Preliminary Analysis of Effect of Random Segment Errors on Coronagraph Performance

Are we alone in the Universe is probably the most compelling science question of our generation. To answer it requires a large aperture telescope with extreme wavefront stability. To image and characterize Earth-like planets requires the ability to block 10(exp 10) of the host stars light with a 10(exp -11) stability. For an internal coronagraph, this requires correcting wavefront errors and keeping that correction stable to a few picometers rms for the duration of the science observation. This requirement places severe specifications upon the performance of the observatory, telescope and primary mirror. A key task of the AMTD project (initiated in FY12) is to define telescope level specifications traceable to science requirements and flow those specifications to the primary mirror. From a systems perspective, probably the most important question is: What is the telescope wavefront stability specification? Previously, we suggested this specification should be 10 picometers per 10 minutes; considered issues of how this specification relates to architecture, i.e. monolithic or segmented primary mirror; and asked whether it was better to have few or many segmented. This paper reviews the 10 picometers per 10 minutes specification; provides analysis related to the application of this specification to segmented apertures; and suggests that a 3 or 4 ring segmented aperture is more sensitive to segment rigid body motion that an aperture with fewer or more segments.