Comparison of fast Fourier transform and convolution in wavelength scanning interferometry

The assessment of surface finish has become increasingly important in the field of precision engineering. Optical interferometry has been widely used for surface measurement due to the advantages of non-contact and high accuracy interrogation. In spite of the 2π; phase ambiguity that can limit the measurement scale in monochromatic interferometry, other optical interferomtry have succeeded to overcome this problem and to measure both rough and smooth surfaces such as white light interferometry and wavelength scanning interferometry (WSI). The WSI can be used to measure large discontinuous surface profiles by producing phase shifts without any mechanical scanning process. Where the WSI produces the phase shifts by altering the wavelength of a broadband light source and capturing the produced interferograms by a CCD. This paper introduces an optical setup and operation principle of a WSI that used a halogen white light as a broadband illumination source and an acousto-optic tunable filter (AOTF) as a wavelength scanning device. This setup can provide a wide scan range in the visible region. The scanned range is being operated from 682.8 nm to 552.8nm and the number of captured frames is 128. Furthermore, the obtained interferograms from a Linnik interferometer have been analyzed by two methods, Fast Fourier Transform and Convolution. A mathematical description of both methods is presented then a comparison in results accuracy is made between them. The Areal measurement of a standard 4.707μm step height sample shows that FFT and convolution methods could provide a nanometer measurement resolution for the surface finish inspection.