Spatiotemporal speckle in optical lithography via integrated speckle theory: interpretation and numerical modeling

We revisit the expression for the contrast of spatiotemporal speckle encountered in optical lithography, in a manner different from previous studies, by exploiting the statistical properties of speckle integrated over both space and time. The necessary conditions under which this framework applies are stated explicitly, and it is emphasized that the required spatiotemporal separability is invoked at the level of the correlation function rather than the optical field. To gain physical insight into the derived expression, we present a numerical method for simulating such speckle, enabling direct evaluation of its contrast. The simulation results agree well with theoretical predictions, validating both the formulation and our interpretation of speckle behavior. We also discuss the practical significance of this type of simulation.