Evaluation The following example shows that the suggested calibration scheme gives the required accuracy. Figure 4.6: Fit between star positions from sky map and the star positions found in the image. $\times$'s are the calculated positions of the stars with the rotations and optical parameters found from optimisation and the $+$'s are the positions of the stars in the image. As can be seen there are only very small deviations between the marker pairs. Figure 4.6 shows a plot of the star positions found in the image and those projected from the sky map onto the image using the optical transfer function. The overall fit between the ``image stars'' and the ``catalogue stars'' is good. To prove quantitatively that the accuracy requirement is met we have to prove that the distribution of the errors has a width corresponding to less than 0.02. This is equal to 1/3 of a pixel field-of-view. Figure 4.7: Here the two-dimensional error between the stars in the image and the projection of the star catalogue with the optimal optical parameters is plotted. Clearly the spread is essentially confined to one pixel width. The scatter plot of the errors shown in figure 4.7 shows that only a few errors excede $\pm1$ pixel. Finally we compare the histograms of the radial error with optical parameters determined from 20 identified stars and optical parameters determined from 175 identified stars. As can be seen in Figure 4.8 the error distribution becomes a bit narrower as the number of stars increase when the optical parameters are determined. The width is less than a pixel for both cases but narrower in the lower panel, and there are less outliers due to the fact that the larger number of stars is more evenly distributed over the image. Figure 4.8: Top panel: The radial error histogram of 175 stars with optical parameters determined from optimisation with 20 identified stars. Lower panel: The radial error histogram of 175 stars with optical parameters determined from optimisation with all 175 identified stars.