Determining the aberrations in a nearly diffraction-limited spectrograph

We present a method to determine the static aberrations in a nearly diffraction-limited spectrograph introduced, for example, by alignment or manufacturing errors. We consider an instrument with two stages separated by a slit or image slicer located in the intermediate focal plane. In such a spectrograph, it is not trivial to distinguish aberrations in the first stage, before the slit, from those in the second, after the slit. However, our method achieves this. Measuring these aberrations separately opens the possibility of reducing them, by realignment or other means, and thereby improving the optical performance of the instrument. The method is based on fitting models to multiple images of a point source, with controlled displacements of the source perpendicular to the slit and controlled defocuses of the second stage or the detector. Fitting models to these images allows the determination of the aberrations in both stages. Our key discovery is that the displaced and defocused images provide additional information which allows us to break the ambiguity between the two stages. We present simulations that validate the performance of the method.