Modelling and tolerance analysis of volume-phase gratings in complex dispersive units

In the present study we consider an approach to design and tolerance analysis of a spectrograph with a complex dispersive unit. The design uses a mosaic dispersive unit consisting of two VPH gratings imposed on the same substrate. This solution allows to detect spectra in two intervals - visible (375-625 nm) and near infrared (600-1000 nm) simultaneously. The modeling results show that the spectra resolution reaches 0.78 and 1.25 nm in the visible and NIR channel, respectively. The diffraction efficiency varies between 74.3% and 99.7% for the entire working range. However, the design is sensitive to the manufacturing and assembly errors. Some design parameters have influence on both the image quality and the diffraction efficiency. We developed a set of design tools allowing to include diffraction efficiency data into the tolerance analysis process. The analysis performed with these tools shown that maintenance of the nominal efficiency together with the image quality requires special control over the holographic layer parameters and also tightening of the tolerances on the lenses parameters. The developed analysis approach and tools may be useful in the future for design of spectral instruments with VPH gratings, especially when they are used to build a complex dispersive element.