Relation between Transmission Densities and Reflection Densities of a Photograhic Image Layer

Abstract

The author has theorecically derived the following general formula describing the relation between transmission densities and reflection densities of a photographic image layer;
R=(1-R_a)R_bT^a/1-R_aR_bT^A+S_T
where R and T are respectively reflectance and transmittance of the layer and S_T is the total light scatter at the image layer of a reflection print. Also R_a is internal reflection at the surface of the image layer, and R_b is reflectance of the base layer or the support. Usually R_b is 1.00 when the support has a white diffuse reflective coating (i.e., baryta or titanium oxide) and theoretically R_a is 0.614 when the image layer consists of gelatin or similar binders and the surface is completely flat and smooth, and A is theoretically 2.13 when reflection densities are measured by a 45°-90° densitometer.
Actually, however, in author's experiments where strips of a reversal color film and some sorts of black and white (silver image) films are, after exposing, processing and transmission-density-measurement, pasted on to a piece of baryta paper, making the surface of the image layer in optical contact with the baryta coating, and the reflection densities are measured by a “Macbeth” densitometer, A is usually lower than 2.13, e.g. 2.10-1.99, and in an exceptional case of D.T.R. prints the values are further lower, e.g. 1.76 (nega.) and 1.61 (posi.), and R_a is also usually lower than the theoretical value of 0.614, e.g. 0.52 for a color print and 0.47-0.34 for silver images, and the values are the lower for the coarser grains. This means that the internal reflection of the image layer becomes lower if the layer contains light scattering substances in it.
The higher density part of a reflection print is practically limited by incident-light-scattering property at the image layer, total value of which is S_T and consists of outer-surface scatter (S_S) and inner-layer scatter (S_I). Finally maximum reflection density (max. D_R) is defined as-logS_T.