| A new signal processing algorithm for white light interferometry has been proposed and investigated theoretically and experimentally. The goal of the algorithm is to determine the absolute length of an interferometer with very high precision ({dollar}ll{dollar}one optical wavelength). The algorithm features cross-correlation of interferometer fringe, patterns and hypothesis testing. The key to making the signal processing algorithm work efficiently is that all photons in a fringe scan are fully utilized through the cross-correlation of fringes and matched filtering. The hypothesis test looks for a zero order fringe peak candidate about which the cross-correlation is symmetric minimizing the uncertainty of misidentification. The shot noise limited performance of the proposed signal processing algorithm has been analyzed using Monte-Carlo simulation. Simulation results were extrapolated to predict the misidentification rate at Signal-to-Shot noise ratio higher than 31 dB. Root-mean-square phase error between the computer-generated zero order fringe peak and the estimated zero order fringe peak has been calculated for various parameter changes.; Results of simulation and comparison with experimental data showed the ability of the proposed signal processing algorithm to identify the zero order fringe peak correctly and the proposed signal processing algorithm proved to be a good diagnostic tool to show the quality of the white light interferometry fringe scan. The proposed signal processing algorithm uses a software approach which is potentially inexpensive, simple and fast. |
