Improvement of the depth resolution in depth-resolved wavenumber-scanning interferometry using multiple uncorrelated wavenumber bands

Abstract

In this article, we provide a method to improve the depth resolution of wide-field depth-resolved wavenumber-scanning interferometry (DRWSI), because its depth resolution is limited by the range of the wavenumber scanning and mode hopping of the light source. An optical wedge is put into the optical path to measure the series of the wavenumber on time using a 2D spatial Fourier transform (FT) of the interferograms. Those uncorrelated multiple bands of the wavenumbers due to mode hopping of the diode laser can be synthesized into one band, to enlarge the range of the wavenumber scanning. A random-sampling FT is put forward to evaluate the distribution of frequencies and phases of the multiple surfaces measured. The benefit is that the depth resolution of the DRWSI is enhanced significantly with a higher signal-to-noise ratio. Because of its simplicity and practicability, this method broadens the way to employing multiple different lasers or lasers with mode hopping as the light sources in the DRWSI.

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

“…The first two surfaces S 1 and S 2 are from an optical wedge. These are used as the reference planes in the Michelson interferometer as well as for monitoring the light wavenumber of the diode laser [6]. S 3 ; …; S M are the surfaces measured.…”

“…The Fourier transform (FT) is widely used in optical depthresolved interferometry applications such as wavelengthscanning interferometry (WSI), swept source interferometry, and spectral OCT [1][2][3][4][5][6][7]. The main drawback of these methods is that their profile depth resolution is limited by the width of the sampling window.…”

“…Attempts were made to use light sources with tunable wavelength in the hundreds-of-nanometers range, either in time domain or in spectral domain, for increasing the depth resolution [2][3][4][5]. However, with increasing the wavenumbers range, the light dispersion possibly yields defocus and blurring of the sharp images obtained using a CCD camera, and mode hops of the light source make the optical system and data processing algorithm complicated [2,3,6]. Therefore, new theoretical solutions are desired for solving the depth resolution problem in optical depth-resolved interferometry.…”

Perspective Measurement of the Out‐of‐plane Displacement and Normal Strain Field Distributions Inside Glass Fibre‐reinforced Resin Matrix Composite

“…The series of the fringe patterns photographed by the CCD camera can be expressed as where ( x , y ) represents spatial coordinates; I p and I q are reflective light intensity from surfaces p and q , respectively; M is the number of the surfaces of the sample and the optical wedge; φ pq 0 is the initial interference phase between surfaces p and q ; Λ pq is the optical path difference between surfaces p and q ; and the wavenumber k = 2π/ λ , where λ is the light wavelength.…”

“…Fourier transform of the fringe patterns I ( x , y , k ) in the k space can be written as where F denotes the Fourier transform; f is the frequency in the Fourier space k ; w is a window function (Hanning window); is the sampling function; k ( n ) is the value of the wavenumber as the CCD camera takes the n ‐th image; N is the total number of the images, which are photographed by the CCD camera. According to the property of δ function, Equation can be rewritten as where k ( n ) is non‐linear and randomly sampled.…”