PAN Wei-qing, ZHU Yong-jian, WANG Jian-zhong. Phase-space analysis for fractional Fourier transform of first-order optical system[J]. Journal of Applied Optics, 2009, 30(4): 596-600.
Citation: PAN Wei-qing, ZHU Yong-jian, WANG Jian-zhong. Phase-space analysis for fractional Fourier transform of first-order optical system[J]. Journal of Applied Optics, 2009, 30(4): 596-600.
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Phase-space analysis for fractional Fourier transform of first-order optical system

  • 1.

    Zhejiang University of Science and Tecnology,Hangzhou 310023,China;

  • 2.

    Hunan University,Changsha 410082,China

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    • Abstract
  • The fractional Fourier express of the first-order optical system was derived by decomposing the transfer matrices of first-order optical system into coordinate rotation matrix, scale matrix and chirp matrix in Wigner phase space. The results show that an arbitrary first-order optical system can be expressed as the scaled and chirp modulation fractional Fourier transform. The transfer matrix and diffractive integral formula in frequency domain were acquired by rotating the input and output optical field /2 in the phase space. Accordingly the fractional Fourier transforms of a first-order optical system in frequency domain were also obtained. By comparing the transfer matrices of two first-order optical systems in space and frequency domains respectively, it is found that the two first-order optical systems in different domain can be expressed as two different expressions of one and the same transfer based on different coordinates. At last the condition is derived for an optical system to implement the fractional Fourier transform in space and frequency domains with the same order.
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  • ［1］COLLINS S A,Jr. Lens-system diffraction integral written in terms of matrix optics［J］. J. Opt. Soc. Am.,1970,6(9):1168-1177.
    ［2］OZAKTAS M H,MENDLOVIC D. Fractional Fou-rier optics［J］. J. Opt. Soc. Am.A,1995,12(4):743-751.
    ［3］OZAKTAS M H, ZALEVSKY Z, KUTAY M A. The fractional Fourier transform with applications in optics and signal processing［M］. John Wiley& Sons, LTD,2000.
    ［4］ZHAO D, WANG S. Collins formula in spatial-domain written in terms of fractional Fourier transform or fractional Hankel transform［J］. Optik, 2000,111(8):371-374.
    ［5］LIU Z, WU X, FAN D. Collins fomula in fre-quency-domain and fractional Fourier transform［J］. Opt.Commu.,1998,155(1):7-11.
    ［6］BASTIAANS M J. Wigner distribution function and its application to first-order optics［J］. J.Opt.Soc.Am.,1979,69:1710-1716.
    ［7］LOHMANN A W. Image rotation, Wigner rota-tion, and the fractional Fourier transform［J］. J.Opt.Soc.Am.A,1993,10(10):2181-2186.
    ［8］MOSHINSKY M., QUESNE C. Linear canonical transformations and their unitary representations［J］. J. Math.Phys.,1971,12(8):1772-1783.
    ［9］BASTIAANS M J. Application of the Wigner distr-ibution function in optics［J］. Proceedings of AIP Conference,1980:292-312.
    ［10］《数学手册》编写组.数学手册［M］.北京：高等教育出版社，1979.
    Compiling group of mathematical handbook. Mathematical handbook［M］.Beijing: Higher Education Press, 1979.(in Chinese)
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