Hi,
The calculation is as follows:
T* = Binv(radiance)
BT = (T* – offset) / slope
where:
Binv is the inverse Planck function
T* is the temperature equivalent of the radiance without band correction
offset, scale are the band correction coefficients from the rtcoef file
BT is the band-corrected brightness temperature
The reference for this is available in the RTTOV docs directory:
docs/sharp_1983_radiance_to_bt_conversion.pdf
We apply the effective temperature method described at the top of page 4.
Best wishes,
James