AUTOMATED PHASE-MEASURING PROFILOMETRY USING DEFOCUSED PROJECTION OF A RONCHI GRATING

A new method is presented for automatic phase measuring profilometry (PMP), in which a defocused image of the projected square-wave Ronchi grating and a phase shifting technique are chosen for the optical phase evaluation. This makes it possible to design all-electronic LCTV-based PMP systems. In this paper a detailed analysis of the applied phase evaluation algorithm as function of the number of steps, N, is given. The alternating feature of the phase measurement precision epsilon(N), which lead to the obvious choice of seven or five steps, is clearly demonstrated. Then an analytical description is presented of the low-pass optical filtering performed by defocused imaging of the projected and video-frame-grabbed Ronchi grating. It is followed by an analytical description of the additional low-pass digital filtering of the same signal due to the inherent properties of the N-step phase shifting algorithm. The figure of merits are estimated in comparison to the simulated perfect imaging of a sinusoidal grating. The results are verified experimentally by a relief determination of a typical object. For this purpose the five accurately shifted defocused projections of the original Ronchi grating, spread over the object, were captured by a CCD based video-digitizing system and evaluated with a PC.