Calibration Access and Data Handbook

Procedure

For this calculation the grating assembly is approximated by an imaginary grating placed at the center of the grating assembly at point $\vec{G}$.

The angle of incidence on the facets of the gratings

$$\gamma_0 = \alpha_0 + \delta \ ,$$

where $\delta$ is the blaze angle, which is available from CCF MiscData, item BLAZE_ANGLE, and $\alpha_0$ is the angle of incidence measured from the grating surface for an on axis source. $\alpha_0$ is available from CCF MiscData, item INCIDENCE_ANGLE, or from CCF Lincoord, item G_ALPHA.

Since the RGA may be rotated around $\rm R_y$, the actual angle of incidence for an on-axis source is

$$\alpha'_0 = \alpha_0 + G_{\rm Ry} \ .$$

$G_{\rm Ry}$ is stored in CCF Lincoord, item G_RY.

With an off-axis source at given angular pair $(\theta, \phi)$ in the TELCOORD reference frame, the component along the RGS dispersion direction is

$$\phi' = -\theta\cos\phi \ ,$$

and the angle of incidence on the gratings is given by

$$\alpha = \alpha'_0 + \frac{F}{2 R \cos\gamma_0} \, \phi' \ ,$$ (20)

and The distance between $\vec{G}$ and a virtual focus of the telescope $L$ is

$$L = 2 R \,\cos \left ( \gamma_0 + \frac{F}{2 R \cos\gamma_0}\,\phi' \right ) \ .$$ (21)

The hardware related dispersion angle $\beta$ is calculated from the ray from point $\vec{G}$ to the detector coordinates of the event $\vec{P}(DETX,DETY)$, as

$$\beta = \tan^{-1} \left [ \frac{-\left ( \vec{P} - \vec{G}... ...t ( \vec{P} - \vec{G} \right ) _{\rm x}} \right ] - \alpha'_0$$ (22)

with the radius of the Rowland circle $R$ available from CCF MiscData item ROWLAND.

And finally the defocus value $\Delta x$ is defined as X-component of the distance between $\vec{P}$ and the intersection of the ray $\bar{GP}$ with the Rowland circle, and is calculated by

$$\begin{array}{ll} \Delta x = & \left ( \vec{P} - \vec{G} \... ...\frac{\sin\alpha}{\sin\beta} + \Delta x_{\rm offs} \end{array}$$ (23)

The first component is the distance between detector bin and mid-point of the grating assembly along the TELCOORD X-axis; the second item is the distance between point G and the intersection of the dispersed ray with the Rowland circle; the third component is a correction term for a shift of the Rowland circle from it nominal geometry due to a shift of point G during the integrations. $F$ is the focal length of the telescope, which is available from CCF MiscData, item FOCAL_LENGTH, and

$$F' = F\cos\phi'$$ (24)

is the X-component of the shift of the focus due to off-axis sources.

$\Delta x_{\rm offs}$ is a linear offset that is taken from the CCF LINESPREADFUNC, table FIGURE. This is a convenient quantity to vary the defocus, without a distortion of the wavelength scale.