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Spatial carrier interferometry from M temporal phase shifted interferograms: Squeezing Interferometry

机译:来自M个时间相移干涉图的空间载波干涉测量法:挤压干涉测量法

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摘要

It is well known that having 3 temporal phase shifting (PS) interferograms we do not have many possibilities of using an algorithm with a desired frequency spectrum, detuning, and harmonic robustness. This imposes severe restrictions on the possibilities to demodulate such set of temporal interferograms. It would be nice to apply for example a 7 step PS algorithm to these 3 images in order to have more possibilities to phase demodulate them; even further, it would be even better to apply a quadrature filter having a spatial spread given by a real number to these 3 interferograms. In this paper we propose to do just that; namely we show how to demodulate a set of M-steps phase shifting images with a quadrature filter having a real-number as spatial spread. The interesting thing in this paper is to use a higher than M spread quadrature filter to demodulate our interferograms; in traditional PS interferometry one is stuck to the use of M step phase shifting formula to obtain the searched phase. Using a less than M PS formula is not interesting at all given that we would not use all the available information. The main idea behind the "squeezing" phase shifting method is to re-arrange the information of the M phase shifted fringe patterns in such a way to obtain a single carrier frequency interferogram (a spatio-temporal fringe image) and use any two dimensional quadrature filter to demodulate it. In particular we propose the use of Gabor quadrature filters with a spread given by real-numbers along the spatial coordinates. The Gabor filter may be designed in such way that we may squeeze the frequency response of the filter along any desired spatio-temporal dimension, and obtain better signal to noise demodulation ratio, and better harmonic rejection on the estimated phase.
机译:众所周知,拥有3个时间相移(PS)干涉图,我们不太可能使用具有所需频谱,失谐和谐波鲁棒性的算法。这对解调这种时间干涉图的可能性施加了严格的限制。最好对这3张图像应用例如7步PS算法,以便有更多的相位对其进行解调;更进一步,将具有由实数给定的空间扩展的正交滤波器应用于这三个干涉图会更好。在本文中,我们建议这样做。即,我们展示了如何使用具有实数作为空间扩展的正交滤波器对一组M步相移图像进行解调。本文有趣的事情是使用一个高于M的扩展正交滤波器来解调我们的干涉图。在传统的PS干涉测量中,人们一直坚持使用M步相移公式来获得搜索到的相位。鉴于我们不会使用所有可用信息,因此使用小于M PS的公式根本没有意义。 “压缩”相移方法背后的主要思想是以这种方式重新排列M个相移条纹图案的信息,以获得单载波频率干涉图(时空条纹图像)并使用任意二维正交过滤器将其解调。特别是,我们建议使用Gabor正交滤波器,其实数沿空间坐标给出了扩展。 Gabor滤波器的设计可以使我们沿着任意所需的时空方向压缩滤波器的频率响应,并获得更好的信噪解调比,以及在估计相位上获得更好的谐波抑制。

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