The Absolute Reflectance and New Calibration Site of the Moon

Yunzhao Wu; Zhenchao Wang; Wei Cai; Yu Lu

doi:10.3847/1538-3881/aabaf5

1. Introduction

The absolute reflectance of the Moon, one of its important intrinsic properties, is crucial for calibrating the optical instruments on board either planetary explorers or Earth-orbiting satellites that use the Moon as an illumination standard. Among all of the extraterrestrial bodies, the Moon's absolute reflectance is the most studied. Studies include laboratory measurements of lunar samples (Pieters et al. 2000), remote measurements from Earth-based telescopes (Shkuratov et al. 2001; Kieffer & Stone 2005; Saiki et al. 2008; Buratti et al. 2011; Velikodsky et al. 2011), and lunar-orbiting spacecraft (Hillier et al. 1999; Ohtake et al. 2010; Yokota et al. 2011; Boyd et al. 2012; Besse et al. 2013a; Wu et al. 2013; Mahanti et al. 2016). At present, however, the absolute reflectance of the Moon is still largely debated. Lunar sample reflectance measured in the laboratory is much higher than the reflectance of the actual lunar surface (Hillier et al. 1999; Shkuratov et al. 2001; Ohtake et al. 2010). The reflectance measured by Earth-based telescopes suffers from atmospheric effects, low spatial resolution, and the difficulty of obtaining an accurate radiometric calibration. The Robotic Lunar Observatory (ROLO), the Earth-based telescopic system operated by the USGS in Flagstaff, uses star flux to establish the Moon as a radiance source for on-orbit calibration of spacecraft instruments. ROLO has been widely used as an optical standard in the lunar calibration of spacecraft instruments. Its results remain open to question (the above effects and the need for new measurements have been noticed by the team; Stone 2015). The absolute reflectance derived from ROLO is 0.87 times lower than the recent Earth-based observations at the peak of Mt. Haleakala, Hawaii, USA (Saiki et al. 2008) and at the Maidanak Observatory, Uzbekistan (Velikodsky et al. 2011). Although the lunar-orbiting missions launched recently such as SELENE, Chandrayaan, Chang'E, and the Lunar Reconnaissance Orbiter (LRO) do not suffer from atmospheric effects, they lack an on-board calibration device. It has been noted that the reflectance measured by these sophisticated missions are considerably different (Besse et al. 2013b; Wu et al. 2016).

In addition to using sophisticated instruments, researchers have recommended many lunar sites (e.g., Apollo 16 highlands, Apollo 15, Lichtenberg rim, MS-2 in Mare Serenitatis, and Tycho) as calibration sites (Pieters et al. 2008). Among them, the Apollo 16 calibration site (about 10 km west of the Apollo 16 landing site) is the one that is used the most for both Earth-based telescopic observations (Pieters 1999) and orbital data (Hillier et al. 1999; Ohtake et al. 2009; Wu et al. 2012). The reason for this is that researchers thought that its spectra could be represented by the laboratory spectra of Apollo 16 bulk soil 62231 (Pieters 1999). However, it has been demonstrated that the composition between the Apollo 16 calibration site and the real sampling site of Apollo 16 bulk soil 62231 is different (Ohtake et al. 2010). More importantly, the roughness, compactness, maturity, and particle size between the laboratory sample and the actual lunar surface differ by large amounts. The in situ spectra measured by the Visible-Near Infrared Spectrometer (VNIS) on board the China's Chang'E-3 (CE-3) "Yutu" rover revealed that the uppermost surficial regolith is much richer in weathered products, which significantly darken the lunar surface and suppress spectral bands, than the regolith immediately below, and samples returned to Earth could not represent actual lunar surface (Wang et al. 2017; Wu & Hapke 2018). Therefore, a spacecraft calibration using the laboratory spectra will have a very large error. For example, the reflectance measured by Clementine and calibrated using the Apollo 16 calibration site has been noted to be a factor of 2.5 (Shkuratov et al. 2001), 1.87 (Hillier et al. 1999), 1.69 (Saiki et al. 2008), or 1.41 (Velikodsky et al. 2011) higher than that inferred from ground-based measurements. The comparison with recent orbital instruments demonstrates that the laboratory spectra of soil 62231 are too high: from 1.38 times higher than that of the Lunar Reconnaissance Orbiter Camera (LROC) Wide Angle Camera (WAC) to 2.25 times higher than that of the Optical Period 1B (OP1B) M³ (Figure 1). All of the other sites do not have standard reflectance data. Moreover, most of them are very old, rugged, and mixed due to numerous impacts.

