We present the optical principle of a white-pupil collimator made up of two mirrors with unequal focal lengths. Analytic formulas for third-order aberrations are derived and compared with the results of ray-tracing experiments. It is shown that the image quality is good if the second mirror has a suitable conic coefficient and the F ratio is not too small. Furthermore, third-order coma and astigmatism can be zeroed simultaneously if the angles are also appropriately selected. When implemented in high-resolution echelle spectrographs, this design permits smaller cross dispersers and cameras, with considerable savings in cost.
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