Geometrical calibration

The task of mapping the field-of-view of each pixel to the observed object is called geometrical calibration. As this topic is extensively covered in Gustavsson [2000, Chapter 4-5] it will only be briefly touched upon here. First a set of star-images are obtained for the viewing direction under consideration. Then the positions of the stars are calculated from a star-catalogue (Bright Star Catalogue (BSC))^4.1and mapped down to the image coordinates. Then preferably more than 100 stars, evenly distributed across the image, are identified. Finally a transfer function is adjusted so that the calculated and actual positions of the stars overlap. This transfer function is then used for calculating the field-of-view of each pixel of the CCD. Table 4.6 displays the fields-of-view of the ALIS imagers as calculated from the transfer-function.

Table 4.6: Measured fields-of-view for the ALIS imagers. These values are obtained from the geometrical calibration procedure using star images. Note that the CCD is a square inscribed in a circular field-of-view. Also note that the fields-of-view are calculated in a spherical geometry.

	field-of-view
ccdcam	$\mathit{FoV_{o}}$	$\mathit{FoV_{x}}$		$\mathit{FoV_{y}}$
1	$90.4^{\circ}$	$59.3^{\circ}$	$\times$	$60.5^{\circ}$
$\langle \mathit{FoV_{}} \rangle$	$1.2^{\circ}$	$1.1^{\circ}$		$0.9^{\circ}$
2	$71.8^{\circ}$	$48.5^{\circ}$	$\times$	$48.7^{\circ}$
$\langle \mathit{FoV_{}} \rangle$	$0.2^{\circ}$	$0.1^{\circ}$		$0.1^{\circ}$
3	$71.7^{\circ}$	$48.8^{\circ}$	$\times$	$48.8^{\circ}$
$\langle \mathit{FoV_{}} \rangle$	$0.1^{\circ}$	$0.6^{\circ}$		$0.3^{\circ}$
4	$72.2^{\circ}$	$49.9^{\circ}$	$\times$	$49.6^{\circ}$
$\langle \mathit{FoV_{}} \rangle$	$0.1^{\circ}$	$0.1^{\circ}$		$0.1^{\circ}$
5	$71.8^{\circ}$	$49.6^{\circ}$	$\times$	$49.1^{\circ}$
$\langle \mathit{FoV_{}} \rangle$	$0.2^{\circ}$	$0.2^{\circ}$		$0.1^{\circ}$
6	$102.1^{\circ}$	$66.1^{\circ}$	$\times$	$68.6^{\circ}$
$\langle \mathit{FoV_{}} \rangle$	$1.1^{\circ}$	$0.4^{\circ}$		$0.2^{\circ}$

The optics used for the ALIS imagers is aberration limited, rather than diffraction limited. The effect of this aberration limited focus is shown in Figure 4.5.

Figure 4.5: A typical ALIS background image with a selection of magnified stars displaying the variation of the point spread function (PSF) over the image. [after Gustavsson, 2000, Figure 5.6].

As can be seen the point spread function varies over the image plane, from 1-2 pixels in the centre to a few pixels at the edges. This will smoothen and widen images of sharp and narrow structures, in particular in the corners of the images. At the present no attempts are made to deblur/sharpen the effect of the PSF [Gustavsson, 2000, pp. 46-47].