Setting parameters of the echelle and cross-disperser

The setting parameters of the echelle (ESP) and cross-disperser (XSP) gratings are related to the offset angles from the nominal setting with $\alpha_e =$ 67$.^{\circ }$5 and $\alpha_c =$ 24$.^{\circ }$0 for the echelle and cross-disperser, respectively. The ESP and XSP are input parameters on GUI for controlling of IRCS. The offset angles are find by fitting the positions of comparison lines on between observational data and calculated data with the Echelle simulator for IRCS. Eqs. 42 and 43 show the relations between the offset angles and ESP or XSP, which are as follows

$$\delta \alpha_e = (-1.2751 \pm 0.0019){\rm ESP} + (3026.47 \pm 12.30) ,$$ (42)

$$\delta \alpha_c = (1.0383 \pm 0.0044){\rm XSP} + (159.00 \pm 14.41) .$$ (43)

Figures 24 and 25 show the relations and residuals. The standard deviations of the residuals are about 40 arcseconds. The mismatches are within 10 pixels for the position of the spectral lines.

Figure 24: Relation between the echelle setting parameters (ESP) and offset angles from the nominal incident angle ($\alpha =$ 67$.^{\circ }$5). The lower panel shows the residuals after subtracting the offset angles of Eq. 42 obtainded by a least square fitting from measured offset angles.

Figure 25: Relation between the cross-disperser setting parameters (XSP) and offset angles from the nominal incident angle ($\alpha =$ 24$.^{\circ }$0). The lower panel shows the residuals after subtracting the offset angles of Eq. 43 obtainded by a least square fitting from measured offset angles.