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| Measuring attenuation of light: Sample and reference cells with the same pathlengths | Prev topic | Next topic Fig. 1 |
An alternative experimental arrangement for measuring transmission of light by a medium uses two identical sample and reference cells containing respectively the examined medium (sample) and a transparent reference medium (transmission, T = 1). (Fig. 1). The reference medium must have negligible attenuation and the refractive index which is equal to that of the sample. This latter requirement stems from the need to minimize refraction effects at the windows of the cells.
The power of light, Φ, transmitted through a cell medium of thickness, z, and attenuation coefficient, c, is:
| Φ(z) = Φ0 exp(-cz) | (1) |
according to the Lambert law,
The power of light transmitted through a cell with the sample medium is less than that given in Eq. 1 by a factor Tc < 1, due to the attenuation of light by the cell itself:
| Φs(z) = Tc Φ0 exp(-cz) | (2) |
where c > 0 is the attenuation coefficient of the sample. In the case of the reference cell, the attenuation coefficient of a medium enclosed in that cell vanishes. Hence
| Φr(z) = Tc Φ0 | (3) |
where Tc is assumed the same for both cells (the cells are assumed to be identical). By taking a ratio of Eq. 1 and Eq. 2, we have
| Φs(z) / Φr(z) | = exp(-cz) | |
| = T(z) | (4) |
where we used the definition of transmission, T (Eq. 1 in Transmission, optical density and thickness).
The sample-reference arrangement simplifies the handling of the sample (only one cell needs to be re-filled with each new sample). However, it places stringent requirements on the preparation and maintenance over the time of the measurements of a "perfectly clean" reference medium. This may pose problems, for example, when measuring the transmission of light by pure water (for example, Pope RM and Fry 1997).
A single cell can also be used to sequentially measure the power of light transmitted though the sample and reference media. This eliminates problems with small differences between the geometries of the two separate "identical" cells. However, this also introduces the problem of repeatability of the cell position on re-insertion into the optical path. It also requires a relatively long-term stability of the light source, or monitoring of the incident beam power, because the measurements with the medium and the reference medium are spaced further away in time.
With either arrangement, synchronous detection can be used to improve the signal-to-noise ratio of the transmission measurement (see end of note Two sample cells with different pathlengths and Fig. 1).
See also: Two sample cells with different pathlengths
| CITATION: Swanson N. L., Jonasz M. 2007. Measuring attenuation of light: Sample and reference cells with the same pathlengths (www.tpdsci.com/Tpc/AtnCfMsSetSamRef.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 21-Nov-2007 Modified: 22-Dec-2007 Peer-reviewed: 22-Dec-2007 |
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