Optical influences
Introduction
The non-contact temperature measurement is based on an optical measuring method. The optical properties of a pyrometer have a large and often underestimated influence on the measuring accuracy. In many cases, only the parameters specified in the data sheet are compared when testing the measurement uncertainty. However, simple, incorrectly selected or incorrectly adjusted lenses can result in very serious measurement errors. The following report explains the principles and effects of optical aberrations and the specification of the optical parameters of pyrometers. We want to present a way for the user to control the quality of the pyrometer's lens.

Fig.1 CellaTemp PA pyrometer with high-resolution precision lens.
Optical aberrations
Spherical aberration (opening error)
Rays of light that fall close to the edge of a lens are focused at a different distance than rays of light that fall in the centre. The result is a slightly blurred image. Spherical aberration can be reduced in optical systems consisting of several lenses by a suitable combination of several lens surfaces.
Chromatic aberration (longitudinal colour aberration)
The focal length of lenses depends on the wavelength. Light or radiation of different wavelengths is focused at different points. The image of an object then appears with coloured borders around the image. Chromatic aberration can be greatly reduced by using lenses that are corrected for two (achromat) or three (apochromat) wavelengths (Fig. 2). The materials of the lenses are selected in such a way that the aberrations of the lenses compensate each other for two or three wavelengths.
Rays of light that fall close to the edge of a lens are focused at a different distance than rays of light that fall in the centre. The result is a slightly blurred image. Spherical aberration can be reduced in optical systems consisting of several lenses by a suitable combination of several lens surfaces.
Chromatic aberration (longitudinal colour aberration)
The focal length of lenses depends on the wavelength. Light or radiation of different wavelengths is focused at different points. The image of an object then appears with coloured borders around the image. Chromatic aberration can be greatly reduced by using lenses that are corrected for two (achromat) or three (apochromat) wavelengths (Fig. 2). The materials of the lenses are selected in such a way that the aberrations of the lenses compensate each other for two or three wavelengths.

Fig. 2 Focal length deviation due to longitudinal colour aberration for uncorrected and colour-corrected lenses.

Fig. 3 Representation of the measuring field sizes in relation to 90, 95 and 98 % of the maximum receivable energy.
Specification of the pyrometer's lenses
To specify the lens, either the measuring spot size for a certain distance or the distance ratio, i.e. the ratio of the measuring distance to the measuring field diameter, is specified.
The measuring spot size of pyrometers is related to a fixed percentage of the maximum energy that can be received in a half-space. 100 % corresponds to an infinitely large measuring object. The measuring field size is typically related to 90, 95 or 98 % of the maximum receivable energy (Fig. 3).
If the radiation component is set to 95 % instead of 90 %, this results in a larger measuring field. Information on the measurement field size is therefore only comparable if it relates to the same percentage. Some manufacturers do not specify the percentage of radiation or define it as a low percentage. As a result, these manufacturers feign a very small measuring field in the data sheets, knowing full well that they would have to specify a significantly larger value if they had defined it differently. In addition, some manufacturers specify the size of the measuring field without taking lens tolerances into account.
The measuring spot size of pyrometers is related to a fixed percentage of the maximum energy that can be received in a half-space. 100 % corresponds to an infinitely large measuring object. The measuring field size is typically related to 90, 95 or 98 % of the maximum receivable energy (Fig. 3).
If the radiation component is set to 95 % instead of 90 %, this results in a larger measuring field. Information on the measurement field size is therefore only comparable if it relates to the same percentage. Some manufacturers do not specify the percentage of radiation or define it as a low percentage. As a result, these manufacturers feign a very small measuring field in the data sheets, knowing full well that they would have to specify a significantly larger value if they had defined it differently. In addition, some manufacturers specify the size of the measuring field without taking lens tolerances into account.
Effects of optical errors
With pyrometers, a distinction is made between devices with focusable lenses and fixed-focus lenses. The measuring field is only in focus at the focus distance. If the pyrometer is operated outside the focal range, uniform distribution of the infrared radiation on the sensor is no longer guaranteed (Fig. 4).
The radiation received via the measuring surface is then detected to varying degrees. Temperature changes in the centre have a greater effect than at the edges of the measuring field.
This has a particular effect on the calibration of the pyrometer in front of a "blackbody". The opening of the furnace must be several times larger than the measuring field of the pyrometer. For devices with simple lenses and a large measuring field, extremely large-area emitters must be used as a calibration source in order to reduce the measuring errors that can occur during calibration. This is one of the main sources of error for the high measurement uncertainty of low-cost devices.
The radiation received via the measuring surface is then detected to varying degrees. Temperature changes in the centre have a greater effect than at the edges of the measuring field.
This has a particular effect on the calibration of the pyrometer in front of a "blackbody". The opening of the furnace must be several times larger than the measuring field of the pyrometer. For devices with simple lenses and a large measuring field, extremely large-area emitters must be used as a calibration source in order to reduce the measuring errors that can occur during calibration. This is one of the main sources of error for the high measurement uncertainty of low-cost devices.

Fig. 4 Comparison of the intensity distribution with focused and defocused lenses.
Especially with small measuring objects that are only slightly larger than the measuring surface of the pyrometer, an incorrect focus setting can lead to considerable measuring errors. However, even if the pyrometer looks at the measuring object through openings, inspection glasses, furnace walls or sight tubes, poorly adjusted lenses or incorrect focusing can quickly lead to a constriction of the sight cone and thus to incorrect measurements. If measurements are taken on objects that are significantly larger than the pyrometer's measuring field, the displayed temperature will change with simple lenses if the size of the measuring object or the measuring distance changes. Fig. 5 shows the comparison of the reduced display of the measured value for a high-quality and a simple lens in relation to the diameter of the measuring object. With a simple lens, the measured value drops considerably when the size of the measuring object changes. The same effect is achieved by changing the measuring distance with a constant object size. This means that devices with a simple lens display different measured values at different measuring distances. Especially when using simple hand-held devices, which are certainly used at different distances, this source of error must be taken into account. This effect is called the size-of-source effect (SSE) and is a more or less significant source of error in all pyrometers. The causes are aberrations in the lens, scattered light and reflection from optical components and housing parts as well as diffraction due to the wave nature of the light. The size-of-source effect decreases as the measuring wavelength becomes shorter. This influence can be minimized by careful correction of optical imaging errors, the use of anti-reflective optical components and the avoidance of scattered light and reflections in the device. The user can minimize this error in practice by focusing precisely on the measuring distance.

