Wednesday, April 25, 2018

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Non-Contact Temperature Sensors

Virtually any mass above absolute zero temperature emits electromagnetic radiation (photons, or light) as a function of that temperature. This basic fact makes possible the measurement of temperature by analyzing the light emitted by an object. The Stefan-Boltzmann Law of radiated energy quantifies this fact, declaring that the rate of heat lost by radiant emission from a hot object is proportional to the fourth power of the absolute temperature:


 = Radiant heat loss rate (watts)

   e = Emissivity factor (unitless)

   σ = Stefan-Boltzmann constant (5.67 × 108 W / m2 K4)

   A = Surface area (square meters)

   T = Absolute temperature (Kelvin)


The primary advantage of non-contact thermometry (or pyrometry as high-temperature measurement is often referred) is rather obvious: with no need to place a sensor in direct contact with the process, a wide variety of temperature measurements may be made that are either impractical or impossible to make using any other technology.

It may surprise some readers to discover that non-contact pyrometry is nearly as old as thermocouple technology1, the first non-contact pyrometer being constructed in 1892.

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):

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:

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, 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 Radiamatic2, 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:


 Target temperature (K) 
 Millivolt output 
4144 K 34.8 mV
3866 K 26.6 mV
3589 K  19.7 mV
3311 K  14.0 mV
3033 K 9.9 mV
2755 K  6.6 mV
2478 K  4.2 mV
2200 K  2.5 mV
1922 K 1.4 mV
1644 K 0.7 mV

We may test the basic3 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.

For example, if we were to take 4144 K and 3033 K as our two test temperatures, we find that the ratio of these two temperature values is 1.3663. Raising this ratio to the fourth power gives us 3.485 for a ratio of millivolt values. Multiplying the 3033 K millivoltage value of 9.9 mV by 3.485 gives us 34.5 mV, which is quite close to the value of 34.8 mV advertised by Honeywell.

If accuracy is not terribly important, and if the range of measured temperatures for the process is modest, we may take the millivoltage output of such a sensor and interpret it linearly. When used in this fashion, a non-contact pyrometer is often referred to as an infrared thermocouple, with the output voltage intended to connect directly to a thermocouple-input instrument such as an indicator, transmitter, recorder, or controller. An example of this usage is the OS-36 line of infrared thermocouples manufactured by Omega.

Infrared thermocouples are manufactured for a narrow range of temperature (most OS-36 models limited to a calibration span of 100 oF or less), their thermopiles designed to produce millivolt signals corresponding to a standard thermocouple type (T, J, K, etc.) over that narrow range.

A counter-intuitive characteristic of non-contact pyrometers is that their calibration does not depend on the distance separating the sensor from the target object4. This is counter-intuitive to anyone who has ever stood to an intense radiative heat source: standing in close proximity to a bonfire, for example, results in much hotter skin temperature than standing far away from it. Why wouldn’t a non-contact pyrometer register cooler target temperatures when it was far away, given the fact that infrared radiation from the object spreads out with increased separation distance? The fact that an infrared pyrometer does not suffer from this limitation is good for our purposes in measuring temperature, but it doesn’t seem to make sense at first.

One key to understanding this paradox is to quantify the bonfire experience, where perceived temperature falls off with increased distance. In physics, this is known as the inverse square law: the intensity of radiation falling on an object from a point-source decreases with the square of the distance separating the radiation source from the object. Backing away to twice the distance from a bonfire results in a four-fold decrease in received infrared radiation; backing way to three times the distance results in a nine-fold decrease in received radiation. Placing a sensor at three integer distances (x, 2x, and 3x) from a radiation point-source results in relative power levels of 100%, 25% (one-quarter), and 11.1% (one-ninth) received at those locations, respectively:

This is a basic physical principle for all kinds of radiation, grounded in simple geometry. If we examine the radiation flux emanating from a point-source, we find that it must spread out as it travels in straight lines, and that the spreading-out happens at a rate defined by the square of the distance. An analogy for this phenomenon is to imagine a spherical latex balloon expanding as air is blown into it. The surface area of the balloon is proportional to the square of its radius. Likewise, the radiation flux emanating from a point-source spreads out in straight lines, in all directions, reaching a total area proportional to the square of the distance from the point (center). The total flux measured as a sphere will be the same no matter what the distance from the point-source, but the area it is divided over increases with the square of the distance, and so any object of fixed area backing away from a point-source of radiation encounters a smaller and smaller fraction of that flux.

