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[Abridged] We determined the luminosity function (LF) of the Coma clustergalaxies selected by luminosity, and the LF bi-variate in central brightness.The Coma cluster and control fields were imaged using the CFH12K (42x28 arcmin)and UH8K (28x28 arcmin) wide-field cameras at the CFHT. Selected HST imageswere used for testing. Quantities were derived from measurements in at leasttwo colors, which have the following features: (1) Galaxies as faint as threetimes the luminosity of the brightest globular clusters are in the completenessregion of our data. (2) We have a complete census (in the explored region) oflow surface brightness galaxies with central surface brightness galaxies almostas low as the faintest so far cataloged ones. (3) The explored area is amongthe largest ever sampled with CCDs at comparable depth for any cluster ofgalaxies. (4) The error budget includes all sources of errors known to date.Using HST images we also discovered that blends of globular clusters, notresolved in individual components due to seeing, look like dwarf galaxies whenobserved from the ground and are numerous and bright. The derived Coma LF isrelatively steep (alpha=-1.4) over the 11 magnitudes sampled, but the slope andshape depend on color. A large population of faint low surface brightnessgalaxies was discovered, representing the largest contributor (in number) tothe LF at faint magnitudes. We found a clear progression for a faintening ofthe LF from high surface brightness galaxies (mu~20 mag/arcsec2) to galaxies ofvery faint central brightnesses (mu~24.5 mag/arcsec2), and some evidence for asteepening. Compact galaxies, usually classified as stars and therefore notincluded in the LF, are found to be a minor population in Coma.Comment: ApJ, in pres

Dissecting the Luminosity Function of the Coma Cluster of Galaxies Using Canada‐France‐Hawaii Telescope1 Wide‐Field Images