,
The Specific filters are implemented according to general standard specifications:
ISO 11562 Gaussian Profile Filter for surface analysis
ISO 13565 Deep Valley - Gaussian Profile Filter for surface analysis.
The ISO standard ISO 11562 describes how to separate the long and short wave content of a surface profile (roughness and waviness). Here the specifications are extended to cover images as well.
The filter kernel for a Gaussian filter is expressed as:
,
where l is the cutoff wavelength.
The two dimensional Gaussian kernel is constructed by multiplication of horizontal and vertical 1D Gaussian kernels:
In the image below a Gaussian kernel is shown in a one-dimensional form by a cross section of the 2D filter kernel. Notice that the height of the kernel is normalized to 1 and the values at the beginning and end of the 1D-kernel approaches zero.
The transmission characteristic for a Gaussian filter can be obtained by Fourier transformation of the filter kernel and the damping factor as function of wavelength l can be expressed as:
This is shown graphically for a filter with a cutoff wavelength l corresponding to 51 pixels. It is seen that the damping factor is 0.5 at the cutoff wavelength.
The kernel size can be defined individually for the x and y directions. It should be selected so that a significant part of the Gaussian function is included in the kernel. This is obtained if the kernel size is 5 times or larger than the cutoff wavelength measured in pixels. It is possible to have the kernel size adjusted automatically by checking the Auto Size checkbox.
The Cutoff wavelength can be defined by physical units, e.g., nanometers and the corresponding pixel length will automatically be displayed.
The cutoff wavelength can also be chosen from the drop down menu with sizes varying from 1/1 to 1/10 of the image size. The standard prescribes a cutoff wavelength of 1/5 of the profile evaluation length.
When the "Relative Cutoff" checkbox is checked the corresponding cutoff wavelength is calculated from the chosen value in the drop down menu.
When this option is checked the filter kernel size is automatically calculated so that a significant part of the Gaussian function is included in the kernel. This means that the kerned width and length will be 1 or two pixels larger than the cutoff wave length.