THE OPTICAL REDSHIFT SURVEY .2. DERIVATION OF THE LUMINOSITY AND DIAMETER FUNCTIONS AND OF THE DENSITY FIELD

We quantify the effects of Galactic extinction on the derived luminosi ty and diameter functions and on the density field of a redshift sampl e. Galaxy magnitudes are more affected by extinction than are diameter s, although the effect on the latter is more variable from galaxy to g alaxy, making it more difficult to quantify. We develop a maximum like lihood approach to correct the luminosity function, the diameter funct ion, and the density field for extinction effects. The effects of rand om and systematic photometric errors are also investigated. The derive d density field is robust to both random and systematic magnitude erro rs as long as these are uncorrelated with position on the sky since bi ases in the derived selection function and number counts tend to cance l one another. Extinction-corrected luminosity and diameter functions are derived for several subsamples of the Optical Redshift Survey (ORS ). Extinction corrections for the diameter-limited subsamples are foun d to be unreliable, possibly due to the superposition of random and sy stematic errors. The ORS subsamples are combined using overall density scaling factors from a full-sky redshift survey of IRAS galaxies, all owing the reconstruction of the optical galaxy density field over most of the sky to 8000 km s(-1).