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Polarimeter - Instrument Simulation


Simulations offer valuable insights into how an instrument can be expected to perform and can also point to areas for improvement. In the case of the polarimeters described here, it is of interest to simulate the motion of the analysing polarizer relative to the fixed defining polarizer as this forms the basis for the optical rotation measurements. To make the simulation more realistic we have incorporated additional factors including (i) the broadband nature of the LED’s emission spectrum, (ii) the variation of the specific rotation of the sample as a function of wavelength, (iii) the spectral response of the detector and (iv) the temperature at which measurements are performed.

The instrument simulations to be described were performed using a commercially available modelling package, ExtendSim CP. Spectroscopic libraries that enhance the capabilities of this package have previously been available in the public domain. These were developed by Assoc. Prof. Ed Voigtman who is now an emeritus faculty member at the University of Massachusetts (Amherst). Voigtman’s libraries contain pre-built “blocks” – optoelectronic components that can be “wired-up” to create both a pictorial and functional representation of an instrument. Of particular interest here are a series of "polychromatic" blocks that are used in the simulations described below.

An ExtendSim model of our instrument is shown below. In this model, the LED source is represented by the polychromatic “lamp” block (A). The output of this block passes through a polarizer (B), then through the optically active sample (C) and finally a Faraday rotator (D) and second polarizer (E) before reaching the detector (F) – the latter is a photodiode/preamplifier block.

The Faraday rotator block as supplied in the library rotates the polarization of incident light by an amount that is proportional to a control voltage applied at its input terminal. Consequently, we used a ramp voltage to drive this input (G), thereby simulating the motion of the analyzing polarizer in the real instrument. If desired, a noise component can also be added in to the ramp, although this was not used in this work.

As can be seen, the model also incorporates an independent beam path having a second photo-detector that simply omits the sample (C), thereby simulating the behaviour for a non-optically active “blank”.

Also included on the model sheet is a “global parameters” block – this is used to define a vector of wavelengths that are used in the calculations at each step in the simulation. Importantly, this allows the simulation to model the behaviour of our instrument over the LED’s full spectrum of emission wavelengths.
For polarimetric measurements on sucrose the International Commission for Uniform Methods of Sugar Analysis (ICUMSA) specification and standard SPS-1 specifies a weight fraction of 0.23701775, corresponding to 26.000 g of sucrose per 100 cm3 of solution at 20C. This solution has a density of 1097.6393 kgm-3. The standard quotes an optical rotation of 40.7770 for this solution when measured in a 20.000 cm cell at a wavelength of 546.2271 nm.

The ICUMSA standard supplies the necessary coefficients to calculate the specific rotation α546 via a quintic polynomial in the weight fraction of sucrose with an additional cubic correction applied with respect to the temperature deviation from 20C. Additional coefficients allow the result to be converted into an alpha value at any other wavelength αλ by means of the reciprocal of a sextic polynomial in even powers of the wavelength.

Several important modifications were thus made to the code in the initsim block for the general optical activity component (block C) that is supplied in the Voigtman library :

(1) α546 is first calculated at the specified temperature and this value is used to determine αλ using the method and coefficients prescribed in the ICUMSA standard.

(2) αλ is next converted into units of deg/(g/ml.dm)

At the start of an ExtendSim simulation the initsim block repeats these calculations for each of the wavelengths to be used in the simulation. For reference, a sucrose solution at 0.26000 g ml-1 then has an optical rotation of 17.3130 (10 cm cell) and a specific rotation α=66.547 deg/((g/ml)(dm) at the Na D line wavelength (589.44 nm).

Prior to running the simulation, various ASCII files need to be loaded into the model – these include the measured emission profile of the LED (into the lamp block), the molar extinction coefficient of the sample, if relevant (into the optical activity block) and the spectral response of the TSL250 photo-detector (into the photodiode/preamplifier block). Each of these files has an entry corresponding to each of the wavelengths assigned in the global parameters block.

As the simulation is running an oscilloscope block on the worksheet displays the outputs of the two photo-detectors as well as the ramp voltage that is applied to the Faraday rotators. The two detector outputs are also written to a spreadsheet file that is used for subsequent analysis.
Typical results simulating a single full rotation of the analyzing polarizer can be seen in the plot above, in which the “blank” trace appears in black and the sample trace in red. The simulation (run at T = 20C) shows the predicted response of the instrument assuming (i) a yellow LED source having λmax= 591 nm and FWHM of 15 nm and (ii) using a TSL250 detector (whose peak response is actually at 770 nm) - for a sucrose sample having a concentration of 9.785 g sucrose/100 ml and a cell length of 1 dm.

Motion of the analyzing polarizer results in a sinusoidal modulation of the light intensity as recorded on the two photo-detectors. The blue trace shows the modulation waveform that is applied to the Faraday rotators with the simulation commencing with (assumed) crossed polarizers (-900), then parallel (00), then crossed again (+900) before the cycle is repeated to model a full 3600 rotation of the analyzing polarizer in the actual instrument.

The sample trace shows a phase-shifted response compared to the blank; in this simulation we’ve assumed no optical attenuation of the beam accompanying passage of light through the sample (i.e. the sample’s extinction coefficient was set to zero at all wavelengths).

The data sets generated by the simulation are post-processed using IGOR Pro and curve fitting to the functional form I(t) = Asin(ωt+φ)+B allows determination of the phase shift φ between blank and sample. This latter quantity is converted into a predicted optical rotation.

For comparison to a conventional polarimeter we ran an additional simulation assuming the source is a vapor lamp emitting the yellow Na D lines.

At the stated sucrose concentration the results of the simulations are as follows : θLED = 6.370, and θNa = 6.430 . The simulation results predict that measurements made using a low cost LED with an emission maximum close to that of the Na D lines will give a measured optical rotation within 1% of the true value for sucrose. Importantly, the model developed here allows the performance of the instrument to be accurately predicted for any source/detector combination that might be used.

For interest, measurements of the sucrose optical rotation were made using a batch of ten different LED’s, yielding θmean = 17.440 and σ = 0.0280. Taking the literature value of 17.3130 (10.00 cm cell) the indicated error is 0.7%.

Additional simulations of the instrument were performed to predict the influence of source wavelength and bandwidth on the measured optical rotation.

The findings of these simulations are as follows :

(a) For a fixed center wavelength, the optical rotation decreases slightly (0.0150) as the FWHM of the source varies from 2 nm to 20 nm.

(b) for fixed source bandwidth, the optical rotation of a standard sucrose solution changes by ~ +0.06250 per nm relative to the value measured at the Na D line wavelength of 589.44 nm.

The main source of error in an LED-only measurement is the variability in the LED’s wavelength; the spectral width of the source is much less important.