# Explaining the Accuracy and Uncertainty of Infrared Cameras in Laymans Terms

## Introduction

The lack of adequate knowledge about how the sensitivity and accuracy of an instrument is derived will affect its reliability. Infrared (IR) cameras often fall in this category. The discussion of infrared camera measurement accuracy generally involves complicated terms and jargon, which can confuse or mislead people.

Due to these issues the potential benefits of thermal measurement could not be realized for research and development applications. This article discusses measurement uncertainty in plain language, providing people with a foundation that will help them to gain knowledge about IR camera calibration and accuracy.

## Camera Accuracy Specs and the Uncertainty Equation

An accuracy specification, such as ±2°C or 2% of the reading, is seen in most IR camera data sheets. This specification is the result of “Root-Sum-of-Squares”, or RSS, a commonly used uncertainty analysis method. The idea is to determine the partial errors for each variable of the temperature measurement equation, square each error term, then add them all together, and take the square root. Although this equation looks like complicated, it is fairly straightforward.

Conversely, calculating the partial errors can be tricky. “Partial errors” can stem from one of the following variables expressed in the typical IR camera temperature measurement equation:

• Emissivity
• Calibrator (blackbody) temperature Accuracy
• Camera response
• Atmosphere temperature
• Reflected ambient temperature
• Transmittance

Once reasonable values are identified for the “partial errors” for each of the above variables, the overall error equation can be expressed as below:

Where, the ΔT1 , ΔT2 , ΔT3 , etc., are the partial errors of the variables in the measurement equation. Why is this required? Sometimes, random errors add in the same direction, deviating further away from the true value. Sometimes, they add in the opposite direction and negate each other. Taking the RSS provides a value that is ideal for an overall error specification. This has traditionally been the specification illustrated on the data sheets of FLIR cameras.

It is to be noted that the computations described so far can be only valid when the camera is used in the laboratory or at a short range outside (below 20 m). Longer ranges will introduce measurement uncertainty due to atmospheric absorption and its emission to a certain extent.

When a camera R&D engineer carries out an RSS analysis for virtually any advanced IR camera system under laboratory conditions, the ensuing number is roughly ± 2°C or 2%. This can be considered as a reasonable accuracy rating to utilize in camera specifications. Practically however, high performance cameras like the FLIR X6900sc provide better results, compared to economical cameras such as the FLIR E40. More work does still need to be done to better explain this observation.

## Laboratory Measurements and ±1°C or 1% Accuracy

The temperature measurements produced by a camera by pointing it at a target of known temperature and emissivity is discussed in this section. Such a target is generally called a “blackbody.” Figure 1 shows one of FLIR’s calibration labs, with its quarter circle of at least 21 cavity blackbodies. In laboratory measurements of uncertainty, a calibrated camera is pointed at a calibrated blackbody and the temperate readings are then plotted over a period of time. Some random error will always occur in the measurement despite the careful calibrations. It is possible to quantify the resulting data set for accuracy and precision. The results obtained from calibrated blackbody measurement are shown in Figure 2.

Figure 1. FLIR thermography calibration lab in Niceville, FL

The plot in Figure 2 illustrates over two hours of data from an FLIR A325sc camera pointing at a 37°C blackbody at a range of 0.3 m in an indoor environment. The temperature is recorded by the camera once per second. The data graphed is the average of all of the pixels present in the image. A histogram of this data would provide a better explanation. However most of the data points were in the range of 36.8-37°C, with the widest temperature range of 36.6-37.2°C.

Based on this data, an expected accuracy of 0.5°C could be claimed for the average of all the pixels or even ±1°C for the FLIR A325sc and for other cameras that use the same detector. However, it could also be claimed that the aforementioned graph illustrates an average of all of the pixels present, and may not be representative of an individual pixel.

Figure 2. Typical FLIR A325sc camera response when looking at a 37°C blackbody

How well all of the pixels agree with one another can be understood by looking at the standard deviation versus time (Figure 3). The graph reveals that the typical standard deviation is below 0.1°C. The occasional spikes to roughly 0.2°C are a result of the 1-point update of the camera, a type of self-calibration approach that all microbolometer-based cameras need to perform periodically. So far, data collection from uncooled microbolometer cameras has been discussed, how will the results vary for high- performance quantum detector cameras?

