Lawrence Berkeley National Laboratory

We analyze the random noise and the systematic errors of the positioning of the interference patterns in the long trace profilers (LTP). The analysis, based on linear regression methods, allows the estimation of the contributions to the positioning error of a number of effects, including non-uniformity of the detector photo-response and pixel pitch, read-out and dark signal noise, ADC resolution, as well as signal shot noise. The dependence of the contributions on pixel size and on total number of pixels involved in positioning is derived analytically. The analysis, when applied to the LTP II available at the ALS optical metrology laboratory, has shown that the main source for the random positioning error of the interference pattern is the read-out noise estimated to be ~;0.2 rad. The photo-diode-array photo-response and pixel pitch non-uniformity determine the magnitude of the systematic positioning error and are found to be ~;0.3 rad for each of the effects. Recommendations for an optimal fitting strategy, detector selection and calibration are provided. Following these recommendations will allow the reduction of the error of LTP interference pattern positioning to a level adequate for the slope measurement with 0.1-rad accuracy.