**Figure 1.** Comparison of reflectance spectra of orbital (IIM, M³, and SP), Earth-based telescopic (ROLO), and laboratory sample (62231) data of the Apollo 16 standard site. Multiple observations of IIM and M³ are shown (note that the IIM reflectance match well with relative accuracy <1%). The IIM data come from Wu et al. (2013), the SP data come from and Yokota et al. (2011) (http://l2db.selene.darts.isas.jaxa.jp/index.html.en), the M³ and ROLO values come from Besse et al. (2013a) (https://pds-imaging.jpl.nasa.gov/data/m3/ for M³), the LROC WAC data are from Boyd et al. (2012) (http://wms.lroc.asu.edu/lroc/view_rdr/WAC_EMP_NORMALIZED), and the laboratory sample data are from the RELAB data set (http://www.planetary.brown.edu/pds/LSCCsoil.html). Data used for the comparison in Figure 8 are also from these data sources.
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In summary, the value for the absolute reflectance of the Moon has puzzled the field for a long time and still remains an open question. State-of-the-art electro-optical sensors needed for many applications require higher and higher calibration accuracy. This leads to a tight requirement for the accuracy of the absolute reflectance of the Moon. The in situ measurement of reflectance with a calibration panel on the surface of the Moon is crucial for obtaining the accurate absolute reflectance. This type of measurement, although common on the Earth, suffers because of the difficult access to the Moon, and it was not achieved until the end of 2013 when CE-3 spacecraft landed on the Moon. In this paper, we report the absolute reflectance of the Moon measured by the VNIS on board the CE-3 "Yutu (Jade Rabbit)" rover and suggest the CE-3 landing site as a new calibration site. Definitions of various reflectance quantities presented in this paper are provided in Appendix A.

2. Materials and Methods

2.1. Introduction to VNIS

The VNIS uses acousto-optic tunable filters (AOTF) as dispersive components and consists of a VIS/NIR imaging spectrometer (0.45–0.95 μm, 256 × 256 pixels, field of view: 8 fdg 5 × 8 fdg 5), a shortwave IR (SWIR) spectrometer (0.9–2.4 μm, 1 pixel, field of view: 3 fdg 6), and a white calibration panel that is protected from dust. The default spectral sampling interval is 5 nm, and the total number of sampling bands is 400 (100 bands for the VIS imaging spectrometer and 300 bands for the SWIR spectrometer; note that the bands between 900 and 945 nm overlap). The VNIS is mounted on the front of the rover and detects lunar surface objects from a height of 0.69 m above the lunar surface at 45° emission angle (Figure 2). The nominal spatial resolution of the VIS imaging spectrometer is 0.53–0.80 mm/p, and the field of view (FOV) is an isosceles trapezoid with a height of 20.6 cm and two parallel sides of 13.5 and 15.7 cm. The field of view of the SWIR spectrometer is approximately oval with diameter of 6.14 cm and 8.68 cm. The center of the SWIR corresponds to (X96, Y128) of VIS. To match the FOV of the VIS and SWIR bands, the VIS spectra is an average of a circle centered at the coordinate (96, 128) in the images, with a diameter of 108 pixels. When compared with the solar illumination, both the specular and diffuse reflection of the rover body on the calibration panel can be neglected because the panel is embedded in the rover body and the rover body right above it is coated black (Figure 2(c)). When compared with the solar illumination, the diffuse reflection of the rover body on the lunar surface can also be neglected because most of the light is specular reflected out of the FOV of the VNIS.

**Figure 2.** Schematic of detection by VNIS. (a) looking at the ground; (b) detection, calibration, and dust-proofing modes of VNIS; (c) white calibration panel and black coating directly above it.
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A calibration unit whose material is polytetrafluoroethylene (PTFE) was located at the light entrance; hence, it functions as both a calibration reference and as a cover to exclude dust. Its directional-hemispherical reflectance (DHR), reflectance factor (REFF), and surface uniformity were measured and traced to the National Institute of Metrology (NIM), China. It is based on a standard diffusion screen that was tested by the NIM and uses an integrating sphere system with a double light path to set the standard. Three modes were designed for the diffuser panel (Figure 2(b)). When the spectrometer is in detection mode, it can be completely opened (55°), and hence does not affect the entrance of light into the instrument. When the spectrometer is in calibration mode, the diffuser panel is oriented parallel to the mounting plane. When the spectrometer is not in use, the calibration unit is closed to protect the spectrometer and also to provide good thermal insulation.

