PHALIN THAKKAR
What linear analyzer readings leave out
Can intensity readings recover a complete polarisation state?
Note 11 · Research extension
Analytical result · Hypothetical examples are not physical measurements.
A calibrated ideal linear analyzer measures:
S0 describes total intensity. S1 and S2 describe linear polarisation components. S3, which contains circular polarisation information, does not appear.
Consider three states with the same total intensity S0 = 1:
- Unpolarized: S = (1, 0, 0, 0).
- One circular handedness: S = (1, 0, 0, +1).
- The opposite handedness: S = (1, 0, 0, −1).
Every rotating linear analyzer returns ½ for all three. The handedness sign convention does not affect this conclusion.
Consequently, equal readings at every linear setting do not establish that the input is unpolarized. A general elliptical state can reveal a linear component and its azimuth, but linear analyzer readings do not determine its full state.
Additional calibrated optics, such as a waveplate before the analyzer, can convert otherwise inaccessible components into measurable intensity variation.
The current hidden direction model assumes fully linear input. Extending it to a full state reconstruction is a further question, not a completed laboratory result.
Continue the reasoning
Wilkinson and colleagues: Complete Stokes vector analysis with a compact, portable rotating waveplate polarimeter. A reading reference showing how calibrated optics can recover additional components, not a publication by Phalin.