Aberrations of varied line-space grazing incidence gratings in converging light beams

Analyses of the imaging properties of several designs for varied-line space gratings in converging beams of light in grazing-incidence spectrometers are presented. An explicit model is defined for the case of a plane-reflection grating intercepting light that converges and is reflected to a stigmatic point associated with the zero-order image of the grating. Smooth spatial variation of the grating constant then permits aberration correction. The aberrations are expressed as polynomials in the grating lens coordinates using power series expansions. Application of the model is illustrated in terms of aberrations experienced with the short wavelength spectrometer on the EUVE satellite. Attention is given to straight and parallel in-plane grooves, curved groove in-plane designs and off-plane grooves. Aberrations due to dispersions and misalignment are also considered.