If non-contact pyrometers really were “looking” at a point-source of infrared radiation, their signals would decrease with distance. The saving grace here is that non-contact pyrometers are focused-optic devices, with a definite field of view, and that field of view should always be completely filled by the target object. As distance between the pyrometer and the target object changes, the cone-shaped field of view covers a surface area on that object proportional to the square of the distance. Backing the pyrometer away to twice the distance increases the viewing area on the target object by a factor of four; backing away to three times the distance increases the viewing area nine times:

So, even though the inverse square law correctly declares that radiation emanating from the hot wall (which may be thought of as a collection of point-sources) decreases in intensity with the square of the distance, this attenuation is perfectly balanced by an increased viewing area of the pyrometer. Doubling the separation distance does result in the flux from any given area of the wall spreading out by a factor of four, but the pyrometer’s view now covers four times as much area on the object as it did previously. The result is a perfect cancellation, with the pyrometer providing the exact same temperature measurement at any distance from the target where the target fills the entire field of view.

Perhaps the main disadvantage of non-contact temperature sensors is their inaccuracy. The emissivity factor (e) in the Stefan-Boltzmann equation varies with the composition of a substance, but beyond that there are several other factors (surface finish, shape, etc.) that affect the amount of radiation a sensor will receive from an object. For this reason, emissivity is not a very practical way to gauge the effectiveness of a non-contact pyrometer. Instead, a more comprehensive measure of an object’s “thermal-optical measureability” is emittance.

A perfect emitter of thermal radiation is known as a blackbody. Emittance for a blackbody is unity (1), while emittance figures for any real object is a value between 1 and 0. The only certain way to know the emittance of an object is to test that object’s thermal radiation at a known temperature. This assumes we have the ability to measure that object’s temperature by direct contact, which of course renders void one of the major purposes of non-contact thermometry: to be able to measure an object’s temperature without having to touch it. Not all hope is lost, though: all we have to do is obtain an emittance value for that object one time, and then we may calibrate any non-contact pyrometer for that object’s particular emittance so as to measure its temperature in the future without contact.

Beyond the issue of emittance, other idiosyncrasies plague non-contact pyrometers. Objects also have the ability to reflect and transmit radiation from other bodies, which taints the accuracy of any non-contact device sensing the radiation from that body. An example of the former is trying to measure the temperature of a silver mirror using an optical pyrometer: the radiation received by the pyrometer is mostly from other objects, merely reflected by the mirror. An example of the latter is trying to measure the temperature of a gas or a clear liquid, and instead primarily measuring the temperature of a solid object in the background (through the gas or liquid).

Nevertheless, non-contact pyrometers have been and will continue to be useful in specific applications where other, contact-based temperature measurement techniques are impractical.

A very useful application of non-contact sensor technology is thermal imaging, where a dense array of infrared radiation sensors provides a graphic display of objects in its view according to their temperatures. Each object shown on the digital display of a thermal imager is artificially colored in the display on a chromatic scale that varies with temperature, hot objects typically registering as red tones and cold objects typically registering as blue tones. Thermal imaging is very useful in the electric power distribution industry, where technicians can check power line insulators and other objects at elevated potential for “hot spots” without having to make physical contact with those objects. Thermal imaging is also useful in performing “energy audits” of buildings and other heated structures, providing a means of revealing points of heat escape through walls, windows, and roofs. In such applications, relative differences in temperature are often more important to detect than specific temperature values. “Hot spots” readily appear on a thermal imager display, and may give useful data on the test subject even in the absence of accurate temperature measurement at any one spot.


1Although Seebeck discovered thermo-electricity in 1822, the technique of measuring temperature by sensing the voltage produced at a dissimilar-metal junction was delayed in practical development until 1886 when rugged and accurate electrical meters became available for industrial use.

2Later versions of the Radiamatic (dubbed the Radiamatic II ) were more than just a bare thermopile and optical concentrator, containing electronic circuitry to output a linearized 4-20 mA signal representing target temperature.

3Comparing temperature ratios versus thermopile millivoltage ratios assumes linear thermocouple behavior, which we know is not exactly true. Even if the thermopile focal point temperatures precisely followed the ratios predicted by the Stefan-Boltzmann law, we would still expect some inconsistencies due to the non-linearities of thermocouple voltages. There will also be variations from predicted values due to shifts in radiated light frequencies, changes in emissivity factor, thermal losses within the sensing head, and other factors that refuse to remain constant over wide ranges of received radiation intensity. The lesson here is to not expect perfect agreement with theory!

4An important caveat to this rule is so long as the target object completely fills the sensor’s field of view (FOV). The reason for this caveat will become clear at the conclusion of the explanation.

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