The plate overlay tool derives a virtual plate using either a four parameter or six parameter plate solution. The four parameter model adjusts for translation, rotation, and relative scale, while the six parameter model adjusts the relative scales along the x and y axis independently. Formally the six parameter model requires at least three common reference stars in each plate, but in order to avoid over-constraining the plate solution, you should not apply the six parameter model with fewer than five reference stars.
Ideally the object under scientific investigation should not enter into the virtual-plate solution. Only the mapping functions should be applied to the object, so that any apparent motion of the object with respect to the reference frame will not be identified simply as a large residual. Unfortunately, some observers may find it necessary to include the science target in the solution if in fact one or more of the reference stars must be disqualified, as would be necessary if the reference star were a binary.
Applying the six parameter model to a plate with fewer than five reference stars might over constrain the solution, making it vulnerable to contamination from unknown and unaccounted for proper motion or parallax in one or more of the reference stars. Such motion would be absorbed undesirably into the solution. Clearly, if the mapping of the individual plates onto the virtual plate is flawed in any way, the scientific objectives will be compromised.
When the six parameter solution is suitably constrained, it noticeably enhances the overall quality of the plate overlays. Indeed, the known tendency of HST's magnification to oscillate or "breathe" by small amounts during an orbit alters FGS3's plate scale by different amounts in the x and y directions. The same effect occurs on longer time scales, owing to the continual desorption of the optical telescope assembly and consequent refocusing every several months. Therefore the focus of HST varies with time, resulting in different relative scales along the x and y axes among a set of astrometric visits. A six-parameter model is most appropriate in such situations, but again, it can be risky if fewer than five reference stars are available.
The four-parameter model has so far been the workhorse for obtaining FGS astrometric plate solutions because the reference fields around the scientific targets have frequently been too sparse for a six-parameter model. Formally only two reference stars are needed to apply the four-parameter model, but obviously such a solution is highly constrained and vulnerable to motions of the reference stars and errors in their measured positions.
It is not uncommon for an observer to delete at least one reference star from the plate solution for a variety of reasons. For example, the star could be double, fooling the FGS into locking onto one component on the x-axis and the other on the y-axis during one visit, then some other combination on subsequent visits. Or, the star might be significantly fainter than anticipated, preventing the FGS from reliably acquiring it in FineLock.
Another frequently encountered problem with the plate solutions is for one or more of the reference stars to display an unanticipated but detectable proper motion or parallax. If the star field is observed frequently enough over a sufficiently long period of time, at various HST roll angles to optimize sensitivity to proper motion, then these motions can usually be determined with acceptable accuracy. If so, the measured position of such an object at a given epoch can be adjusted for its apparent motion before the data from that visit are mapped onto the master plate. Unfortunately, corrections of this nature are usually only possible if the observer has the luxury of an adequate number of otherwise well behaved reference stars. Figure 13.3 shows the residuals from a four-parameter plate solution for two visits to a standard astrometric field. The agreement is all the more impressive in this case because HST rolled by more than 25 mas in one of the visits during the observing sequence.
When the plate overlay software becomes publicly available, it will be announced and documented on the STScI web pages.
Figure 13.3: Residuals of Two Virtual Plates Overlaid with a Four-Parameter Plate Solution