The PPI value of open foams and its estimation using image analysis

The mean number of pores per inch (PPI value) is one of the most important geometric characteristics of cellular materials such as open or closed foams. It is defined as the number of pores (cells) along a straight test line related to the line length. Counting cells along a test line sounds very simple, but on the surface of an open foam specimen it is often hard to decide whether a cell hits the line or not. Thus, there exists no quick and safe method to estimate the PPI value from an optical image taken from the specimen's surface. In this article, we present a very efficient method of estimating the PPI value of foams from optical dark-field images of the surface of a foam sample. The method is based on the computation of the spectral density of the (two-dimensional) dark field images. It turns out that the radius of the first interference ring in the spectral density is proportional to the PPI value. The constant of proportionality can be determined from geometric models for open foams or analysis of three-dimensional images of foam samples. These techniques allow calibration of the estimation of the PPI value from the spectral density of two-dimensional dark field images.