Herein we derive an expression for direct determination of the geometric autocorrelation function W of a polycrystalline material from images of its grain boundary network (e.g., those delivered by orientation imaging microscopy). We also obtain an identity that relates the mean linear intercept function to a directional derivative of the geometric autocorrelation function. These formulae were applied to examine whether a widely-used formula for W, particularly in theoretical studies of attenuation of elastic waves in polycrystalline media, would be valid for the grain boundary structure of a commercial aluminum alloy. The conclusion was negative. © 2005 Elsevier B.V. All rights reserved.
Man, C. S., Paroni, R., Xiang, Y., & Kenik, E. A. (2006). On the geometric autocorrelation function of polycrystalline materials. In Journal of Computational and Applied Mathematics (Vol. 190, pp. 200–210). https://doi.org/10.1016/j.cam.2005.01.044