Infrared Telescopes
Jansky Units and Infrared Radio Telescopes
1 Jansky is 1e-26 W/m2-Hz. Hz implies bandwidth. The bandwidth of a radio telescope is obvious - the bandwidth in Hertz, probably after a chilled reflector into a chilled low noise amplifier, then through a filter. A wider filter picks up more power, and more thermal noise. So the power in Janksy units for a source is Jy = 1e26 * Power~Received / ( Area * ( f_2 - f_1 ) with power in watts, Area of the receiving surface in square meters, and frequencies in Hertz.
Infrared telescopes have much wider bandwidth, and infrared is typically characterized with wavelength (usually micrometers) rather than Hertz. We can recast the formula as
Jy~=~1e26*(P/A)*c*(1/\lambda_2-1/\lambda_1)~=~1e26*(P/A)*c(\lambda_1-\lambda_2)/(\lambda_1\lambda_2)
where c is the speed of light. Defining \Delta\lambda~=~\lambda_1-\lambda_2 and center wavelength \lambda = \sqrt{\lambda_1\lambda_2}, this simplifies to:
Jy ~=~ 1e26*(P/A)*c~\Delta\lambda/\lambda^2
So, how much is that? A parsec is 3.26 light years or 3.0857e16 meters, like a star that appears to move one arcsecond in the sky as the earth moves 1 AU across its orbit. So, a sphere 1 AU in diameter would appear one arc-second across from 1 parsec away. From 200 parsecs away ( 6.1714e18 meters ), a sphere 100 AU in radius or 200 AU in diameter, and heated by the entire sun's output (3.86e26 W), would be about 60K, and deposit all that power on a 200 parsec diameter sphere with an area of 4.786e38 square meters, a power density of 8.07e-13W/m2. We still don't know enough to compute the Jansky units, because we don't know the bandwidth. That is a function of the filtering and imager on our telescope - and if the telescope is not in orbit, the passband and emissions of the atmosphere.