Transmitted-light spectra

Schematic representation of an apparatus that measures the absorption spectrum of a gaseous element. The gas in the tube absorbs light at specific wavelengths, called lines, so the intensity of transmitted light is low at these particular wavelengths.

We usually use white light from a Xe discharge arc lamp for the measurement of near-field transmission images and spectra [9]. The spectrum of transmitted light... 

The y-axis of a UV spectrum may be calibrated in terms of the intensity of transmitted light i.e. percentage of transmission or absorption), as is shown in Figure 2.2, or it may be calibrated on a logarithmic scale i.e. in terms of absorbance (A) defined in Figure 2.2. 

Fig. 2. Absorption spectrum of oxygen in the Schumann-Runge band system. The absorption coefficient, k, is defined by the equation I = la exp ( — kx), where h and I are the incident and transmitted light intensities and x is the layer thickness of the absorbing gas reduced to STP. This figure is taken from ref. (101) with the permission of The Journal of Chemical Physics.

To convert an optical signal into a concentration prediction, a linear relationship between the raw signal and the concentration is not necessary. Beer s law for absorption spectroscopy, for instance, models transmitted light as a decaying exponential function of concentration. In the case of Raman spectroscopy of biofluids, however, the measured signal often obeys two convenient linearity conditions without any need for preprocessing. The first condition is that any measured spectrum S of a sample from a certain population (say, of blood samples from a hospital) is a linear superposition of a finite number of pure basis spectra Pi that characterize that population. One of these basis spectra is presumably the pure spectrum Pa of the chemical of interest, A. The second linearity assumption is that the amount of Pa present in the net spectrum S is linearly proportional to the concentration ca of that chemical. In formulaic terms, the assumptions take the mathematical form... 

The photograph presented in Figure 13.10 shows a typical interface used to collect these noninvasive spectra. Light is incident on one side of the skinfold and a fraction of the transmitted light is collected directly from across the input fiber. Bundles of low-hydroxy silica fibers are used to deliver and collect the near-infrared radiation for the measurement. For the experiments described here, the noninvasive spectra were collected with a Fourier transform spectrometer set for a resolution of 16 cm-1 and 128 coadded interferograms. Each recorded spectrum required approximately 60 s to acquire and save. A total of 370 spectra were collected over a period of nearly 7h while in vivo glucose concentrations varied from 6 to 33 mM (108-594 mg/dL). 

Fig. 7 Experimental scheme of a LiNbOs waveguide with an electro-optical interrogation. Here, two electrodes are present, which allow to apply a potential across the electro-optically active waveguide. This leads to a change in the k-vector of the propagating waveguide mode. The transmission of either a single wavelength or a white light spectrum can be measured, as well as the phase between the transmitted single wavelength and a reference beam can be measured...

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