A theoretical limit on the number of effective pixels that can be optically resolved on a non-planar subject

In normal imaging systems, the depth of field is inversely-proportional to the lens aperture. If we assume the system is diffraction limited, then the maximum resolution (i.e. pixels per mm) is proportional to the lens aperture. Thus there is a tradeoff between depth of field and resolution. This tradeoff creates an upper limit on the number of pixels that can be resolved on a nonplanar subject. This paper presents the theoretical limit on the number of pixels. The derivations of the limit show that the limit is only a function of the subject size and depth. The subject distance, focal length, and sensor size do not matter. For small subjects, the limit is well below the capabilities of modern imaging systems. For example, a subject 15 cm wide and 10cm deep can only be imaged with 300,000 pixels even though sensors with 10 times that many pixels are readily available. The resulting limit has obvious applications in machine vision, particularly when specifying optics and imaging sensors. Experimental results are provided to validate the main result of the paper.