The faint end of the differential galaxy number counts , n ( m ) , in the Hubble Deep Field ( HDF ) North has been determined for the F450W , F606W , and F814W filters by means of surface-brightness fluctuation ( SBF ) measurements .
This technique allows us to explore n ( m ) beyond the limiting magnitude of the HDF , providing new , stronger constraints on the faint end of n ( m ) .
This has allowed us to test the validity of previous number count studies and to produce a new determination of the faint end of n ( m ) for magnitudes fainter than 28.8 in the AB system and to extend this estimate down to 31 .
This value represents an extension of more than two magnitudes beyond the limits of previous photometric studies .
The obtained n ( m ) slopes are \gamma = 0.27 , 0.21 , and 0.26 in B _ { 450 } , V _ { 606 } , and I _ { 814 } , respectively .