Shape of a Slit Image

The following equations represent the shape of a slit image,

$$x_s = f_{cam,e} \tan \left\{ \sin^{-1} \left( \frac{m_e \lambda}{\sigma... ...e + \delta \gamma_e )} - \sin (\alpha_e + \delta \alpha) \right) \right\} - x ,$$ (13)

$$y_s = f_{cam,c} \tan \left\{ \sin^{-1} \left( \frac{m_c \lambda }{ \sigma_c \cos \gamma_c} - \sin ( \alpha_c + \delta \gamma_e) \right) \right\} - y ,$$ (14)

where $(x_s, y_s)$ is the coordinates of the edge of the slit image relative to the center at ($x, y$), which are calculated by Eqs. 3 and 4. The parameters $\delta \alpha$ and $\delta \gamma_e$ are the angles corresponding to the half-width and half-length, respectively, of the slit against the echelle grating. The definitions of the other parameters are the same as those of Eqs. 3 and 4.