© The Author(s), published by EDP Sciences, 2024

1 Introduction

Industrial bulk oven processes require stable and precise temperature monitoring and control, and thus require accurate temperature measurements. One such process is the hardening of bulk ceramics, primarily kaolinite, in a newly designed kiln, for which the advanced multi-channel pyrometer shall be designed.

The Institute of Space Systems (IRS) at the University of Stuttgart has extensive experience in the field of pyrometry; particularly with the PYREX system which flew onboard the European Space Agency (ESA) mission EXPERT, which was designed to measure the heat flux through a ceramic thermal protection system during atmospheric entry by measuring its backside temperature. [1]

Further developing the IRS pyrometer technology, a new advanced multi-channel pyrometer is designed. The pyrometer shall measure temperatures of kaolinite, in a range of 100–1750 °C where the measurement error shall not exceed 2 K. The surface of the bulk material allows the assumption of diffuse emission and reflection. Six measurement channels shall be used. The measurement frequency shall not be lower than 0.5 Hz. These requirements are reflected in the various design aspects.

Additionaly, the system shall conduct temperature measurements independent of the emissivity of the bulk material. The main target application of the designed pyrometer is a closed oven system, where a blackbody environment can be assumed because the ambiance is isothermal [2]. Since the goal is to develop a versatile product, a filter system and an algorithm for multi-color pyrometry are part of the pyrometer design. The signal path of each pyrometer channel consists of collimator optics, an optical fiber, a combination of interference filters and a photo diode. Of those components, the filters and diodes have the largest impact on the resulting signal strength and its wavelength dependence. It is decided that the diodes are the same for all channels, while the filters can be interchanged between channels. This interchangeability enables two-color multi-color pyrometry approaches for emissivity independent measurements.

2 Fundamentals

In the following sections, the physical principles used in pyrometry are laid out.

2.1 Thermal radiation

All bodies with non-zero temperatures emit electromagnetic radiation, according to the Stephan-Boltzmann law:(1) is the radiated power over all wavelengths, σ is the Stephan-Boltzmann constant, ε is the emissivity of the radiator, A is its surface and T its temperature [3].

The radiated power is non-uniformly distributed over all wavelengths. The spectral distribution of radiation density is described by Planck’s radiation law,(2)where L _λ is the spectral radiance, M _λ is the spectral radiant exitance, h is Planck’s constant, c is the speed of light, λ is the wavelength and k is the Boltzmann constant [4].

In the context of pyrometry, Planck’s radiation law is frequently simplified using the Wien approximation.

The Wien approximation is(3)

In other publications on multi-color pyrometry like [5–7], the Wien approximation is used to make the emissivity independent temperature determination possible by simplifying the temperature dependence of the spectral radiance in Planck’s radiation law. The approximation is feasible in the Wien region . Its error is less than 1% if λT < 2898 μmK [8]. For the given temperatures, that means that the measuring wavelengths would have to be between around 1.4 μm for the high end of the temperature range and 7.8 μm for the low end of the temperature range. Measurements must be taken at high wave lengths though, around 5.0–8.0 μm, as explained in Section 4.1. This means that for high temperatures in the specified measuring range, the Wien approximation would introduce large errors – up to around 41.1% (see Fig. 1) – and thus cannot be used.

Figure 1 Relative error intruduced by using the Wien approximation in equation (2).

2.2 View factor

To measure the radiation emitted by a body, a detector of a finite size must be used. The fraction of the radiation leaving the source that is seen by the detector is indicated by the view factor. The view factor between the radiation source and a pyrometer diode that receives all the radiation that is collected by a collimator is the view factor between two disks on the same axis. It is(4)with , r _i denoting the radii of the source surface (i = 1) and receiving surface (i = 2) and a denoting the distance between the two surfaces [9]. For a pyrometer with collimator optics, r ₁ is the radius of the measuring point and r ₂ is the radius of the collimator aperture.

2.3 Emissivity independent temperature determination

Single-color pyrometers offer highly accurate temperature measurements in clean environments when the emissivity of the investigated object at the measuring wavelength is known. However, in industrial environments contaminants on the surface and in the line of sight, varying surface geometries and emissivities cause significant measurement errors. In contrast, two-color and multi-color pyrometers offer more robust and accurate measurements as the measurement principle mitigates the influence of the stated measurement errors.

