spectrum properties of partially coherent beams in the fractional Fourier transform plane
    • Y. Cai and Q. Lin, "Transformation and spectrum properties of partially coherent beams in the fractional Fourier transform plane," Journal of the Optical Society of America A, vol. 20, no. 8, pp. 1528-1536, 2003.
    • (2003) Journal of the Optical Society of America A , vol.20 , Issue.8 , pp. 1528-1536
    • Cai, Y.1    Lin, Q.2
  • 143
    • 0036800754 scopus 로고    scopus 로고
    • Fractional Fourier transform for partially coherent Gaussian Schell model beams
    • Q. Lin and Y. Cai, "Fractional Fourier transform for partially coherent Gaussian Schell model beams," Optics Letters, vol. 27, no. 19, pp. 1672-1674, 2002.
    • (2002) Optics Letters , vol.27 , Issue.19 , pp. 1672-1674
    • Lin, Q.1    Cai, Y.2
  • 144
    • 0346361667 scopus 로고    scopus 로고
    • Simple scheme for the astigmatic transformation of laser modes
    • A. A. Malyutin, "Simple scheme for the astigmatic transformation of laser modes," Quantum Electronics, vol. 33, no. 11, pp. 1015-1018, 2003.
    • (2003) Quantum Electronics , vol.33 , Issue.11 , pp. 1015-1018
    • Malyutin, A.A.1
  • 145
    • 1542345333 scopus 로고    scopus 로고
    • True beam smoothing in the fractional Fourier transform domain
    • Q. Tan, Y. Yan, G. Jin, and D. Xu, "True beam smoothing in the fractional Fourier transform domain," Journal of Modern Optics, vol. 50, no. 14, pp. 2147-2153, 2003.
    • (2003) Journal of Modern Optics , vol.50 , Issue.14 , pp. 2147-2153
    • Tan, Q.1    Yan, Y.2    Jin, G.3    Xu, D.4
  • 146
    • 0347022767 scopus 로고    scopus 로고
    • Resolution enhancement of low resolution wavefields with POCS algorithm
    • A. E. Cetin, H. Ozaktas, and H. M. Ozaktas, "Resolution enhancement of low resolution wavefields with POCS algorithm," Electronics Letters, vol. 39, no. 25, pp. 1808-1810, 2003.
    • (2003) Electronics Letters , vol.39 , Issue.25 , pp. 1808-1810
    • Cetin, A.E.1    Ozaktas, H.2    Ozaktas, H.M.3
  • 147
    • 0038476080 scopus 로고    scopus 로고
    • Motion detection, the Wigner distribution function, and the optical fractional Fourier transform
    • J. T. Sheridan, B. Hennelly, and D. Kelly, "Motion detection, the Wigner distribution function, and the optical fractional Fourier transform," Optics Letters, vol. 28, no. 11, pp. 884-886, 2003.
    • (2003) Optics Letters , vol.28 , Issue.11 , pp. 884-886
    • Sheridan, J.T.1    Hennelly, B.2    Kelly, D.3
  • 148
    • 0036821495 scopus 로고    scopus 로고
    • Application of the fractional Fourier transform to moving target detection in airborne SAR
    • H.-B. Sun, G.-S. Liu, H. Gu, and W.-M. Su, "Application of the fractional Fourier transform to moving target detection in airborne SAR," IEEE Trans. Aerosp. Electron. Syst., vol. 38, no. 4, pp. 1416-1424, 2002.
    • (2002) IEEE Trans. Aerosp. Electron. Syst. , vol.38 , Issue.4 , pp. 1416-1424
    • Sun, H.-B.1    Liu, G.-S.2    Gu, H.3    Su, W.-M.4
  • 149
    • 0036887604 scopus 로고    scopus 로고
    • Using Fourier/Mellin-based correlators and their fractional versions in navigational tasks
    • D. Sazbon, Z. Zalevsky, E. Rivlin, and D. Mendlovic, "Using Fourier/Mellin-based correlators and their fractional versions in navigational tasks," Pattern Recognition, vol. 35, no. 12, pp. 2993-2999, 2002.
