Applicability of the Van Cittert–Zernike theorem in a Ronchi shearing interferometer

Abstract

Ronchi shearing interferometry is a promising technique for in situ wavefront aberration measurement of the projection lens in advanced photolithography systems. The Van Cittert–Zernike theorem has been used to analyze the interference signal of a Ronchi shearing interferometer in the effective interference area (overlapping area of the $\pm 1$ st diffraction orders produced by the image grating). However, the applicability of this theorem has not been systematically studied. In this work, the analytical expression of the Ronchigram in this area is derived based on the theory of scalar diffraction and incoherent imaging. The results show that only the object and image grating with infinite diffraction orders can fully satisfy the Van Cittert–Zernike theorem. In the finite diffraction orders case, the theorem can be considered approximately applicable in the overlapping area of the $\pm 3$ rd diffraction orders produced by the image grating. The applicable area extends to the overlapping area of the $\pm 2$ nd diffraction orders under a shear ratio of less than 1%, which accounts for 97% of the effective interference area. The theoretical analysis has been verified by simulation and fundamental experiments.