Introduction

The photometric features of planetary surface simulants have been already studied from several authors. Gunderson et al. (2006, 2007) observed the photometric properties for visible (VIS) and near-infrared (NIR) reflectance measurements of Martian regolith simulants. Shepard and Helfenstein (2007) tested the Hapke photometric model with a goniometer in the 0.4- to 0.9-µm spectral range. Hapke (himself) et al. (2009) tested its theoretical model on bidirectional reflectance with the help of goniometric measurements in the visible spectral range. Again a goniometer study in the VIS spectral range was carried out from Shepard and Helfenstein (2013) to study the bidirectional reflectance spectra from particulate samples. Beck et al. (2012) measured the bidirectional reflectance phase function of several meteorite samples in the VIS spectral range. Pommerol et al. (2013) measured the bidirectional reflectance of Martian analogues in dry, wet, and frozen conditions over a wide range of phase angles in the visible spectral range. Visible/near-infrared reflectance measurements of lunar soil simulants, Apollo soils, and Martian analogue samples as functions of illumination and emission angles were described in Johnson et al. (2013).

The influence of emergence (or observing) angle (θ) on the measured emissivity of natural surfaces has already been observed. Labed and Stoll (1991) studied the angular variation of the thermal infrared emissivity of natural samples under laboratory conditions. They observed that a decrease of the emissivity with increasing viewing angle does exist, and it is not simply related to the optical properties of the material, but it depends also on the scattering mechanism, grain size, porosity, etc. However, the setup they used for the experiment was very rudimentary, so they could only measure samples in air and had to restrict their spectral range to three segments: 3.2–4.2, 4.4–5.5, and 8.0–13.5 µm. In their conclusions, they state that the emissivity decreases with increasing viewing angle. For sand and silty material in small pieces, the effect is very weak up to θ = 60°. A very simplified experiment on water and ice showed the same kind of angular dependence for emissivity in the thermal infrared (8–14 µm) region (Rees and James 1992). Wald and Salisbury (1995) measured in air thermal infrared (7–14 µm) directional emissivity of quartz for several particle size ranges and packing fractions. Emissivity was found to be a strong function of each of these variables. In particular, for small grain sizes (where thermal gradients in the samples are higher), the angular dependence is non-monotonic, with a peak at θ = 45°. A successive study conducted to provide angular emissivity measurements for five representative samples (water, clay, sand, loam, and gravel) in one thermal IR broadband (8–13 µm) showed a general decrease in emissivity with increasing viewing angles (Cuenca and Sobrino 2004). The authors acknowledged that for all the samples, there is no significant difference in measured emissivity for θ from 0° to 30°. Finally, a recent study on the angular variation of thermal infrared (7.7–14.3 µm) emissivity (ε) for twelve inorganic bare soil (IBS) types concluded that ε of all IBS studied is almost azimuthally isotropic, and also zenithally up to θ = 40°, from which ε values decrease significantly with the increase of θ (García-Santos et al. 2012).

Building on these coherent indications from previous literature, we decided in this work to focus on the experimental verification of the effect of increasing emergence angle on emissivity measurements for asteroid analogue materials, taking into high consideration the results from the Hayabusa mission (Okada et al. 2015). We therefore selected a fine particle sample of meteorite Millbillillie, an achondritic eucrite originating from asteroid Vesta (Hiroi et al. 1995; McSween et al. 2013; Mittelfehldt 2014), and a synthetic enstatite to represent E-type asteroids (Zellner et al. 1977), both reduced to <25 µm as analogues for asteroid surface. The selection of those two samples does not explore the vast collection of asteroid analogues. Nevertheless, our intent in this study is to show that deviation of directional emissivity from ideal case has a trend that is independent from the kind of target sample we chose for the measurements; also our choice of two powdered samples plus two slab samples is reasonable from a statistical point of view.

We measured their emissivity under purging air and vacuum (<0.8 mbar) conditions, at 100 °C surface temperature, using the setup described in Helbert et al. (2013) and adjusted for measuring at lower temperature, for emergence angles from 0° to 60°. The choice of measuring at 100 °C surface temperature is not fully representative for NEOs, but it was a set point high enough to have good signal for measuring emissivity and low enough to remain a realistic approximation for the daily surface temperature of many asteroids.

