## Abstract

Formulations for specular optical density as a function of incident x-ray intensity are shown to be inadequate, theoretically and compared with available data. Approximations assuming low intensities, grain densities, or energies yield significant error in typical emulsions. Unjustifiable simplifications limit analysis and consequent results. The avoidance of assumptions leads to models for rough and smooth emulsion surfaces, which correspond to Kodak 101-01 and DEF-392 emulsion types. The self-consistent use of spherical grains yields scaling that is dependent on emulsion roughness. We obtained improvement over standard formulations, avoiding the empirical character of earlier models and associated parameterization. The correlation of grain locations and occluded emulsion area is approximated within monolayer depths but neglected between layers. Effects of the incident angle from a broad source, scattering, and photoelectrons are considered. The models presented herein apply to the vacuum UV and x-ray energies from 9 eV to 20 keV and may be preferred over alternative models at lower energies, densities greater than unity, emulsions with high grain fractions, or where interpolation over energy ranges is desired. Error contributions may be dominated by intensity statistics or densitometry statistics. Both are inadequate in medium-density regimes. We have derived estimates including pseudo-binomial grain development statistics, using a summation over layers.

© 1993 Optical Society of America

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