Optical systems, particularly those involving refractive elements, do not have a constant plate scale over the field, but there is a radial distortion pattern which takes the form:-
where is the distance of an object from the optical axis, as measured on the sky (in arcseconds), and is its distance from the optical axis in mm. is rarely significant. Table lists the significant terms for imaging focal stations.
Table: The Optical Distortion terms for ING Imaging stations
A popular technique for obtaining deep imaging data is ``dithering'', or subdividing the long exposure into a number of shorter exposures, and moving the telescope pointing position by a small amount (typically in the range 5 to 30 arcsec) between exposures. Image frames are then transformed to a common reference frames by appropriate resampling software, and then combined. In the presence of optical distortion about a field centre which changes on the sky between exposures a simple shift will not necessarily register the images correctly, and a proper correction for the optical distortion may be necessary. This is discussed in more detail by D. Carter in Gemini, number 39, page 14, where techniques for recombining images are also discussed. If dithering is to be employed, then it is important to chose a focal station where the distortions are small, and if a complete correction for the distortion is necessary to ensure that the image sampling is good enough for this.