Reflectance spectra were measured (for samples at room temperature, a standard condition in this kind of measurements) with minimal incidence angle (i = 13°) and emergence angles ranging from 13° to 80° (see Maturilli et al. 2014). A solid serpentinite sample, used for the calibration of MARA instrument on MASCOT lander and for the thermal infrared imager instrument of the Hayabusa 2 mission (Helbert et al. 2014), was measured in emissivity and reflectance under the same conditions. A second basalt slab was used to confirm the results found by measuring the serpentinite slab sample. Even if igneous rocks like basalts are not to be found on asteroids, this sample contained large phenocrysts of olivine and pyroxenes, commonly considered as asteroid analogue materials (Gaffey et al. 1993). This second slab was measured not because of its nature of asteroid analogue material, but as a thin slab sample, whose measurements were easier, trustworthy, and useful to confirm our findings on the other asteroid analogues we measured in this work. Furthermore, the surface of asteroids is composed of fine particle as well as larger particles. It is impossible to measure coarse particles in our setup, because the larger grains tend to slip away, even for small emergence angles. For this reason, the slab measurements are really important to support the results we found for finer particles, because the slabs offer the possibility to have reliable measurements on a target with physical features close to those of large grain size particles.

Methods

At PEL, we use two instruments equipped with external chambers to measure emissivity. The Bruker Vertex 80 V Fourier transform infrared (FTIR) spectrometer is operated under vacuum to remove atmospheric features from the spectra. An external evacuable chamber is used to measure emissivity: It contains a motor-driven carousel for up to 12 samples in the same working session, thermal sensors for each sample, and a webcam for monitoring the activities inside the chamber. The induction heating system allows heating up the samples (in stainless steel cups) from 50 °C to higher than 800 °C (Helbert et al. 2013). A Bruker A513 accessory mounted in the same spectrometer is used to obtain bi-conical reflectance with variable incidence angle i and emission angle e between 13° and 85° at room temperature, under purged (dry air, H2O, and CO2 removed) or vacuum conditions, in the 1- to 100-µm spectral range (Maturilli et al. 2014). In the whole spectral range, a gold sandpaper-coated surface is used as reference for reflectance measurements, measured with the same incidence and emission angles as the samples. The incidence beam cone angle is of 17°, the incidence beam size depends on the incidence angle, and it is however smaller than 10 mm, being the sample cup/reference diameter size for reflectance measurements.

The air-purged Bruker IFS 88 FTIR spectrometer has an attached emissivity chamber for measurements at low to moderate temperatures (Maturilli et al. 2006, 2008) that can be cooled down to 0 °C. Samples can be heated from room temperature to 150 °C in a purging environment. A Harrick Seagull™ variable-angle reflection accessory allows measurement of the bi-conical reflectance at room temperature, under purging conditions in the extended spectral range from 0.4 to 55 µm, for i and e from 5° to 85°.

In this work, emissivity in vacuum was measured with the Bruker Vertex 80 V, emissivity under purged air with the Bruker IFS 88. The two instruments have similar optical design, but some design differences cause the field of view (FOV) of the Vertex 80 V to be double in size to the one for the IFS 88 instrument. Emissivity was always measured using sample cups having 50 mm diameter. For emissivity measurements at 5° and 10°, emergence angle aluminum wedges were used, while for all the emergence angles from 20° to 60° (in 10° steps) we used custom-designed stainless steel wedges (see Fig. 1). Powdered meteorite Millbillillie, synthetic enstatite (grain sizes <25 µm), and a serpentinite slab were chosen as analogues for asteroid surface. Furthermore, a second basalt slab was used to confirm our results.

Fig. 1
figure 1

Wedges for inclined emissivity measurements; for 5° and 10° emergence angles aluminum wedges were manufactured, while for 20°–60° emergence angle, custom-designed and custom-made stainless steel wedges were used to heat up the samples at the proper emission angle

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To avoid slipping, the powdered samples were packed by mixing them with ethanol and then dried in oven at 350 K. Ethanol allows particles to rearrange and homogeneously distribute. As ethanol evaporates, the particles network results compressed into a denser packing, increasing the frictional resistance to sliding. Desiccation treatment in an oven removes residual capillary bridges. Since ethanol is not effective as solvent on the minerals of both samples, no solid bridges occurrence is expected during the evaporation (Gohering et al. 2013). For each sample a temperature sensor was carefully placed in contact with the emitting layer to ensure a sample surface temperature of 100 °C. Each sample was calibrated in emissivity with respect to a blackbody measured at exactly the same temperature and for emergence angle 0° to reproduce the calibration procedure of an instrument onboard a spacecraft orbiting around an asteroid. A waiting time of 1 h was observed before each measurement to stabilize the sample temperature.

