We determined the relative spatial density of the Coma cluster galaxies selected by luminosity , and the contribution of the galaxies of each central brightness to the luminosity function ( i.e .
the luminosity function bi–variate in central brightness ) .
The Coma cluster and control fields were imaged using the CFH12K ( 42 \times 28 arcmin ) and UH8K ( 28 \times 28 arcmin ) wide–field cameras at the Canada–France–Hawaii Telescope .
Selected Hubble Space Telescope images were used for testing .

Quantities were derived from measurements in at least two colors , which have the following features : ( 1 ) Galaxies as faint as three times the luminosity of the brightest globular clusters are in the completeness region of our data .
( 2 ) We have a complete census ( in the explored region ) of low surface brightness galaxies with central surface brightness galaxies almost as low as the faintest so far cataloged ones .
( 3 ) The explored area is among the largest ever sampled with CCDs at comparable depth for any cluster of galaxies .
( 4 ) The error budget includes all sources of errors known to date .
Using Hubble Space Telescope images we also discovered that blends of globular clusters , not resolved in individual components due to seeing , look like dwarf galaxies when observed from the ground and are numerous and bright .
When mistaken as extended sources , they increase the steepness of luminosity function at faint magnitudes .
The derived Coma luminosity function is relatively steep ( \alpha = -1.4 ) over the 11 magnitudes sampled , but the slope and shape depend on color .
A large population of faint low surface brightness galaxies was discovered , representing the largest contributor ( in number ) to the luminosity function at faint magnitudes .
We found a clear progression for a faintening of the luminosity function 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 } ) , and some evidence for a steepening .
Compact galaxies , usually classified as stars and therefore not included in the LF , are found to be a minor population in Coma .