  Photometric measurements show that as a group nearby type Ia supernovae
follow similar lightcurves and reach similar peak magnitudes Thus, these
supernovae can serve as standard candles or calibrated candles at cosmological
distances. Magnitudes of local and distant supernovae, both in the same filter
band, are compared using a $K$ correction to account for the different spectral
regions incident on that filter. A generalized approach compares magnitudes in
different bands for the nearby and distant supernova, bands that are selected
to give sensitivity in corresponding regions of the redshifted and unredshifted
spectra. Thus at a redshift of $z \approx 0.5$, local $B$ magnitudes are
compared with distant $R$ magnitudes. We compute these generalized $K$
corrections over a range of redshifts and bandpass pairs and discuss their
advantages over the traditional single-band $K$ correction. In particular,
errors near maximum light can be kept below 0.05 mag out to at least $z=0.6$,
whereas the traditional $K$ correction is difficult to use beyond $z > 0.2$.

Astrophysics