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The measurement of transmission, T, of light by an attenuating medium involves normalization of the power, Φ(z), transmitted through a layer of a medium of thickness, z, by the power of light incident at that layer, Φ(0), i.e. it involves taking a ratio
| T = Φ(z) / Φ(0) | (1) |
Given that Φ(z) = Φ(0) exp(-cz), according to the Lambert law, the incident power, Φ(0), cancels out in the expression for transmission, T. This implies that we do not need to know the light source power. In addition, it doesn't matter what type of output the detector gives (current, voltage, frequency, etc.).
However, given that the sample is enclosed in a cell, the power of light incident onto the cell, Φin, and transmitted by the cell, Φout, can only be measured. By following the power flow through the cell, we have:
| Φ(0) = Φin Tw1 | (2) |
| Φout = Φ(z) Tw2 Tr | (3) |
where, Tw1 and Tw2 represent transmissions of the entrance and exit windows, and Tr is the transmission of the cell due the refraction of the beam by the cell, for example, due to non-parallel windows. Hence,
| T | = Φ(z) / Φ(0) | |
| = [Φout / ( Tw2 Tr ) ] / [ Φin Tw1 ] | ||
| = [ Φout / Φin ] / [ Tw1Tw2 Tr ] | (4) |
Thus, in order to calculate T by using Φout and Φin, we need to know a product of Tw1Tw2Tr = Tc, i.e. the overall cell transmission. In the following notes we discuss two ways in which this product can be determined.
The cancellation of the incident light source power, referred to earlier, is conditional on it being constant over the time of the measurements. Alternatively, a reference channel may be used to continuously monitor the light source power and replace both the power incident and transmitted through a sample cell by the ratios of those powers to the reference power.
| CITATION: Swanson N. L., Jonasz M. 2007. Measuring attenuation of light: Normalization of the transmitted power (www.tpdsci.com/Tpc/AtnCfMsNorm.php). In: Top. Part. Disp. Sci. (www.tpdsci.com). |
HISTORY: Published: 21-Nov-2007 Modified: 18-Dec-2007 Peer-reviewed: 22-Dec-2007 |
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