The effect of piston errors on the image quality of ground-based segmented mirror telescopes

The errors associated with a segmented primary mirror limit the image quality obtainable with those astronomical telescopes which employ them. It is necessary to derive the effects of segmentation errors on image quality in order to determine realistic error budgets for such telescopes. The main segmentation errors are misalignment and piston of the segments as well as figure errors. Here, the effect of segmentation on image quality is studied analytically by considering a two-ring telescope. Approximate expressions for the MTF and CIR (Central Intensity Ratio) are derived following the technique described by Dierickx (1992). It is found by numerical simulation that the results may be applied to telescopes with realistic segmentation schemes for piston errors up to ≈ 80nm.