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Abstract
Longwave downward radiation measurements are fundamental for investigating the surface and atmospheric energy budget of the Earth. Such measurements are performed using broadband infrared radiometers that have a hemispherical acceptance angle. A new hemispherical reference blackbody has been developed to provide a new traceability path of longwave downward radiation measurements to the SI. The Hemispherical Blackbody (HSBB) was specifically designed to meet the large opening angle of radiometers used for measuring longwave downward radiation. The first step was to find a suitable design candidate for the HSBB by simulating the effective emissivity using the Monte Carlo ray-tracing software STEEP. The most promising candidate was then realized in two versions with similar coatings and both versions were taken into operation.
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1. Introduction
Specific broadband infrared radiometers with a hemispherical acceptance angle are used for longwave downward radiation measurements. In most cases, pyrgeometers are typically employed for such measurements, which are performed at research and weather stations around the world and organized, for example, within the Baseline Surface Radiation Network (BSRN) [1]. Measurements of the longwave downward radiation are relevant for investigating the surface and atmospheric energy budget of the Earth [2]. Longwave downward radiation originates from infrared radiation that is incident on the Earth after being emitted in and transmitted through the atmosphere [3]. The new calibration source, the Hemispherical Blackbody (HSBB), must be operated between approximately $-20\,^{\circ }$C and $20\,^{\circ }$C, the temperature range corresponding to the irradiance levels of atmospheric longwave downward radiation at middle latitudes. The relevant part of the corresponding infrared radiation for this temperature range is within the wavelength range from approximately 4 $\mathrm {\mu }$m to approximately 50 $\mathrm {\mu }$m.
For a long time now, the Tilted Bottom Cavity BB2007 at the Physikalisch-Meteorologisches Observatorium Davos / World Radiation Center (PMOD/WRC) has provided the reference for longwave downward radiation measurements within the BSRN [4]. In addition, the PMOD/WRC developed the Infrared Integrating Sphere (IRIS) instruments as windowless transfer radiometers, and it operates the World Infrared Standard Group (WISG), a set of pyrgeometers that serve as an international standard [5].
The new HSBB has been developed as a novel calibration approach to provide the basis for efforts aimed at reducing the measurement uncertainty of longwave downward radiation to 2 W/m2 with traceability to the SI.
This publication presents the development process, the setup, and the operation of the new blackbody. It describes the specific design aspects of the HSBB, highlights its main technical features, and reports on a characterization approach carried out by means of effective emissivity simulations.
2. Computational method of effective emissivity simulations
For the development and characterization of the HSBB, simulations were carried out using the Monte Carlo optical ray-tracing programme STEEP3 version 321. The computational method of the programme is described in detail in various publications [6–8]. Based on these, the main concept of the simulations is given very briefly as follows.
The general procedure for computing the effective emissivity involves comparing the simulated radiance emitted by the blackbody cavity to the radiance that would be emitted by a physically ideal blackbody at the same temperature. Simulations start by creating rays using the so-called backward ray tracing algorithm. This means that the rays, i.e., trajectories, are traced in the opposite direction, namely from the detector to the cavity. The rays are traced until, after multiple reflections, they fall below a flux threshold to be specified. The computation of the effective emissivity then takes place following the trajectories leading from the cavity to the detector, starting at the so-called “birth point” [8]. Based on the created trajectories, the actual computation of the total effective emissivity is performed according to Eq. (1) by applying the Stefan-Boltzmann law [9].
The reference temperature is denoted by $T_{\text {ref}}$ and is a matter of definition for each cavity individually. An average over $n$ trajectories is formed by summing over the trajectories and then dividing by $n$. The number of ray-cavity interactions amounts to $m_i$. The index $k$ accounts for reflections of the ray inside the cavity. The hemispherical total wall emissivity, hemispherical total wall reflectivity, and temperature of a point $j$ on the cavity surface are denoted by $\varepsilon _j$, $\rho _j$ and $T_j$, respectively [9].
3. Development of the design
The effective emissivity was simulated in this study in order to find the most promising design of the new blackbody cavity with respect to coating and geometry. Several design aspects were considered. Past studies on blackbody cavities, given in [10,11], suggest that blackbody cavities with highly reflecting side walls may have a different effective emissivity compared to cavities with highly emitting side walls. In addition, cavities with highly reflecting side walls may show a different dependence of the effective emissivity on the observation angle. This idea was used to find an optimal design for the new HSBB.
