The Measurement of Spatially Random Phenomena

The assay of material is of importance in numerous branches of science and industry. In many applications the analyte is randomly distributed in the matrix of the sample. The design of a system to assay such a sample is complicated by the difficulty of assessing the effect of the spatial randomness of the analyte. Traditionally, the designer has had to choose from among a large number of conceivable designs without precise knowledge of the sensitivity of each design to the random spatial distribution of the analyte. Costly and time-consuming trial and error in the design process has usually been unavoidable. In the present paper a performance criterion is developed which allows analytical comparison of alternative proposed designs. The criterion rigorously accounts for all possible spatial distributions of the analyte. The problem is formulated in terms of geometrical properties of convex sets, which leads to an efficient computerizable algorithm for evaluating the performance criterion, even for complex ...