Shear test of the off-axis surface with an axis-symmetric parent

Interferometers with additional test optics are frequently used for measuring aspherical optical surfaces. In optical testing it is desirable to separate the figure measurement errors due to the test surface from figure errors that arise in the test equipment. For axially symmetric optics this is accomplished by rotating the surface being measured with respect to the test system. The data can then be processed to separate the non-axially symmetric errors that are fixed in the test system and those that rotate with the part. The axially symmetric errors cannot be distinguished with this technique. In this paper we present a variation of this technique for off-axis aspheric optics. The rotation is performed by rotating the test surface about the optical axis of its parent asphere, which may be outside the physical boundary of the test surface. As these rotations cannot be large, this motion is better described as a shear of the optical surface with respect to the test optics. By taking multiple measurements with different amounts of rotational shear and using maximum likelihood estimation methods, one can separate the errors in the test optics from the irregularity in the optical surface.