Bi-conical reflectance measurements were taken in vacuum with an A513 accessory unit, setting incidence angle to the minimum possible (i = 13°) and varying the emission angle between 13° and 80°. In a recent paper, we show that bi-conical reflectance spectra of samples measured at PEL under purging or under vacuum conditions are identical (Maturilli et al. 2015).

Emissivity and reflectance measurements with both instruments were achieved by using a nitrogen-cooled MCT detector coupled with a KBr beam splitter. For emissivity and reflectance measurements, 4 cm−1 was used as spectral resolution.

Results and discussion

The study presented in this manuscript is designed to investigate the influence of increasing emergence angle on the emissivity measurements of asteroid’s analogue materials. Figure 2 shows emissivity spectra measured under purged air for a powdered Millbillillie sample for emergence angle from 0° to 60°. Each spectrum was calibrated with respect to a “flat” or “nadir” (θ = 0°) blackbody measured at the same temperature as the sample. 1−R (R is bi-conical reflectance at minima i and e angles) is shown for mere comparison too. For θ < 40°, the spectral variations are very limited, and from θ = 40°, we can observe that the emissivity spectra of the inclined surfaces tend to diverge from the one measured in nadir geometry. The band peaking at the Christiansen feature (CF, a maximum in emissivity, see Maturilli et al. 2006) around 8.1 µm is narrowing with increasing θ, while the whole continuum tends to lower. To numerically quantify the effect of increasing emergence angle on measured emissivity, we calculated the average percent difference between emissivity with θ = 0° and all the other values for θ. For each point in the 5- to 14-µm spectral range, the absolute value of (ɛ θ  − ɛ θ=0) was divided for ɛ θ=0 to express the difference in percent. The average value (expressed in %) of those differences along all the point in the 5- to 14-µm spectral range is used as average error between ɛ θ and ɛ θ=0.

Fig. 2
figure 2

Millbillillie emissivity measured under purged air for increasing θ; emissivity spectra of meteorite Millbillillie <25 µm sample measured under purged air at 100 °C surface temperature, for increasing emergence angle (θ), calibrated with respect to a blackbody at the same surface temperature, measured under nadir viewing geometry

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In the paper of Maturilli and Helbert (2014), the maximum error on a single emissivity measurement along the whole continuum at PEL was studied and found to be σ = 0.35 %. We decided to apply those results to our current work, proposing that the divergence from emissivity measured in nadir geometry can be considered significant when exceeding the value of 2σ = 0.7 %. Table 1 shows those results for emissivity difference of Millbillillie measured under purged air.

Table 1 Percent deviation from nadir (θ = 0°) for emissivity of Millbillillie measured under purging environment
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Table 1 highlights that emissivity variations become significant for θ ≥ 40°.

Figure 3 shows the same kind of measurements for a synthetic enstatite sample. Again, the spectra show that emissivity deviation from “nadir”-like measurements occurs around θ = 40°. We can detect the same narrowing of the band peaking at the CF and lowering of the continuum like for the Millbillillie sample. Deviations originating from increasing values of θ for the synthetic enstatite sample are reported in Table 2. Emissivity variations become again relevant for θ ≥ 40°, in agreement with deviations observed for the Millbillillie sample under the same conditions.

Fig. 3
figure 3

Synthetic enstatite emissivity measured under purged air for increasing θ; emissivity spectra of synthetic enstatite <25 µm sample measured under purged air at 100 °C surface temperature, for increasing emergence angle (θ), calibrated with respect to a blackbody at the same surface temperature, measured under nadir viewing geometry

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Table 2 Percent deviation from nadir (θ = 0°) for emissivity of synthetic enstatite measured under purging environment
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Similar emissivity measurements have been performed on two slabs, except for the measurements at 5° emergence angle, which was omitted because they would be redundant for this study. The first sample is a serpentinite slab, already used as a calibration body for the instrument MARA on MASCOT lander and the thermal infrared imager on the JAXA Hayabusa 2 mission (Helbert et al. 2014). The slab is much thicker than the usual samples used in the PEL laboratory (20 mm with respect to 3–5 mm as usual sample thicknesses). The resulting change in the measurement geometry could potentially affect the measured emissivity, because the FOV of the measurements could include the side portion of the slab. Figure 4 shows the serpentinite slab emissivity dependence on the increasing emergence angle θ. In this case too it can be noted that starting from θ = 40° the emissivity spectra show larger divergence from a nadir measurement. The relative deviations of emissivity from θ = 0° for increasing angle θ are listed in Table 3. We believe that the high value of emissivity deviation occurring for θ = 20° is a measurement error, probably caused from a not perfect position of the sample (because of its geometrical dimension) under the mirror collecting the emitted radiation to the spectrometer.

