Thermal cameras and distance detection claims.
If you are about to invest in a thermal imaging device be very wary of many published claims that are more marketing biased for a good story than factual. Especially of note are many examples of video footage or image grabs claiming distances to object that do not withstand any logical scrutiny when you consider the size of the object displayed relative to the size of the display. Up front there is no simple answer. The issue of specific distance detection is a very vexed issue due to so many variables. There are established scientific formulas and we will quote the following as being a good summation.
"There are several formulas used to estimate the detection capability of a thermal camera, including the Johnson Criteria, the Resolvability Limit formula, and the Minimum Resolvable Temperature (MRT) formula. These formulas are used to estimate the distance at which a thermal camera can detect an object or the minimum temperature difference that can be resolved by the camera.
However, these formulas can be problematic as they make assumptions about ideal conditions, such as high emissivity of the target object, clear atmospheric conditions, and no camera noise or artefacts. In the real world, these conditions may not always be met, and other factors such as the reflectivity of the target object, the temperature of the surrounding environment, and the presence of atmospheric interference can affect the detection capability of the camera. As a result, the formulas may not accurately reflect the real-world performance of the camera and should be used with caution."
That being said what we will say is for a human size object the FYRLYT FTV-640 camera will resolve a standing 180cm human up to 1800M in ideal conditions. Note there are two measures commonly used and that is DETECT and IDENTIFY and they themselves can be quantumly differential. This is where we are adamant that a thermal camera must be used understanding its limitations regardless of cost and why you will often see it used in conjunction with another optical device that can enhance detail when required. The ethical and safety considerations are obvious.
The other thing to be looking for in claims and we see it often is this. Look for the relative size of the object occupying the image frame. You can reverse engineer this by knowing the camera specifications to quantify is the distance claimed accurate. We see many examples of claimed distances in footage of still captures that are grossly exaggerated and common to see what is claimed as being 400M to being 200M or even less.
The Johnson Criteria is a formula used to estimate the detection capability of thermal cameras, specifically for military applications. It is based on the premise that an object must produce enough contrast against its background to be detectable by the camera. The formula is expressed as:
D = 2.7 x SQRT(RT / deltaT)
where D is the maximum range at which the object can be detected in meters, RT is the background radiation temperature in Kelvin, and deltaT is the minimum temperature difference required for detection in Kelvin.
The Resolvability Limit formula is a method used to estimate the spatial resolution or the ability of a thermal camera to distinguish between two closely spaced objects. It is based on the Rayleigh Criterion, which states that two objects can be resolved if the central maximum of the point spread function of one object does not overlap with the first minimum of the point spread function of the other object.
The Resolvability Limit formula for thermal cameras is expressed as:
deltaX = 1.22 x Lambda x F/# / deltaT
where deltaX is the minimum resolvable distance between two objects in meters, Lambda is the wavelength of the thermal radiation in meters, F/# is the f-number of the camera lens, and deltaT is the minimum temperature difference required for resolution in Kelvin.
The Minimum Resolvable Temperature (MRT) formula is a method used to estimate the sensitivity of a thermal camera or the minimum temperature difference that the camera can detect. It is also known as the Minimum Resolvable Temperature Difference (MRTD) formula.
The MRT formula for thermal cameras is expressed as:
MRT = 0.94 x Lambda / (N x ln(1 + DeltaT/T))
where MRT is the Minimum Resolvable Temperature in degrees Celsius, Lambda is the wavelength of the thermal radiation in micrometers, N is the Noise Equivalent Temperature Difference (NETD) of the camera in degrees Celsius, DeltaT is the threshold temperature difference that can be detected, and T is the absolute temperature of the object being imaged in Kelvin.
This formula provides an estimate of the minimum temperature difference that can be detected by the camera. It is commonly used in the field of thermal imaging to compare the performance of different cameras and to evaluate the sensitivity of the camera under different conditions.
However, it also has limitations as it assumes ideal conditions such as a uniform target temperature and no atmospheric attenuation. In the real world, factors such as target emissivity, background temperature, and atmospheric conditions can affect the sensitivity of the camera. Therefore, the MRT formula should be used with caution and in conjunction with other methods to accurately estimate the camera's sensitivity in real-world scenarios.
Minimum Resolvable Temperature (MRT) formula:
LaRocque, J. J. (1985). Minimum Resolvable Temperature Difference (MRTD) for Thermal Imaging Systems: A Review. Optical Engineering, 24(4), 583–588. https://doi.org/10.1117/12.7973494
Jacobs, R. N. (2002). Handbook of thermal analysis and calorimetry (Vol. 4). Elsevier.
Resolvability Limit formula:
Arvanitis, C. D., Papageorgas, P. G., & Georgiades, A. V. (2016). A comparative study of the Johnson, the resolvability, and the limiting resolution criteria for thermal imaging systems. Journal of Imaging, 2(1), 6. https://doi.org/10.3390/jimaging2010006
Diakides, N. A. (1983). Infrared systems design. New York: Marcel Dekker.
Johnson, R. C. (1965). Detectability and resolvability in optical systems. Journal of the Optical Society of America, 55(4), 433–436. https://doi.org/10.1364/JOSA.55.000433
Mavroidis, M., Alexandridis, A. A., Papageorgas, P. G., & Kandarakis, I. (2017). On the Use of the Johnson Criteria for the Evaluation of Thermal Camera Performance. Journal of Infrared, Millimeter, and Terahertz Waves, 38(4), 476–487. https://doi.org/10.1007/s10762-017-0367-5