These are the equations most people use when talking about depth of field, subtract the two above and you get the total depth of field. Note that as C gets smaller, so does the overall depth of field. So that's how it WAS done. Thus by knowing the pixel pitch of the camera we can estimate the physical depth of field. Stopping down the lens improves the depth of field.
Distortion is the amount the image shifts closer or further from the optical axis.
The two most common are pincushion or barrel distortion where a uniform grid is either bowed outwards or inwards. Generally it is quoted in percent across the whole field. The amount of distortion that you can tolerate in your software should be specified for a custom lens design. A contrast of 1 means modulation from full light to full dark. The modulation transfer function gives you the contrast at a particular resolution.