Absolute testing for cylindrical surface

Cylindrical surfaces are typically inspected using null-testing relative interferometry. This paper proposes an absolute testing for cylindrical surfaces by conducting three testing at distinct configurations: focal line position, confocal position, and 180° rotated confocal position. The measured phase data are fitted using orthogonal Chebyshev polynomials, and the absolute surface figure is determined through solving a equation matrix established based on the inherent flip-symmetry characteristics of the polynomial basis. This approach effectively eliminates systematic errors inherent in conventional interferometric testing, enabling high-precision absolute characterization of cylindrical surfaces without requiring additional reference optics.