Optical system analysis based on prolate spheroidal wave functions

被引：0

作者：

Zhang B. ^{[1
]}

Fu D. ^{[1
]}

Chen J. ^{[1
]}

Xiang H. ^{[1
]}

机构：

[1] School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai

来源：

Zhongguo Jiguang/Chinese Journal of Lasers | 2016年 / 43卷 / 06期

关键词：

Energy-preservation ratio; Fourier optics; Offset linear canonical transform; Optical system; Spheroidal wave functions;

D O I：

10.3788/CJL201643.0609005

中图分类号：

学科分类号：

摘要：

The prolate spheroidal wave function is a set of complete orthogonal functions set in both the finite and infinite space domain, which is suitable to analyze the practical optical systems with finite aperture size. The linear canonical transform is a kind of important time-frequency analysis tool, and the Fresnel transform is a special case of linear canonical transform. So, the linear canonical transform can model optical system. The offset linear canonical transform of prolate spheroidal wave functions in finite space domain and frequency domain is instituted, and the offset linear canonical transform models a two-dimension optical system. Using the spheroidal wave functions as signal functions, the signal's energy loss after passing through the system is analyzed. Based on prolate spheroidal wave functions' eigenvalue property, the eigenvalue reflects the energy-preservation ratio. The numerical calculation result suggests that the signal function's energy ratio after passing through the system is consistent with the energy ratio's estimation value gained by the function's eigenvalue, which indicates the validity of this method. © 2016, Chinese Lasers Press. All right reserved.

引用

页数：7

共 15 条

[1]

Chen Z., Wang H., Zhong P., Et al., The peak-to-average power ratio reduction method for prolate spheroidal wave function based on Givens rotation transformation, Journal of Electronics & Information Technology, 35, 6, pp. 1406-1412, (2013)

[2]

Tao C., Tao C., Optical Information Theory, pp. 6-7, (2005)

[3]

Liu L., 2D Fourier-transform imaging algorithm for synthetic aperture imaging ladars, Acta Optica Sinica, 34, 1, (2014)

[4]

Zhang W., Lu X., Liu S., Et al., Generalized phase-shifting phase retrieval approach based on time-domain Fourier transform, Chinese J Lasers, 42, 9, (2015)

[5]

Sun Q., Ma J., Yang Y., Et al., Talbot effect in linear canonical transformation, Acta Optica Sinica, 34, 7, (2014)

[6]

Xiang Q., Qin K., Zhang C., Linear canonical transform and time-frequency filtering, Journal of Electronic Measurement and Instrument, 23, 4, pp. 69-73, (2009)

[7]

Xu T., Li B., Linear Canonical Transform and its Implication, (2013)

[8]

Chen J., Su X., The Principle and Application of Optical Information Technology, pp. 37-38, (2002)

[9]

Yu D., Tan H., Engineering Optics, pp. 384-386, (2011)

[10]

Chen J., Zheng Z., Lian G., Digital realization method for Fresnel transform of multiple three-dimensional objects, Laser & Optoelectronics Progress, 51, 4, (2014)

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