Calibration Access and Data Handbook

Procedure

The shape of the dispersed image in the cross-dispersion direction is parameterized as a function of dispersion angle $\beta$. The parameterization is a superposition of Gaussian and a Lorentzians.

This parameterization is independent of the source position in the FOV along the dispersion direction. In the cross-dispersion direction, the location of the dispersed image is shifted according to

$$\Delta XDISP = L \times \tan{\theta} \ ,$$

where $\theta$ is the component of the off-axis angle in the cross-dispersion direction, and $L$ is the distance between RGA and RFC.

The parameterizations are evaluated at each bin in $\beta$ by integration over the entire width of the bin.

The functions have the following forms. The Gaussian function is parameterized by

$$G(XDSP) = a(\beta)\ e^{-\frac{1}{2} \left (\frac{XDSP-\mu(\beta)}{\sigma(\beta)} \right)^2} \ ,$$

and the Lorentzian is parameterized by

$$L(XDSP) = \frac{1}{\pi} \frac{b(\beta)\ w(\beta)/2} {(XDSP-\nu(\beta))^2 + \frac{ w^2(\beta)}{4}} \ .$$