Optical Design of a Slitless Astronomical Spectrograph with a Composite Holographic Grism

In the present work, we consider an optical design of a slitless spectrograph for an existing 0.5 m-class telescope. This design concept has a number of advantages such as compact size, simplicity, and simultaneous coverage of a large field of view. A challenge with this design is correcting aberrations caused by placing a dispersing element in a converging beam. To overcome this issue, we propose to use a composite grism, which represents a combination of a prism and a volume-phase holographic grating, the latter which is split into zones with independently optimized parameters. We demonstrate two designs of such a grism. In both designs, the spectrograph operates in the range of 450–950 nm in an F/6.8 beam and covers a field of view of 35.6′ × 7.2′. Through advanced modeling, it is shown that a composite grism having four rectangular zones with different thickness and index modulation depth of the hologram and recorded with an auxiliary deformable mirror decreases the astigmatic elongation by a factor of 85, increases the spectral resolving power by 4.4 times, and reaches R1389 while increasing the average diffraction efficiency by a factor of 1.31. If we reduce the number of zones to only two, replace the deformable mirror with two static corrector plates, and fix the hologram thickness, the corresponding performance gains still remain high: the astigmatism is reduced by a factor of 61, the spectral resolving power is up to 1.7 times higher, reaching R1067, and the efficiency is increased by a factor of 1.27. This shows that the proposed design allows the construction of a simple and compact instrument, providing high performance over the entire field of view and spectral range.