The method employed by Streifer and Stark to calculate toner pile height due to the development to field neutralization of weak sinusoidal image patterns superposed on a solid area is extended to cover realistic development systems by applying more general boundary conditions on the free surface of the toner layer. We found that as long as the altered boundary conditions do not vary spatially, the effects of the new boundary conditions are propagated via a single parameter: the toner pile height corresponding to a solid area part of the image. This finding allows us to extend the realm of the analysis to the case of partial neutralization, provided some conditions are met by the development process. A theoretical development modulation transfer function (MTF) is derived from the toner pile height calculations. The variation of this MTF as a function of the solid area toner pile height is exploited to obtain the theoretical MTFs for the development of multiple layers in color xerography.
S. Jeyadev, H. M. Stark, "Modulation Transfer Function for Development to Complete Field Neutralization" in Journal of Imaging Science and Technology, 1996, pp 369 - 372, https://doi.org/10.2352/J.ImagingSci.Technol.1996.40.4.art00017