2.1

Geometry

Our cavity radiometer geometry builds on the knowledge of previously developed radiometers. Prior to the monitoring of the Earth’s radiation budget with WFOV radiometers, the first radiometers were used for Total Solar Irradiance monitoring, and were developed in different geometries, such as a cone shape (ACRIM,¹³ TIM¹⁴), an inverted cone shape (PMO¹⁵), or a cylinder (DIARAD¹⁶). Our cavity radiometer is an improvement of the cavity radiometer from the Sun-Earth IMBAlance (SIMBA) mission,¹⁷ developed at the Royal Meteorological Institute of Belgium, and which inherited its measurement principle using electrical substitution from the DIARAD-type radiometer. Thanks to its novel cavity shape, our radiometer features a wide field-of-view of 135°, exceeding the 127° that is required to observe the Earth from limb-to-limb from a nominal altitude of 700 km, enabling to monitor the Earth’s total outgoing radiation while allowing for pointing errors. This radiometer and its functioning are described in detail in.¹¹ The cavity is composed of a near-hemispherical part and a conical part supplemented with an appropriate baffle. In our model, the diameter of the cavity aperture equals 6 mm. Below the cavity radiometer, there is a baffle featuring a precision aperture with a diameter of 5 mm. The cavity radiometer aperture is slightly larger than the precision aperture to allow for alignment errors, ensuring that no radiation is stopped by the cavity aperture.

An alternative to the cavity radiometer is to use an integrating sphere, which features an easier geometry. Also, an integrating sphere offers the advantage to enable a stronger versatility, e.g. placing a spectrometer at the detector or using filters in front of the entrance aperture. Here, we use a full sphere with a standard size of 5 cm of diameter. The entrance aperture equals 1 mm diameter, while the detection area equals a circular area with a diameter of 1 cm. These pameters have been determined according to best practices, i.e. targeting to obtain a port fraction f ≈ 0.01, as to achieve an optimal performance of the integrating sphere.¹⁸ Therefore, we have:

where A_e is the area of the entrance aperture, A_d is the area of the detector, and A_s is the area of the sphere.

A major difference with the cavity radiometer is that the latter has been shaped solely in the purpose of observing the Earth from limb to limb, without needing for an interior baffle. While for the integrating sphere, an interior baffle is needed in the case of Earth observation, to avoid that incoming radiation falls directly onto the detector.

2.2

Sources

Two pointing modes, therefore two cases, are considered: Solar radiation and Earth’s radiation (Figure 1). Solar radiation is only used for calibration purposes. This source can be modeled as a 5 mm diameter beam (since it passes through the precision aperture first) entering the aperture of the cavity, with a full emission angle of 3°. Regarding the Earth’s emitted radiation, we consider a Lambertian source¹⁹ with an emission angle of 127°, corresponding with the acception angle of the baffle.

Figure 1.

Earth viewed by the WFOV radiometer. Occasional Solar pointing will allow intercalibrating the Incoming Solar Radiation and the Earth’s Total Outgoing Radiation measurements. SW stands for shortwave and LW for longwave.

2.3

Coating and absorption factor

The interior cavity walls of the radiometer are coated with Black Velvet, a black paint, that allows to absorb incoming radiation.²⁰ The absorption factor of Black Velvet equals 0.97 +/- 0.01, for both spectral regions of interest (SW and LW), and considering perpendicular illumination. Also, we consider three illumination cases: (1) LW Earth, for which a Lambertian source of 127° is simulated in the 8 μm – 14 μm spectral range; (2) SW Earth, featuring the same angle but considering the 400 nm – 1100 nm spectral range; (3) Solar, a SW source with an emission angle of incidence of ±1.5°. This definition implies that all generated rays will first encounter the hemispherical part of the cavity, since the source rays are only defined with a total emission angle of 127°, while the conical part of the cavity features a larger acceptance angle of 135°. For this analysis performed in ASAP®, Breault Research, we use the commands SPLIT 2 for specular reflection and LEVEL 2 for scattered light, a total flux of 100 (in arbitrary units), and 50000 rays.

Considering the integrating sphere, a space-based Spectralon® coating from LabSphere is considered.²¹ This coating features a diffuse reflectance higher than 99% (scattering) until 250 nm, then decreases to 95% until 2500 nm (Figure 2). In our simulations, we will assume 99% of diffuse reflectance and 1% of absorption, to see if the integrating sphere has a better performance than the cavity radiometer, even in certain spectral regions of interest only. In addition, a second simulation with 100% of scattering will be done to assess the influence of the geometry only. For this analysis, we use the command LEVEL 750 for scattered light, while with the HALT command we allow 10¹⁸ interactions between the rays and the coating, in order to avoid that the lights are wrongly trapped in the integrating sphere.

