The optical redshift survey. II. Derivation of the luminosity and diameter functions and of the density field

We quantify the effects of Galactic extinction on the derived luminosity and diameter functions and on the density field of a redshift sample. Galaxy magnitudes are more affected by extinction than are diameters, although the effect on the latter is more variable from galaxy to galaxy, making it more difficult to quantify. We develop a maximum likelihood approach to correct the luminosity function, the diameter function, and the density field for extinction effects. The effects of random and systematic photometric errors are also investigated. The derived density field is robust to both random and systematic magnitude errors as long as these are uncorrelated with position on the sky since biases in the derived selection function and number counts tend to cancel 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 found to be unreliable, possibly due to the superposition of random and systematic errors. The ORS subsamples are combined using overall density scaling factors from a full-sky redshift survey of IRAS galaxies, allowing the reconstruction of the optical galaxy density field over most of the sky to 8000 km s^-1.