PHALIN THAKKAR
More measurements, same ambiguity
Which ambiguities can new settings remove, and which remain even with perfect readings?
Note 4 · Explanatory note
Analytical result · Hypothetical examples are not physical measurements.
Repeated independent readings at one setting can reduce the standard error of a mean by 1/√n. A shared calibration bias does not average away.
With a known intensity scale, measurements only at 0° and 90° determine cos2φ but leave the sign of sin2φ unresolved. For example, φ = 30° and φ = 150° both give 0.75I0 at 0° and 0.25I0 at 90°.
At 45°, they differ:
That new setting resolves the reflection ambiguity.
By contrast, φ and φ + 180° give identical predictions at every linear analyzer angle. They label the same physical linear axis. Repeating or adding linear analyzer settings cannot turn that axis into an arrow.