Flux Density/Surface Brightness measured by a Radio Telescope

The monochromatic intensity $\it I(\nu)$ has units of W m$^{-2}$ s$^{-1}$ Hz$^{-1}$ sr$^{-1}$. where, sr means steradians and is the unit of solid angle. By comparing these units with the Planck function, we see that they are the same.

The Planck function gives the monochromatic intensity of the blackbody represented by it, whereas, the intensity, or the surface brightness, is the integration of Planck function over all frequencies, i.e.,

$$\rm {I = \int{I(\nu) d\nu}}$$ (1..1)

(units: W m$^{-2}$ s$^{-1}$ sr$^{-1}$).

Integrating this equation once again over an angular area, we obtain the flux, i.e.,

$$\rm {F = \int{I dW}}$$ (1..2)

(units: W m$^{-2}$ s$^{-1}$).

The flux is the power per unit area. In radio astronomy, we often use a related quantity called as the flux density. It is the monochromatic intensity (or the Planck function) integrated over the solid angle, i.e.,

$$\rm {S = \int{I(\nu) dW}}$$ (1..3)

(units: W m$^{-2}$ Hz$^{-1}$).

In fact, it is the flux density, which is a fundamental quantity measured by radio telescopes. 1 Jansky (Jy) = 10$^{-26}$ W m$^{-2}$ Hz$^{-1}$.

The quantity that a radio telescope measures is the flux density over some wavelength band, so the strength of radio sources in the sky are often specified in 'Jy'.

(Ref : Introduction to Radio Astronomy, Prof. Dale E. Gary, NJIT,
http://web.njit.edu/$\sim$dgary/728/Lecture1.html).