Applications of the Lambert W function to analyze digital camera sensors

Abstract

The Lambert W function is applied via Maple to analyze the operation of the modern digital camera sensors. The Lambert W function had been applied previously to understand the functioning of diodes and solar cells. The parallelism between the physics of solar cells and digital camera sensors will be exploited. Digital camera sensors use p-n photodiodes and such photodiodes can be studied using the Lambert W function. At general, the bulk transformation of light into photocurrent is described by an equivalent circuit which determines a dynamical equation to be solved using the Lambert W function. Specifically, in a camera senor, the precise measurement of light intensity by filtering through color filters is able to create a measurable photocurrent that is proportional to image point intensity; and such photocurrent is given in terms of the Lambert W function. It is claimed that the drift between neighboring photocells at long wavelengths affects the ability to resolve an image and such drift can be represented effectively using the Lambert W function. Also is conjectured that the recombination of charge carries in the digital sensors is connected to the notion of “noise” in photography and such “noise” could be described by certain combinations of Lambert W functions. Finally, it is suggested that the notion of bias, and varying the width of the depletion zone, has a relationship to the ISO “sped· of the camera sensor; and such relationship could be described using Lambert W functions.