2.3.1 Two-color pyrometry

Two-color pyrometers measure the radiation intensity in two narrow wave bands. The ratio of the two signal strengths is then a function of temperature and independent of emissivity, assuming that the emissivity is equal in both wavebands. Since this assumption generally does not hold in practice, the accuracy of two-color pyrometers is too low for the use case at hand [10].

2.3.2 Multi-color pyrometry

Multi-color pyrometers measure the radiation intensity within four or more narrow wave bands. A least-squares technique is used to solve for the unknown emissivity as well as the surface temperature. For this to work, prior knowledge on the functional dependence of the emissivity on the wavelength is required. Typically, the spectral emissivity function is assumed to be continuous and single-valued in the wavelength region in which the measurements are taken. With these assumptions, the spectral function of emissivity can be approximated using an exponential operating on a polynomial or a polynomial [7].

The obtained systems of equations can then be used to determine the surface temperature as explained by Neupane [7].

3 Simulation software

To save on protoyping costs and time that would arise from testing many different combinations of optical components, a simulation software for pyrometers is created at the beginning of the design process. This software, “PyroSim”, is implemented using the Python language and the Qt5 graphical user interface library. The software simulates the whole signal path seen in Figure 2. For given temperatures, the software calculates the corresponding voltage signal.

Figure 2 Optical signal path per channel.

3.1 Structure

A modular approach was chosen for the code. The simplified schematic of the PyroSim software structure is shown in Figure 3. Modules for the optical and electrical components as well as a radiation module and a geometry module make up the data model. It is independent of the graphical user interface (GUI). The GUI is connected to the data model via a controller module, which is also connected to a module for saving and loading pyrometer configurations for improved user experience.

Figure 3 Simplified schematic of the software structure.

Within the data model, the different component types are implemented as independent modules. All optical component modules are supersets of a common base. This makes it easy to add more component types if necessary.

Specific components of the implemented types are saved as text files. Components can easily be added to the software’s database by extracting the relevant information from their respective data sheets.

3.2 Logic

The software simulates the signal path from the radiation source to the photo diode as well as the electronic amplification of the photo current. The radiation source is assumed to be a blackbody radiatior. The photocurrent is calculated as(5)with(6) L _λ denotes the thermal radiation emitted by the radiation source, F _s−d denotes the view factor between the source and a diode. τ _fiber is the transmissivity of an optical fiber(7)where δ is the attenuation of the fiber and l is its length, τ _filters is the transmissivity of a combination of optical filters(8)

τ _lens and τ _collim denote the transmissivities of any lenses in the system and the collimator assembly, respectively. Lastly, R _diode is the responsivity function of a given photodiode.

4 Optical design

Based on the PyroSim simulation results, as well as optical and physical considerations, the optical configuration was determined. The design considerations for all components seen in Figure 2 are discussed in the following sections.

4.1 Photo diode

First, a photo diode capable of detecting weak infrared signals was chosen. As is shown in Figure 4, the intensity of a black body radiator at 100 °C is several orders of magnitude lower than that of a black body radiator at 1750 °C, even at the wavelength of maximum radiation intensity at 100 °C. Thus, the sensitive range of the diode is governed by the intensity distribution of a black body at the lowest temperature of the measuring range, 100 °C. A suitable photo diode is the two-stage thermoelectrically cooled Hamamatsu P12691-201G, which is an Indium Arsenide Antimonide detector, as it has a high responsivity across a large part of the relevant wavelength range (around 5.0–8.0 μm) [11]. Its spectral responsivity along with the radiation intensity for a 100 °C blackbody can be seen in Figure 5.

Figure 4 Radiation intensity distribution for the upper and lower temperature limit of the measuring range.

Figure 5 Radiation intensity distribution for the lower temperature limit of the measuring range and diode sensitivity.

4.2 Optical fiber

The optical fiber needs to have a transmission range that corresponds well to the detection range of the diode. Thus, chalcogenide glass fibers as well as hollow core glass fibers are possible. Since hollow core fibers are susceptible to high bending losses, the IRF-Se-100R by IRflex is chosen [12].

4.3 Optical filters

Optical filters are used to enable a multi-color pyrometry approach. The filters are mounted on a rotating revolver so that each filter can be used for each channel (see Section 5). To achieve the best possible accuracy of emissivity independent temperature determination, six different filters are used, as accuracy increases with the number of wavelength channels [13]. More channels are not possible as explained in Section 7.

