A new linear transfer theory and characterization method for image detectors. Part I: Theory

A new generalized linear transfer theory describing the signal and noise transfer in image detectors is presented, which can be applied to calculate the pixelwise first and second statistical moment of arbitrary experimental images including correlation between pixels. Similar to the existing notion of a point spread function describing the transfer of the first statistical moment (the average), a noise spread function is introduced to characterize the spatially resolved transfer and generation of noise (second central moment, covariance). It is also shown that previously used noise characteristics like the noise power spectrum and detection quantum efficiency, derived from plainly illuminated images, contain only partial information of the complete noise transfer.