We present the definition of a new quantity, the pupil difference probability density (PDPD), and describe its use in the study of imaging systems. Formally, the PDPD is defined as the probability density that two random points over the pupil, with given separation, have a given wavefront error difference. Under this definition, the PDPD is the one-dimensional Fourier transform, of the error difference variable, of the OTF. Using the PDPD, we show that it is possible to understand how certain sources of error affect the OTF. Further, given its geometric interpretation, this formalism is useful for finding accurate analytic approximations to the OTF.