Voltage calculation from RF rigid line directional wattmeter
At the bottom of that description it says that the rf is rectified, filtered and displayed on a meter.  The diode that does the rectifying is inside your directional coupler somewhere.  What that does is introduce some non-linearity, making the DC voltage out not exactly proportional to the RF voltage or to the RF power.  Especially when the DC voltage is low.  At higher DC voltages the voltage out is roughly proportional to the RF voltage.  At lower voltages people like to say you're in the &quot;square law&quot; region and the voltage is roughly proportional to the power.  I've never found either approach very accurate. Usually the meter scale on the Bird wattmeter has the calibration built into it.
Probably the best thing to do is get out some software like Matlab or python (or maybe Excel if you're of that persuasion) and take your calibration data and fit a polynomial or a spline to the power vs DC voltage for each of your plug-in elements.  It all depends on how accurate you want to be.
Note that your calibration depends on what load resistance you have on your DC output.  If you plan on putting the DC voltage on an oscilloscope and you want good time resolution then you'll want to put a fairly low load resistance on it, and you'll need to do your calibration with that load present.