Misfit of rigid tools and interferometer subapertures on off-axis aspheric mirror segments

Rigid tools can confer advantages at certain stages of manufacturing off-axis mirror segments, but the misfit due to surface asphericity and asymmetry poses constraints on their application. Types of misfit are classified and, using least squares, the best-fit tool forms with different distances from the pole of the parent asphere are calculated. The outer mirror segment for the European extremely large telescope is taken as a case-study, assuming a rigid tool size of 150 mm. A simple independent approximation validates the calculation. A close parallel is wavefront misfit in subaperture interferometry, which is also considered. © 2011 Society of Photo-Optical Instrumentation Engineers (SPIE).