2.2. Data and Methods

At 13:11:18 UTC on 2013 December 14, CE-3 landed in the northern Mare Imbrium with the landing site at (44 fdg 1281N, 19 fdg 5110W). The unit of the landing site belongs to the last major phase of lunar volcanism (Eratosthenian high-Fe, middle to high-Ti basalts) with an age newly dated as ~2.35 Ga (Wu et al. 2018). During the 114 m travel of the Yutu rover, four measurements of the soil were made by the VNIS. Both the soil and the diffuser calibration panel were measured by the VNIS, except for Site 6 where only the soil was measured. The integration time used to obtain the VIS and SWIR spectra was ~2 minutes and 7 minutes, respectively. The total time finishing each pair of panel and soil measurements is ~40.4 minutes during which the change in solar illumination is negligible. Data acquisition conditions of the four sites analyzed by VNIS are shown in Table 1. Figure 3 shows the locations of the four spectral measurements (sites 5–8) and the increased reflectance zone around the lander caused by the rocket exhaust during the spacecraft descent. Out of the four measurements, Site 8 (~40 m from the lander) was visually undisturbed; hence, it is primarily used in this paper.

**Figure 3.** Before (a; NAC image M1127248516R) and after (b; NAC image M1147290066R) images of the CE-3 landing site. The locations of the four spectral measurements (numbered 5–8), the lander, and the final position of the rover are also shown.
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Table 1. Data Acquisition Conditions of the Four Sites Analyzed by VNIS and Orbital Data

	Date (UTC)	Sun Zenith Angle	Sun Azimuth Angle	View Zenith Angle	View Azimuth Angle	Phase Angle	Sun–Moon Distance
5	20131223	60.02	238.48	48.27	55.01	108.21	0.985
6	20131224	67.48	248.44	47.42	355.47	86.56	0.984
7	20140112	69.57	108.72	47.03	6.00	85.01	0.985
8	20140114	53.95	131.20	44.39	287.12	95.50	0.986
SP	20090508	51.57	136.14	1.58	20.15	52.35	1.012
IIM	20080523	47.62	213.60	4.09	98.15	49.74	1.014
M³ (OP1B)	20090207	62.98	119.18	10.63	273.46	72.64	0.988
M³ (OP2A)	20090416	67.15	248.42	2.076112	251.68	65.09	1.004
M³ (OP2C1)	20090610	43.54	191.43	13.53	276.78	44.07	1.017

Note. Angles are in degrees and Sun–Moon distance is in astronomical unit (au).

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The dimensionless raw data were radiometrically calibrated to the spectral radiance using the calibration coefficients derived from the two measurements of the calibration panel at a larger solar elevation angle and same measurement mode (sites 5 and 8). (Details of the data processing and calibration are provided in He et al. 2014 and Liu et al. 2014). Hence, the radiance of the calibration panel at Site 7 can be used as a test by comparing the reflectance measured on board (the Bidirectional Reflectance Factor (BRF) was used) with that provided by the manufacturer (the REFF was used). The comparison shows that the SWIR reflectance of the calibration panel for the three measurements matches those provided by the manufacturer quite well (around 1.2 for Site 5, around 1.1 for Site 8, and 0.96 for Site 7), indicating that the absolute radiance at the SWIR bands is reliable. Although the order of the VIS reflectance of the calibration panel for the three measurements is also Site 5 > Site 8 > 1 > Site 7, they do not match those provided by the manufacturer well, forming a gap at the overlapping wavelengths between the VIS and SWIR segments.

