Eigenvalue decomposition and least squares algorithm for depth resolution of wavenumber-scanning interferometry

Abstract

Depth resolution of depth-resolved interferometry evaluated by Fourier transform is limited by the range of phase shifting. A novel algorithm, the eigenvalue decomposition and least squares algorithm (EDLSA), is proposed. Experimental results obtained using depth-resolved wavenumber-scanning interferometry demonstrate that the EDLSA performs better than the Fourier transform and complex number least squares algorithm. Not requiring any a priori information, the algorithm can replace the Fourier transform in depth-resolved interferometry with improved depth resolution.

Estimating the number of layers for precise wavelength scanning interferometry

“…In such cases, instead of the direct discrete Fourier transform method, we usually use more precise methods, e.g. the wavenumber-domain least-squares algorithm [10], eigenvalue-decomposition and least-squares algorithm [14] and complex-number least-squares algorithm (CNLSA) [7], to guarantee depth resolution [10]. For such precise methods, we need to estimate/evaluate the number of layers in advance.…”

“…For this reason, in 2015, Bai et al proposed an eigenvalue decomposition algorithm (EDA) to estimate the number of layers for WSI unsupervised [14], where the idea behind it is to estimate the number of eigenvalues of the interference autocorrelation matrix, pixel by pixel. Then, the number of layers is determined by counting the valid rank of the matrix [15][16][17][18].…”