Characterizing the texture of a surface depends on the roughness and waviness of the surface. We can use various filtering techniques to restrict profiles at different scales.
Filtered profiles are divided into low-pass and high-pass. The roughness profile is obtained using a high-pass filter, so filtering removes long wavelength components and allows high-frequency changes to be obtained. Therefore, the roughness profile also emphasizes fine, detailed surface features. There is also a waviness profile, which is the opposite of the roughness profile and is obtained by using a low-pass filter. As the name suggests, the low-pass filter only allows low-frequency (long wavelength) components to pass through and reduces high-frequency components, which will cause the surface to appear smoother and highlight larger changes. So, when we apply low-pass and high-pass filters in sequence using the same cutoff frequency, they create a bandpass filter. This filter effectively isolates a narrow band of wavelengths around the cutoff frequency, allowing for focused analysis of surface characteristics at that specific scale.
Characteristics of Bandpass Filters
1. Asymmetry: Bandpass filters exhibit asymmetric Gaussian transmission characteristics due to the inherent process of obtaining roughness from waviness by subtraction. In contrast, conventional signal and audio processing filters are typically symmetrical in design.
2. Attenuation at the cutoff frequency: Both types of filters typically have an attenuation factor of 50% at the cutoff frequency. This means that the amplitude of the transmitted signal is reduced to one-fourth of its original value. To compensate for this reduction, the resulting data can be multiplied by four, resulting in 100% transmission at the cutoff frequency. This approach is outlined in the VDA2007 standard for detecting the dominant wavelength in a surface profile.
Filter Banks and Multiscale Analysis
Based on the above characteristics, the application of bandpass filters facilitates multiscale analysis, allowing researchers to generate a series of profiles or surfaces, each filtered at a different cutoff value. This concept can be likened to a filter bank, which breaks up the spectrum into individual bands, similar to how an audio equalizer works. Octave Definition: The number of scales in this analysis can be determined by the number of bands per octave, where an octave is defined as the interval between a wavelength and its double or half.
Cascading Symmetric Filters: By cascading symmetrical filters, second-, fourth-, or eighth-order filters can be created to provide more selective transmission curves and reduce overlap. This enhances the ability to decompose the spectrum into finer bands, thereby improving the resolution of surface texture analysis.
Summary of Bandpass Filters
In summary, bandpass filters are an essential tool in surface analysis, allowing detailed examination of surface properties at different scales. By utilizing the principles of filtering and multiscale analysis, researchers can gain a deeper understanding of the texture and properties of materials.