Magnitude Equation Correction

A key feature of the SPM plate material is the use of an objective grating
in conjunction with two exposures of different duration. This not only
produces measureable images of both galaxies and bright reference stars,
but just as importantly, provides a means of correcting *each individual
plate* for the effects of magnitude equation. (Magnitude equation
is the undesired correlation between the position of the image center and
the magnitude of the star producing the image. It is due to inevitable
guiding errors or optical misalignments in combination with the nonlinear
response of the photographic plate.) The effectiveness of the technique
we employ to correct for magnitude equation, (which we adopt from a formulation
by Jefferys, 1962, A.J. 67), is illustrated in the figure above.
Differences between proper motions derived from our blue plate pairs
and those from our visual plate pairs are shown as a function of magnitude.
In the upper panel, the plates have not been corrected for magnitude
equation. In the lower panel, they have. For details concerning
the SPM magnitude-equation corrections, see Girard et al. 1998, A.J. 115,
855.