High Precision Signal Processing Algorithm for White Light Interferometry

Abstract

A new signal processing algorithm for absolute temperature measurement using white light interferometry has been proposed and investigated theoretically. The proposed algorithm determines the phase delay of an interferometer with very high precision (≪ one fringe) by identifying the zero order fringe peak of cross-correlation of two fringe scans of white light interferometer. The algorithm features cross-correlation of interferometer fringe scans, hypothesis testing and fine tuning. The hypothesis test looks for a zero order fringe peak candidate about which the cross-correlation is symmetric minimizing the uncertainty of mis-identification. Fine tuning provides the proposed algorithm with high precision sub-sample resolution phase delay estimation capability. The shot noise limited performance of the proposed algorithm has been analyzed using computer simulations. Root-mean-square (RMS) phase error of the estimated zero order fringe peak has been calculated for the changes of three different parameters (SNR, fringe scan sample rate, coherence length of light source). Computer simulations showed that the proposed signal processing algorithm identified the zero order fringe peak with a miss rate of 3 × 10-4 at 31 dB SNR and the extrapolated miss rate at 35 dB was 3 × 10-8. Also, at 35 dB SNR, RMS phase error less than 10-3 fringe was obtained. The proposed signal processing algorithm uses a software approach that is potentially inexpensive, simple and fast.

Dynamic coherence scanning interferometry based on an optical phase mask for simultaneous measurement of local induced vibration and local topology change of a mirror

“…We can assume that the white light source shape of the bandpass is a Gaussian. In that case, we can define the interference pattern as the combination of the normal probability density function and the fundamental equation of interferometry, 19 – 21 obtaining the following equation: I(OPD)=0.5·I0·(1+exp[−(OPDlc)2])·cos(2·k0·OPD),where k0 is the wavenumber (k0=2 π/λ), λ is the central wavelength of the source, and lc is the coherence length defined in Eq. (2) 4 .…”

“…We can assume that the white light source shape of the bandpass is a Gaussian. In that case, we can define the interference pattern as the combination of the normal probability density function and the fundamental equation of interferometry, [19][20][21] obtaining the following equation:…”

Nondestructive surface profiling of hidden MEMS using an infrared low-coherence interferometric microscope

“…A phase inconsistency between the envelope and the interference may also arise due to highly curved or tilted surfaces [61,62]. Various signal processing techniques of the LCI correlogram have been developed to determine the object's height position [17,[63][64][65][66][67][68][69][70][71][72][73][74][75].…”

White-light interferometers with polarizing optics for length measurements with an applicable zero-point detection

“…Signal processing is a challenge for any white-light interferometer because the signature is influenced by different curve distortions (for example fringe beating effects [11]) and signal noise. In his paper, Kim describes some algorithms simulated and tested for a precise signal processing in the field of whitelight interferometry [12]. Ma and Bock published their work for white-light signal processing and fringe analysis in [13].…”