Klosterboer and Rutledge developed a mathematical model for photothermograp
hic systems consisting of silver halide grains, silver carboxylates, develo
pment chemistry and binder. The Klosterboer-Rutledge (K-R) model incorporat
es several simplifying assumptions, the most limiting of which is the assum
ption that the spheres of influence do not overlap. This assumption effecti
vely restricts the validity of the model to low grain-number densities. The
model has now been modified to remove this restriction resulting in a more
general model that resolves the discrepancy between the Klosterboer-Rutled
ge model and the observed dependence of D-MAX, contrast and speed on grain-
number density The Klosterboer-Rutledge model also treats the spheres of in
fluence as spheres with perfectly sharp boundaries.. The generalized model
was derived with an arbitrarily shaped region of influence thereby extendin
g the validity to more realistic model films. In addition, other simplifyin
g assumptions were addressed to complete the generalization of the K-R mode
l.