This is the same four-axis NV vector-magnetometry reconstruction as the 3D version, drawn as a stereographic pole figure — the standard 2D projection crystallographers use to plot crystal directions on paper instead of a 3D model. Each 3D unit vector (x, y, z) maps to a single 2D point via
u = x / (1 + |z|), v = y / (1 + |z|)
Δf_i = 2·γ·|B · n̂_i| (i = 1..4)
γ ≈ 28 MHz/mT (0.028 MHz/µT)
Upper-hemisphere directions (z ≥ 0) land inside the disk as filled dots; lower-hemisphere ones (the antipodal ⟨111⟩ partner, z < 0) are drawn as hollow rings — a real pole-figure convention. Dot radius scales with each axis's measured ODMR splitting, so a glance at the figure shows both direction and signal strength at once, something a single 3D camera angle can't show without occlusion.
- Pole figure (left disk) — the four fixed ⟨111⟩ NV axes (colored), the true field direction (white) and the reconstructed field direction (orange), all projected onto the same 2D disk.
- Residual diagnostic (right panel) — a measured-vs-predicted scatter plot: each axis's actual ODMR splitting (x) against what the reconstructed field predicts for that axis (y). A perfect fit places every point on the diagonal; noise pushes points off it, and the plot's spread is the least-squares residual — a genuinely 2D-native way to see an over-determined fit (4 equations, 3 unknowns) that the 3D arrow view can't visualize directly.
- Add readout noise — adds photon-shot-noise-like Gaussian jitter to each splitting before reconstruction, visibly scattering the reconstructed point off the true one and the residual points off the diagonal.
Real-world relevance: this four-axis reconstruction is exactly how diamond-based vector magnetometers (biomagnetic imaging, current sensing, geophysics) recover a full 3D field from a single crystal with no moving parts, and pole figures are exactly how the underlying crystal geometry is published in papers.