The choice of filters is limited to the responsive range of the diode, so roughly 5.0 μm to 8.0 μm. The oven contains combustion products CO, CO₂ and H₂O, of which only the H₂O absorbs thermal radiation in the relevant wavelength range [14]. The filters are chosen to minimize the absorption by water (see Fig. 6), which is only successful for the three filters at higher wavelengths (Fig. 6). Other factors for the filter choices were the availability and the total transmission of the filters. The chosen filters are listed in Table 1. All filters are manufactured by Northumbria Optical Coatings Ltd. [19].

Figure 6 Spectral transmissivties of the filters used and of water vapour at 1 bar and 300 K, HITEMP [14] data visualized using RADIS [15–18].

4.4 Water vapour

Even though the filters are chosen to minimize the influence of water vapour absorption and emission, it cannot be avoided completely.

Absoprtion occurs in the air flushed section of the path, that is in the tube described in Section 5.2. It must be taken into account by incorporating the transmission spectrum of water vapour, at the temperature and concentration of the surrounding air, into the signal chain computation, using HITEMP[14] and RADIS [15–18].

Emission occurs in the oven between the tube and the bulk material. In this area, the oven is heated by burning natural gas, which burns at 1937 °C (adiabatic flame temperature) [20]. This flame temperature is assumed to be constant, so the emission spectrum can be calculated and subtracted from the signal before further processing, using HITEMP [14] and RADIS [15–18]. These assumptions regarding water vapour absorption, emission, and constant flame temperature must be validated through comprehensive test measurements to ensure the accuracy of the signal processing approach.

5 Mechanical design

Mechanically, the pyrometer system has two special features: a filter revolver and sensor heads that are decoupled from the base unit. The general mechanical layout can be seen in Figure 7.

Figure 7 Schematic of the pyrometer system design.

5.1 Filter revolver

The filter revolver is a disk inside the base unit which holds one filter for each of the six measurement channels. The disk is connected to a stepper motor so that the narrow band filters can be interchanged between the six channels. This means that each measurement channel can be used as a six-color pyrometer. Since the required measurement frequency is very low, positioning time is not critical; the six positions can be switched through in less than 0.5 s.

5.2 Sensor heads

The sensor heads consist of a collimator which focusses light into an optical fiber which is connected to the base unit. This ensures that the base unit is far away from the heat source. Furthermore, it allows for high flexibility in terms of sensor placement. The sensor heads are placed on special viewports in the oven walls wherever temperature measurements are required. These ports consist of a tube that leads through the insulating layers (see Fig. 8), which is threaded outside the oven so that the sensor heads can be screwed on. The tube, whose dimensions are yet to be determined, limits the size of the measuring area. The measuring area otherwise depends on the collimator’s beam divergence. Since spacial accuracy is not a requirement, no further measures to limit the measuring area were taken. Between the tube and the sensor head, there are ports for air flushing, minimizing the heating of the sensor heads and preventing dust buildup on optical components.

Figure 8 Conceptual drawing of the sensor head placement in the oven wall with the cone of vision of the sensor head in red.

6 Electronic design

The electronic design is required to provide data aquisition and stepper motor control as well as data processing. For these tasks, Stange Elektronik GmbH has designed four printed circuit boards inside the base unit: A sensor board, a sensor acquisition board, a micro controller board and a power supply board (see Fig. 7). The sensor board houses the photo diodes. On the sensor acquisition board, the photo current of the diodes is converted into a voltage using transimpedant amplifiers. Depending on the photo current, different amplification circuits can be selected for each channel using relays. The micro controller board houses an ATSAMD51N19A-AU micro controller. The controller controls the stepper motor and calculates the target temperature from the measurement voltages for each channel. Lastly, the power supply boards provides power to all other boards as well as the stepper motor.

7 Emissivity independent temperature determination

Emissivity independent temperature determination can be achieved using multi-color pyrometry approaches, as explained in Section 2.3. These approaches are made possible via the optical, mechanical and electronic design discussed so far.

