WIYN Open Cluster Study. XVII. Astrometry and membership to V=21 in NGC 188

We present techniques for obtaining precision astrometry using old photographic plates from assorted large-aperture reflectors in combination with recent CCD Mosaic Imager frames. At the core of this approach is a transformation of plate/CCD coordinates into a previously constructed astrometric reference frame around the open cluster NGC 188. This allows us to calibrate independently the optical field angle distortion for all telescopes and field correctors used in this study. Particular attention is paid to computing the differential color refraction, which has a marked effect in the case of NGC 188 as a result of the large zenith distances at which this cluster has been observed. Our primary result is a new catalog of proper motions and positions for 7812 objects down to V = 21 in the 0.75 deg(2) area around NGC 188. The precision for well-measured stars is 0.15 mas yr(-1) for proper motions and 2 mas for positions on the system of the Tycho-2 catalog. In total, 1490 stars have proper-motion membership probabilities P-mu greater than or equal to 10%. The sum of membership probabilities indicates that NGC 188 contains similar to 1050 stars down to V = 21. Comprehensive lists of the candidate blue stragglers and red giant stars substantially enlarge the number of such stars known in NGC 188. We have also obtained a small correction to the proper motions from the mean motion'' of background galaxies. Thus, the absolute proper motion of NGC 188 is labs mu(x)(abs) = - 2.56 +/- 0.2 and mu(y)(abs) = +0.18 +/- 0.2 mas yr(-1).