It is difficult to trust the measurements of instruments when it is not clear what mechanism underlies their sensitivity and accuracy. This is often the case with infrared cameras. Furthermore, discussions about the measurement accuracy of infrared cameras are usually mired in complex terminology and jargon that can lead to confusion and error. This may ultimately lead some researchers to reject all such tools. However, in doing so, they miss out on the potential benefits of thermal measurements for R&D applications. In the following discussion, we review technical terms and explain measurement uncertainty in plain language, to provide a basis for understanding the calibration and accuracy of infrared cameras.
Camera accuracy specifications and uncertainty equation
You will notice that most data sheets for infrared cameras have an accuracy specification of ±2ºC or 2% of the measurement. This specification is the result of a widely used uncertainty analysis technique called "Root-Sum-of-Squares" or RSS. The idea is to calculate the partial errors for each variable in the temperature measurement equation, square each error term, add them up and extract the square root. Although this equation looks complicated, it is actually quite simple. On the other hand, determining the partial errors can be complex.
Partial errors" can arise from several variables in the temperature measurement equation of a standard infrared camera, including
- Emissivity
- Reflected ambient temperature
- Transmittance
- Atmospheric temperature
- Camera response
- Calibrator temperature accuracy (black body)
When reasonable values are determined for the "partial errors" for each of the above terms, the general error equation will look like this:
Where the ΔT1, ΔT2, ΔT3, etc. are partial errors of the variables in the measurement equation.
What's the point? It turns out that sometimes random errors accumulate and take you away from the true value, while other times they cancel out. Taking the RSS gives you a value that is more suitable for a general error specification.
It is necessary to clarify that the calculations discussed so far are only valid if the camera is used in the laboratory or at short distances (less than 20 m) outdoors. Longer distances will introduce uncertainty into the measurements due to atmospheric absorption and, to a lesser extent, emissions. When a camera R&D engineer performs an RSS analysis for almost all modern infrared camera systems under laboratory conditions, the figure he or she obtains is around ±2ºC or 2%, a reasonable accuracy rate for use in camera specifications.
However, practice has shown that high-performance cameras perform much better than low-cost cameras, and therefore we still have work to do to better explain this observation.
Laboratory measurements and accuracy of ±1ºC or 1%.
In this section we look at the temperature measurements that a camera produces when it scans an object of known emissivity and temperature. Such an object is usually referred to as a "blackbody". You may have heard this term before in reference to the theoretical concept of an object with a known emissivity and temperature.
The laboratory's uncertainty measurements include pointing a calibrated camera at a calibrated blackbody and tracing the temperature over a period of time. Despite accurate calibrations, there will always be random errors in the measurements. The resulting data set can be quantified for precision and accuracy. Figure 2 below shows the results of calibrated blackbody measurements.
The plot below shows more than two hours of data from a camera analysing a black body at 37°C at a distance of 0.3 m in an indoor environment. The camera recorded the temperature once per second. The plotted data is the average of all pixels in the image. A histogram of the data would have provided a better understanding, but most of the data points were between 36.8°C and 37°C. The furthest recorded temperatures were 36.6°C and 37.2°C.
Given this data, it would be tempting to define an expected accuracy of 0.5°C for the average of all pixels. One could even define ±1ºC for any other camera using the same detector. However, it could also be said that the graph above is an average of all pixels and does not necessarily represent an individual pixel.
One way to see how well the pixels match each other is to look at the standard deviation as a function of time. Figure 3 is an example. The graph shows that the standard deviation is less than 0.1°C. The occasional spikes around 0.2°C are the result of the camera's '1-point' update, a type of self-calibration procedure that all microbolometer-based cameras must perform regularly.
So far we have discussed data collection from uncooled microbolometer cameras. How will the results be different for a high performance quantum detector camera?
Figure 4 shows the response of a standard 3-5 μm camera equipped with an indium antimonide (InSb) detector. The documentation for this camera shows the accuracy tested to ±2 ºC or 2%. In the graph below, we can see that the results correspond well to these specifications: the precision measurement that day was around 0.3°C and the accuracy measurement around 0.1°C. But why was the offset error 0.3°C? It could be due to the blackbody calibration, the camera calibration or any of the partial error terms mentioned in section 2. It is also possible that the camera was simply warming up at the start of the measurement. If the optics or the inside of the camera body change temperature, they may distort the temperature measurement.
