Multi-wavelength digital holography for shape measurement of grinded surfaces with ultimate accuracy

Abstract

The entry of CNC machining processes into optics brought the possibility of nearly arbitrary shape generation. Obviously the measurement of the generated shape increasingly gains the importance, because the generation has to be performed in an iterative manner as the required precision increases. Often mid spatial frequency error is neglected because it is not an easy task to be measured. Unfortunately those unwanted residual deviation in a shape left after grinding could dramatically complicate a subsequent polishing procedure. Mid spatial frequency content if not controlled well could spoils significantly the performance of the optical system. Elimination of mid spatial residuals originated in grinding process is nearly impossible or very difficult by sub-aperture polishing. Hence it is important to measure the grinded surface with sufficient lateral resolution. Tactile probes (usually used for shape measurement of grinded surfaces) can measure with sufficient lateral resolution but only at the expense of time. Interferometer based techniques fail when applied to scattering surfaces due to speckles. The authors have proposed multi-wavelength multi-directional digital holography – the method perfectly suitable for grinded surfaces shape measurement. Naturally, reconstructed phase maps are affected by speckle noise implying significant errors in the calculation of the shape of the surface. In order to reduce the effect of speckle noise and hence to increase the sensitivity of the measurement of the grinded surface shape, we propose to apply windowed digital holography. This paper describes the principle of the windowed digital holography and the way of straightforward application of the method in shape measurement of grinded surfaces.