    • (2002) Pattern Recognition , vol.35 , Issue.12 , pp. 2993-2999
    • Sazbon, D.1    Zalevsky, Z.2    Rivlin, E.3    Mendlovic, D.4
  • 150
    • 0037645696 scopus 로고    scopus 로고
    • Beamforming using the fractional Fourier transform
    • I. S. Yetik and A. Nehorai, "Beamforming using the fractional Fourier transform," IEEE Trans. Signal Processing, vol. 51, no. 6, pp. 1663-1668, 2003.
    • (2003) IEEE Trans. Signal Processing , vol.51 , Issue.6 , pp. 1663-1668
    • Yetik, I.S.1    Nehorai, A.2
  • 151
    • 84888904163 scopus 로고
    • Fresnel holograms: Their imaging properties and aberrations
    • J. A. Armstrong, "Fresnel holograms: their imaging properties and aberrations," IBM Journal of Research and Development, vol. 9, no. 3, pp. 171-178, 1965.
    • (1965) IBM Journal of Research and Development , vol.9 , Issue.3 , pp. 171-178
    • Armstrong, J.A.1
  • 152
    • 0037238935 scopus 로고    scopus 로고
    • Fresnelets: New multiresolution wavelet bases for digital holography
    • M. Liebling, T. Blu, and M. Unser, "Fresnelets: new multiresolution wavelet bases for digital holography," IEEE Trans. Image Processing, vol. 12, no. 1, pp. 29-43, 2003.
    • (2003) IEEE Trans. Image Processing , vol.12 , Issue.1 , pp. 29-43
    • Liebling, M.1    Blu, T.2    Unser, M.3
  • 154
    • 0036460174 scopus 로고    scopus 로고
    • Principle and application of multiple fractional Fourier transform holography
    • Y. Zeng, Y. Guo, F. Gao, and J. Zhu, "Principle and application of multiple fractional Fourier transform holography," Optics Communications, vol. 215, no. 1-3, pp. 53-59, 2003.
    • (2003) Optics Communications , vol.215 , Issue.1-3 , pp. 53-59
    • Zeng, Y.1    Guo, Y.2    Gao, F.3    Zhu, J.4
  • 155
    • 0036648047 scopus 로고    scopus 로고
    • Fractional cosine, sine, and Hartley transforms
    • S.-C. Pei and J.-J. Ding, "Fractional cosine, sine, and Hartley transforms," IEEE Trans. Signal Processing, vol. 50, no. 7, pp. 1661-1680, 2002.
    • (2002) IEEE Trans. Signal Processing , vol.50 , Issue.7 , pp. 1661-1680
    • Pei, S.-C.1    Ding, J.-J.2
  • 156
    • 0036538082 scopus 로고    scopus 로고
    • Eigenvalues and eigenvectors of generalized DFT, generalized DHT, DCT-IV and DST-IV matrices
    • C.-C. Tseng, "Eigenvalues and eigenvectors of generalized DFT, generalized DHT, DCT-IV and DST-IV matrices," IEEE Trans. Signal Processing, vol. 50, no. 4, pp. 866-877, 2002.
    • (2002) IEEE Trans. Signal Processing , vol.50 , Issue.4 , pp. 866-877
    • Tseng, C.-C.1
  • 157
    • 0038367706 scopus 로고    scopus 로고
    • Eigenmodes of fractional Hankel transform derived by the entangled-state method
    • H.-Y. Fan and H.-L. Lu, "Eigenmodes of fractional Hankel transform derived by the entangled-state method," Optics Letters, vol. 28, no. 9, pp. 680-682, 2003.
    • (2003) Optics Letters , vol.28 , Issue.9 , pp. 680-682
    • Fan, H.-Y.1    Lu, H.-L.2
  • 158
    • 0037381231 scopus 로고    scopus 로고
    • Linear and radial canonical transforms of fractional order
    • A. Torre, "Linear and radial canonical transforms of fractional order," Journal of Computational and Applied Mathematics, vol. 153, no. 1-2, pp. 477-486, 2003.
    • (2003) Journal of Computational and Applied Mathematics , vol.153 , Issue.1-2 , pp. 477-486
    • Torre, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.