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The frequency footprint of ID and 2D profiling instruments needs to be carefully considered in comparing ID surface roughness spectrum measurements made by different instruments. Contributions from orthogonal direction frequency components can not be neglected. The use of optical profiling instruments is ubiquitous in the measurement of the roughness of optical surfaces. Their ease-of-use and non-contact measurement method found widespread use in the optics industry for measuring the quality of delicate optical surfaces. Computerized digital data acquisition with these instruments allowed for quick and easy calculation of surface roughness statistics, such as root-mean-square (RMS) roughness. The computing power of the desktop computer allowed for the rapid conversion of spatial domain data into the frequency domain, enabling the application of sophisticated signal processing techniques to be applied to the analysis of surface roughness, the most powerful of which is the power spectral density (PSP) function. Application of the PSD function to surface statistics introduced the concept of 'bandwidth-limited' roughness, where the value of the RMS roughness depends critically upon the spatial frequency response of the instrument. Different instruments with different spatial frequency response characteristics give different answers when measuring the same surface.

2-D Spatial Frequency Considerations in Comparing 1D Power Spectral Density Measurements