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The Smithsonian Hectospec Lensing Survey (SHELS) is a magnitude limitedspectroscopically complete survey for R<=21.0 covering 4 square degrees. SHELSprovides a large sample (15,513) of flux calibrated spectra. The wavelengthrange covered by the spectra allows empirical determination of k-correctionsfor the g- and r-band from z=0 to ~0.68 and 0.33, respectively, based on largesamples of spectra. We approximate the k-corrections using only two parametersin a standard way: Dn4000 and redshift. We use Dn4000 rather than the standardobserved galaxy color because Dn4000 is a redshift independent tracer of thestellar population of the galaxy. Our approximations for the k-correctionsusing Dn4000 are as good as (or better than) those based on observed galaxycolor (g-r) (sigma of the scatter is ~0.08 mag). The approximations for thek-corrections are available in an on-line calculator. Our results agree withpreviously determined analytical approximations from single stellar population(SSP) models fitted to multi-band optical and near-infrared photometry forgalaxies with a known redshift. Galaxies with the smallest Dn4000-the galaxieswith the youngest stellar populations-are always attenuated and/or containcontributions from older stellar populations. We use simple single SSP fits tothe SHELS spectra to study the influence of emission lines on the k-correction.The effects of emission lines can be ignored for rest-frame equivalent widths<~ 100 A depending on required photometric accuracy. We also provide analyticapproximations to the k-corrections determined from our model fits for z<=0.7as a function of redshift and Dn4000 for ugriz and UBVRI (sigma of the scatteris typically ~0.10 mag). Again, the approximations using Dn4000 are as good (orbetter than) those based on a suitably chosen observed galaxy color. We provideall analytical approximations in an on-line calculator.

Empirical optical k-Corrections for redshifts <= 0.7