Measuring Spectral Sensitivity

When we look at lights or reflecting surfaces of objects, two of the features we notice are their color and brightness. In this section I focus on the subject of brightness and the related concept of luminance which will be discussed below.

It turns out that the brightnesses of colored objects is not as simple as one might initially expect. Without prior knowledge, one might expect that when under a given illumination a red book appears brighter than a blue one, this red book will continue to appear brighter even when the illumination to both books is reduced. Under this condition, one might expect both books to appear less bright but the red one to still appear brighter. A Czech physiologist, Johannes Purkinje, noticed that when red objects in bright light appeared brighter than blue ones these same red objects would appear dimmer than the blue ones when the illumination was much less. It is said that he noticed this phenomenon while looking at the colors in a rug as daylight changed to dusk in the late afternoon or evening (depending on the time of year). This observation is called the Purkinje Phenomenon and the Purkinje Shift.

An important consideration, for all kinds of applied reasons, is the brightness measurement of colored sources. Often, for legal and safety reasons, it is necessary to specify the amount of chromatic light that is needed. Consider, for example, traffic lights. It is important to ensure that there is an adequate amount of light in the traffic signal so that drivers can easily see the lights, correctly interpret their colors and respond in time to guarantee safety.

So now one has the problem of finding an appropriate method of light measurement. Fortunately there are light measuring instruments available. They come in two general types: radiometers and photometers. Radiometers measure the energy emitted or reflected by the source. This is a strictly physical measurement. Unfortunately the radiometric measurement of light does not represent what people see.

For example, suppose that the red, yellow and green traffic signals were adjusted so that they emitted equal energies of light (i.e., they are radiometrically equal). All observers would report that the yellow light is much brighter than the red and green. Most would also say that the green is brighter than the red. If our goal is to make the lights approximately equally bright, radiometry is not the way to go.

The reason that radiometry is an inadequate means for measuring the perception of chromatic brightness is that the visual system is differentially sensitive as a function of wavelength. That is to say it exhibits spectral sensitivity. Light measuring instruments, called photometers, attempt to take into account the average spectral sensitivity of human observers. Because they take into account the spectral sensitivity of an average observer, photometers measure luminance. Recall that radiometers measure radiance. In 1931 the Commission Internationale de l'Eclairage (CIE) an international standardizing body for illumination defined a standard photopic luminous efficiency function. In plain English they defined a standard spectral sensitivity function that is appropriate to young adults and for targets that subtend a 2 degree visual angle. Most photometers use this CIE function. That is the good news. The disconcerting news is that if one adjusts the wavelengths of the visible spectrum so that they are photometrically equal (i.e., of equal luminance) these stimuli will not all appear equally bright. The results will be a lot better than they were when equated radiometrically (i.e., made of equal radiance). In the middle of the spectrum (the yellow-greens, yellow, yellow-orange and even the oranges will appear approximately equally bright. The short wavelengths, i.e. the blues and violets will deviate the most from equal brightness as will the long wavelength reds. The CIE photopic luminous efficiency function is only a reasonably good approximation of the average human spectral sensitivity.

Let us now consider how to measure human spectral sensitivity. There are many methods for doing this, unfortunately they do not all yield exactly the same results. The reader may be thinking, "what is the big deal? Why not just determine how much physical energy is required to make all the visible wavelengths appear equally bright?" Brightness matching results in a technical difficulty dealing with the concept of additivity which I will discuss below. It also turns out brightness matching is not a very reliable method.

Let's deal with reliability first. Consider, for example, two lights: a white and a yellow. Assume that we consider the white our reference source and that we wish to make the yellow equally bright to the white. It is well known that when an observer makes such a match many times that there will be variability in these matches. This is true even when such matches are made all, say, with in an hour. But when this same observer repeats this procedure on a subsequent day the variability between days will be even greater than the variability within a day. This is the problem of intra-subject variability. Then there is the problem of inter-subject variability which can be considerably greater than the intra-subject variability. These variability problems caused visual scientists to seek for more objective means of assessing human spectral sensitivity. The list of methods include:

The interested reader can select each of the methods listed above to learn how the experiments are conducted.

Even if the reader does not want to get involved with the nitty gritty research methods it is worth outlining the major ideas behind all of these methods.

Each of the above methods uses an explicit or and implied reference stimulus. The white light in the brightness matching paradigm, discussed above, is an example of an explicit reference. An example of an implicit reference will be come clear when you read about absolute thresholds.

A second concept that is required for all methods is a criterion response. Such criterion responses are frequently implicit in the name of the method: e.g., equal brightness, minimum flicker, minimum border, criterion visual acuity, criterion electrophysiological response, criterion change in pupil area etc.

The basic idea behind most of the above methods is that one measures the physical energy required for the observer to make the criterion response. The criterion response is made as a function of wavelength. Then the reciprocal of the energy required for the criterion response (relative sensitivity) is plotted as a function of wavelength .

Above I mentioned the problem of additivity. By additivity I mean that when, for example, two lights that are equally bright are added together the result should be a new light that is twice as bright as either of the two components. In simple obvious example of additivity would be that 1 + 1 = 2. So, for example, let us take a reference white light of a certain brightness (luminance) and adjust a green light to be equally bright to this reference white. Then we take a red light and also adjust it to be equally bright to this same reference white light. Now suppose we take this green and red light (both of which are equally bright to the reference white) and mix them together. The first thing we will notice that this green + red light will have a distinct yellowish appearance. But, the question of interest here is how bright will it be? We might expect that it will be twice as bright as the reference white. However, we would be wrong. In fact the mixture of the green + red which appears yellowish will be distinctly less bright that we would expect. We can see this graphically. OK, now that we understand that brightness matching leads to additivity failure, the question arises, what is so important about additivity? The significance of additivity is grounded in the luminance equation. The funny symbol that appears like an elongated "S" is an integral sign and signifies that all of the data following the equal sign is integrated. Integration is really just a fancy mathematical term referring to addition. As can be seen in the luminance equation the radiance as a function of wavelength is multiplied by the sensitivity of the visual system as a function of wavelength.

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