Summary: Some general results are derived on the chromatic properties of diffraction images for arbitrary wavefront errors. Although the theoretical results are probably of limited practical use, they are nevertheless important for understanding the behaviour of actual centroiding algorithms in real optical systems. The main results are: (1) the centre-of-gravity (CoG) of the diffraction image can only be defined as a mathematical limit, and in practice cannot be computed to reasonable accuracy and stability in presence of noise; (2) for arbitrary wavefront errors, the limiting CoG is independent of wavelength and thus without chromaticity; (3) practically useful centroiding algorithms exhibit chromatic behaviour which depends strongly on the details of the algorithm and wavefront errors. Certain limiting behaviours are identified and explained.
 

Bibtex entry for this abstract:

@UNPUBLISHED{LL:LL-064,
author = {L.~Lindegren},
title={{A} theoretical investigation of chromaticity},
institution={Lund Observatory},
year={2005},
month={November},
url={http://www.rssd.esa.int/doc_fetch.php?id=511774},
note={GAIA-CA-TN-LU-LL-064},
type={Technical note}
}