Calibration of scanners and cameras usually involves measuring the point spread function (PSF). When edge data is used to measure the PSF, the differentiation step amplifies the noise. A parametric fit of the functional form of the edge spread function (ESF) directly to the measured edge data is proposed to eliminate this. Experiments used to test this method show that the Cauchy functional form fits better than the Gaussian or other forms tried. The effect of using a functional form of the PSF that differs from the true PSF is explored by considering bilevel images formed by thresholding. The amount of mismatch seen can be related to the difference between the respective kurtosis factors.
Barney Smith, Elisa H.. (2006). "PSF Estimation by Gradient Descent Fit to the ESF". Proceedings of SPIE-IS&T Electronic Imaging, 6059. http://dx.doi.org/10.1117/12.643071