Fig. 4
figure 4

Serpentinite slab emissivity measured under purged air for increasing θ; emissivity spectra of serpentinite slab sample measured under purged air at 100 °C surface temperature, for increasing emergence angle (θ), calibrated with respect to a blackbody at the same surface temperature, measured under nadir viewing geometry. 1−R (R = bi-conical reflectance) is shown for comparison too

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Table 3 Percent deviation from nadir (θ = 0°) for emissivity of serpentinite slab measured under purging environment
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Nevertheless, despite the different height of this slab sample making the measurements trickier, the emissivity variations become significant for θ ≥ 40°.

To avoid the effects caused by the excessive height of this slab on the measured emissivity (cf. excessive deviation for θ = 20°), we repeated the measurements on a basalt slab with a thickness of 5 mm, closer to the standards used at PEL. While we do not consider the basalt itself as an analogue for asteroid surfaces, the measured sample provides several phenocrysts of olivine and pyroxenes, whose solid-solution phases are commonly identified as possible asteroid surface components. Figure 5 shows the results of emissivity measurements for this material, while Table 4 lists the emissivity differences with respect to nadir geometry data.

Fig. 5
figure 5

Basalt slab emissivity measured under purged air for increasing θ; emissivity spectra of basalt slab sample measured under purged air at 100 °C surface temperature, for increasing emergence angle (θ), calibrated with respect to a blackbody at the same surface temperature, measured under nadir viewing geometry

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Table 4 Percent deviation from nadir (θ = 0°) for emissivity of basalt slab measured under purging environment
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For the two powdered samples, we measured emissivity for increasing θ under vacuum (P < 0.8 mbar), at surface temperature of 100 °C. Figure 6 shows the spectra we measured for a Millbillillie sample. Again, we detect the narrowing of the band peaking at the CF and lowering of the continuum like for the measurements under purged air. We do not perform a direct comparison between emissivity and reflectance in vacuum because of the complications originating from the effect of thermal gradients (see Salisbury et al. 1994) on emissivity measurements of powdered samples in vacuum. Typical effects of thermal gradients on the measured emissivity spectra of powdered samples are band shifting, loss of spectral contrast, and band narrowing. However, in this paper we are only comparing measurements taken under the same conditions, and as our results show, the deviation of directional emissivity from the ideal case is not depending on the atmospheric pressure used for the experiment.

Fig. 6
figure 6

Millbillillie emissivity measured under vacuum for increasing θ; emissivity spectra of meteorite Millbillillie <25 µm sample measured under vacuum at 100 °C surface temperature, for increasing emergence angle (θ), calibrated with respect to a blackbody at the same surface temperature, measured under nadir viewing geometry. 1−R (R = bi-conical reflectance) is shown for comparison too

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Table 5 confirms the trend we already observed for purged measurements, showing that emissivity variations become significant for θ ≥ 40°. High emissivity deviation for θ = 20° is probably originating from a not precise positioning of the sample on the wedge under the parabolic mirror.

Table 5 Percent deviation from nadir (θ = 0°) for emissivity of Millbillillie measured under vacuum
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Figure 7, picturing the same results for a synthetic enstatite under vacuum, shows that for θ ≥ 50° measured emissivity undergoes a first important step in its changing.

Fig. 7
figure 7

Synthetic enstatite emissivity measured under vacuum for increasing θ; emissivity spectra of synthetic enstatite <25 µm sample measured under vacuum at 100 °C surface temperature, for increasing emergence angle (θ), calibrated with respect to a blackbody at the same surface temperature, measured under nadir viewing geometry. 1−R (R = bi-conical reflectance) is shown for comparison too

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Table 6 confirms the trend we already observed for purged measurements, with emissivity variations again becoming significant for θ ≥ 40°. Small deviations from this general behavior (like the apparent maximum at θ = 30°) are due to difficulties in optimizing the geometrical/optical setup for the measurements. In fact, our instrument field of view for measurements under vacuum doubles the one for measurements under purging. Therefore, tilting the sample when increasing the emergence angle results in diminishing the amount of sample surface exposed to the mirror collecting the emitted radiation, hence increasing the portion of cup and wedge (made of steel) radiation included in the measurements, and since the emissivity of steel is much lower than for the sample, this explains the high variations that we see in Figs. 6 and 7 for measured emissivity at values of θ ≥ 50°.

