The results of an optical and infrared investigation of a complete sub-sample of the Leiden-Berkeley Deep Survey are presented . Optical counterparts have been identified for 69 of the 73 sources in the two Hercules fields , and redshifts obtained for 49 of them . Photometric redshifts are computed from the griK data for the remaining 21 sources . This complete sample is compared with the radio luminosity functions ( RLFs ) of Dunlop and Peacock ( 1990 ) [ 1 ] . The RLF models successfully trace the evolution of the radio sources with redshift , but there is some disagreement between the luminosity-dependence of the models and the data . The observed RLF for the lower luminosity population ( \mathop { { log } _ { 10 } } P < 26 ) shows evidence for a cut-off at lower redshifts ( z \sim 0.5 –1.5 ) than for the more powerful objects .