The raw radiance of the four measurements released by the team is at 1 au Sun–Moon distance, for which we first performed the distance correction. The gap is clearly shown in the radiance for both regolith and diffuser panel data (Figures 4(a) and (b)). For the calibration panel, the gap was eliminated by multiplying an adjustment factor, which was the ratio of the BRF over REFF of the calibration panel. For soil, because there is no reflectance standard, the radiance of VIS was adjusted to the radiance of SWIR using a multiplicative factor considering the higher signal-to-noise ratio (S/N) and increased stability of the SWIR. The gap ratio was calculated for the overlapping bands between VIS and SWIR (900–945 nm). The adjustment factor is the average of the gap ratios of the overlapping bands by eliminating abnormally large values. Adjustment factors for sites 5–8 are 1.023, 0.702, 0.716, and 0.993, respectively. The final radiance after the gap removal and Sun–Moon distance correction for both regolith and the diffuser panel are show in Figures 4(c) and (d), and the data are in Appendix B.

**Figure 4.** Radiance of the diffuser panel and the lunar regolith. (a) diffuser panel before gap adjustment; (b) regolith before gap adjustment; (c) diffuser panel after gap adjustment; (d) regolith after gap adjustment. Note that at Site 6, the diffuser panel was not measured.
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The CE-3 VNIS measured the lunar spectra with the on-board calibration panel, and its results are used here for comparing optical instruments on board orbital missions. This comparison is very important. For such missions, it is critical to assess the characteristics of each data set and to know the brightness of the Moon. Comparing the orbital missions' data with the in situ data, however, is not easy because the spatial resolution, observation, and illumination geometry vary with each mission. In this study, we try to accomplish the comparison with several state-of-the-art sensors in terms of both radiance and reflectance. By comparing the radiances, we can avoid the error caused by the photometric correction. Similarly, by comparing the reflectance, we can minimize the effects of illumination geometry. During the comparisons, we kept in mind the differences in composition, particle size, maturity, spatial resolution, and illumination geometry.

For the radiance, all of the measurements were standardized to 1 au. For the reflectance, generally one normalizes to the photometric angle of incidence i = 30°, emergence e = 0°, and phase angle α = 30°, which are commonly used for orbital data (Hillier et al. 1999; Ohtake et al. 2010; Buratti et al. 2011; Yokota et al. 2011; Boyd et al. 2012; Besse et al. 2013a; Wu et al. 2013). Unfortunately, existing spectrophotometric models were developed with a more restricted range of phase angles than were seen at sites 5 and 8. Our testing found that the models derived from the ROLO (Buratti et al. 2011), Clementine (Hillier et al. 1999), M³ (Besse et al. 2013a), and IIM (Wu et al. 2013) all over-normalized the VNIS data from sites 5 and 8. For these spectra, the models produced unreasonably high reflectance because their phase functions steadily decreased with increasing phase angles. This suggests that at large phase angles, the lunar soil has more forward scattering than indicated by current models. Only the reflectance of sites 6 and 7 were normalized to an angle of i = 30° and e = 0° using three models (Hillier et al. 1999; Buratti et al. 2011; Besse et al. 2013a) that provide a comprehensive reflection of their relatively large range of phase angles and numerous bands. The only model that was derived from the high-Fe basalts (i.e., the CE-3 landing unit), the IIM model (Wu et al. 2013), cannot be applied to the VNIS data because the model's range in phase angle is less than 80°.

Moreover, for the comparison, it is necessary to use the measurements from the undisturbed regolith (for this study, Site 8 is used). Unfortunately, accurate comparison is impossible due to the lack of a photometric model suitable for normalizing the illumination geometry seen at Site 8. To obtain approximate comparison using the CE-3 in situ measurement at Site 8, the comparison was performed using (1) radiance and (2) BRF, which just corrects for the solar incidence angle.

3. Results

3.1. In Situ Radiance

Figure 4 shows the radiance for both the calibration panel and the soil. The regolith radiance data have peaks at 570–600 nm while the radiance of the diffuser panel exponentially decreases with increasing wavelength. These observations are consistent with the fact that the reflectance of the lunar soil increases toward longer wavelengths while maintaining a consistent reflectance value for the calibration panel. The strong Fraunhofer lines (e.g., 485, 515, 655, and 855 nm) are evident in the soil radiance data, and the diffuser panel captured most of the Fraunhofer series, even the very weak 2165 nm absorption for both the visible and SWIR bands. The accurate match between the absorption of the diffuser panel and the Fraunhofer series (ASTM 2014, Thuillier et al. 2003; Gueymard 2004) indicates that the wavelength calibration of the VNIS is reliable, and hence it can be used for the wavelength calibration of orbital data. We note that the absolute calibration of the VNIS is the on-board calibration using the data of Gueymard (2004) as the irradiance source. The re-calibration for the VNIS data using the laboratory calibration would be desirable for double checking not only the solar Fraunhofer lines but also the absolute reflectance. Note that the small jumps around 630 and 1380 nm are due to the sudden change of the spectral resolution at the switching point of high and low radio frequency (RF) of the AOTF crystal and not a real absorption of lunar minerals.

