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The science
The NV centre has a spin-1 ground state. At zero field the ms = +/-1 levels sit D = 2870 MHz above ms = 0. A field B along the NV axis shifts them by the Zeeman term f(+/-) = D +/- gamma B, with gamma = g muB / h = 28.03 MHz/mT (the 3D page uses 28). The two fluorescence dips are therefore separated by 2 gamma B, so B = (f+ - f-)/(2 gamma).
Each dip is a Lorentzian of half-width w = 6 + 10 P MHz and depth min(0.15 + 0.28 P, 0.82) (power P in arbitrary units, same law as the 3D page): more microwave power gives deeper but broader dips (power broadening).
Every point of the sweep is a photon count, so the noise is shot noise: relative sigma 1/sqrt(N). The fit uses the known line shape, scans both centres and keeps the least-squares pair. A temperature change shifts D by about -0.074 MHz/K but moves both dips the same way, so the splitting (and B) is unchanged: the centre of the two dips reads temperature, the spacing reads the field.
Simplifications: field exactly along the NV axis, one NV orientation, no hyperfine structure, constant laser, no spin-lattice relaxation.
What to try
- Press Low field (B near 0.3 mT): the dips merge and the page warns that they are unresolved.
- Raise the photon number per point and watch the scatter of the estimated field shrink like 1/sqrt(N).
- Change the temperature shift: the dips slide together, the readout B does not change.