The requirements and prior design decisions lead to a six-color approach: More wave bands tend to produce more accurate temperature measurements as seen in [13], but several limitations lead to just six channels being feasible. Firstly, the requirements state that the six measurement channels of the pyrometer shall measure simultaneously. This means that, given the mechanical design and the filter revolver assembly, the number of wave bands must be a multiple of the number of measurement channels. For 12 or more wave bands, it is not possible, with the available sources for narrow band pass filters, to find a filter configuration without substantial overlap between the channels.

7.1 Application on ceramics

The emissivity of ceramics is dependent on the temperature of the surface and the wavelength at which the radiation is measured [21]. Here, the temperature dependence can be ignored, as the temperature is assumed to be constant during a multi-color measurement cycle, since the observed bulk oven processes are slow moving. Thus, only the wavelength dependence has to be considered.

7.2 Method

There are multiple methods of determining the temperature from the radiation intensity measurements in the different wavelength bands. The relevant methods are linear least-squares fitting and a non-linear least-squares fitting as described by Neupane et al. [7]. Here, the output signals (voltages) from the six wave bands are used to determine the photocurrent of the diode. From those photocurrents, the spectral radiance at the center wavelength of each channel is obtained from equation (6). Since the Wien approximation is not applicable, a nonlinear least squares approach has to be taken to obtain the measured temperature: the linear least-squares method as described by Neupane et al. [7] requires the simplifications that the Wien approximation makes possible. The objective function to optimize for is(9)where λ _j is the center wavelength of each wave band, L _λ,meas is the spectral radiance derived from the measurements and L _λ,guess is the guessed spectral radiance. L _λ,meas is obtained from the measurement voltage using(10)where U _meas is the voltage signal and R _meas is the measuring resistance. This calculation is error prone due to uncertainties in the view factor, as the distance between the sensor head and the measured object changes during the oven process. Since this error is not wavelength dependent though, it only scales the emissivities that the method described here yields, but doe not change the temperature.

L _λ,guess is obtained using equation (2) with a third degree polynomial, with four coefficients a ₀–a ₃ describing the spectral emissivity distribution. The least squares minimization was accomplished using the Nelder-Mead algorithm as implemented in the lmfit Python library [22], and imposing bounds of 0.8 < ε < 1, which are taken from the known emissivity values of kaolinite [23]. The parameters for the optimization are the four coefficients of the emissivity polynomial as well as the measured temperature. More information on this method of temperature determination can be found in [7].

7.2.1 Problems

The method described above can be used for temperature (and emissivity) determination with better accuracy than simply assuming black body radiation in a closed, potentially isothermal environment. When simulated input values calculated with the emissivity distribution of kaolinite [23] are used, which represents a best case scenario neglecting noise and other error sources, several problems for the implementation in the final product present themselves. First, this simulated best case accuracy is still too high for the requirement of 2 K, in fact, absolute error values go up to 90 K. As seen in Figure 9, the higher the temperature gets, the more the estimated temperature oscillates. Algorithms other than Nelder-Mead oscillate a lot less, but their error is considerably higher. The emissivity estimations produced by the Nelder-Mead algorithm (see Fig. 10) are almost perfectly straight, first order polynomials, even though the parameters of the least squares minimization allow for third order polynomials. More investigation to obtain better fits is necessary here. Secondly, the narrow wave band filters are not sufficiently narrow to assume monochromaticity, a multi-band pyrometry approach must be chosen (where L _meas and L _guess in equation (9) are substituted by(11)[24]). With this approach, no least-squares fit that is better than assuming a constant emissivity of unity could be achieved. Further investigation is necessary to improve the accuracy using the multi-band approach.

Figure 9 Temperature estimation error.

Figure 10 Comparison of estimated emissivity functions and real emissivity of kaolinite [23].

Lastly, the computing time of the temperture determination algorithm is high, taking a few seconds per temperature determination on consumer hardware, which is obviously not acceptable given the desired measuring frequency of 0.5 Hz. Expected performance on the microcontroller in the finished product would be much worse.

8 System test and calibration

The pyrometer system has to be tested during the design process, and calibrated before it can be used for temperature determination. For both tasks, the same test setup is used. It consists of a radiation source, a reference thermometer and the pyrometer prototype.

8.1 Radiation source

The radiation source is a cavity radiator that was built at the IRS. It approximates a black body radiator with an effective emissivity ε _BB > 0.99 [2]. It can operate at temperatures up to 2400 °C. Below around 700 °C, the temperature of the radiation source can not be kept stable by the control system.

