What We Measure. Part 2: Transmittance

Last month 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:

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.

Configuration for transmittance measurement of the sample.

Configuration for transmittance standardization.

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:

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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, we will also need to consider the measurement geometry. That is, the optical configuration. But that will be another posting.

What We Measure. Part 1: Reflectance

Welcome to the first Spectroscopy at Avian Technologies blog post.  Over the next few months, my colleagues and I hope to give you an idea of what we are all about when it comes to measurements — instruments, capabilities, traceability, uncertainties, and anything else you would like to discuss. We hope your comments and questions will guide where we go with this blog.

First of all, we’d like to review what we have for measurement capabilities. The material properties we measure are reflectance and transmittance. The specific definitions can be complex and confusing, but we will present an explanation at the level of the non-expert in the spectroscopy and color measurement communities. Reflectance is the more complex measurement, and this post will contain technical details explaining what it is. Measuring transmittance is a simpler procedure, but it comes with its own set of complications that we will cover in turn.

So, reflectance is simply a ratio: light reflecting off an object divided by the light incident on the object.  We use Φ to indicate the amount of light, the subscripts r and i for reflected and incident light. Sorry for the math, but a little bit is going to be required:

What’s so complicated about that? In principle, nothing, but consider this graphic showing one common arrangement of light source, sample and detector. We have some white light incident on the blue sample, and the blue light reflects off. We position a detector to measure the reflected light. The problem is that besides measuring the reflected light — the numerator of the equation — we also need to measure the incident light for the denominator. That would require positioning the detector where the sample is, or someplace else in the optical path. For higher-end or research instruments this is often possible, but for most devices this is not practical and would be too expensive to enable. 

How then to we measure reflectance, when the vast majority of instruments cannot even measure the simple values in our reflectance equation? We need some help from others. Usually that help comes from the manufacturer of the instrument. In any case, what we need is a sample that is of known reflectance. The measurement community has a special word for such samples: standards; in this case reference standards. 

Imagine you are trying to make accurate voltage readings. You purchase a battery that always produces exactly 5V.^‡ In the morning, you hook up this perfect battery and adjust the voltmeter so it reads 5V. An advanced voltmeter might also have the ability to dial in 0V. Between these two calibration steps, your meter can now accurately measure voltage. When we do the equivalent of the 5V and 0V measurements in our calibration procedure, we are measuring the reference standard and a black standard. The final form of reflectance is this:

Here Φ_d is the dark measurement and the reference reflectance data R_s.

In a real instrument, we cannot measure light quantities directly, but we infer the amount of light from the detector signal. This signal (current or voltage) is digitized and the processed in the control software.

The above measurement is carried out at every point in the spectrum. Depending on the application, this could be 250nm to 2500nm sampled every 1nm or 400nm to 700nm sampled every 10nm. Or mid-IR all the way out to 20µ. And from the reflectance spectrum, derivative values can be calculated, such as color, whiteness, and more. Or you can infer chemical composition, fading, and even counterfeit products! But that is another column...

‡ You may well ask, “how close to 5V does it have to be for me to say exactly 5V?” Good question. That depends on the uncertainty of the measurement process. We will cover that in our discussion about Traceability.

Welcome

The goal of this blog/FAQ is to foster interactive discussions across the spectroscopy community. There are many common (and many uncommon!) questions that we seem to repeatedly field for customers. We would like to make this information more directly available to you. More informed customers and colleagues make our jobs more productive and enjoyable.