Optimization of the size and shape of the scanning aperture in autocollimator-based deflectometric profilometers

Deflectometric profilometers based on industrial electronic autocollimators (ACs), as the ELCOMAT-3000, have become indispensable tools for precision form measurements of optical surfaces. A growing number of labs at synchrotron and free electron laser x-ray facilities are going for BESSY-II NOM-like versions of the AC-based profilometers. These tools have proven capable of characterizing state-of-the-art aspherical x-ray optics with an accuracy on the level of 100 nrad (root-mean-square) over the spatial frequency range limited by the size of the aperture used in the profilometer. Typically, a round aperture with a diameter of about 2.5 mm is used. Previous investigations have shown that with the optimally aligned 2.5-mm aperture, the spatial resolution of a NOM-like profilometer corresponding to the first zero-crossing of the optical transform function (OTF) is ∼1.2 mm. In this paper, we investigate the performance of an AC ELCOMAT-3000 for a slope profilometer with different aperture sizes and shapes. The results of angular calibration of the AC equipped with circular and rectangular apertures placed at different distances from the AC are discussed. The calibration was performed at the Physikalisch-Technische Bundesanstalt using the original experimental arrangements, also discussed in the paper. The OTF measurements with the specially developed test sample with chirped surface slope profiles were performed at the Advanced Light Source X-Ray Optics Laboratory (XROL) in application to a new optical surface measuring system under development at the XROL. In the OTF measurements, we have shown that application of a rectangular aperture with dimensions of 1.5 mm × 3 mm improves the spatial resolution in the tangential direction by a factor of ∼1.4 compared to that of the standard circular aperture of 2.5-mm diameter. We believe that the results of our investigations are crucial for reaching fundamental metrological limits in deflectometric profilometry utilizing state-of-the-art electronic autocollimators.