Question: Mini spectrophotometer - how does this deviate from the Beer-Lambert law?

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FoxClass asked on June 23, 2016 05:04
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I'm looking at using the mini foldable spectrophotometer (from Public Lab) to monitor qualitative colour changes of a solution in a glass vessel over a short period of time. I'm curious if the simple hardware and SpectralWorkbench could do this, since the colour change in the image should, I suppose, be able to detect a subtle change in the spectrum so long as the room lighting remains constant.

I'm also curious how the measurements taken on the mini spec would relate to concentration of analyte, since there's not really a 'path-length' involved. Would it be a logarithmic relationship to concentration?

Thanks for your thoughts!



7 Comments

The spectrometer requires intensity calibration in order to detect color consistently. The active research is here: https://publiclab.org/notes/stoft/03-06-2015/plab-3-gain-correction @warren @stoft have a clearer answer?

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The Beer-Lambert law primarily states there is a relationship between attenuation and wavelength of light through a substance. The attenuation is linear with path length through a uniform substance. If the attenuation is small and the signal level is high, then the spectrometer will have a better SNR (signal to noise ratio) and RELATIVE measurements are possible. Absolute measurements require sensitivity calibration over the detection wavelength range -- SWB does not yet do this.

Assuming just relative measurements, it is best to 1) provide a stable, broadband light source (Solux 4700K halogen for eg.), 2) no room light as that is hard to control and 3) set the max non-clipped signal level to handle the lowest attenuation configuration. You are then left with the sensitivity range for measurement defined by the spectral curve you observe over the typical range of the spectrometer (eg: 400-650nm).

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Yes, as @stoft mentions, an absolute intensity calibration is not required for demonstrating the Beer Lambert law; @mathew refers to a post about getting closer to absolute intensity calibration, which is one way to enable comparison between different devices (say, with different sensors). But that's not needed here.

@stoft, I'm curious, did you mean attenuation and concentration? I see there are ways to use wavelength with Beer-Lambert, but the main relationship is that attenuation and concentration of the sample are linearly related. But curious if there are other aspects or applications of the law I'm not familiar with.

But yes, I think @stoft is also right that choosing your own stable light source, and not room lighting, is a good way to control light in your scans, and that using a full-spectrum source like a halogen or incandescent will let you measure a larger set of wavelengths.

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However, if it's possible to either turn off exposure compensation between your two scans, or to scan both spectra at the same time (side by side), you'll be able to better ensure a consistent light intensity between the samples. @cristoforetti has been using a Raspberry Pi camera to do this.

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Hi @FoxClass,

This is a great question. As the other commenters have mentioned, to compare intensities across different wavelengths, an intensity calibration would need to be done because the webcam is not equally sensitive at all wavelengths of the visible spectrum. However, if you want to compare relative intensities at the same wavelength, then that is not necessary. If you want any sort of quantitative analyte concentration calculation, a sensitivity calibration would be necessary.

Since you said you are looking for qualitative results, I think you can indeed conduct your experiment without calibration, if you focus on comparing one wavelength at a time. One of the important things here is to make sure you have a blank or control so that you can observe the incident light versus the light coming through your sample. The Beer-Lambert law is generally reduced to A = ELC, where A is absorption, E is an empirical value for molar absorptivity, L is path length, and C is molar concentration. However, A = log(I-initial / I-sample), or the log of the ratio of the incident light intensity versus the light intensity through a sample at a given wavelength. The spectrometer can measure (in relative, non-quantitative terms) the light intensities that will allow you to calculate A, and thus calculate relative C. For your set-up, the path length L is the diameter of your sample bottle (since the incident light will shine through your sample vial before entering the spectrometer. It looks like you have the same size bottles for your control and your samples, so L won't be important unless you're looking for quantitative results (in which case you would need to know E too).

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@warren has a good point; the smaller the change in transmitted light (as a function of attenuation caused by concentration change) the greater the potential for error contributed by the stability of the camera. So, yes, ideally any AGC or auto-exposure should be turned off so the only residual error becomes noise. Recall that the default PLab device only provides 8-bit data and that the measurable dynamic range is, therefore, less than that.

The steady-state measurement limits could be tested by comparing pre-prepared exact concentrations where the attenuation for each remains constant over time. Time-relative measurement limit testing would be more difficult (increasingly as the (dA/dT) [attenuation change per unit of time] increases). For several-second intervals, it might suffice to observe the 'step-function' of changing the concentration by adding a known quantity of the 'sample' or the 'solvent' to the sample under test -- assuming the mixing is quick [and, ideally, taking spectral data at regular intervals during that procedure.]

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Just another note here -- starting to look for someone interested in creating an activity out of a beer's law demonstration -- for determining concentration of a solution.

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