We describe the algorithm that selects the main sample of galaxies for spectroscopy in the Sloan Digital Sky Survey from the photometric data obtained by the imaging survey. Galaxy photometric properties are measured using the Petrosian magnitude system, which measures flux in apertures determined by the shape of the surface brightness profile. The metric aperture used is essentially independent of cosmological surface brightness dimming, foreground extinction, sky brightness, and the galaxy central surface brightness. The main galaxy sample consists of galaxies with r-band Petrosian magnitude r < 17.77 and r-band Petrosian half-light surface brightness < 24.5 magnitudes per square arcsec. These cuts select about 90 galaxy targets per square degree, with a median redshift of 0.104. We carry out a number of tests to show that (a) our star-galaxy separation criterion is effective at eliminating nearly all stellar contamination while removing almost no genuine galaxies, (b) the fraction of galaxies eliminated by our surface brightness cut is very small (0.1%), (c) the completeness of the sample is high, exceeding 99%, and (d) the reproducibility of target selection based on repeated imaging scans is consistent with the expected random photometric errors. (abridged)
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