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.