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Colorimetry (and it's cousin visible-UV spectroscopy) is a form of chemical analysis that works by sending visible light of one wavelength through the sample. It then analyses how much of the light was absorbed in that process so you can determine concentration.

What I don't understand is why only one wavelength is used. Apparently, even for Infrared Spectroscopy, only one wavelength is analysed at one time yet the whole spectrum is needed. Why not send in white light (with all the wavelengths at once)? The output light could be split through dispersion and every wavelength could be analysed for its absorbance. Perhaps some wavelengths of light aren't worth measuring or too many frequencies at once cause interference?

Why not send in white light (with all the wavelengths at once)?

This is certainly and routinely done today. The main thing is how much price are we willing to pay? In a rigorous sense, colorimetry refers to the fact that we use optical filters to isolate wavelengths rather than monochromators. When the latter are used, you call them spectrophotometers. Basically, the question is referring to scanning instruments versus diode array or multiplexing instruments. Both exist today and both have their advantages and disadvantages.

In scanning spectrophotometers, one wavelength passes through the sample at a time. In diode array instruments, all light passes through the sample at once and it is dispersed later. The dispersed light falls on an array of detectors (thousands of tiny detectors, usually 1024). The detectors do not know what wavelength is falling on them, however, they are calibrated.

Similarly, if you were working in the 1970s-80s you would use a scanning infrared spectrophotometer (one wavelength at a time). One needed a prism made of salt or a very special diffraction grating to disperse the infrared radiation. This made life very difficult. Imagine working with a salt prism!

In Fourier transform infrared spectroscopy, all wavelengths are passed at once, but there is no array of detectors. Unfortunately, there is no detector which can differentiate wavelengths on the basis of their frequency and separate them. We need to modulate them in such a way that an ordinary detector can "follow" the frequency of wavelengths. Here comes in the Michelson interferometer. The raw output does not look like a spectrum at all, but it has all the information "hidden" there. You need Fourier transform to recover a typical infrared spectrum.

Now one may ask why don't we use FT for UV-Vis? The answer is that the required precision of a moving mirror is so high that it is rather difficult to make one.

An explanation is provided in this abstract (1):

Fourier transform spectrometry in the UV-Vis region (FT/UV-Vis),
because it is source shot-noise limited, has a signal-to-noise ratio
(S/N) disadvantage in comparison to dispersive spectrometry,
especially with dense spectra. At the expense of poorer S/N, FT/UV-Vis
can be satisfactory for high-resolution measurements. However,
low-resolution spectroscopic studies, such as molecular absorption
measurements, are not expected to be performed advantageously by
FT/UV-Vis. The broad, dense spectra with high intensity throughout a
wide spectral range should show a significant S/N degradation, in
comparison to results with dispersive spectrometry.

Further explanation of the subject of noise and why FT does not provide an advantage here can be found in course notes made available by U. Delaware Prof. S. L. Neal:

Filters do not always improve the quality of spectral data.
Measurements that are dominated by noise from the source, e.g.,
fluorescence, are often distorted by flicker noise. Whereas white
noise is frequency independent, flicker noise is larger at low
frequencies. In fact, it is sometimes called pink noise (since low
frequencies are associated with red rather than blue light).
Filtering techniques are based on the idea that the noise does not, in
general, consist of the same frequency components as the signal. In
the case of flicker noise, this condition is not met. This is one
reason that FT-UV-VIS spectrometers are not widely used. The
improvement in signal to noise that comes from measuring the entire
spectrum many times using an interferometer during the time a single
spectrum can be measured on a dispersive (monochromator based)
spectrometer is the square root of the number of times the spectrum
was measured for shot noise limited (FT-IR) measurements. In other
words, a ten point spectrum measured by the interferometer has a
signal to noise ratio that is about three times ($sqrt10$ ) larger than the
same spectrum measured using a dispersive device because signal
averaging reduces random noise by the square root of the number of
acquisitions. (Remember this is called the multiplex or Fellgett
advantage.) This improvement is always smaller in the presence of
flicker noise, and in very crowded spectra, a multiplex disadvantage
in which the signal-to-noise ratio in the data acquired by the
interferometer is lower than in the dispersive instrument can be
observed.

Reference

1. Mark R. Glick, Bradley T. Jones, Ben W. Smith, and James D. Winefordner
   Applied Spectroscopy Vol. 43, Issue 2, pp. 342-344 (1989)




2. V. Saptari, Fourier-Transform Spectroscopy Instrumentation Engineering, SPIE Press, Bellingham, WA (2003).