Cosmology From Type IA Supernovae: Measurements, Calibration Techniques, and Implications

Our search for high-redshift type Ia supernovae (SN Ia) has so far discovered ~ 50 supernovae. Using a ``batch'' search strategy, almost all were discovered before or at maximum light, and were observed over the peak of their light curves with ground-based photometry and spectroscopy, and some HST photometry. The spectra and light curves indicate that almost all were type Ia supernovae at redshifts z=0.18 -- 0.83. We have developed methods to measure the cosmological parameters Omega and Lambda , by studying the SN Ia Hubble diagram at a wide range of redshifts. This presentation will focus on the techniques used to calibrate SNe Ia luminosity distances, the sources of measurement uncertainty, procedures for determining and correcting for systematic effects, and the cosmological implications of these high-redshift supernovae from our ongoing project.