Deflectometry encoding the measured angle in a time-dependent intensity signal.

We propose a new concept of a deflectometer, aimed to provide high accuracy measurements with high sampling rate and low noise, as required by state-of-the-art slope-measuring profilometers, like Long Trace Profilometers or Nanometer Optics Measuring instruments. For this purpose, we introduce certain modifications to the usual working principle of autocollimators so that the measured angle is not given by the displacement of the pattern captured by a CCD, but by the harmonic contents of the time-modulated intensity signal acquired by a photodiode. By doing this, the signal can be sampled not by just a few thousand pixels but by millions of samples/s.

Completeness condition for unambiguous profile reconstruction by sub-aperture stitching.

We describe the conditions required for a set of displaced sub-aperture measurements to contain sufficient information to reconstruct the stitched mirror profile removing all additive systematic errors of the measuring instrument, independent of the reference surface and of the guidance error of the linear stage used for the translation. We show that even-spaced stitching must be avoided and that the pitch error of the linear stage or the curvature of the reference must be measured, to avoid periodic errors and curvature errors in the reconstructed profile. We show that once these uncertainties are solved, the 1D profile can be reconstructed free of any additive systematic error. The theory is supported by computer simulations and by experimental results using two different instruments.