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 subsample 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 x 10^-4 at 31 dB SNR and the extrapolated miss rate at 35 dB was 3 x 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.