Frequency domain position estimation for lithographic alignment

A frequency-domain-based algorithm for estimating the position of a symmetric pulse is described. The algorithm exhibits low estimation error variance and low computational complexity, making it ideal for the lithographic alignment task in integrated circuit manufacturing. It is shown that for additive, white stationary noise the position estimation is unbiased and that if the noise is also Gaussian this algorithm asymptotically achieves the Cramer-Rao bound as the noise power decreases. An adaptive algorithm that optimizes the position estimation of a pulse of unknown shape given a training set is also described. This adaptive procedure does not require knowledge of the position of the training pulses and is therefore a blind, adaptive optimizer. It achieves a steady-state mean squared estimation error that is smaller than that of the LMS (least mean square) algorithm.<>