# Demo — AoA Accuracy Explorer
A phase interferometer turns the wavefront's tilt into a bearing. Stretch the baseline and the bearing sharpens — but past a half-wavelength the phase wraps, and the naive estimate snaps to a confidently wrong angle. This demo lets you walk that accuracy–ambiguity trade directly.
## The relation
$$
\Delta\phi = \frac{2\pi d}{\lambda}\,\sin\theta
\qquad\Longrightarrow\qquad
\theta = \arcsin\!\left(\frac{\lambda\,\Delta\phi}{2\pi d}\right).
$$
A phase meter only reads $\Delta\phi$ modulo $2\pi$, so unambiguous coverage across $\pm 90^\circ$ requires $d \le \lambda/2$ — a short, coarse baseline.
## Interactive demo
Open in full screen
## Walkthrough
1. **Start short.** With $d \le \lambda/2$ the ambiguity flag is green and the estimate tracks the true bearing — but coarsely; raise the noise (lower SNR) and the error swings widely.
2. **Stretch the baseline.** Increase $d$ and watch the estimate tighten against the same noise — a fixed phase error maps to a smaller angle error as $d/\lambda$ grows.
3. **Cross the half-wavelength.** When $d > \lambda/2$ the flag turns red. On the phase plot you can see several bearings now share one wrapped reading, and the naive estimate jumps to the wrong one.
4. **Read the polar plot.** The navy ray (truth) and red ray (estimate) agree at short baselines and diverge dramatically once the long baseline wraps.
## Key observations
- **Accuracy wants a long baseline; unambiguity wants a short one.** No single pair gives both.
- **Multi-baseline buys both** — the short pair picks the $2\pi$ cycle, the long pair sets the precision. That is the resolution the type-along implements.
- **Amplitude comparison never wraps** because it reads a monotone power ratio, not a periodic phase — it trades that safety for poor accuracy.
## Source
MATLAB · code/L13_InterferometricAoA.m↓
The in-class script turns a true AoA into the phase across a short and a long baseline, shows the long baseline wrapping, and uses the short baseline to unwrap it into a fine, correct bearing.