The first goal of the simulations was to identify a design that shows an almost constant total effective emissivity over all observation angles, especially for normal incidence and the hemispherical opening angle, given on the one hand that experimental characterization is easier to carry out at normal incidence with a radiation thermometer, and on the other hand that the hemispherical opening angle is needed for the calibration application. The ability to transfer measurements at normal incidence to the hemispherical opening angle is a decisive advantage for later characterization measurements.
The hemispherical total wall emissivity values of the materials employed in the simulations originate from measurements at the Physikalisch-Technische Bundesanstalt (PTB) and are given in Table 1. The instrumentation for these measurements is described in detail in [12,13]. For the measurements, samples of the same batch of material that was applied to the cavity of the HSBB are used. For the values given in Table 1, the diffusity is defined as the diffuse reflectivity divided by the sum of specular and diffuse reflectivity. The gold surface is assumed to exhibit entirely specular reflection with neglectable diffusity. The coatings used show particularly flat spectral emissivity distributions with respect to the relevant spectrum and are therefore very suitable for the HSBB as a calibration source for the broadband infrared radiometers. Plots of the directional spectral emissivity of the coatings in the most relevant wavelength range from 6 $\mathrm {\mu }$m to 22 $\mathrm {\mu }$m are shown in Fig. 1.
Table 1. Coatings of the Hemispherical Blackbodies (HSBBs).a
Fig. 1. Spectral plots of coating emissivity. Shown are the directional spectral emissivities of Vantablack S-IR and Nextel 811-21 in (a) and of highly specular reflecting gold in (b) in the 6 $\mathrm {\mu }$m to 22 $\mathrm {\mu }$m wavelength range, which is most relevant for the temperature range between $-20\,^{\circ }$C and $20\,^{\circ }$C. All three distributions are sufficiently spectrally flat for application to the HSBBs. The results in the plots correspond to measurements under an angle of 10$^{\circ }$. The uncertainties shown as shaded areas are given for $k$=1.
For the simulations carried out in this work, the number of simulated rays was set to $10^5$ and the flux threshold to $10^{-8}$. The background temperature was set to 0 K.
A selection of four possible design cavity candidates is shown in Fig. 2(a) together with the simulation results. All geometries feature the same aperture size. In the simulations the detector was the same size as the cavity aperture. Each column in Fig. 2(a) corresponds to the same geometry while each row represents a certain coating or coating combination. In total, 16 variants are shown. Only isothermal cavities are considered here. The presented curves of the effective emissivity depend on the observation angle.
Fig. 2. (a) Simulation results of the total effective emissivity for different design candidates. The two most promising designs with stable and flat total effective emissivity curves are marked red. The gold surfaces exhibit highly specular reflection. The observation angles correspond to the 2D plane with 0$^{\circ }$ for normal incidence and 180$^{\circ }$ representing the hemispherical opening angle. (b) Variation of the detector position to achieve different observation angles. In order to simulate different observation angles, the detector position is changed with respect to the aperture of the blackbody cavity.
The given values for the observation angles in Fig. 2(a) are shown with respect to two-dimensional angles in the top view plane, meaning that the three-dimensional solid angle is projected onto a two-dimensional plane, as shown in Fig. 2(b). The observation angle 0$^{\circ }$ corresponds to normal incidence while the angle 180$^{\circ }$ is the hemispherical observation with the detector positioned directly in the cavity aperture. To achieve more observation angles, the detector was placed at different positions with a varied distance from the cavity in the simulations. The detector was placed such that the average of the angle defined by one detector point and the cavity aperture over all detector points corresponded to observation angles of 36$^{\circ }$, 72$^{\circ }$, 108$^{\circ }$ and 144$^{\circ }$, respectively. This procedure is a good approximation for solid angles and gives a good impression of how the total effective emissivity may change for different solid angles. All simulations were carried out with cylindrical symmetry and with the centre of the detector coinciding with the optical axis of the cavity.
Two similar designs with good results indicating almost constant total effective emissivity were selected and are highlighted in red in Fig. 2(a). They both correspond to a cavity geometry with a cone angle of 150$^{\circ }$ and a reflective dome. The two designs can be considered the most promising design candidates of the HSBB.
