By means of wide–field ( 42 \times 28 arcmin ) CCD images of the Coma cluster of galaxies and of control fields , taken at the Canada–France–Hawaii telescope with the CFH12K and UH8K cameras , we determine the luminosity function bi–variate in central brightness .
We found a clear progression for a steeping and weakening of the FL going from high surface brightness galaxies ( \mu \sim 20 mag arcsec ^ { -2 } ) to galaxies of very–faint central brightnesses ( \mu \sim 24.5 mag arcsec ^ { -2 } ) .
Compact galaxies , usually rejected in the star/galaxy classification , are found to be a minor population in Coma .
A huge population of low surface brightness galaxies red and faint are discovered , representing the largest contributor to the LF at faint magnitudes .
Among them , there could be the remnant of high redshift starbursting galaxies responsible for the Butcher–Oemler effect .