Random errors for the measurement of central positions in white-light interferometry with the least-squares method

This paper analyzes the effect of random noise on the measurement of central positions of white-light correlograms with the least-squares method. Measurements of two types of central positions, the central position of the envelope (CPE) and the central position of the central fringe (CPCF), are investigated. Two types of random noise, intensity noise and position noise, are considered. Analytic expressions for random error due to intensity noise (REIN) and random error due to position noise (REPN) are derived. The theoretical results are compared with the random errors estimated from computer simulations. Random errors of CPE measurement are compared with those of CPCF measurement. Relationships are investigated between the random errors and the wavelength of the light source. The REPN of CPCF measurement has been found to be independent of the wavelength of the light source and the amplitude of the central fringe.