The size-of-source effect (SSE) in pyrometry might be a major cause of temperature measurement uncertainty. It describes the effect by which the measurement signal and thus the temperature show a change in conjunction with changing size of the measured object. Its cause is diffraction, scattering, reflection and aberration of the infrared radiation to be measured in the optical channel. In pyrometry, this effect is well understood and extensively described in the literature, e.g. in Gutschwager et al. (2008) and Machin and Sergienko (2001).

This effect also occurs in thermography. The displayed temperature of an object in the thermoscene depends on the size of the object. Particularly for very small objects (forming an image of less than 4 pixel × 4 pixel), the temperatures measured are regularly erroneous. Alongside the previously mentioned reasons for the SSE, in thermography the digitization of the thermal image (sampling and pixelization) provides a further important cause. In principle, the SSE represents a reduction in contrast and can be described as such. In contrast to scattering, reflection and aberration, diffraction and digitization can be described with the modulation transfer function MTF, as is common in image processing.

In the following, this contrast reduction is described for an uncooled thermal imaging camera using the MTF. With the aid of the MTF, the SSE can then be calculated for very small and very large objects and subsequently a scene (Siemens star) presented to measure the image quality.

For optoelectronic systems, the optical transfer function OTF describes the image quality (DIN ISO 9335, 2015; DIN ISO 15529, 2010). The modulation transfer function MTF is the magnitude of the OTF (Budzier and Gerlach, 2011). In uncooled infrared cameras with microbolometers, the system MTF is obtained through multiplication of the optical MTF of the lens used and the pixel MTF.

At this point it must be explicitly stated that all considerations of the MTF always refer to the radiation flux and not to temperatures. Thus, an MTF of 0 means an averaging of the radiation in the image, which does not correspond to the average value of the temperatures in the thermal image due to the non-linear correlation of radiation flux and temperature (Planck's radiation law).

In addition to the thermal image (temperature in ∘C), an infrared camera also outputs values proportional to the radiation flux, which correspond to the digital voltages of the pixels. These values are converted to temperatures in the calibration process and are called relative radiant flux. Figure 1 shows the measured relationship between the object temperature and the relative radiation flux of the uncooled infrared camera used. The relationship shown is typical for uncooled infrared cameras. However, since the exact values are very specific for each camera, these relationships are determined during the calibration process of the individual infrared camera (Budzier and Gerlach, 2015).

For small objects, e.g. images of hotspots extending a few pixels in the image, the measured object temperature is always less than the actual temperature (Fig. 7). For very small objects, e.g. smaller than 4 pixel × 4 pixel in the image, significant deviations occur.

When imaging large objects, such as area radiators, not only the edges are blurred, but the entire surface is also affected (Fig. 8). For example, the profile of the hot surface is rounded (Fig. 9). The measured temperature decreases from the centre of the image of the surface to the edge. Colder objects are accordingly measured warmer than their true temperature. Colder or hotter refers to the average temperature of the thermoscene. All profiles have been calculated with the measured MTF from Fig. 5 (image centre) and for a QVGA microbolometer with a pixel size of 25 µm and a lens with f/1.0–18 mm. In addition, it has been assumed that the same MTFs apply in both the vertical and horizontal directions.

The Siemens star offers a good opportunity to test the quality of an optical imaging system. To this end, a suitable scene was created (Fig. 10). In the thermal image (Fig. 11) it can clearly be seen how small structures are blurred out and approach the average temperature of approx. 62 ∘C. The small opening at the centre of the Siemens star, required for manufacture, shows 72.4 ∘C, that is, 20 K less than the real temperature.

If the distance between the camera and the scene is increased, the structures shown on the thermal image become smaller (Fig. 12). In the profile, there is clearly an area at average temperature (MTF → 0). At the centre of the Siemens star, where there ought to be a hotspot, the temperature is below this average (Fig. 13). This is where spurious resolution occurs.

The modulation transfer function MTF is suitable for explaining the phenomena of contrast reduction and the size-of-source effect (SSE). Therefore, it provides a good and above all impartial description of the image quality. The MTF of uncooled infrared cameras is determined by the diffraction of the lens and the sampling caused by the pixel size. It also allows an estimate of how large an object needs to be that the displayed temperature shows a sufficient accuracy.

The SSE leads to blurring in the image. This is of particular importance for the imaging of small objects, where the displayed temperatures are particularly incorrect. Since the size of an object in the image depends on the measuring distance, there is an apparent distance dependence of the temperature measurement. When imaging large objects, not only the edges become blurred, but the entire image is also affected.

However, other image errors such as reflections in the optical channel or defects in sensor electronics cannot be explained by the MTF.