Figure 2.

Typical 8° Hemispherical Reflectance (SRM-990) of the Space-grade Spectralon® Reflectance Material, between 250 nm and 2500 nm.²¹

2.4

Optimization

Both the cavity radiometer and integrating sphere were optimized towards minimal light loss. Specifically, the optimization targets to minimize the light flux leaving the cavity by considering the flux at the detector surface, positioned at the entrance of the geometry, as merit function.

Considering the cavity radiometer, our initial design composed a perfect hemispherical cavity, supplemented with a bottom conical part. After including the coating in the design, optimization of the hemispherical part was done, by considering its semi-length along the Z-axis as variable. Considering the integrating sphere, an optimization is performed when considering the size of the entrance aperture and detector area as variables, relatively to the size of the sphere.

3.1

Cavity radiometer

The investigation on the geometry and the coating of the cavity radiometer was the object of a precedent paper,²² of which the key results will be repeated for benchmarking purposes. Considering a total Earth’s outgoing radiative flux of 340 W/m² (Figure 1), Table 1 gives the relative and absolute outgoing fluxes when observing the Earth and the Sun from space. In all cases, the outgoing flux is less than 1 W/m². This excellent result originates from a combined effect from the optimized geometry and good coating properties. In fact, the cavity geometry has been designed solely in this purpose. An optimization has been performed on that cavity geometry, and the results show that the initial geometry (Figure 3) performed the best. In comparison to pure flat sensors, the coating absorption factor is of less importance when associated with a proper cavity geometry. In fact, a purely flat sensor coated with Black Velvet would absorb 97% of the incoming flux, resulting in a loss of 10.2 W/m² when observing the Earth (in the SW range, which is the best case scenario), indicating the importance of the optimized radiometer geometry.

Figure 3.

The cavity radiometer is composed of a hemispherical part, a conical part, and has an aperture where the radiation is entering. In our ASAP model, the gap of 2 mm between the hemispherical part and the conical part is an absorptive layer that stops the propagation of light (in red). In yellow, another absorptive structure intercepts the outgoing light. The source has an emission angle of 127° to illustrate the Earth’s case. Rays are plotted in black.

Table 1.

Computed outgoing flux (in % of the incoming flux) for the cavity radiometer model with the gap, when applying a Black Velvet coating, when measuring Earth’s radiation (SW and LW) and Solar calibration. The absolute outgoing flux is the light loss when observing Earth from space, considering a total Earth’s outgoing radiative flux of 340 W/m2.

3.2

Integrating sphere

We investigate the integrating sphere as a possible alternative for the cavity radiometer, since integrating spheres are generally used in laboratory to measure radiation, and thus might offer a valuable alternative. The model for our integrating sphere is illustrated in Figure 4.

Figure 4.

The integrating sphere. The rectangle (red) at the left is the detector measuring the signal. The yellow plane at the bottom quantifies the outgoing flux. The source, placed at the entrance of the integrating sphere, has a full emission angle of 127° and a diameter of 1 mm. Rays are plotted in black.

In our simulations, the Spectralon coating is 1% absorbing, while 99% of the incoming rays are scattered. The total light loss of the integrating sphere is, however, the superposition of the light that is escaping by the entrance aperture due to the geometry and the light that is absorbed by the coating. Despite the fact that the Spectralon absorption seems only a minor percentage, this shows to be a major contributing factor due to the multiple reflections on the interior of the integrating sphere (typically 24347 interactions until the end of the simulation). Consequently, in this case, the outgoing flux due to the geometry and the light absorption by the Spectralon are studied separately to identify their individual contributions. Specifically, when determining the geometrical influences, we investigated the outgoing flux and the detected flux, as indicated by the detectors in Figure 4, in case we consider 0% of light absorption by the Spectralon. Following, the influence of the Spectralon absorption is studied, by including the 1% absorption and studying again the outgoing and detected flux. Both of these cases where considered for Earth and Solar observation, giving rise to the results presented in Tables 2. Comparing Table 2 to Table 1, it shows that in all cases, even when considering the infuence of the geometry only, the flux reaching the detector is smaller than when using the cavity radiometer.

Table 2.

Distribution of fluxes for the integrating sphere with interior baffle and a coating with 1% and 0% of absorption. The flux is whether absorbed by the sphere and the baffle, outgoing or detected. The observation cases are Earth observation and Solar calibration. The flux is relative and expressed in %.

Considering Solar illumination, an optimization was carried out on the angle of incidence of the source, showing that the best results are found for a collimated input beam. Additionally, the merit function is reaching its minimum when the source is tilted with a small angle of -0.4°. However, it should be noted that the flux gain is very low, even negligible.