We present a measurement of the K -band luminosity function ( LF ) of field galaxies obtained from near-infrared imaging of a sample of 345 galaxies selected from the Stromlo-APM Redshift Survey .
The LF is reasonably well-fit over the ten magnitude range -26 \leq M _ { K } \leq - 16 by a Schechter function with parameters \alpha = -1.16 \pm 0.19 , M ^ { * } = -23.58 \pm 0.42 , \phi ^ { * } = 0.012 \pm 0.008 Mpc ^ { -3 } , assuming a Hubble constant of H _ { 0 } = 100 km s ^ { -1 } Mpc ^ { -1 } .
We have also estimated the LF for two subsets of galaxies subdivided by the equivalent width of the H \alpha emission line at \mbox { EW ( H$ \alpha$ ) } = 10 Å .
There is no significant difference in LF shape between the two samples , although there is a hint ( \sim 1 \sigma significance ) that emission line galaxies ( ELGs ) have M ^ { * } roughly one magnitude fainter than non-ELGs .
Contrary to the optical LF , there is no difference in faint-end slope \alpha between the two samples .