Figure 3.

Numerical calculation (blue solid line) of $J_{\overline{\mathrm{\Omega }},\overline{\mathrm{\Omega }}}$ and the corresponding Voigt based approximation (dashed grey line). A finely pixelated detector with $N_p=5000$ pixels was assumed. The width of the response function of the dispersive element was taken as ${\gamma }_{\mathrm{disp}}=8.4\mathrm{nm}$ and the relay lens assumed to have a numerical aperture of $\mathrm{NA}=0.01$ such that the spectrometer is diffraction limited. See Table 1 for other simulation parameters. Individual contributions to the Voigt approximation are shown by the dot-dashed light blue, green and purple lines corresponding to Eqs (37) (see also text), (51) and (55) respectively.