Compared to the selected designs, the geometry on the far right in Fig. 2(a) appears to exhibit a similarly low correlation between the total effective emissivity and the observation angle. However, this geometry turns out to be more sensitive to the diffusity uncertainty of the black coatings: For the hemispherical opening angle, for example, the uncertainty contribution of the diffusity uncertainty is more than three times larger compared to the selected designs. The geometry on the right was therefore rejected. For the selected designs, the calculation of the uncertainty of the total effective emissivity, including the diffusity uncertainty of the black coatings (which turned out to be the major uncertainty component), is described in section 5.
When considering the optimal design candidate of the HSBB, a highly diffuse reflecting hemisphere with $D=1$ instead of a highly specular reflecting hemisphere would produce a large difference in the total effective emissivity between normal incidence and the hemispherical opening angle of approximately $0.006$ and is therefore unfavorable.
Consequently, a blackbody cavity is now realized to consist of a highly emitting black cone and a highly specular reflecting golden hemisphere. It should be highlighted that the reflective hemisphere is also less sensitive to the inevitable temperature gradients which arise when attaching a radiometer to the HSBB.
4. Experimental realization and operation
Based on the outcome of the simulations in the previous section, it was decided that the new blackbody should consist of two parts, a black coated cone and a specular reflecting golden hemisphere. When assembled, the two parts form the cavity with the aperture found in the golden hemisphere. A 3D-schematic and a sectional view are seen in Fig. 3 with the main features of the HSBB labelled. When calibrating pyrgeometers and IRIS instruments, for instance, achieving a hemispherical opening angle is only possible if the radiometer is attached directly to the aperture of the HSBB, as shown in Fig. 3(b). Actual photographs of the HSBB components are presented in Fig. 4. The hemisphere has a diameter of 200 mm. Four different apertures with opening diameters of 20 mm, 26 mm, 32 mm, and 40 mm are available to properly adapt the blackbody to the radiometers. The ideal aperture diameter may be determined in the experimental setup itself to fit each radiometer individually. However, the largest aperture diameter of 40 mm is expected to be the most practical for the measurements. Completing the hemisphere, the apertures were also coated with gold. All gold coatings were applied by a galvanic coating process. In the electroplating process, a thin copper layer was first applied to the aluminium and then polished with a polishing paste by hand in order to produce a very smooth surface. The latter is important as a specular reflecting gold surface on the hemisphere is the goal of the gold coating process. Once a smooth copper surface was obtained, gold was applied.
Fig. 3. (a) Rendered photo of the HSBB. The HSBB is shown together with an Infrared Integrating Sphere (IRIS) instrument positioned below the blackbody aperture. (b) Sectional view of the HSBB. Here, the HSBB is presented with its main technical features labelled and the outer insulation shown in green. The geometry of the cavity with cone and golden hemisphere is clearly visible. An IRIS instrument is positioned below the HSBB aperture to demonstrate the need to directly attach such radiometers to the aperture of the HSBB in order to achieve a hemispherical opening angle during calibration.
Fig. 4. Photos of the HSBB. Presented are photos of the HSBB with (a) the golden hemisphere, (b) the black cone with Nextel 811-21 coating and (c) the cooling channels in a bifilar winding on the back of the cone.
Two versions of the HSBB were realized based on the optimization simulations described in the previous section. One version, named HSBB1, was coated with Nextel 811-21, the other, called HSBB2, had the coating Vantablack S-IR applied to the cone. Apart from the cone coating, the two versions were identical in construction.
For each HSBB, two thermostats with appropriate cooling fluid are used to control the temperature of the blackbody cavity in two separate cooling sections, one on the back of the cone and one around the blackbody aperture. The first and larger of the two sections is the back channel section and includes a bifilar winding on the back of the blackbody behind the cone. The bifilar winding can be seen in Fig. 4(c) and consists of two interlocking spirals. After passing the inlet to the blackbody, the fluid passes through the first spiral, continues through a channel around the hemisphere and then flows through the second spiral on the back of the blackbody before exiting the blackbody through the outlet and returning to the thermostat.