The conclusion we can draw from these two calibration tests is that microbolometer cameras and photon counting quantum detector cameras can be factory calibrated to provide accuracies of less than 1°C when examining objects at 37°C with known emissivity under standard indoor environmental conditions.
Ambient temperature compensation
One of the most important steps in factory calibrations is compensation for ambient temperature. Infrared cameras, whether thermal or quantum detection, respond to the total infrared energy that falls on the detector. If the camera is properly designed, most of this energy will be from the scene: very little energy comes from the camera itself. However, it is impossible to completely eliminate the contribution of the materials surrounding the detector and the optical path. Without proper compensation, any change in the temperature of the camera body or lenses will significantly alter the temperature measurements provided by the camera.
The most suitable method of obtaining ambient temperature compensation is to measure the camera temperature and the optical path in up to three different locations. The measurement data is then included in the calibration equation. This ensures accurate measurements over the entire operating temperature range (typically -15°C to 50°C). This is particularly important for cameras that will be used outdoors or that will be subject to temperature changes.
Even with ambient temperature compensation, it is important to let the cameras warm up completely before making critical measurements. In addition, keep the camera and optics out of direct sunlight or other heat sources. Changing the temperature of the camera and optics will have an adverse effect on measurement uncertainty.
It should be noted that not all camera manufacturers include ambient temperature compensation in their calibration process. But by not properly compensating for ambient temperature, the data from these cameras could show significant inaccuracies, up to 10°C or more. Therefore, be sure to ask questions about calibrations and how they are performed before investing in an infrared camera.
Other measurement parameters to be taken into account
Although these parameters are not directly related to camera calibration, emissivity and spot size can have an impact on the accuracy of the camera. An incorrect emissivity setting or unsuitable test conditions will affect the camera's ability to correctly measure your subject.
Emissivity (or the ability of an object to emit rather than reflect infrared energy) must be properly considered. This means taking the time to determine the emissivity of your subject and entering this information into the camera. It also means knowing if the subject is fully reflective and taking steps to resolve this (i.e. covering the surface with non-reflective paint) before making the measurements. All InfraTec cameras provide a means of setting a suitable emissivity. If you make a mistake, all InfraTec software allows you to change the emissivity during the analysis (live view or post analysis). This modification can usually be done on a full image or region-by-region basis.
Another factor to consider is the point size, or the area each pixel covers on your target. Let's say an A325sc camera with a default 25 degree lens measures a burning match that is 18 cm away. Each pixel covers about 2.5 cm² of the total scene. But a match head measures only 0.31 cm², a much smaller area than the pixel that covers it. Almost all of the infrared energy hitting this pixel actually comes from the area behind the glowing match head. Only 1/64th of the contribution comes from the glowing head we wanted to measure. If the background is at room temperature, the camera will significantly underestimate the temperature of the glowing head.
The solution would be to attach a telescopic lens to the camera or simply move it closer to the target. Both solutions would generate a pixel size closer to a 1:1 ratio with the head glowing. If we want the most accurate absolute temperature accuracy possible, we need to ensure that the smallest object is completely covered by a 10 x 10 pixel grid. However, taking a single pixel or a 3 x 3 pixel grid as the point size will get you very close to the actual measurement.
Conclusion
As we have seen, the RSS uncertainty analysis technique allows us to determine the accuracy of infrared cameras and to ensure that they have a maximum margin of error of 2°C. With proper calibration and taking into account factors such as ambient temperature, emissivity and spot size, the possible margin of error can be less than 1°C.
A final note: the information presented in this document was originally written with factory-calibrated infrared cameras in mind. While the physical data is applicable to user calibrations, the tools and methods needed for user calibrations vary depending on the system involved. In addition, knowing how to perform a proper calibration would allow you to perform a custom uncertainty analysis, so the generalized specifications presented in this document would be less relevant.
