There isn't a single, inherent "exact" cut-off wavelength for any Gaussian filter; rather, the cut-off wavelength is a parameter chosen based on the specific application. However, certain values are widely recommended and used, particularly in surface texture analysis.
Recommended Cut-off Wavelength Values
Based on common standards and practices, several specific cut-off wavelengths are frequently recommended when applying a Gaussian filter to separate surface features (like roughness from waviness).
The recommended cut-off wavelength values provided are:
- 0.25 mm
- 0.8 mm
- 2.5 mm
These values serve as standard choices depending on the scale of the surface features being analyzed.
Understanding Cut-off Wavelength
In the context of filtering surface profiles or other signals, the cut-off wavelength (often denoted by λc) defines the threshold between components of different spatial frequencies.
- Purpose: A filter with a specific cut-off wavelength allows features larger than the cut-off to pass through (long wavelengths) while attenuating features smaller than the cut-off (short wavelengths), or vice versa.
- Gaussian Filter: The Gaussian filter uses a weighting function based on the Gaussian bell curve. It is known for providing a good balance between separating features and minimizing phase distortion. The cut-off wavelength for a Gaussian filter is typically defined as the wavelength where the filter transmits 50% of the amplitude of a sinusoidal signal.
Practical Application of Recommended Values
The choice of cut-off wavelength depends heavily on the nature of the surface being measured and the type of texture information required (e.g., roughness, waviness).
| Recommended Cut-off Wavelength | Typical Application | What it Filters Out (Roughly) |
|---|---|---|
| 0.25 mm | Analyzing finer surface textures | Very fine irregularities |
| 0.8 mm | Standard surface roughness measurement | Standard roughness components |
| 2.5 mm | Analyzing coarser textures or surface waviness | Larger texture features |
Choosing the appropriate cut-off is crucial for obtaining meaningful and comparable results in surface texture analysis according to standards like ISO 16610.
These recommended values (0.25 mm, 0.8 mm, and 2.5 mm) represent common industry practices for setting the parameter of a Gaussian filter when analyzing surface profiles.
