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.