One difficulty in determining the magnitude of fainter stars is that the
USNO-A2.0 Catalogue (a catalogue of 526,280,881 stars) “only” goes down to around mag 19. It was a 6Gb+ download!
To go dimmer than mag 19, I use the
USNO Flagstaff Station Integrated Image and Catalogue Archive Service which is based on the POSS-I (1st epoch Palomar Obs. Sky Survey) and POSS-II (2nd epoch Palomar Obs. Sky Survey). The data lists the Red and Blue magnitudes.
Cheers
Dennis