= Dipole-axis ambiguity from three intensity measurements
The <angular distribution of electric dipole radiation> measures squared projections of the dipole axis, so a few <intensity> measurements need not determine that axis or the total radiated <power> uniquely. For a real unit dipole axis $\mathbf d$, the radiation-zone formula is $I(\mathbf n)=3P[1-(\mathbf d\cdot\mathbf n)^2]/(8\pi R^2)$. Equal intensities along $\hat{\mathbf z}$, $(\hat{\mathbf x}+\hat{\mathbf z})/\sqrt2$ and $(\hat{\mathbf y}+\hat{\mathbf z})/\sqrt2$ permit four axes, up to reversal:
$$
\mathbf d\ \parallel\ (s_1\sqrt2-1,\ s_2\sqrt2-1,\ 1),\qquad s_1,s_2\in\{+1,-1\}.
$$
Three generally different radiated powers are compatible with the same intensity data. Additional directional measurements or polarization information can remove the ambiguity.
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