Off-axis Hartmann wavefront sensing for the GMT-Consortium Large Earth Finder (G-CLEF) red camera optics

The Hartmann test is a method used to measure the wavefront error in a focal optical system, wherein a mask with a pattern of small holes is placed at the system's aperture stop. By taking an image at a defocused plane, the differences between the ideal and real positions of the reimaged holes (called the transverse ray aberrations) can be measured, which can then be used to estimate the wavefront error. However, the Hartmann test is usually used with an on-axis field. In this paper, we present a wavefront sensing method which generalizes the classical Hartmann test for off-axis field angles and arbitrary reference wavefronts. Our method involves taking images at two defocused planes, and then using the real reimaged hole positions on both planes to estimate the trajectories of rays from the system's exit pupil, at which the reference wavefront is situated. We then propagate the rays forward from the reference wavefront to one of the two defocused planes, in order to find the ideal reimaged hole positions, from which we can compute transverse ray aberrations. We derive and solve a pair of nonlinear partial differential equations relating transverse ray aberrations to wavefront error, using Zernike decomposition and nonlinear least squares. Our method has been verified on simulated data from the 7-lens f/2.25 red camera system of the GMT-Consortium Large Earth Finder (G-CLEF), a high resolution optical echelle spectrograph which will be a first light instrument for the Giant Magellan Telescope (GMT).