Five thermometers are used in the setup of each HSBB. One of them is used for temperature regulation and four of them are used to measure the temperatures of the HSBB. Aged and calibrated sheath platinum Pt100 resistance thermometers are employed for these temperature measurements. The temperature sensors are placed at the very end of the bores close to the surfaces whose temperatures are to be measured. The standard calibration uncertainty of the Pt100 thermometers is approximately 5 mK to 10 mK. Three thermometer bores are in the cone, one each for the cone vertex, cone middle and cone edge temperature. The cone middle thermometer is directly connected to the thermostat for external temperature regulation. The temperatures to be measured are the cone vertex and cone edge temperature as well as two temperatures on the hemisphere. The resistance thermometers are read out by a calibrated resistance measurement device. The positions of the thermometers are shown in Fig. 5. The two thermometers in the hemisphere, referred to as “left” and “right” when looking at the blackbody, are placed at opposite locations symmetric to the optical axis of the HSBB. They are positioned at a distance of 29 mm to the blackbody aperture outer surface and 72 mm to the blackbody cone edge, with the distances corresponding to the dimensions along the optical axis of the HSBB.
Fig. 5. Thermometer positions. Shown are the positions of the Pt100 resistance thermometers that are used in the setup of each HSBB. The cone middle thermometer is used for temperature regulation and the other four thermometers are used to measure the temperatures of the HSBB.
Parts of the golden hemisphere extending approximately from the latitude circle of the hemisphere thermometers to the pole of the hemisphere or aperture can be considered a buffer zone for the thermal gradient between the housing temperature of the attached radiometer and the main blackbody temperature. The housing of a radiometer will have in general a different temperature than the blackbody. A direct attachment to the front of the blackbody will very likely produce temperature non-uniformities in the very front area of the blackbody cavity, the buffer zone, because of thermal conduction between blackbody and radiometer. But due to the low emissivity of the golden hemisphere the induced temperature gradient in the buffer zone and its influence on the irradiance provided by the blackbody can be neglected. The buffer zone in the front of the golden hemisphere to ensure proper thermal connection can be considered a major design attribute of the HSBB for its specific application. All other parts of the golden hemisphere, although also highly reflecting, are intended to have the same temperature as the blackbody cone in order to not induce any thermal gradients into the blackbody cone. For this reason, a second cooling section regulates the temperature in the front of the HSBB and features a cooling channel around the blackbody aperture, as shown in Fig. 3(b) (label 4). This second cooling section is used to compensate for different values of heat input into the blackbody when applying radiometers of different shape, size and housing temperature and restrict the thermal gradient between blackbody and radiometer housing to the small buffer zone. Consequently, a reproducible temperature non-uniformity of the HSBB is achieved when the hemisphere thermometers measure the same temperature as the blackbody cone and blackbody edge thermometers. In all investigated cases this was possible by setting the thermostat of the front cooling section to appropriate temperature values.
Exemplary independent measurements of the thermometers in setups with a radiation thermometer, an IRIS instrument and a Kipp and Zonen CG4 pyrgeometer are shown in Fig. 6, demonstrating that the temperature non-uniformity of the HSBB is highly reproducible. The data points correspond to measurements with a 40 mm opening performed with the HSBB1. In each measurement, the temperature non-uniformity is small with respect to the measurement uncertainty. The data in Fig. 6 show that the idea of manually setting the thermostat of the front cooling section to different temperature values depending on the setup is successful and provides reproducible temperatures of the HSBB and therefore reproducible measurement conditions.
Fig. 6. Temperature non-uniformity. Shown here are the temperatures measured with calibrated Pt100 thermometers at different locations in the HSBB1. The temperatures correspond to independent measurements with a radiation thermometer, a Kipp and Zonen CG4 pyrgeometer attached, and with an IRIS instrument attached. The shown data points are exemplary and correspond to measurements carried out with the HSBB1 at a nominal blackbody temperature of $-20\,^{\circ }$C and $0\,^{\circ }$C. The data show good reproducibility of the temperature non-uniformity, which is small in relation to the absolute measurement uncertainty. To illustrate the reproducibility with the same instrument, two different measurements with the radiation thermometer are shown for $-20\,^{\circ }$C and are labelled “Open (radiation thermometer)”. The uncertainty range ($k$=1) of the measured temperatures is represented by the grey shaded areas.