3.2. In Situ Absolute Reflectance

Figure 5 and Appendix B show the in situ reflectance of the lunar soil. The VNIS images at 750 nm for the four sites are shown in Figure 6. Compared with existing lunar spectra, the CE-3 data are referenced to the on-board calibration panel and acquired at different photometric geometry with large emission and phase angles. These new measurements extend the range of photometric geometries of current data and for a large range of wavelengths. Among the four spectra, their emission angles are the same, their phase angles are all large, and it can be expected that their phase function values will not vary much, and their solar incidence angles will be normalized. Therefore, the variation of the reflectance spectra shown in Figure 5 mostly reflects the property of the lunar soil. Both the spectra and images show that Site 8 is the darkest. The measured reflectance increases for sites closer to the lander. This is consistent with the image brightening observed by the LROC Narrow Angle Camera (NAC; Figure 3(b)) and reflects the brightening of the soil from the disturbance of the regolith by rocket exhaust during descent of the spacecraft. The soil brightened because rocket exhaust from the spacecraft blew away the uppermost mature dust and exposed less-mature material. The REFF of lunar soil at Site 8, taken at angles of i = 54°, e = 44°, α = 95°, is 4.53% at 750 nm with an average of 3.86% for the visible bands (450–760 nm). This indicates that the CE-3 landing site is very dark, consistent with that of the CE-3 (the unsampled Eratosthenian high-Fe, middle- to high-Ti basalts).

3.3. Comparison among In Situ and Other Measurements

3.3.1. Radiance Comparison

Radiances obtained by the CE-3 in situ measurement and three recent orbital hyperspectral measurements of the CE-3 landing site are compared in Figure 7 (see Table 1 for the measurement geometry for each observation). The in situ radiance exhibits many Fraunhofer lines while the orbital measurements do not. This indicates that the CE-3 VNIS provides high-quality radiance data. It is important to accurately detect compositionally related spectral features because most lunar spectral variations are subtle. In terms of the shape, the in situ radiance is a better match to M³ than Spectral Profiler (SP). The radiance of the SP has a broader peak between 550 and 660 nm and a sharper fall toward the blue band and much higher radiance in its NIR 1 detector (wavelength: 894–1686 nm). This indicates that the slope of spectral reflectance of the SP is larger than the others, which is consistent with previous comparisons (Besse et al. 2013b; Wu et al. 2016). In theory, the SP NIR-2 detector (wavelength 1694–2582 nm) should be consistent with the NIR1 detector. However, as shown in Figures 7 and 8 they are not consistent. Therefore, the radiance of the SP NIR 2 detector is reduced so that it matches the CE-3 VNIS and M³ radiance. The CE-3 in situ radiance also confirms that the 626 nm absorption seen in all of the SP data of the Moon is not a real absorption. The IIM has the lowest S/N among all the instruments. Our check of the global IIM data found that the oscillation in the IIM curve is systematic and confirmed the response stability of IIM (Wu et al. 2016). (It is a Sagnac-based spatially modulated Fourier transform imager and has no moving parts.) The first five bands (480–513 nm) and last band (946 nm) of the IIM are abnormal and should be eliminated before use. The comparison in Figure 7 also confirms that the IIM measurements of the three bands with the high quantum efficiency of a silicon detector (721, 738, and 757 nm) are low. This indicates that a re-calibration of the IIM to remove the systematic miscalibration is needed.

