The problem of monitoring the quality of concave gratings is solved by means of an optical system based on a Wyko interferometer and by computer modelling of the wavefront. The optical system transforms a plane wavefront into a toroidal one with two foci, coinciding with the meridional and sagittal foci of the grating. The aberrations of the grating result from the interference of an incident plane wavefront and a modified diffracted wavefront. The mathematical model gives an interferogram corresponding to an ideally fabricated grating. The difference between the computed and the experimental interferograms indicates that the grating has fabrication errors.
E. A. Sokolova, V. Kruizinga, D. De Bruijn, and M. Broxterman, "Computer modelling of a wavefront diffracted at a concave grating," J. Opt. Technol. 70, 600-606 (2003)