Sometimes it is useful to visualize an optical design and calculate the optical quality. A free program for doing that is BEAM4 from

I had used an earlier test version, but now it is available as a free version and more user friendly, so I gave it a try.

I chose the Czerny spectrograph example and modified it to calculate spot diagrams.

first result, optimized for resolution
quick spot diagram, only a few rays calculated, showing nicely the astigmatism of this design (focus optimized for spectral resolution)

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