This article and the following one will discuss the effect on resolution of digitizing a continuous optical image.
The sampling process carried out by the sensor results in digital values corresponding to an intensity at each pixel’s location. These so-called Data Numbers are stored ideally as-is in the raw file and are proportional to infinitesimal point samples of a new continuous image: the optical image smoothed by the characteristics of the pixels’ effective active area, known as the pixel aperture function.
Figure 1. Simulated Pixel Aperture Function of a 4um pitch Back Side Illuminated pixel in isolation. Note diffusion beyond the -2/+2um theoretical pixel boundaries suggested by pitch.
Physicists and mathematicians over the last few centuries have spent a lot of their time studying light and electrons, the key ingredients of digital photography. In so doing they have left us with a wealth of theories to explain their behavior in nature and in our equipment. In this article I will describe how to simulate the information generated by a uniformly illuminated imaging system using open source Octave (or equivalently Matlab) utilizing some of these theories.
Since as you will see the simulations are incredibly (to me) accurate, understanding how the simulator works goes a long way in explaining the inner workings of a digital sensor at its lowest levels; and simulated data can be used to further our understanding of photographic science without having to run down the shutter count of our favorite SLRs. This approach is usually referred to as Monte Carlo simulation.
