DIFFERENTIAL INTERFEROMETRY

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Interferometry is a typical technique for high precision measurement of mirror shapes, but one can only get the defference between the object and the reference wavefronts, rather than the absolute shape. In this research, we propose differential interferometry to get absolute shapes of the mirrors.The method consists of the measurement of two phase distributions before and after shifting the object, and taking the difference of them to subtract out the influence of the reference phase. We used a zone plate interferometer for the measurement to reduce the influences from vibration and air turbulence, and employed an electro-optical phase modulator to change the reference phase for the phase shifting technique. The following results are obtained in the research.1.To verify this technique experimentally, it is applied in the measurement of the radius of a concave mirror, and we propose a new optical system with an additional interferometer to measure the inclination of the stage, and an equation to reduce the error due to the inclination.2.We compare the object shifting direction, perpendicular to and parallel to the optical axis of the interferometer, and achieve better accuracy by the latter technique.3.A technique to measure a parabolic mirror's shape is proposed, in which the mirror is rotated to the center of the curvature, instead of linear translation.4.Experiments show the accuracy of the measurement of a concave mirror's radius is about 0.1% for a mirror of 1m radius and 100mm diameter.