Confidence Limits in (Infrared )Temperature Measurements

This depends on a few other things, but certainly no better than the manufacturer’s calibration specification. We’ll get back to those later. Typically the result of careful measurements is reported as a number, plus or minus an uncertainty value or a standard deviation value for the data set used to calculate the estimate.

Say, for discussion’s sake, that the average measured value is 87.677777 °C ± 1.833 °C, where the 1.833 °C is further specified as the estimated standard deviation.

The technically correct way to report these values for an instrument having a fundamental measurement capability of ±2 °C would be to round the values up to the nearest increment of resolution capability, or as: 88 °C ± 2 °C.

Since a thermal imager is an expensive, complex temperature measurement device, it is a primary, essential requirement that the measurement calibration uncertainty is well known, traceable, and its measurement stability known usually by a calibration history record.

An expensive instrument without regular, periodic checks of one of its key capabilities is a wasted resource. If it is a prime source of income or plant evaluation, then you need to be sure that it functions at its best at all times.

Since a thermal imager is an expensive, complex temperature measurement device, it is a primary, essential requirement that the measurement calibration uncertainty is well known, traceable, and its measurement stability known usually by a calibration history record.

An expensive instrument without regular, periodic checks of one of its key capabilities is a wasted resource. If it is a prime source of income or plant evaluation, then you need to be sure that it functions at its best at all times.

Many Thermographers will fall prey to the argument that is often made that they are not really measuring temperatures; they are measuring temperature differences in a scene. Therefore absolute calibration of a thermal imager is not a problem or concern.

To any paranoid ear, that sounds like an excuse for not understanding how an instrument functions. The fact is, like so many “sales pitches”, there is an appeal to the argument, but it is seldom true.

There are two very important aspects of instrument performance that bear on the subject of calibration stability and uncertainty whether measuring temperatures or temperature differences:

1. The error in a measured temperature level varies with both errors in the instrument zero and gain values, whereas errors in temperature differences vary with the error in the calibration gain and not the zero level.

If the calibration gain is off, then there will be a temperature level sensitivity in measurements of true temperatures and temperature differences or gradients.

For instance, say the temperature difference in a scene between two points is 20 °C. One part is at 120 °C, the other at 140 °C.

Now suppose that the system zero calibration has shifted by 30 °C. In that case the difference is still 20 °C. (Most people associate zero shifts that with a temperature difference-but, in fact gain shifts are just as likely to occur and are the source of serious measurement errors.)

If the system gain has shifted, the difference will vary according to the amount of the gain shift. Take the same example where the output is related by a typical linear relationship; for example, where we assume that the bias is 0.0 and the gain is 10.0:

Output =gain x Input + bias

Table 1-Output effects of zero and gain changes.

If the gain shifts by +10%, a 20 °C difference will look like a 22 °C difference. It’s actually a lot worse than the example given, because thermal imager calibration is not linear, it is noticeably non-linear and gain calibration errors result in much larger temperature errors.

2. Knowing that your calibration is good under the fixed, stable conditions of a calibration environment is not enough. If you measure the same object in an hour or a day or a month from now, chances are very good that the measurement conditions, and possibly even the person making the measurements will not be the same.

You need to know the calibration stability and the effect of each of the variables that can influence the measurement results. You need to be aware of how a measuring instrument behaves when conditions that could influence its measurements change.

One set of “simple” tests for stability and calibration checking is given for spot radiation thermometers in ASTM Standard E1256. It’s a good starting point for testing the stability of thermal imagers although more complete practices need to be available.

Work on them has begun in ASTM Subcommittee E20.02, Radiation Thermometry. So, in order that a temperature differential measurement at one point in time can be compared fairly to another requires that the instrument be calibrated during both sets of measurements and that the effects of the likely influencing factors, that may be different each time, be known and any corrections carefully made.

Making absolute temperature measurements is yet another step in complexity, but it has the very same basics as a differential temperature measurement. Knowing that your calibration is correct is but the first step. You need also to know the effect of the major influencing factors involved in making practical measurements.

You learn about and understand measurement science. It stands to reason that if you are reporting measurements that you understand their believability.

Also, your calibration checking procedures need to have a root source that is at least 4 times better than the calibration sensitivity you are seeking.

As an example, consider the case where one uses the boiling point of water as a “reality check” on one equipment calibration.

Unless one uses traceably calibrated thermometer to verify the boiling temperature of water, one must be careful to correct for local air pressure since the boiling point is pressure sensitive. Normal weather-related atmospheric air pressure variations introduce about a 0.8 °C uncertainty in the boiling point and the altitude at which the water is boiling can introduce an even larger error.

The boiling point of water changes about –1 °C for each 355 meters increase in altitude. In fact, a boiling point apparatus makes a pretty good altitude meter. You need to know how your instrument calibration is established and maintained.

If you use boiling water without an independent, reference temperature sensor to indicate the actual boiling point, you can expect that your system calibration to have an uncertainty of at least 3 °C, assuming you correct for altitude effects. It’s more if you don’t!

Now, assuming that you have a calibrated instrument and go into the field and make a temperature difference measurement, is one measurement enough? How many is enough?

Do you know the ambient temperature, the atmospheric humidity level, the solar intensity, the temperature of the objects surrounding your measurement spot, who is operating the unit, what the various instrument settings are? Good, glad you do.

Do you also know the impact each of these factors has on your resulting measurement values?

Unless the manufacturer of the equipment provides that relationship, you will need to test the equipment yourself, or have it tested by a qualified laboratory. We recommend that you use some established practices as, for example, recommended in ASTM E 1256.

How well do you know the thermal settling time of your imager, say, when leaving an air-conditioned vehicle and walking into an area at an ambient that is 30 °F hotter?

How does your thermal imager correct for the fact that it stabilizes (in one or two hours more or less) at a temperature that is 30 °F hotter than the temperature at which its calibration is certified?

Do you know? If you don’t, you could be making significant measurement errors.

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Tagged as: confidence limit, gage r&r, grr, irinfo, irinfo2003, nist, r&r, traceable calibration, uncertainty