Finite-length line-spread function

In this paper we derive a formula for calculating the point-spread function (PSF) of a rotationally symmetric imaging system from measurements along a line through the image of an arbitrary separable input object. An important special case of this formula is when the input object is a finite-length slit. The set of measurements in this case is called the finite-length line-spread function (FLSF). The FLSF differs from the infinite-length line-spread function (LSF) only in the assumed finite length of the line that is input into the system. This difference between the FLSF and the LSF becomes important for imaging systems for which the PSF is large in extent and in which the isoplanatic patch is relatively small. The usual LSF-to-PSF conversion formulas cannot be applied accurately to such systems.