Section 7.2.3.3. Geometric distortion

Geometric distortions arise in the optical coupling of the system. If they are stable, the distortions can be mapped and corrected. Long-term stability is possible for a phosphor fibre-optically coupled directly to a CCD, since all distortions are mechanically fixed. Intensifier-based systems are subject to changes in magnetic and electric fields, hence stability is more of a problem.

Geometric distortions may be either continuous or discontinuous. Fibre optics often have shear between adjacent bundles of fibres. In this defect, one group of fibres will not run parallel to a neighbouring group, causing a discontinuity in the image. Rather than dealing with such discontinuities, tapers with low shear (less than one pixel maximum) are usually specified. Even with low shear, there is a continuous distortion (several per cent), which varies slowly over the face of the detector. Such distortion is inevitable, as the temperature profile cannot be precisely controlled in the large block of glass comprising the fibre optic as it is processed. To map this distortion, an image is taken of a regular array of spots. Such an image can be made by illuminating a shadow mask of equally spaced holes with a flood field of X-rays. Holes 75 µm in diameter spaced on a 1 × 1 mm square grid are adequate for mapping the distortions present in most fibre-optic tapers. Such masks have been lithographically fabricated in an X-ray opaque material, such as 50 µm tungsten foil (Barna et al., 1999).

Given an image produced with this X-ray mask, the displacement map for every pixel in the original image can be computed as follows: find the centroid of each mask spot and its displacement relative to an ideal lattice. The array of spot positions and associated displacements can then be interpolated to find the displacement for each pixel in the original distorted image.

The displacement of a pixel from original to corrected image will not in general be a whole number. Rather, the intensity of a pixel will be distributed in a local neighbourhood of pixels in the corrected image centred about the position given in the displacement map. The size of the neighbourhood depends on the local dilation or contraction of the image; typically the intensity will be distributed in one to nine pixels. This distribution procedure yields a smooth intensity mapping. Applying corrections to mask images that have been arbitrarily displaced shows that the distortion correction algorithm is good to better than 0.25 pixels (Barna et al., 1999).

The geometrical distortion is tied intimately to the correction of the response of the system (see below). Since distortions produce local regions of dilation or contraction of the image, pixels will, in general, correspond to varying sizes. This variation must be included in the flat-field calibration.