How to determine power from emitted light using a photodiode?
First, you consult the photodiode data sheet to find the quantum efficiency of the PD at the wavelength of interest.

Then, you measure the PD current. Using the standard relationship, you convert this to electrons/second. (1 amp equals 1 coulomb/sec).

Now, knowing the electrons/second impinging on the PD, you use the QE to determine the number of photons hitting the PD.

Finally, since you know the photon flux, and you know the wavelength of the photons, you can calculate the power.

If you are looking for total power, you take the PD active area and calculate the total area illuminated by the Cerenkov radiation, calculate the ratio of the two, and apply this to the PD power.