  A novel method for generating coded mask patterns based on Gaussian random
fields (GRF) is proposed. In contrast to traditional algorithms based on cyclic
difference sets, it is possible to construct mask patterns that encode a
predefined point spread function (PSF). The viability of this approach and the
reproducibility of the PSFs is examined, together with studies on the mean
transparency, pixel-to-pixel variance and PSF deterioration due to partial
shadowing. Sensitivity considerations suggest the construction of thresholded
realisations of Gaussian random fields (TGRF) which were subjected to the same
analyses. Special emphasis is given to ray-tracing simulations of the pattern's
performance under finite photon statistics in the observation of point sources
as well as of extended sources in comparison to random masks and the pattern
employed in the wide field imager onboard BeppoSAX. A key result is that in
contrast to traditional mask generation schemes, coded masks based on GRFs are
able to identify extended sources at accessible photon statistics. Apart from
simulating on-axis observations with varying levels of signal and background
photon counts, partial shadowing of the mask pattern in the case of off-axis
observations and the corresponding field-of-view is assessed.

Astrophysics