A high-resolution polarimeter formed from inexpensive optical parts

We describe a high resolution laser polarimeter built from commodity optical components. The optical rotation angle is determined by measuring the phase difference between two harmonically modulated polarised laser beams – an ‘object beam’ that passes through the sample under test and a ‘reference beam’ that bypasses the sample. The complete polarimeter may be assembled from low cost off-the-shelf parts for less than £300 (UK Sterling). Data acquisition and analysis are carried out on a microcontroller running an efficient algorithm based on the sliding Discrete Fourier Transform. Despite its low cost, the polarimeter is a fully automatic, research-grade instrument with an accuracy of ±0.0013° and a precision of ±0.0028° – comparable to far costlier commercial instruments. The polarimeter’s ease of use, compact size, fast measurement times and high angular resolution make it a capable and versatile tool for analytical science, while its low cost means it is ideally suited for use in resource-constrained environments and process monitoring. The polarimeter is released here as open hardware, with technical diagrams, a full parts list, and source code for its firmware included as Supplementary Information.


Fig. S2
Photograph of the assembled polarimeter. The beam from the laser is passed through a 1-mm aperture (A1), a neutral density filter (ND) and a second 1-mm aperture (A2). A 50:50 plate-type beam-splitter (BS1) divides the laser beam into an object beam and a reference beam. The reference beam is directed by a plane mirror (M1) through a fixed thin-film polariser (P1) onto the centre of a rotatable thin-film polariser (P3), which is mounted on a hollow-shaft motor. The motor is driven at a continuous speed of approximately eight revolutions per minute by an electronic speed controller (ESC). The object beam is directed by BS1 through a fixed thin-film polariser (P2), and onto plane mirror (M2); it then passes through a 5-cm optical cell, before striking the same central point on the rotating polariser (P3). The object and reference beams pass through the centre of P3 and are then directed by a third mirror (M3) onto a pair of amplified photodiodes (AP1, AP2). The beam splitter BS2 is a glass slide, which directs a small fraction (~ 4 %) of the initial beam onto a light-to-frequency converter (LTFC). The polarimeter components are mounted on a 12"×12" breadboard using standard optical mounts. The microcontroller (µC) is soldered to a custom printed circuit board (PCB) which provides electrical connections to the optical sensors and power connections for the motor. The two amplified photodiodes are mounted on a separate PCB. The two PCBs sit in custom 3D-printed mounts.

Fig. S3
Annotated photograph of the assembled polarimeter, showing optical beam paths. The initial laser beam (L) strikes a beam-splitter formed from a glass slide. The (weak) reflected beam acts as a low-intensity "monitor beam" (M), allowing variations in laser intensity to be observed using a light-to-frequency converter. The transmitted beam strikes a 50:50 plate beam-splitter, where it is divided into an object beam (O) and a reference beam (R). See Fig. S2 for further details.

Fig. S4
Circuit diagram of detection circuitry, comprising one microcontroller development board (Teensy 3.6, PJRC), two amplified photodiodes (OPT 101, Texas Instruments) and a light-to-frequency converter (TSL235R-LF, AMS). The analogue signals from the amplified photodiodes are measured using the microcontroller's two built-in analogue to digital converters, while the digital signal from the light-to-frequency converter is read using one of its digital I/O pins. The object and reference signals are divided by the measured laser intensity prior to calculating the phase difference. The calculated phase difference is sent via the microcontroller's USB port to a PC or other remote device for data visualisation.   The secondary x-axis shows the corresponding optical density at the 650-nm probe wavelength. The accuracy is better than 0.003º for optical densities of 1.1 or less, increasing rapidly above this value due to inadequate use of the dynamic range of the analogue to digital converters (ADCs) on the microcontroller. To maintain accuracy at optical densities substantially greater than one, the neutral density filter ND should be removed from the optical set up and/or a stronger laser should be used. Extrapolating to 100 % volumetric concentration yields a lactose concentration of 33 ± 10 mg/ml lactose for the original milk sample in agreement with literature values [1].
Experimental procedure. A whole milk sample was obtained from Tinemelk SA (Tinemelk Helmelk, 3.5 % fat content). Following Ref. 2, the milk solution was deproteinated by adding 7.5 ml of concentrated H2SO4 to 50 ml of whole milk, followed by 7.5 ml of 1M aqueous potassium iodide to induce precipitation of milk fats and proteins. The product was filtered, and the collected filtrate was diluted in water to a volume of 100 ml, creating a colourless (non-scattering) stock solution with half the volumetric concentration of the original sample. The stock solution was used to prepare solutions with volumetric concentrations in the range ten to fifty percent of the original sample, i.e. with relative concentrations of 0.1 to 0.5. The specific angle of rotation at 650 nm was calculated using the Drude model / = /( 4 − 6 4 ), with A = 1.47 ± 0.70 nm 2 dm -1 g -1 mL and 6 = 254 ± 70 nm, see Ref.  Table S1 Parts list for the polarimeter. The £300 cost is dominated by the expensive laser diode, which could be replaced by a low-cost laser pointer at < £15, bringing the build cost to £170. Further savings could be achieved by replacing the legacy ESC (a manual device with potentiometric control) by a modern ESC with PWM control (< £10). It would also be possible to amend the sDFT algorithm to use integer or fixed-point arithmetic, which would reduce the microcontroller cost to < £10 by removing the need for a Floating Point Unit. Making all three changes would bring the build cost below £100 without substantially reducing the performance of the polarimeter.

Manufacturer Model
Quoted Accuracy

Quoted Precision
Quoted measurement times

Appendix S1 Brief derivation of the sliding DFT
Consider a digitised function (0), (1), (2) (S1) and F = abs( ( )) and F = arg( ( )). The sDFT is based on a sliding window of the N most recent data points. It follows from Eq. (S1) that, for a window starting at time = , the DFT is given by: Recognising the first term in brackets as \ ( ) and writing AB4RF = 1 (for integer values of ), we obtain the following recurrence formula for the -th bin of the DFT: