What We Measure, Part 2: Transmittance

Previously, we reviewed the first of the basic units we measure: reflectance. We presented a simplified but rigorous definition of the way we quantify the flux reflected from a surface. In a similar way, this post addresses transmittance, which describes the flux that passes through an object, in particular if the spectral properties of the light have been affected. Science words for asking "is the sample colored?"

There are several applications for transmittance, the most common being quantifying the color of filters. Most likely you are viewing this posting with an LCD monitor, and each pixel is actually a tiny back-lit triplet containing a red, green, and blue filter. The selection of these filters was a careful engineering decision based on the output of the backlight and many other factors. Filters serve this and many many other roles in science and technology, but we are getting ahead of ourselves.

The basic equation for calculating transmittance is almost the same as that for reflectance:

Transmittance equation

Similar to what we defined for reflectance, we use Φ to indicate an amount of light, the subscripts t and i for transmitted and incident light. The diagram below shows the flow of light through the system. We have a light source, a beam of incident light passing through the sample, and then a detector measuring the amount of transmitted light. Since this measurement will depend on the specific optical path (properties of the illumination beam, and detection optics, etc) we refer to this as "transmittance factor."

Transmittance diagram

Transmittance Diagram 2

The good news with transmittance is that standardizing the instrument is a bit easier than with reflectance. To measure the incident light Φi we need only remove the sample and make a measurement. The incident light passes through to the detector unaffected. We assume Φi = Φt and the standardization is complete. To be strictly correct, we need to compensate for the detector dark signal Φd and the transmittance of the standard Ts:

Transmittance equation complete

For many applications. Ts is 1.0 since our reference standard was simply air. For measuring liquids, a clear glass cuvette is used. For the standardization step, a cuvette is installed, usually filled with the carrier in your sample (water or a solvent) and then measured for Ts. In this case Ts can be slightly less than 1.0.

These measurements are quite straightforward so long as the sample is non-scattering. That is, it does not affect the direction of light travel, only the spectral properties of the light (via absorption). For scattering samples, transmittance factor is much more dependent on the measurement geometry. That is, the optical configuration. But that will be another post.

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