Statistical Measurement of Real Contact Area on the Basis of Image Intensity Histograms (Part 1) - Using Gaussian Distribution of Light Interference Image

The target contact zone was visualized using LED (light-emitting diode) polarized interferometry. Under the condition of non-lubricated static Hertzian contact between a sapphire plate and a plano-convex or a lenticular lens made of PMMA (polymethyl methacrylate), a statistical measurement of the real contact area was carried out by using image intensity histograms. The results are as follows: (I) The Gaussian distribution characteristics at the lowest region of the intensity histogram distribution were obtained, and the size of the domain as extracted through Gaussian distribution fitting was in good agreement with the theoretically obtained Hertzian contact area. By using the right and left symmetricalness of Gaussian distributions, it was possible to statistically measure the size of the domain, that is, the real contact area, in a straightforward manner. (2) It was suggested to measure the real contact area statistically by using the proposed method, which is capable of detecting gaps of the order of nanometers without requiring a threshold value for binarization. (3) In the case of a rough model surface when using a lenticular lens, the results agreed with the theoretical results for the Hertzian contact area as obtained by performing background correction. Thus, the effectiveness of measuring the real contact area by using Gaussian distribution fitting was demonstrated.