Part of our work compares how chiral molecules respond to left- and right-circularly polarised light. If the beam is less circular than we think, part of the difference we measure belongs to the light, not the molecule.
Checking the polarisation by hand took over two hours. The software I specified now does it in about five minutes, and it runs in our lab every day.
The method
The method is rotating quarter-wave-plate polarimetry, as described by Schaefer and co-workers in 2007. The beam passes a quarter-wave plate, then a fixed linear polariser, then a power meter. As the plate turns through an angle θ, the power rises and falls in a pattern set by the polarisation.
That pattern has only four terms: a constant, one part that repeats twice per turn, and two parts that repeat four times per turn. Fit them, and the Stokes parameters follow directly. The twice-per-turn term gives the circular part, S3. The four-times terms give the linear parts, S1 and S2.
I(θ) = ½ [A + B sin 2θ + C cos 4θ + D sin 4θ]
S0 = A − C, S1 = 2C, S2 = 2D, S3 = B
What the automation does
The software steps a rotation stage, reads an Ophir power meter at each angle and fits the four terms. It runs with our Newport ESP301 controller and with the newer Trinamic TMCM-6110. Scan range, step size, dwell time and averaging are all set in the interface.
It reports the full Stokes vector, the degree of polarisation, and the ellipticity and orientation of the light. Each value carries an uncertainty from the fit, shown next to the fit quality. A flag marks light as near-perfectly circular when |S3/S0| is at least 0.98.
I chose to talk to each device over its own protocol rather than through a general automation framework. A timeout or a stalled motor then shows up as exactly that. It does not disappear inside a layer nobody in the lab controls.
What limits the accuracy
The fit itself is simple. Four things in the hardware set the accuracy.
The retardance of the plate. A quarter-wave plate gives a quarter wave only near its design wavelength. Away from it, the formulas above no longer hold as written. They need the real retardance of the plate.
The zero angle. The fit assumes you know where the fast axis of the plate sits at 0°. An offset mixes S1 and S2, so the measured orientation of linear light rotates. Calibrate it with light whose polarisation you know.
Laser drift during the scan. The method reads polarisation from changes in power. If the laser power itself drifts while the plate turns, the fit takes that for polarisation. Dwell time and averaging help, and a five-minute scan gives the laser far less time to drift than two hours did.
The polariser and the detector. The polariser must block the unwanted direction well. The power meter must respond linearly over the range the scan covers.
If you want to do the same
You need a rotation stage, a quarter-wave plate made for your wavelength, a fixed polariser and a power meter. The fit is a few lines of linear algebra. Report an uncertainty with every Stokes vector, and set a threshold you can act on, such as the 0.98 flag above.
You can try the method on simulated light on my Projects page.
Method: B. Schaefer, E. Collett, R. Smyth, D. Barrett and B. Fraher, "Measuring the Stokes polarization parameters", Am. J. Phys. 75, 163 (2007), doi:10.1119/1.2386162.