Edit (months later): In hindsight, I was asking about the theoretical limits of multivariate curve resolution (see Lawton & Sylvestre: Self-modeling curve resolution) in chemometric applications.

NIR spectra are commonly used to estimate analyte concentrations. The common approach is to measure the spectra of different samples with known concentration (training data) and then estimate the unknown concentrations by regression.

My question is whether we could determine analyte concentrations of any substance just from the following:

1) Infinitely precise spectra of all elements.
2) Infinitely precise spectrum of the sample.

If not, would it help if we relaxed on the NIR range assumption?
If still not, would it help if we knew the spectra of all possible molecules with infinite precision?

The first step in determining the answer is probably determining whether there are two different atoms identical in their spectra. I don't know the answer. Unfortunately my knowledge of physics and chemistry is very limited.

  • $\begingroup$ "Infinitely precise spectrum of the sample" ? Precise in what? BTW I find this question unclear and rather strange. $\endgroup$ – Mithoron Jan 9 '18 at 21:25
  • $\begingroup$ @Mithoron precise as in free from measurement errors. $\endgroup$ – user1127 Jan 9 '18 at 21:33
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    $\begingroup$ Firstly, atoms do not have an IR spectrum. You mean molecules, or any kind of chemical substance. Anyway. Then, by "infinite precision", you mean noise-free. Yes of course, no two molecules have the same vibrational modes, except if it's the identical substance. But this is completely pointless, because there is no such thing as a noise-free measurement, and also because you can't just split a single absorption spectrum into the individual spectra of an arbitrary number of possibe components. This approach is 100% wilful nonsense, imo. $\endgroup$ – Karl Jan 9 '18 at 23:56
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    $\begingroup$ to continue comments by @karl, molecular spectra have transitions that have a finite spectral width and because of this spectra from one molecule will always overlap that of another to a greater of lesser extent. You only have to look at an IR spectrum to see this. This means that it can be impossible to properly measure different species as some lines will be hidden under those from different species. Having noise free signals will not help much as you will have to fit data anyway and this will in itself introduce uncertainty is assignments. $\endgroup$ – porphyrin Jan 10 '18 at 14:22
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    $\begingroup$ Thank you for your feedback! I will do some more reading and possibly refine my question. I'll add an analogy to mass spectroscopy, where it is feasible to generate a database of all possible peptide spectra (de novo approach) and then search for the measured spectrum in this database e.g. by the cosine distance metric. I don't hope to build such database for NIR spectra. The goal of this question is just to understand the data at hand 'from bottom up'. $\endgroup$ – user1127 Jan 10 '18 at 16:54

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