Both magnitude and flux representations are widely used. Flux density of a source is defined as the flux per unit frequency.
Flux density is the physical unit used for point sources.
The unit of flux density is Wm -2 Hz . For practical purposes in the infrared it is often convenient to scale this SI unit and use Jansky instead. For extended objects, the surface brightness is used instead of flux density. Also background emission for e.g. point sources is expressed in brightness units. Brightness is defined as the flux density per unit solid angle.