In order to avoid water condensation and icing from air humidity at lower temperatures, the cavity is purged with dry air inside. As can be seen in Fig. 3(b), the small inlet holes for the dry air are placed on the hemisphere very close to the cone and are distributed evenly along the cone. The flux for the dry air is usually a few litres per minute. Before purging the cavity, the dry air passes through a temperature-controlled heat exchanger and a channel around the hemisphere to equalize the temperature of the dry air with that of the blackbody. Moreover, an isolation enclosure covers the complete blackbody in order to improve the performance of the temperature control section.
To underpin the simulation results, radiation temperature measurements of the HSBB1 were performed under a limited angular range, i.e., under normal incidence, 10$^{\circ }$, 20$^{\circ }$, and 30$^{\circ }$ with respect to the optical axis of the HSBB1. These measurements were performed using a calibrated radiation thermometer with a narrow opening angle. The results obtained for the nominal temperatures of $-15\,^{\circ }$C, $0\,^{\circ }$C, and $15\,^{\circ }$C are shown in Fig. 7. The measurements were performed with a prior version of the HSBB1, which among other things did not yet have the second cooling section. However, it is expected that the new HSBB1 would show the very same results. For the measurements, an opening diameter of 40 mm was used and the HSBB1 was operated in an upright position with its optical axis in a horizontal orientation. The angles between the optical axis and the measurement direction of the radiation thermometer corresponded to the horizontal plane. The results show that the radiation temperature of the HSBB1 is indeed independent of the observation angle within the measurement uncertainties in the observed angular range, as was expected. A small difference in radiation temperature between normal incidence and angles of $\ge$10$^{\circ }$ is observed at all three nominal measurement temperatures and appears to be more pronounced at lower blackbody temperatures. This difference may be attributed to an effect similar to the size-of-source effect [14] that is inherent to any radiation thermometer. More specifically, the difference might be explained by specular reflections at the golden aperture edge of the HSBB1, which are more pronounced at normal incidence. Measurements under angles beyond 30$^{\circ }$ were assumed to be unreliable due to the projected opening area of the HSBB1, which decreases with increasing observation angles.
Fig. 7. Radiation temperature measurements of the HSBB1 under different angles. The measurements were performed under normal incidence and under different angles with respect to the optical axis of the HSBB1 to verify that the radiation temperature of the HSBBs is independent of the observation angle.
5. Uncertainty of effective emissivity from simulation
As described in section 2, the simulated total effective emissivity $\varepsilon _{\text {eff}}$ of a blackbody cavity may be understood as a function of the parameters used in the simulations. Consequently, the effective emissivity needs to be understood as $\varepsilon _{\text {eff}}=f(\varepsilon _{\text {V/N}},\varepsilon _G,D_{\text {V/N}})$ even though the expression cannot be written analytically. Here, the parameters to be considered are the hemispherical total wall emissivity values of Vantablack S-IR or Nextel 811-21, denoted by $\varepsilon _{\text {V/N}}$, and that of the gold surface, denoted by $\varepsilon _{\text {G}}$. In addition, the diffusity $D_{\text {V/N}}$ of Vantablack S-IR or Nextel 811-21 is considered. Using only these parameters is reasonable considering the otherwise constant simulation conditions such as the observation angle.
The uncertainty of the simulated total effective emissivity can be calculated by taking into account the individual uncertainties of the relevant input parameters $\varepsilon _{\text {V/N}}$, $\varepsilon _{\text {G}}$ and $D_{\text {V/N}}$. Using Gaussian uncertainty propagation, the uncertainty of the simulated total effective emissivity can be obtained according to Eq. (2).
Following Eq. (2), the individual partial derivatives are approximated and calculated by performing two STEEP simulations with slightly different values of the respective parameter and the results are used to compute the respective difference quotient. The data from Table 1 are used for the uncertainty calculations.