**Figure 7.** Radiance values (a) and the values normalized to unity at 750 nm (b) comparison among different instruments. Because OP2C1 M³ does not exactly cover the CE-3 landing site, the nearby location (−20403W, 44063N) is used.
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fdg — **Figure 7.** Radiance values (a) and the values normalized to unity at 750 nm (b) comparison among different instruments. Because OP2C1 M³ does not exactly cover the CE-3 landing site, the nearby location (−20403W, 44063N) is used.
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**Figure 8.** (a) Comparison of the RADF from VNIS sites 6 and 7 normalized to (30°, 0°, 30°) using the photometric function derived from ROLO (Buratti et al. 2011). Also shown are the Apollo sample spectrum (71501, <45 μm) and orbital spectra of the CE-3 landing site from IIM, LROC WAC, SP, and M³. Site 8 is also shown for an approximate comparison (see the text for its normalization). (b) Comparison of the BRF of the VNIS with those of IIM, SP, and M³.
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The radiance of the three optical periods in the M³ data (OP1B, OP2A, and OP2C1) increases with the decrease of solar zenith angle. The amplification between the two cold OPs (OP1B and OP2A) is consistent with the angle of reducing solar incidence, indicating that the M³ instrument response during these OPs is stable. For the warm OP (OP2C1), the extent of the radiance increase is much larger than the contribution of the angle of reducing solar incidence. For such large amplification (the radiance of OP2C1 is 2.6 times that of OP2A), the contribution of the angle of reducing solar incidence is 1.86 times that of OP2A, so the contribution of the reducing phase angle is 1.69 times that of OP2A assuming that the scattering dependence on incidence and emission angle uses the Lommel–Seeliger model. That is, the phase function value of OP2C1, i.e., f(44°) should be 1.69 times that of OP2A, i.e., f(65°). For the Moon, there is no such steep phase curve between the phase angles of 44° and 65°. Therefore, the large variations among the different OPs M³ data are inherent. That the measurement of OP2C1 M³ data is much larger than other OPs has been noticed by the M³ team (Besse et al. 2013a). Our large amounts of comparison data (Wu et al. 2016) show the same thing, and the reason for this is unknown. Despite this, the measurement of OP2C1 M³ is much smaller than the SP value based on their similar radiance, but OP2C1 M³ data have a smaller solar incidence angle and phase angle. Similarly, the measurement by the IIM is smaller than the SP and CE-3 in situ measurements. We have large amounts of comparison data all indicating that the IIM data fall close to the OP2C1 M³ data (Wu et al. 2016). Hence, both the IIM and OP2C1 M³ measurements are smaller than the SP and CE-3 in situ measurements. For the comparison of absolute reflectance in the next section, the OP2C1 M³ data were used.

3.3.2. Reflectance Comparison

The reflectance comparison is shown in Figure 8, where (a) shows the reflectance in the form of the radiance factor (RADF) normalized to angles of i = 30° and e = 0°, and (b) shows the reflectance in the form of BRF. Note that Site 8 is also shown. Because it could not be normalized to (30°, 0°, 30°), it was derived from the Site 7 data via multiplying by the ratio of the two curves in Figure 5. Although it is not a true RADF (30°, 0°, 30°), it is useful for an approximate comparison. In addition to orbital data, the laboratory reflectance spectrum of an Apollo bulk soil sample 71501 (<45 μm size fraction) is also shown. It was deliberately selected from the Lunar Soil Characterization Consortium (LSCC) soil from the RELAB data set to be significant when comparing different sampling areas and composition. This sample very nearly has the darkest hue and the highest value for FeO (16.5 wt.%) + TiO₂ (9.31 wt.%) in the LSCC data set. The CE-3 in situ reflectances normalized using the three models (M³, ROLO, and Clementine) are similar, so only the one normalized using the ROLO model is shown.

The comparison in reflectance is consistent with the comparison in radiance, to some extent, which indicates that the photometric correction for the illumination geometry is acceptable. Both the radiance and reflectance comparisons reveal that the very high value at 870 nm and very low values at 1009 and 1449 nm of M³ data are abnormal. Among all of the data, the three SP detectors exhibit the largest variation. In addition to the NIR 1 detector, which is significantly higher than the rest, the VIS detector shows a sharp decline toward the blue band in radiance and reflectance. Of all the orbital reflectance, the LROC WAC is the largest and reddest. The SP value is next. We also find the same situation for many other areas when there are large amounts to compare (Wu et al. 2016). The IIM and OP2C1 M³ data match well and are much smaller and flatter than the LROC WAC and SP data. The IIM and M³ data are also smaller than ROLO (0.85 and 0.92 times around 770 nm, respectively). Note the very low spatial resolution of ROLO (7.4 km/p in the VNIR and 15 km/p in the SWIR for the sub-Earth point). The IIM and M³ data are steeper, and in the visible wavelengths, they are smaller than the CE-3 in situ data; in the SWIR bands, they are larger than the in situ data. The LROC WAC and SP data are larger and redder than the in situ measurement. In the visible bands, the in situ reflectance is in the middle of all the data. The measurements from the four recent orbital missions are considerably different in both absolute value and slope. The difference increases with the wavelength increasing. At 689 nm, the LROC WAC and SP is 1.5 times that of IIM and M³. This difference is outside the limits of uncertainties (usually <5%) of modern sophisticated electro-optical sensors and perhaps indicates the inherent differences in the absolute calibration of these missions, though their spatial resolution is different. Thus, the absolute reflectance and the irradiance of the Moon derived from these missions are different. Although the reflectance properties of the Moon are very stable, one should be cautious about the data source when using the Moon as a radiance source for on-orbit calibration of spacecraft instruments.

