Figure 1. Comparison of ISMAT with commercial software packages for a
Gaussian Filter
In addition, the Gaussian and 2RC
Filters of the ISMAT were validated based on their transmission
characteristics. Simulated sinusoidal profiles of gradually increasing
wavelengths with point spacing of 0.5 µm and traversing length of 11200
for testing the long cutoff, and with point spacing of 0.05 µm and
11200 data points for testing the short cutoff are being used.
The sinusoid profiles are inputted into Gaussian or 2RC filter
subroutine using 0.8 mm for long cutoff wavelength and 0.8 µm for short
cutoff wavelength. The ratio of the Rt parameter of a roughness profile
and the Pt parameter of a primary profile plotted against the
wavelength yields the filter transmission characteristic curve.
Transmission curve is then compared with a theoretical curve. Test was
done for several calculation methods: convolution, Fast Gaussian,
FFT, and recursive method. The results are shown in
figure 2, 3, 4, and 5.
| Figure 2. Comparison of
transmission characteristic curve of Gaussian filter
implemented using the straight convolution, FFT, and a Fast Gaussian
filtering technique [11] with a theoretical transmission characteristic
curve for long cutoff wavelength |
Figure 3. Comparison of
transmission characteristic curve of Gaussian filter implemented using
convolution with theoretical transmission characteristic curve for
short cutoff wavelength
|
| Figure 4. Comparison of
transmission characteristic curve of 2RC
filter implemented using convolution and recursive method with
theoretical transmission
characteristic curve for the roughness long cutoff wavelength |