Fig. 5 Comparison of the lower display of the measured value for a high-quality and a simple lens.
Depending on the temperature, the infrared radiation emitted by a measuring object is in the wavelength range between 0.6 - 20 µm, i.e. usually above visible light. Firstly, this means that the lenses must be corrected for the wavelength range used by the pyrometer. If the user wishes to focus visually or if the devices are equipped with a video camera as a sighting aid, the lenses must be designed in such a way that the optical aberrations are corrected equally for both the visible and infrared wavelength ranges. In simple devices, lenses are used that are not colour-corrected or are only corrected for one wavelength. Then the focus points of the infrared and visible radiation do not match (Fig. 2). If the pyrometer is focused via the sighting device, it is not optimally focused for infrared radiation.
Especially when using lasers to display the measuring point, the laser point does not match the measuring distance with simple lenses.
These errors can only be largely eliminated by optically complex two-lens systems or three-lens systems. The pyrometers in the CellaTemp PA series, for example, have high-quality precision lenses with a broadband anti-reflective lens system.
This means that even wires with a diameter of 0.3 mm can be measured correctly in terms of temperature.
Especially when using lasers to display the measuring point, the laser point does not match the measuring distance with simple lenses.
These errors can only be largely eliminated by optically complex two-lens systems or three-lens systems. The pyrometers in the CellaTemp PA series, for example, have high-quality precision lenses with a broadband anti-reflective lens system.
This means that even wires with a diameter of 0.3 mm can be measured correctly in terms of temperature.
Checking of the imaging qualities
The imaging properties of a pyrometer can be easily checked by the user. The pyrometer is aligned to a defined radiation source for this purpose.
The size of the radiation surface should be several times larger than the measuring field of the pyrometer. Now position an open iris diaphragm at the focal distance (a) of the pyrometer in front of the radiation source and use the pyrometer to determine the temperature at an emissivity setting of ε = 1 (Figure 6). It is advisable to carry out the measurement at the end of the pyrometer's measuring range, as optical measuring errors become more visible at higher temperatures. The emissivity on the pyrometer must then be set to 0.98, which leads to an increase in the temperature display.
The size of the radiation surface should be several times larger than the measuring field of the pyrometer. Now position an open iris diaphragm at the focal distance (a) of the pyrometer in front of the radiation source and use the pyrometer to determine the temperature at an emissivity setting of ε = 1 (Figure 6). It is advisable to carry out the measurement at the end of the pyrometer's measuring range, as optical measuring errors become more visible at higher temperatures. The emissivity on the pyrometer must then be set to 0.98, which leads to an increase in the temperature display.

Fig. 6 Measurement setup for testing the optical properties.
Then reduce the diameter of the diaphragm until the displayed temperature matches the original value again. The diameter of the iris diaphragm opening then corresponds to the size of the measuring field in relation to 98 % of the radiation energy. The ratio to the measuring distance a results in the distance ratio D = . This measurement should then be repeated for a measuring field size of 95 % and 90 % and the result compared with the manufacturer's brochure specifications.
This makes it very easy to test and compare the actual optical imaging properties, including the effects of lens errors, of different devices.
This makes it very easy to test and compare the actual optical imaging properties, including the effects of lens errors, of different devices.
Figure 7, for example, shows the diameters of the measuring objects for 90 % and 95 % of the radiation energy. In relation to 90 %, the differences in the measuring field sizes are still relatively small at Ø 14 mm for the simple lens and Ø 10.2 mm for the high-quality lens. However, at 95 % (Ø 24 mm for the simple lens and Ø 11.5 mm for the high-quality lens), the specifications are very different. In order to be able to specify a better (smaller) value for the measuring field diameter, some manufacturers therefore prefer to specify the value for a lower reference value of the radiation (e.g. 90 %). This makes a simple lens seem much better than it actually is.
For pyrometers with pilot light, video camera or through-the-lens sighting, the test can also be used to determine whether the distance of the focus point from the measuring field and from the field of view is identical and whether the measuring field marking actually corresponds to the position and size of the measuring surface of the pyrometer.
For pyrometers with pilot light, video camera or through-the-lens sighting, the test can also be used to determine whether the distance of the focus point from the measuring field and from the field of view is identical and whether the measuring field marking actually corresponds to the position and size of the measuring surface of the pyrometer.

Fig. 7 Comparison of the diameters of the measuring objects for 90 % and 95 % of the radiation energy for high-quality and simple lenses.
Conclusion
When selecting pyrometers, it is important to compare not only the metrological parameters but also the optical properties. Unfortunately, the information provided by some manufacturers in their brochures is often inadequate, so you should ask in detail how the specified measuring field was determined and whether lens errors and alignment tolerances were taken into account in the specification. It is only possible to compare different pyrometers if the optical specifications and reference values are identical. In critical cases, to be on the safe side, you should check the quality and specification of the brochure information yourself as described. After all, what use is a pyrometer if it is specified with an electrical measurement uncertainty of significantly less than 1 %, but the use of simple lenses and optical setups results in significantly larger measuring errors?