Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform.
作者： Kieran G. Larkin
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摘要: Utilizing the asymptotic method of stationary phase, I derive expressions for Fourier transform a two-dimensional fringe pattern. The assumes that both amplitude and phase pattern are well-behaved differentiable functions. Applying limits in two distinct ways, show, first, spiral (or vortex) approaches ideal quadrature asymptotically and, second, approximation errors increase with relative curvature fringes. results confirm validity recently proposed direct demodulation closed patterns.
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Carl M. Bender, Steven A. Orszag, Asymptotic Expansion of Integrals Springer, New York, NY. pp. 247- 316 ,(1999) , 10.1007/978-1-4757-3069-2_6
J.F. Kaiser, On a simple algorithm to calculate the 'energy' of a signal International Conference on Acoustics, Speech, and Signal Processing. pp. 381- 384 ,(1990) , 10.1109/ICASSP.1990.115702
Hans Knutsson, GFosta H. Granlund, Signal processing for computer vision ,(1994)
Thomas Kreis, Holographic Interferometry: Principles and Methods ,(1996)
J. L. Marroquin, J. E. Figueroa, M. Servin, Robust quadrature filters Journal of the Optical Society of America A. ,vol. 14, pp. 779- 791 ,(1997) , 10.1364/JOSAA.14.000779
A.H. Nuttall, E. Bedrosian, On the quadrature approximation to the Hilbert transform of modulated signals Proceedings of the IEEE. ,vol. 54, pp. 1458- 1459 ,(1966) , 10.1109/PROC.1966.5138
Kieran G. Larkin, Bozenko F. Oreb, Propagation of errors in different phase-shifting algorithms: a special property of the arctangent function Interferometry: Techniques and Analysis. ,vol. 1755, pp. 219- 227 ,(1993) , 10.1117/12.140773
Norden E. Huang, Zheng Shen, Steven R. Long, Manli C. Wu, Hsing H. Shih, Quanan Zheng, Nai-Chyuan Yen, Chi Chao Tung, Henry H. Liu, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 454, pp. 903- 995 ,(1998) , 10.1098/RSPA.1998.0193
Kieran G. Larkin, Donald J. Bone, Michael A. Oldfield, Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform. Journal of The Optical Society of America A-optics Image Science and Vision. ,vol. 18, pp. 1862- 1870 ,(2001) , 10.1364/JOSAA.18.001862
Petros Maragos, Alan C. Bovik, Thomas F. Quatieri, Multidimensional energy operator for image processing visual communications and image processing. ,vol. 1818, pp. 177- 186 ,(1992) , 10.1117/12.131436