Table 6 Percent deviation from nadir (θ = 0°) for emissivity of synthetic enstatite measured under vacuum
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We measured bi-conical reflectance of the same samples, reproducing the optical/geometrical conditions we posed for the emissivity experiment. We put the incident angle to the minimum (the Sun in nadir position with respect to the surface) and moved the emission angle from the minimum (13°) to 20° and then to 80°, step 10°. Figure 8 shows the measurements (we show 1−R, R = reflectance, for a direct comparison with emissivity) for Millbillillie, and Fig. 9 shows the reflectance measured for synthetic enstatite.

Fig. 8
figure 8

Millbillillie 1-reflectance measured under vacuum for increasing emergence angle (e); 1-reflectance spectra of meteorite Millbillillie <25 µm sample measured under vacuum at room temperature, for fixed (minimum) incidence angle (i = 13°) and increasing emergence angle (e), calibrated with respect to a gold sandpaper reference, measured under the same incidence and emission angles

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Fig. 9
figure 9

Synthetic enstatite 1-reflectance measured under vacuum for increasing emergence angle (e); 1-reflectance spectra of synthetic enstatite <25 µm sample measured under vacuum at room temperature, for fixed (minimum) incidence angle (i = 13°) and increasing emergence angle (e), calibrated with respect to a gold sandpaper reference, measured under the same incidence and emission angles

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Table 7 (differences in % for Millbillillie, calculated with respect to R taken for θ = 13°) and Table 8 (differences in % for synthetic enstatite, calculated with respect to R taken for θ = 13°) help us to understand the trend for those measurements. As we did for emissivity spectra, we compare those differences with the 2σ error we characterized in Maturilli et al. (2014). It is interesting to note that for Millbillillie, different and independent measurement methods like emissivity and reflectance produce the same result as can be seen from Table 5 and Table 7: The first detectable deviation from nadir-like measurements is occurring for angles above θ = 30°. Further analysis will be conducted to understand if this effect has a physical explanation.

Table 7 Percent deviation from nadir (θ = 13°) for 1−R of Millbillillie measured under vacuum
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Table 8 Percent deviation from quasi-nadir (θ = 13°) for 1−R of synthetic enstatite measured under vacuum
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The reflectance measurements confirm what we already found with emissivity measurements: For θ ≥ 40° “nadir”-like measurements could be misleading to approximate the spectra we got from a surface with high inclination (hence emergence angle) θ.

Conclusions

To test the influence of increasing emergence angle on measured emissivity and reflectance spectra of small bodies (especially for asteroids), we set up a suite of experiments at the Planetary Emissivity Laboratory (PEL) of the German Aerospace Center (DLR). Two powdered analogue materials, meteorite Millbillillie and synthetic enstatite, were measured in emissivity at 100 °C surface temperature, under vacuum and purged air conditions, for emergence angles from 0° to 60°. A serpentinite slab and a basalt slab were measured under the same conditions. Reflectance measurements on powders were taken for minimum incidence angle (i = 13°) and emergence angle (e) varying from 13° to 80°. All the spectra were measured between 5 and 14 µm.

For all the target samples we found that divergence from nadir-like measurement becomes significant for emergence angles θ ≥ 40°.

Our results have a direct application for different fields of study. For planetary surfaces (where for gravitational effects, the surface slopes and therefore emergence angles are typically low), the effect of emergence angles can be largely neglected. On small bodies, however, large surface slopes and regions of highly irregular surface topographies are observed due to the microgravity environment. The resulting high emergence angles can lead to a misinterpretation of the spectral data if compared to laboratory measurements of analogues measured under nadir viewing geometries. Thermophysical models of small bodies (cf. Davidsson et al. 2015) should take into account our results for regions of high emergence angles (θ ≥ 40°).

Analyses on our emissivity and reflectance measurements show that emergence angles θ < 40° do not affect the spectra significantly, while for θ ≥ 40° we detect significant spectral differences, further increasing for each 10° step of increasing emergence angle θ. Similar results are obtained by a goniometric study on variations of emitted energy depending on the emergence angle carried out with the Oxford Space Environment Goniometer (OSEG) of the Oxford University (Warren et al. 2015).