5.1 Results: The observations were carried out at normal illumination to avoid the shadowing effect. Apart from that, the angle of incidence is frequently zero during laser altimeter observations onboard spacecraft visiting various solar system objects, and therefore this is an important observation condition. Reflectance data obtained from each of the samples in Table-1 are shown in Fig. 3. The curves show a similar trend at low phase angles but quite different at large angles. From these results three observations can be pointed out – (i) At small phase angles (up to 10o) all the curves have a decreasing trend which appears to be the end trail of opposition effect. (ii) At large phase angles ≥ 70o, the reflectance phase curve of SS1 shows an increasing nature while that of Q1 shows a decreasing trend which can be compared with Mie calculations for spherical particles with the Hapke formula (Hapke 1993) for a monodisperse medium as shown in Fig. 4. Since surface roughness is known to be related to particle size, it is expected to affect differently in the above two cases, and hence the nature of phase curves at large angles. The curves of mixed samples are flattened in this region, which may be due to the combined effect of albedo and roughness variation.
(iii) In a region between 5o and 45o phase angle most of the curves are nearly parallel and horizontal. Careful observation reveals that the reflectance in this region is linear with the proportion of sample mixing (Fig. 5). The reflectance of the combined sample can be calculated from their end members with the following relationship
rcalculated= rSS1×(Mass fraction of SS1) + rQ1×(Mass fraction of Q1)………..(5)
Here r SS1 and rQ1 are reflectances of SS1 and Q1 respectively, and rcalculated is the theoretically calculated reflectance assuming linear combination for the intermediate sample with mass fractions of end members as used at the RHS of Eq. 5.
In Fig. 5 experimentally measured values at constant phase angles have been plotted against calculated reflectance for phase angles ≤ 45o. The points clearly show a linear trend about the line of unit gradient, which means that calculated and measured values are in good agreement with each other.
5.2 Discussion: Comparing the results of this experiment with previous studies following observations can be pointed out –
1) Working with mixed samples, Cord et al. 2005 conclude that – “....(1) the textural roughness, essential for the accurate determination of mineralogical abundances”. However, they used reflectance data at a higher angle of incidence (e.g. Figure 3 of Cord et al. 2005) where the shadowing effect comes into play. In our observation, we find that at normal illumination conditions the reflectance values are linearly dependant on the abundance of their components at phase angles ≤ 45o (Fig. 5). At higher phase angles, however, this behavior is destroyed (Fig. 3), which may be due to the hiding effect due to surface roughness (i.e. if we assume that, the rough surface is like hilly terrain, the valleys are visible at small viewing angle but not at large). Hence it turns out that, the effect of textural roughness on abundance determination may be neglected for normal illumination of light and phase angles ≤ 45o.
2) Yoldi et al. (2015 and 2020) experimented with real water-ice samples of two different particle sizes (i) SPIPA-A (4.5 ± 2.5 µm) and (ii) SPIPA-B (67 ± 31 µm), and their intimate mixtures with primary regolith - JSC Mars-1 (24 µm) and Dark Basalt (50wt% of the particles > 109 µm and 50 % < 109 µm). Yoldi et al. 2015 concluded that bigger ice particles (i.e. SPIPA-B) are difficult to detect at low phase angles even if their abundance is as large as 75% in the primary regolith, and therefore laser altimeters are not recommended for ice detection on planetary regolith. The size of our Q1 sample is comparable to SPIPA-B, but Fig. 3 indicates an opposite result. However, if we compare Fig. 3 and phase curves of SPIPA-A mixtures at i = 20o (Fig. 2(a), Yoldi et al 2015), they look similar – which means SPIPA-A is easily detectable, unlike SPIPA-B. Interestingly, the size of Q1 (78 µm) is comparable to SPIPA-B, not SPIPA-A. Instead of size, if we compare their size ratio with primary regolith, we see that SS1/Q1 = 3.24 and JSC Mars-1/SPIPA-A = 5.33, whereas JSC Mars-1/SPIPA-B is < 1. This suggests that it is not the size of ice particles – rather their relative size to the primary regolith which matters when it comes to their detection. If ice particles are relatively larger than primary regolith particles, they are difficult to detect. Also, low phase angle observations may be important if ice particles are relatively smaller than the primary regolith particles.
If we talk about the linearity of mixing, from Fig. 5 we see that intimate mixtures of Q1 and SS1 show a linear trend consistent with their abundance. A similar graph has been plotted in Fig. 6 for three intimate mixtures used in Yoldi et al. 2020 with the help of data derived from Fig. 8 (a)(c) and (d) of Yoldi et al. 2020 at λ = 0.65 µm. The relative albedo of samples are as follows –
JSC Mars-1/ice* ≈ 0.116
Basalt/ice ≈ 0.0779
SS1/Q1 ≈ 0.38
If we compare the relative albedo of the samples we see that brighter the primary regolith – closer it is to the line of unit gradient (i.e. reflectance is linear in terms of abundance). Therefore, it might be easier to detect the abundance of ice as an impurity by using a linear relationship like Eq.(5) in a brighter terrain like silicate-rich S-type asteroids.
*Both SPIPA-A and SPIPA-B have similar reflectance at 0.96 µm, hence their average is considered