| Wavenumber Scanning Interferometry (WSI), whose measurement accuracy of strain field reach to micro-level, can measure the strain field inside a composite material in perspective. WSI is able to nondestructively test the composite material with high accuracy. Currently, it is one of the important ways on nondestructive measurement of micron-size. However, the measurement accuracy and the depth resolution are much lower than that of traditional Optical Coherence Tomography, since the wavenumber scanning range is limited. This disadvantage also causes unsolvable prior information inside the composite material, making improssible to separate the useful interference signals. In addition, due to weak reflected intensities inside the composite material, the interference signals are easily immerse into speckle noises. Those problems of WSI make it difficult for application.To address the problem mentioned above, this paper uses nonlinear least squares and spatial spectrum estimation to improve the depth resolution, measurement accuracy and to blindly separate interference signal from multiple surfaces without broadening the wavenumber scanning range of laser output. In the meanwhile, this paper also focuses on how to reduce speckle noise based on nonlinear least squares algorithm. The main contents and achievements are listed as follows:(1) A complex number least squares algorithm (CNLSA) and a wavenumber-domain least squares algorithm (WLSA) are put forward by fitting the interference spectrum and wavenumber-domain interference intensities in complex number field and real number field respectively. CNLSA and WLSA are able to remove the blurring effect of convolution by a window function, which can replace Fourier transform (FT) for evaluating interference data. The experimental results show that the depth resolution δz is improved from 8z to δz/1.8 by CNLSA and from 8z to δz/6 by WLSA. At the same time, their suppression of sidelope is stronger than that of FT with a hanning window, resulting in a higher accuracy of phase measurement.(2) An eigenvalue decomposition and least squares algorithm (EDLSA) are founded by combining theory of spatial spectrum estimation and principle of date evaluation in phase-shifting interferometry. Firstly, the amount of surfaces is blindly evaluated using eigenvalue decomposition of depth-resolved interference signal autocorrelation matrix. Secondly, the interference frequencies are evaluated using estimation of signal parameters via rotational invariance techniques (ESPRIT). Thirdly, the linear least squares algorithm of phase-shifting interferometry is developed to complex number field so that the interference phases and amplitudes are evaluated. In the end, the interference signals from multiple surfaces are successfully separated without any a prior knowledge. The experimental results show that although the wavenumber scanning range is relatively narrow, EDLSA can still blindly separate the multiple interference signals. Besides, the depth resolution and measurement accuracy are much better than that of FT.(3) A joint Fourier transform and complex number least squares algorithm (JFTLSA) is proposed to reduce depth-resolved speckle noises. The theory is presented as follow: firstly, by making full use of relationship between surfaces on interference amplitudes, frequencies, and phases, the CNLSA is updated for lowering the dimension so that it is more stable in an environment of speckle noise. Secondly, the unstable points in wrapped phase maps evaluated by updated CNLSA are modified according to noise points searching equation and FT. Depth-resolved speckle experiments show that the speckle noises are reduced 20% after using JFTLSA, compared with FT.
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