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We call these energy differences $E_u$ and $E_l$ (subscripts refer to "upper" and "lower"), or in units of frequency, $f_u$ and $f_l$ (where $E_{l,u} = hf_{l,u}$ ).

As a special case, when $\mathbf{B}$ is aligned with the NV axis (i.e., $\theta = 0$ ), the above relation reduces to:

$f_u = D+\gamma B \quad \text{and} \quad f_l = D-\gamma B.$

The key result is:

$B= \frac{1}{\sqrt{3}\gamma}\sqrt{f_u^2+f_l^2-f_u f_l-D^2}$

Here, $\gamma = 28$ GHz/T is the gyromagnetic ratio.