Given a sufficient number of reference stars, measured to high accuracy and evenly distributed over the whole plate, it is possible to supplement the normal 4- and 6-coefficient linear solutions with one in which the plate centre and/or the radial distortion are determined automatically.
The option of fitting the plate centre (i.e. the of the centre of projection, which a priori may well not be known to adequate accuracy) is selected simply by beginning the plate centre record with the tilde character ’~’ (meaning “approximately”):
| ~ 12 53 00.0 -42 00 00 B1950.0 1974.5 * Approx plate centre |
Even though the plate centre is to be adjusted, it is advisable to start off with the best available estimate. The difference between this and the actual centre of the projection pattern is what textbooks refer to as tilt. Determination of the tilt is most secure where the radial distortion is pronounced. Schmidt astrometry is relatively insensitive to tilt, and attempting to fit the plate centre may be unwise unless the reference stars are numerous and well-distributed.
A further option (intended for investigating the properties of previously unmodelled telescopes rather than for routine use), is to fit the radial distortion coefficient. This is selected by prefixing the telescope type record with the tilde character ’~’:
| ~ AAT3 * Guess |
Tilt and distortion may be fitted simultaneously. Neither adjustment will be attempted unless at least 10 reference stars are supplied. If the fit proves to be unacceptably ill-conditioned, or if the adjustments are unrealistically large, the fit is rejected.
Though no check is made, it is clearly unwise to request that the tilt and distortion be included in the model if the reduction is not taking place in observed coordinates (see the previous section).