Uncertainty of wavelength limitation due to stylus tip radius for engineering surface texture based on wavelength and amplitude by FFT

In contact stylus measurement, profiles are affected by the radius of the stylus tip. This fact has been presented in the annex of ISO 3274:1996 as the uncertainty of wavelength limitation due to the stylus on a chart of the transmission characteristics. In this standard, however, the logical process to introduce the wavelength limitation has not been mentioned. This paper reveals that the gain of transmission is given by the enveloping sinusoidal curves of Fourier series with a contact stylus tip. The relationship between wavelength and amplitude for this analysis is introduced by applying power law index to Fractal-like or Markov-process-like power spectral density function of the surface asperities. The results presented in this paper are very close to the wavelength limitation shown in ISO 3274.