Using non-linear least-squares fitting to extract the phase-difference between the object and reference channels is computationally intensive and results here in large measurement errors of ± 0.3°. For real-time analysis, we instead use an algorithm based on the sliding Discrete Fourier Transform (see description under Measurement Details), using a sliding window of the most recent 1024 samples (=1.024 s). The blue lines in Fig. show time series for the sDFT-derived phase differences using ultra-pure water and 200 mg/ml D-sucrose, streamed over the USB interface at a rate of one hundred readings per second (i.e. every tenth value of the internally filtered phase difference). The two blue lines fluctuate about mean values of 2.0514° and 12.6558°, with standard deviations of approximately 0.001°. From Eq. ( ), it follows that the optical rotation angle is 5.3022 ± 0.001°, which is consistent with the values derived by non-linear least squares fitting but with a greatly reduced uncertainty. Fig. shows a time-series of the calculated phase-difference for ultra-pure water obtained by averaging the outputted phase data in 500-sample (i.e. 5-s) batches at 10-min intervals. 5-s is the typical time-resolution we use for collecting data from the polarimeter, but faster update rates may be obtained by adjusting the internal filtering and external averaging. Over the 100-min duration of the measurement, the phase-difference can be seen to fluctuate -without obvious drift -around a mean value of 2.0512° with a standard deviation of σ = 0.0008°. The wander in the measured phasedifference is shown at higher time-resolution in Fig. .