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Lyman-alpha-emitting galaxies (LAEs) are typically young, low-mass, star-forming galaxies with little extinction from interstellar dust. Their low dust attenuation allows their Ly α emission to shine brightly in spectroscopic and photometric observations, providing an observational window into the high-redshift Universe. Narrowband surveys reveal large, uniform samples of LAEs at specific redshifts that probe large-scale structure and the temporal evolution of galaxy properties. The One-hundred-deg ^2 DECam Imaging in Narrowbands (ODIN) utilizes three custom-made narrowband filters on the Dark Energy Camera (DECam) to discover LAEs at three equally spaced periods in cosmological history. In this paper, we introduce the hybrid-weighted double-broadband continuum estimation technique, which yields improved estimation of Ly α equivalent widths. Using this method, we discover 6032, 5691, and 4066 LAE candidates at z = 2.4, 3.1, and 4.5 in the extended COSMOS field (∼9 deg ^2 ). We find that [O ii ] emitters are a minimal contaminant in our LAE samples, but that interloping Green Pea–like [O iii ] emitters are important for our redshift 4.5 sample. We introduce an innovative method for identifying [O ii ] and [O iii ] emitters via a combination of narrowband excess and galaxy colors, enabling their study as separate classes of objects. We present scaled median stacked spectral energy distributions for each galaxy sample, revealing the overall success of our selection methods. We also calculate rest-frame Ly α equivalent widths for our LAE samples and find that the EW distributions are best fit by exponential functions with scale lengths of w _0 = 53 ± 1, 65 ± 1, and 59 ± 1 Å, respectively.

We describe the survey design and science goals for One-hundred-deg ^2 DECam Imaging in Narrowbands (ODIN), a NOIRLab survey using the Dark Energy Camera (DECam) to obtain deep (AB ∼ 25.7) narrowband images over an unprecedented area of sky. The three custom-built narrowband filters, N 419, N 501, and N 673, have central wavelengths of 419, 501, and 673 nm and respective FWHM of 7.5, 7.6, and 10.0 nm, corresponding to Ly α at z = 2.4, 3.1, and 4.5 and cosmic times of 2.8, 2.1, and 1.4 Gyr, respectively. When combined with even deeper, public broadband data from the Hyper Suprime-Cam, DECam, and in the future, the Legacy Survey of Space and Time, the ODIN narrowband images will enable the selection of over 100,000 Ly α -emitting (LAE) galaxies at these epochs. ODIN-selected LAEs will identify protoclusters as galaxy overdensities, and the deep narrowband images enable detection of highly extended Ly α blobs (LABs). Primary science goals include measuring the clustering strength and dark matter halo connection of LAEs, LABs, and protoclusters, and their respective relationship to filaments in the cosmic web. The three epochs allow for the redshift evolution of these properties to be determined during the period known as Cosmic Noon, where star formation was at its peak. The narrowband filter wavelengths are designed to enable interloper rejection and further scientific studies by revealing [O ii ] and [O iii ] at z = 0.34, Ly α and He ii 1640 at z = 3.1, and Lyman continuum plus Ly α at z = 4.5. Ancillary science includes similar studies of the lower-redshift emission-line galaxy samples and investigations of nearby star-forming galaxies resolved into numerous [O iii ] and [S ii ] emitting regions.