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| Measuring attenuation of light: Two sample cells with different pathlengths | Prev topic | Next topic Fig. 1 |
To measure the attenuation of light by a light scattering and absorbing medium, one measures the exponential decay of power of light, Φ, with distance, z, in the medium:
| Φ(z) = Φ0 exp(-cz) | (1) |
according to the Beer-Lambert law, where Φ0 is the power of light for z = 0.
Given that the form of that decay is known and it is strictly decreasing, it is sufficient to make just two measurements of that power: at z1 and z2 = z1 + z, to yield transmission T(z2 - z1) = T(z). Hence, one can use a set of two sample cells with differing pathlengths (z1 and z2) both filled with the medium to be examined and obtain:
| T(z2 - z1) | = Φ(z2) / Φ(z1) | |
| = Φ0 exp( -cz2 ) / Φ0 exp( -cz1 ) | = exp[ -c(z2 - z1) ] | |
| = exp( -cz ) | (2) |
The cancellation of Φ0 implies that the optical transmission through each cell must be the same when both cells are filled with a medium of negligible attenuation and refractive index which is the same as that of the sample. This latter condition is needed to assure that residual refraction for each cell (due to a slight non-paralellism of the windows) is very nearly identical to that occuring when each cell contains the sample. Incidentally, given such non-parallelism it is essential to always place the cells at the same orientation in the beam path.
Note that the transmission of the cell iself, Tc (see Normalization of the transmitted power), modifies Eq. 1 to become:
| Φout | = Tc Φ(z) |
|
| = Tc Φ0 exp(-cz) | (3) |
However, this modification is of no consequence, assuming that the transmission factors for both cells, Tc1 and Tc2 are equal. Indeed, the factors of Tc cancel out when the ratio of the powers transmitted by each cell is taken in Eq. 2.
Hence, it is not necessary to measure the incident power Φ0. In addition, the effects of transmission through the cells are automatically cancelled. The reference and sample cells can be introduced in the optical path sequentially. This may cause errors if the cells are not placed in exactly the same position from measurement to measurement.
Alternatively, the light beam can be split to pass through the two cells and turned on and off for each cell in rapid sequence by using, for example, a mechanical light chopper (Fig. 1). The light chopper offers an additional advantage of exploiting the on-off modulation of the incident light power at a well-defined frequency to use a method of synchronous detection of the transmitted light power (for example, Bissel PR et al 1987, Meade ML 1983, 1982). This method may significantly increase the signal-to-noise ratio of the transmission measurement. It is also referred to as phase-sensitive detection, or lock-in amplification. In this configuration, the powers in the two beam paths must be the same.
See also Sample and reference cells with the same pathlengths
| CITATION: Swanson N. L., Jonasz M. 2007. Measuring attenuation of light: Two sample cells with different pathlengths (www.tpdsci.com/Tpc/AtnCfMsSetTwoPlen.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 21-Nov-2007 Modified: 16-Jan-2008 Peer-reviewed: 22-Dec-2007 |
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