The results of the total effective emissivity with uncertainty for different viewing conditions for the HSBB1 and HSBB2 are presented in Fig. 8. The results correspond to the HSBB with 40 mm aperture. The different viewing conditions correspond to possible application setups with a radiation thermometer, an IRIS instrument, an Absolute Cavity Pyrgeometer (ACP) instrument [15], a Hukseflux IR20/IR20WS pyrgeometer, an Eppley PIR pyrgeometer, an Eko MS-21 pyrgeometer and a Kipp and Zonen CG4/CGR4 pyrgeometer. These instruments are often used in the community for longwave downward radiation measurements. Apart from the radiation thermometer, all viewing conditions correspond to the hemispherical opening and only differ in the diameter of the detecting surface or the pyrgeometer dome diameter. In fact, the viewing conditions with hemispherical opening are sorted by ascending diameter of the detecting surface or dome diameter in Fig. 8, with the PIR and MS-21 pyrgeometers having approximately the same diameter. The data in Fig. 8 demonstrate the characterization of the HSBB by means of effective emissivity simulations. The main uncertainty contribution comes from the diffusity uncertainty of the highly emitting black coatings. It can be pointed out that for each HSBB version, the total effective emissivity values for the different viewing conditions are, as expected, in very good agreement within their uncertainties. In addition, characterization measurements performed at normal incidence with a radiation thermometer can safely be applied to the cases with hemispherical opening in later measurements with the HSBB with no need to correct the effective emissivity.
Fig. 8. Simulation results. Shown here are the results for the simulated total effective emissivity for different viewing conditions, one of which corresponds to measurements with a radiation thermometer. The other viewing conditions correspond to measurements with an IRIS instrument, an Absolute Cavity Pyrgeometer (ACP), a Hukseflux IR20/IR20WS pyrgeometer, an Eppley PIR pyrgeometer, an Eko MS-21 pyrgeometer, and a Kipp and Zonen CG4/CGR4 pyrgeometer. The uncertainties are given for $k$=1.
The reference temperature is defined as the cone vertex temperature of the HSBB. During operation, the temperature non-uniformity along the cavity walls is sufficiently small. The differences in effective emissivity between the HSBB with the measured temperature non-uniformity and an assumed isothermal HSBB turned out to be much smaller than the calculated uncertainties of the effective emissivity resulting from the uncertainties of the coating properties. For this reason, the values for the effective emissivity given in Fig. 8, which were computed using an isothermal temperature distribution and without background radiation, are appropriate.
6. Summary
In the development process for the HSBB, an optimized design with respect to several design aspects was identified in order to achieve a blackbody cavity design showing almost the same effective emissivity for both normal incidence and the hemispherical opening angle. The optimized design was found by carrying out effective emissivity simulations. Based on the simulation results, the HSBB was realized to consist of a highly emitting black cone and a highly specular reflecting golden hemisphere. The HSBB was realized in two different coating versions, the HSBB1 with Nextel 811-21 and the HSBB2 with Vantablack S-IR for the highly emitting blackbody cone. Special attention in the experimental realization of the HSBB was given to the requirements for the calibration of infrared radiometers with a hemispherical acceptance angle.
The HSBB has been established as fit-for-purpose reference and will deliver the basis for reducing the measurement uncertainty of longwave downward radiation measurements directly traceable to the SI. The next step will be to describe the experimental characterization of the HSBB by comparison to the Radiation Temperature Scale of PTB [16]. The results from the characterization measurements are already available for both the HSBB1 and HSBB2. They show that the radiation temperatures of the HSBB1 and HSBB2 are consistent with respect to their absolute uncertainties. Furthermore, comparison measurements will be carried out between the HSBB and the BB2007 operated by the PMOD/WRC. The latter currently serves as the reference for atmospheric longwave downward radiation within the BSRN. The comparison measurements will validate the existing traceability of the BB2007.
Funding
European Association of National Metrology Institutes (16ENV03 METEOC-3, 19ENV07 METEOC-4); European Metrology Programme for Innovation and Research (EMPIR), Participating States, European Union’s Horizon 2020 research and innovation programme.
Acknowledgments
The support of Prof. Paul Fumagalli of Free University of Berlin as supervisor of a Master and a Bachelor thesis written throughout the course of this project is greatly appreciated.
The technical support provided by Detlef Müller, head of the mechanical workshop of the Physics Department of Free University of Berlin, is also gratefully acknowledged.
The constructive comments of three anonymous reviewers are gratefully acknowledged.
Disclosures
The authors declare no conflicts of interest.
Data availability
All relevant data are presented in the paper. Data files of this study are available upon request from the authors.
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