SHELS ( Smithsonian Hectospec Lensing Survey ) is a dense redshift survey covering a 4 square degree region to a limiting R = 20.6 .
In the construction of the galaxy catalog and in the acquisition of spectroscopic targets , we paid careful attention to the survey completeness for lower surface brightness dwarf galaxies .
Thus , although the survey covers a small area , it is a robust basis for computation of the slope of the faint end of the galaxy luminosity function to a limiting M _ { R } = -13.3 + 5 logh .
We calculate the faint end slope in the R-band for the subset of SHELS galaxies with redshifts in the range 0.02 \leq z < 0.1 , SHELS _ { 0.1 } .
This sample contains 532 galaxies with R < 20.6 and with a median surface brightness within the half light radius of SB _ { 50 ,R } = 21.82 mag arcsec ^ { -2 } .
We used this sample to make one of the few direct measurements of the dependence of the faint end of the galaxy luminosity function on surface brightness .
For the sample as a whole the faint end slope , \alpha = -1.31 \pm 0.04 , is consistent with both the Blanton et al .
( 2005b ) analysis of the SDSS and the Liu et al .
( 2008 ) analysis of the COSMOS field .
This consistency is impressive given the very different approaches of these three surveys .
A magnitude limited sample of 135 galaxies with optical spectroscopic redshifts with mean half-light surface brightness , SB _ { 50 ,R } \geq 22.5 mag arcsec ^ { -2 } is unique to SHELS _ { 0.1 } .
The faint end slope is \alpha _ { 22.5 } = -1.52 \pm 0.16 .
SHELS _ { 0.1 } shows that lower surface brightness objects dominate the faint end slope of the luminosity function in the field , underscoring the importance of surface brightness limits in evaluating measurements of the faint end slope and its evolution .