Comparing CVA and ERA in transfer function measurements for lithography applications

Identification of linear, time invariant systems from input and response time series is a demanding problem with applications in virtually every area of science and technology. Recently several important techniques have been developed to derive the state model of a multiple-input, multiple-response system from measured values of the input and response time series. Two algorithms commonly in use are canonical variate analysis (CVA) and the eigensystem realization algorithm (ERA). In this paper we develop a realistic numerical model for a lithographic stage, which is a complex dynamic, structural system. Identification of this model is performed over a range of signal-to-noise ratios using both CVA and ERA techniques. An error measure is developed based on comparisons of the system and model impulse responses. This measure directly compares the two techniques. The CVA estimates of the state model are substantially more accurate than those provided by ERA