The Las Campanas Infrared Survey. IV. The Photometric Redshift Survey and the Rest‐FrameR‐Band Galaxy Luminosity Function at 0.5 ≤ z ≤ 1.5

(Abridged) We present rest-frame R-band galaxy luminosity functionmeasurements for three different redshift ranges: 0.5<=z<=0.75, 0.75<=z<=1.0,and 1.0<=z<=1.5. Our measurements are based on photometric redshifts for ~3000H-band selected galaxies with apparent magnitudes 17<=H<=20 from the LasCampanas Infrared Survey. We show that our photometric redshifts are accuratewith an RMS dispersion between the photometric and spectroscopic redshifts of\sigma_z/(1+z)~0.08. Using galaxies identified in the Hubble Deep Field Southand Chandra Deep Field South regions, we find, respectively, that (7.3\pm 0.2)% and (16.7\pm 0.4)% of the H<=20 galaxies are at z>=1. We first demonstratethat the systematic uncertainty inherent in the luminosity functionmeasurements due to uncertainties in photometric redshifts is non-negligibleand therefore must be accounted for. We then develop a technique to correct forthis systematic error by incorporating the redshift error functions ofindividual galaxies in the luminosity function analysis. The redshift errorfunctions account for the non-gaussian characteristics of photometric redshiftuncertainties. They are the products of a convolution between the correspondingredshift likelihood functions of individual galaxies and a Gaussiandistribution function that characterizes template-mismatch variance. Wedemonstrate, based on a Monte Carlo simulation, that we are able to completelyrecover the bright end of the intrinsic galaxy luminosity function using thistechnique. Finally, we calculate the luminosity function separately for thetotal H-band selected sample and for a sub-sample of early-type galaxies thathave a best-fit spectral type of E/S0 or Sab from the photometric redshiftanalysis.Comment: 42 pages and 12 figures; Accepted for publication in the Astrophysical Journa