Use Gaussian filter to calculate surface roughness.

PURPOSE
This app can be used to smooth data with Gaussian filter, and calculate roughness for surface metrology.

INSTALLATION
Download the file Gaussian_Filter_in_Surface Metrology.opx, and then drag-and-drop onto the Origin workspace. An icon will appear in the Apps Gallery window.
NOTE: This tool requires OriginPro.

OPERATION

1. Make a worksheet or graph active. Click Gaussian Filter in Surface Metrology app icon in Apps Gallery window.
2. In the opened dialog, set a value to Cutoff Wavelength. Click Preview button to preview the waviness.
3. Click OK button. Waviness and roughness data will be created in the worksheet.

SAMPLE OPJU FILE
This app provides a sample OPJU file. Right click on the Gaussian Filter in Surface Metrology icon in the Apps Gallery window, and choose Show Samples Folder from the short-cut menu. A folder will open. Drag-and-drop the project file GaussFilterEx.opju from the folder onto Origin. The Notes window in the project shows detailed steps.
Note: If you wish to save the OPJU after changing, it is recommended that you save to a different folder location (e.g. User Files Folder).

ALGORITHM
An approximation filter with order n=8 is used.

\(H_8( \lambda_c/\lambda ) = \left ( \frac{ \text{sin}( c_8 \pi \lambda_c/\lambda ) } { c_8 \pi \lambda_c/\lambda } \right )^8\), where \(\lambda_c\) is the cutoff wavelength, \(c_8\)=0.2275.

The discrete form is:

\(H_8( N/N_c ) = \left ( \frac{1}{2k+1} \cdot \frac{ \sin( (2k+1) \pi /N )}{ \sin( \pi/N) } \right )^8\), where k is calculated by minimizing \(| 2k+1-C_8N_c |\), and Nc is the cutoff length determined by the cutoff wavelength.

REFERENCE

1. Y.B. Yuan, T.V. Vorburger, J.F. Song, T.B. Renegar, A Simplified Realization for the Gaussian Filter in Surface Metrology, X. International Colloquium on Surfaces, Chemnitz (Germany), Jan. 31 - Feb. 02, 2000

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