Optical counterparts for 70,000 radio sources: APM identifications for the first radio survey

We describe a program to identify optical counterparts to radio sources from the VLA FIRST survey using the Cambridge APM scans of the POSS-I plates. We use radio observations covering 4150 deg(2) of the north Galactic cap to a 20 cm flux density threshold of 1.0 mJy; the 382,892 sources detected all have positional uncertainties of <1 '' (radius of 90% confidence). Our description of the APM catalog, derived from the 148 POSS-I O and E plates covering this region, includes an assessment of its astrometric and photometric accuracy, a photometric recalibration using the Minnesota APS catalog, a discussion of the classification algorithm, and quantitative tests of the catalog's reliability and completeness. We go on to show how the use of FIRST sources as astrometric standards allows us to improve the absolute astrometry of the POSS plates by nearly an order of magnitude to -0.'' 15 rms. Matching the radio and optical catalogs yields counterparts for over 70,000 radio sources; we include detailed discussions of the reliability and completeness of these identifications as a function of optical and radio morphology, optical magnitude and color, and radio flux density. An analysis of the problem of radio sources with complex morphologies (e.g., double-lobed radio galaxies) is included. We conclude with a brief discussion of the source classes represented among the radio sources with identified counterparts.