How can I convert from mJy/beam to mJy?

A common question we receive here at the JCMT is regarding observations with SCUBA-2 and the conversion from mJy/beam to mJy. Before we begin, it should be noted that for a real point source, a peak brightness value reported in units of mJy is the same as a peak brightness value reported in mJy/beam.

Now what happens if we have a map in mJy/beam and we want to obtain an integrated intensity value, a total flux value. We first sum up a number of pixels and now we want to get our units correct from mJy/beam to mJy…

Total Flux = flux summed over a number of pixels/(number of pixels in a beam)

Then your units are:

[mJy*pixels/beam] / [pixels/beam] = [mJy].
Now we know that For a Gaussian:
Beam Area =  2 × π × σ² [arcsec]

where the σ of the Gaussian beam can be calculated from the JCMT FWHM values at 850 and 450 microns (reminder the beam components are provided in Dempsey’s 2013 paper).

FWHM = 2 σ √(2 ln 2)   [arcsec]

So we can use the FWHM to obtain σ to calculate the Beam Area and report the beam area in terms of pixels:

number of pixels in a beam = Beam Area [arcsec] / (pixel length)²
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