  Numerous methods for finding clusters at moderate to high redshifts have been
proposed in recent years, at wavelengths ranging from radio to X-rays. In this
paper we describe a new method for detecting clusters in two-band
optical/near-IR imaging data. The method relies upon the observation that all
rich clusters, at all redshifts observed so far, appear to have a red sequence
of early-type galaxies. The emerging picture is that all rich clusters contain
a core population of passively evolving elliptical galaxies which are coeval
and formed at high redshifts. The proposed search method exploits this strong
empirical fact by using the red sequence as a direct indicator of overdensity.
The fundamental advantage of this approach is that with appropriate filters,
cluster elliptical galaxies at a given redshift are redder than all normal
galaxies at lower redshifts. A simple color cut thus virtually eliminates all
foreground contamination, even at significant redshifts. In this paper, one of
a series of two, we describe the underlying assumptions and basic techniques of
the method in detail, and contrast the method with those used by other authors.
We provide a brief demonstration of the effectiveness of the technique using
real redshift data, and from this conclude that the method offers a powerful
yet simple way of identify galaxy clusters. We find that the method can
reliably detect structures to masses as small as groups with velocity
dispersions of only ~300 km/sec, with redshifts for all detected structures
estimated to an accuracy of ~10%.
