A New Density Function Based on the Poisson Distribution for the Characteristic Curve and Linear at Very Low Densities

Abstract

It is suggested that densitometric data be represented in terms of the density function

$\begin{array}{lll}\Omega \hfill & =\hfill & log(\frac{1}{\text{T}}-1+\delta )\hfill \\ \hfill & =\hfill & log\omega \hfill \end{array}$

which differs from the corresponding Seidel (Baker-Sampson) function² by the addition of the constant δ Use of log ω has distinct advantages if density measurements have to be made in the toe part of the H and D curve The constant δ bears a definite relationship to the inertia threshold The fact that the existence of the inertia threshold can be taken into account considerably improves the linearity of the function at very low densities Relationship of the suggested density function to the characteristic curve based upon a Poisson distribution is discussed and a practical formula for calculating approximate values of δ will be given. Linearization of the H and D curve is possible down to densities where deviations from Beer's law for reduced silver set in, and except for such photometric effects the new characteristic curve can be extrapolated down to inertia threshold Although use of log ω instead of simple density or the Seidel density may be cumbersome in routine applications, it should become an important tool to the research man using the toe part of the H and D curve for measurment of densities.