Figure 3. Standard deviation of typical A325sc when looking at 37°C blackbody

The response of a typical 3-5 µm camera with an Indium Antimonide (InSb) detector like the FLIR X6900sc is depicted in Figure 4. According to the camera’s specification sheet, the accuracy was tested at ± 2°C or 2%. However, the results are well within those specifications. The precision reading on that day was roughly 0.1°C and the accuracy reading was roughly 0.3°C. However, there is an offset error at 0.3°C due to the calibration of the camera, the calibration of the blackbody, or any of the aforementioned partial error terms. Another possibility is warming up the camera at the start of the measurement.

Figure 4. Response of a typical InSb camera looking at a 35°C blackbody

If the optics or the inside of the camera body are changing temperature, they may offset the temperature measurement. The conclusion we can draw from these two calibration tests is that both microbolometer and photon-counting quantum detector cameras can be factory calibrated to provide accuracies of less than 1°C when looking at 37°C objects of known emissivity under typical indoor environmental conditions.

## Ambient Temperature Compensation

In factory calibrations, ambient temperature compensation is one of the most critical steps. IR cameras, both thermal and quantum detecting, respond to the total IR energy incident on the detector. Most of this energy will come from the scene if the camera is designed well, with very few results obtained from the camera itself.

However, it is not possible to fully eliminate the contribution from the materials that surround the detector and the optical path. Without proper compensation, any temperature changes in the camera body or lenses will drastically change the temperature readings provided by the camera.

The best approach to achieve the ambient temperature compensation is measuring the temperature of the camera and optical path in up to three various locations. Then, the measurement data is added to the calibration equation to ensure accurate readings via the entire range of operating temperatures, typically in the range of -15°C to 50°C. This is especially critical for cameras that will be used in outdoor applications or are otherwise subjected to temperature changes. Even with ambient temperature compensation, the camera needs to be allowed to fully warm up before critical measurements are made. The camera and optics must be kept out of direct sunlight or away from other heat sources.

The measurement uncertainty will be adversely affected when the temperature of the camera and optics is changed. It is to be noted that the ambient temperature compensation will not be included by all camera manufacturers in their calibration process. If the ambient temperature drift is not properly compensated, the data obtained from these cameras could have significant inaccuracies up to 10°C or more. Users must understand how calibrations are carried out before making an investment in an IR camera.

## Other Measurement Considerations

Considerations, such as spot size and emissivity are not directly associated with camera calibration, but can influence camera accuracy. Improper testing conditions or an incorrect emissivity setting will have an impact on the ability of a camera to measure a target correctly.

Emissivity is the ability of an object to emit instead of reflect IR energy. It needs to be properly accounted for. The emissivity of a subject needs to be determined, and that data needs to be entered into the camera. If the target is completely reflective, then necessary measures must be taken to resolve the issue before the measurement is performed. For instance, the surface can be coated with a non-reflective paint. All FLIR cameras offer a way to describe an appropriate emissivity. If users make a mistake, then FLIR R&D software helps them to change the emissivity during analysis. This can be carried out on an entire image or on a region-by-region basis.

The spot size is nothing but how much area is covered by a pixel on a target. For instance, if a lit match at a distance of 60ft is measured with an A325sc featuring a default 25 degree lens, each pixel is able to cover about an inch square area of the total scene. However the match head has a size of only 1/8” square, a size much smaller than that is covered by a pixel.

Almost all of the IR energy hitting that pixel actually comes from the region behind the match ember. However, only 1/64ths of the contribution that is coming from the ember is intended to be measured. The temperature of the ember will be severely under reported by the camera when the background is at ambient temperature.

The possible solutions are to simply move the camera closer to the subject, or coupling a telescopic optic to the camera. Either of these solutions would bring the pixel size nearer to a 1:1 ratio with the ember. If the user wants the closest to absolute temperature accuracy, it must be ensured that the smallest target of interest is completely subtended by at least a 10 x 10 pixel grid. However, the user can get very close to true measurement by considering the spot size to be a single pixel or a 3 x 3 pixel grid.

## Conclusion

From the results discussed in this article, the accuracy of IR cameras can be determined using the RSS uncertainty analysis technique. These cameras may have not more than a 2°C margin of error. The margin of error can be reduced to below 1°C with appropriate calibration and attention to considerations such as spot size, emissivity, and ambient temperature.

This information has been sourced, reviewed and adapted from materials provided by FLIR Systems.