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.