Optical Identification of Cepheids in 19 Host Galaxies of Type Ia Supernovae and NGC 4258 with the Hubble Space Telescope

We present results of an optical search for Cepheid variable stars using the Hubble Space Telescope (HST) in 19 hosts of Type Ia supernovae (SNe Ia) and the maser-host galaxy NGC 4258, conducted as part of the SH0ES project (Supernovae and H0 for the Equation of State of dark energy). The targets include 9 newly imaged SN Ia hosts using a novel strategy based on a long-pass filter that minimizes the number of HST orbits required to detect and accurately determine Cepheid properties. We carried out a homogeneous reduction and analysis of all observations, including new universal variability searches in all SN Ia hosts, that yielded a total of 2200 variables with well-defined selection criteria -- the largest such sample identified outside the Local Group. These objects are used in a companion paper to determine the local value of H0 with a total uncertainty of 2.4%.