Gaussian Filter Testing


The Gaussian filter was validated based on its transmission characteristics. We used simulated sinusoidal surfaces of gradually increasing wavelengths in both direction x and y with spacing of 1.0 micron and traversing length of 6 cutoff wavelength. The sinusoidal surfaces were input into a Gaussian subroutine with long cutoff of 0.08mm. The ratio of Sa parameter of the roughness surface and Sa parameter of the raw data plotted against the wavelength to yield the filter transmission characteristic surface. The transmission surface was then compared with the theoretical surface. The test was done for two calculation methods: convolution and FFT. The results are shown in the figures below.

Gaussian Filter implemented based on Convolution method	Gaussian Filter implemented based on FFT method
Transmission characteristic curve of Gaussian filter  at cutoff of 0.08 mm	Transmission characteristic curve of Gaussian filter  at cutoff of 0.08 mm
Transmission characteristic curve of Gaussian filter implemented using the straight convolution	Transmission characteristic curve of Gaussian filter implemented using FFT
Comparison of transmission characteristic curve of Gaussian filter implemented using the straight convolution with theoretical Gaussian transmission characteristic for cutoff of 0.08 mm (absolute maximum value = 1.78%)	Comparison of transmission characteristic curve of Gaussian filter implemented using FFT with theoretical Gaussian transmission characteristic  for cutoff of 0.08 mm (absolute maximum value = 1.78%)