Theoretical analysis of retrace error in Fizeau interferometer for deformed optical flats

Laser Fizeau interferometers are widely used for surface form metrology for optics and silicon wafers. The reference beam and sample beam share a common optical path in Fizeau interferometer when measuring a non-tilted optical flat. However, in the process of measuring surface topography of a wafer, as the form of a wafer often deviates from an ideal flat, such as surface warping caused by the manufacturing process, the so-called retrace error may occur due to the violation of the common path condition. In this paper, we establish two ray tracing models that correspond to the home-built Fizeau interferometer in our lab, and find that the retrace error only occurs in the presence of optical aberrations in the interferometer. In addition, we study the effect of the variation of the wafer surface form on the retrace error by superposing different Zernike polynomials on the flat surface. Based on the simulation results, the tolerance for aberrations in the specific Fizeau interferometer is provided.