A time-honored design for non-contact pyrometers is to concentrate incident light from a heated
object onto a small temperature-sensing element. A rise in temperature at the sensor reveals the
intensity of the infrared optical energy falling upon it, which as discussed previously is a function of the target object’s temperature (absolute temperature to the fourth power):

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The fourth-power characteristic of Stefan-Boltzmann’s law means that a doubling of absolute
temperature at the hot object results in sixteen times as much radiant energy falling on the sensor, and therefore a sixteen-fold increase in the sensor’s temperature rise over ambient. A tripling of target temperature (absolute) yields eighty one times as much radiant energy, and therefore an 81- fold increase in sensor temperature rise. This extreme nonlinearity limits the practical application of non-contact pyrometry to relatively narrow ranges of target temperature wherever good accuracy is required.

Thermocouples were the first type of sensor used in non-contact pyrometers, and they still find
application in modern versions of the same technology. Since the sensor does not become nearly
as hot as the target object, the output of any single thermocouple junction at the sensor area will
be quite small. For this reason, instrument manufacturers often employ a series-connected array of thermocouples called a thermopile to generate a stronger electrical signal.

The basic concept of a thermopile is to connect multiple thermocouple junctions in series so their
voltages will add:

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Examining the polarity marks of each junction (type E thermocouple wires are assumed in this example: chromel and constantan), we see that all the “hot” junctions’ voltages aid each other, as do all the “cold” junctions’ voltages. Like all thermocouple circuits, though, the each “cold” junction voltage opposes each the “hot” junction voltage. The example thermopile shown in this diagram, with four hot junctions and four cold junctions, will generate four times the potential difference that a single type E thermocouple hot/cold junction pair would generate, assuming all the hot junctions are at the same temperature and all the cold junctions are at the same temperature.
When used as the detector for a non-contact pyrometer, the thermopile is oriented so all the
concentrated light falls on the hot junctions (the “focal point” where the light focuses to a small
spot), while the cold junctions face away from the focal point to a region of ambient temperature.
Thus, the thermopile acts like a multiplied thermocouple, generating more voltage than a single
thermocouple junction could under the same temperature conditions.

A popular design of non-contact pyrometer manufactured for years by Honeywell was the
Radiamatic16, using ten thermocouple junction pairs arrayed in a circle. All the “hot” junctions
were placed at the center of this circle where the focal point of the concentrated light fell, while all the “cold” junctions were situated around the circumference of the circle away from the heat of the focal point. A table of values showing the approximate relationship between target temperature and millivolt output for one model of Radiamatic sensing unit reveals the fourth-power function:

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We may test the basic validity of the Stefan-Boltzmann law by finding the ratio of temperatures
for any two temperature values in this table, raising that ratio to the fourth power, and seeing if
the millivolt output signals for those same two temperatures match the new ratio. The operating
theory here is that increases in target temperature will produce fourth-power increases in sensor
temperature rise, since the sensor’s temperature rise should be a direct function of radiation power
impinging on it.

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