Evaluation of the Performance of Polished Mirror Surfaces for the TAMA Gravitational Wave Detector by Use of a Wave-Front Tracing Simulation: Erratum

A nonmechanical scanning Mirau-type spectral interference microscope has been developed for the measurement of three-dimensional surface profiles of discontinuous objects. An acousto-optic tunable filter (AOTF) is used as a highresolution spectral filter, which scans the optical frequency of the broadband light emitted from a superluminescent diode. To generate spectral fringes that make full use of the limited coherence length of the filtered light we unbalanced the Mirau interferometric system by positioning the reference mirror nearly halfway between the top and the bottom of the step height. When the frequency of the broadband light source is scanned by an AOTF, the interference fringes move in opposite directions on the top and the bottom of the object. To uniquely determine the sign of the fringe movement over the large area of the object, we developed a three-dimensional Fourier-transform technique, and from the detected sign of the fringe movement and phase information, we determined the threedimensional step height. Experimental results of the measurement of 100- (mu)m step height are presented. The main advantages of the proposed system are that it provides nonmechanical scanning and a large measurement range without ambiguity in the sign of the phase.