Disordered spheres with extensive overlap in projection: image simulation and analysis.

This article simulates highly overlapped projections of spherical particles that are distributed randomly in space. The size and number of the features in the projections are examined as well as how these features change with particle size and concentration. First, there are discernable features in projection even when particles overlap extensively, and the size of these discernable features is the expected size of an individual particle. Second, the number of features increases with specimen thickness at a rate of t(0.543) when the specimen thickness is below a critical value and becomes independent of specimen thickness at higher thicknesses. A criterion is established for the critical thickness based on particle size and particle volume fraction. When the specimen thickness is known and smaller than the critical thickness, a single representative transmission electron microscopy (TEM) (or scanning TEM) image exhibiting extensive particle overlap can be used to determine the size and number density of the spherical particles.