The Alignment and Phasing System (APS) of the Thirty Meter Telescope (TMT) is an instrument that will be responsible for aligning the primary, secondary, and tertiary mirrors of TMT. The number of mirrors, the segmentation of the primary mirror, and the size of the mirrors make alignment a complicated and challenging problem. The large size of the mirrors means that the mirror surfaces must be highly corrected in order to achieve acceptable image quality. With 492 segments in the primary mirror, APS must control a large number of degrees of freedom simultaneously, align segment edges, and correct segment surfaces. Three mirrors must be aligned, one of which (the tertiary) is a large turning flat that rotates to serve instruments at different focal stations. In this work the telescope and APS are modeled with a ray tracing simulation program. Various sets of initial conditions and alignment procedures are simulated, and results are compared to the image quality specifications for the telescope.

For every simulated alignment procedure, many trials were performed with random initial mirror errors in order to compute reliable statistics. Not all of the alignment procedures studied in this work yielded acceptable image diameters at the 90% confidence level, especially at focal stations far from APS. The procedures that use only APS measurements yield unacceptably large image diameters, while procedures that use measurements from APS and another wavefront sensor at a different location result in telescope alignments that produce acceptable image diameters at the 90% confidence level. The two-sensor procedures require M3 to rotate to point at the second sensor, which rotates the M3 surface errors relative to the rest of the telescope. Used together, measurements from the two sensors provide a better estimate of M3 errors than can be obtained from measurements with APS alone. However, APS-only procedures should be adequate for the restricted configurations of instruments available at first light. In general, APS-only procedures should also be capable of maintaining the alignment produced initially by the more complex two-sensor procedures.