Optical correlation analysis of two-phase micrographs.

The application of coherent optical techniques to the study of correlations in the detailed structure of electron (or light) micrographs was considered for the case when the structure appears to be random. A statistical autocorrelation analysis was made for a random array of transparent disks on an opaque background, relating the radii of the central and first autocorrelation maxima to the radius and mean separation, respectively, of the disks. Experimental determinations of the two-dimensional autocorrelation function were made both for arrays of disks and ellipses. In each case, the shape of the central maximum was similar to the shape of the objects (when all had the same shape and orientation). In addition, the shape of the first autocorrelation maximum was dependent only upon the distribution of centroids of the objects in the array and exhibited the proper asymmetry when the mean separation of centroids differed for the two dimensions. In this latter case, a rectangular first autocorrelation maximum was observed, implying separability of the two-dimensional autocorrelation function and providing a technique for direct quantitative determinations of the mean separations.