Alignment of a Ritchey-Chrétien telescope with primary mirror figure error guided by the rapid measurement of binodal astigmatism

Nodal aberration theory (NAT) is a vectorized aberration theory that was developed to describe systems without rotational symmetry. NAT predicts non-rotationally symmetric aberration field dependences for third-order astigmatism and in particular a "binodal" behavior in which there are two points in the field of view where astigmatism vanishes. This study serves to demonstrate an alignment technique based on an understanding of this binodal behavior using a custom Ritchey-Chretien telescope. A method involving a commercial Shack-Hartmann compact-format wavefront sensor was developed to rapidly measure densely sampled full-field displays of the telescope, which has its secondary mirror mounted on a precision hexapod to allow for repeatable control of the telescope alignment. Real ray-based simulations were carried out on a model of the telescope and were consistent with the observed experimental results for both aligned and misaligned states of the telescope. We then provide guidelines on how to interpret Fringe Zernike astigmatism full-field displays for use during optical system alignment. This method is particularly relevant for freeform systems, which often have asymmetric field dependencies for multiple aberration types including astigmatism.