8.2 Reference thermometer

The reference thermometer is a linear pyrometer, LP3, developed by KE Technology GmbH. In the range between 950 °C and 2400 °C, the measurement error is, for a 95% confidence interval, ±2.1 K as per the last calibration in 2023.

8.3 Validation of the simulation software

For testing and validation of the simulation software, the radiator is set to six different temperatures within the measuring range of both the LP3 and the prototype pyrometer. An early prototype, using an FD1000W photodiode [25], a Thorlabs RC08SMA-P01 collimator [26], a Thorlabs FG200LCC fiber [27], a 6 mm thick barium flouride lens and no filters was tested and compared against simulation results obtained with the PyroSim software.

Measurements were recorded using a LeCroy WaveSurfer 434 oscilloscope [28]. The comparison shows a good agreement between the simulated and measured data (see Fig. 11). The maximum relative error of this dataset is 19.3%, its average relative error is 9.69%. Error sources are the uncertainty of the reference pyrometer, the uncertainty of the oscilloscope and diode degradation. It is worth noting that, due to the instability of the radiator temperature below 700 °C as well as the responsivity of the prototype’s diode in shorter wavelengths, no relevant measurements were obtained in the range of 100–700 °C. A new testbed and prototype will be created in the future to validate the simulation software throughout the whole measuring range of the pyrometer system.

Figure 11 Temperature-signal-relation comparison between experiment and simulation.

9 Conclusion

A pyrometer system is designed as a versatile measuring instrument for the temperature control of industrial bulk oven processes. It features six channels with sensor heads that are decoupled from the base unit which houses the photodiodes. In the design process, a simulation tool is created which can be used for spectral sensitivity studies with different optical components. The expansion of the instruments capabilities to include emissivity independent temperature determination is examined by investigating multi-color pyrometry with regard to the application on ceramics. The requirements on the pyrometer system can not be fulfilled, as the algorithm for the emissivity independent temperature determination is still inaccurate. Further optimization of the fitting algorithm is necessary in the future in order to minimize the measurement error. Additionally, the accuracy must be verified in a controlled laboratory environment and tested in the industrial environment of the planned use case.

Acknowledgments

We would like to thank Stange Elektronik GmbH for their help in the electronic design of the pyrometer system. We also want to thank New Generation Kilns Grün GmbH for providing insight into bulk oven processes.

Funding

This research was funded by the “Zentrales Innovationsprogramm Mittelstand (ZIM)” by the German government, specifically the “Bundesministerium für Wirtschaft und Klimaschutz” under grant number KK5034904SY1.

Conflicts of interest

The authors declare that they have no competing interests to report.

Data availability statement

Numerical data created using PyroSim is available. Data that was experimentally obtained during the verification of the software is available as well.

Author contribution statement

R. Fritzsche wrote the article with contributions from C. Kaiser, who supervised the writing. R. Fritzsche and C. Kaiser carried out experiments and testing with the black body simulator. R. Fritzsche programmed the simulation software, using an earlier prototype of a PyroSim-like tool developed by G. Herdrich, and implemented the least squares optimization algorithm. The conceptualization, funding acquisition and project administration was done by G. Herdrich.

References

All Tables

All Figures

	Figure 1 Relative error intruduced by using the Wien approximation in equation (2).
In the text

	Figure 2 Optical signal path per channel.
In the text

	Figure 3 Simplified schematic of the software structure.
In the text

	Figure 4 Radiation intensity distribution for the upper and lower temperature limit of the measuring range.
In the text

	Figure 5 Radiation intensity distribution for the lower temperature limit of the measuring range and diode sensitivity.
In the text

	Figure 6 Spectral transmissivties of the filters used and of water vapour at 1 bar and 300 K, HITEMP [14] data visualized using RADIS [15–18].
In the text

	Figure 7 Schematic of the pyrometer system design.
In the text

	Figure 8 Conceptual drawing of the sensor head placement in the oven wall with the cone of vision of the sensor head in red.
In the text

	Figure 9 Temperature estimation error.
In the text

	Figure 10 Comparison of estimated emissivity functions and real emissivity of kaolinite [23].
In the text

	Figure 11 Temperature-signal-relation comparison between experiment and simulation.
In the text