Filter with variable transmission characteristics for determination of three-dimensional roughness

In this study, we propose a low-pass filter whose transmission characteristics are determined to be more than 99.99% identical to the designed transmission characteristics at wavelengths greater than the cut-off wavelength. This low-pass filter is realized using a frequency-domain method which uses down-sampling, a frequency filter, and a cubic B-spline. When the frequency characteristics of a Gaussian filter (GF) were used as the designed transmission characteristics, this low-pass filter perfectly replaced the GF. In addition, no end effects and directional characteristics developed, and high-speed computation was possible. Furthermore, we can easily realize a low-pass filter having transmission characteristics that rise sharply at a right angle like a step edge.