Cochran and Wyant have recently proposed the extension of profile measurements by overlapping a number of successive colinear traces to generate a composite trace which is an order of magnitude longer than any individual measurement. This paper presents an error analysis of this method as a guide for its application and improvement. Expressions are derived for: a) the cumulative rms error of the composite profile, b) the trade-off between this error, the number of traces required, and the degree of overlap of successive traces, and c) the power spectral density of the cumulative error. This last is important in the application of the method since -- as expected -- it predicts that most of the error is concentrated in long surface wavelengths, in precisely the region the method was designed to illuminate. The present analysis suggests that the performance of the method may be improved by using a global fitting procedure rather than the serial method originally considered.
E. L. Church, E. L. Church,
"Extension Of The Range Of Profile Measurements By Overlapping Successive Traces", Proc. SPIE 0749, Metrology: Figure and Finish, (20 April 1987); doi: 10.1117/12.939844; https://doi.org/10.1117/12.939844