Figure 8(a) shows that the laboratory reflectance of lunar samples is significantly larger and even redder than the actual lunar reflectance measured from orbit and on the lunar surface. The comparison with in situ spectra supports the previous opinion that the reflectance measured in the laboratory is much larger than the actual reflectance of the Moon. Previous research assumed that roughness and compactness were the major factors responsible for the reflectance of samples being larger than that seen in remote sensing data (Hillier et al. 1999; Ohtake et al. 2010). A detailed analysis using lunar sample revealed that the compactness can be large enough to explain a 40% difference (Ohtake et al. 2010). The CE-3 VNIS data reveal that, in addition to roughness and compactness, lithic fragments and maturity are also very important. The close-up images captured by VNIS show a large number of shadows (Figure 6), indicating the effects of roughness and compactness. The slope of the laboratory reflectance spectra is steeper than that of the in situ spectra, and the in situ spectra have greater absorption depth, indicating that the VNIS sees more lithic fragments than the laboratory samples. As shown in Figure 6, the actual lunar surface has more lithic fragments than the soil samples, which are sieved into bins <45 μm. Figure 5 shows that, when comparing Site 5 with Site 8, Site 5 has a considerable increase in reflectance and absorption strength but has a similar continuum slope. This indicates that the uppermost surface is very mature and thus largely reduces reflectance. The samples analyzed by LSCC are not the uppermost mature dust. Unfortunately, maturity is very complex, and it is difficult to compare the maturity between the in situ and laboratory samples. And of course, the simulation work using lunar samples in the laboratory cannot represent pristine regolith.

Unlike the calibration sites on the Earth, which are generally smooth, homogeneous, and carefully manually maintained, the lunar calibration sites suggested previously (each about 200 km in diameter) are quite rugged and form a mixture of rocks and soil due to innumerable craters. All of them lack the standard spectra of the pristine surface. We propose the CE-3 landing site as a calibration site. Compared to those frequently used calibration sites such as MS-2, Apollo 15, and Apollo 16 Highlands, the CE-3 site is much younger and less impacted and contaminated. The remote sensing image shows that the large area surrounding the landing site has a homogeneous composition and can be extended to North Imbrium (Figure 9), which allows the calibration of instruments with different spatial resolution. (We recommend that the CE-3 calibration site be much more extensive because the landing site belongs to the last major phases of mare basalts, which cover large areas of Oceanus Procellarum, Mare Imbrium, and small regions within several surrounding maria.) Moreover, compared to other lunar calibration sites, one additional advantage of the CE-3 site is that it has chemical compositions acquired in situ by the Active Particle-induced X-ray Spectrometer (APXS) on the CE-3 rover, which are approximately 4.31 wt% TiO₂, 12.11 wt% Al₂O₃, 22.24 wt% FeO, 8.61 wt% MgO, 9.72 wt% CaO, and ~0.15 wt% K₂O (personal communication with the APXS team). In addition to being an optical calibration site, the CE-3 site can also be a compositional calibration site for elemental mapping. Global high-resolution elemental maps of the Moon derived from Clementine (Lucey et al. 2000) and IIM (Wu 2012; Wu et al. 2012) were calibrated using the Apollo and Luna samples. Unfortunately, none of them are from the last major phases of mare basalts that span large areas of maria. The CE-3 site will significantly improve the elemental mapping accuracy for the last major phase basalts.

**Figure 9.** LROC WAC enhanced color mosaic (R-689 nm; G-415 nm; B-321 nm) images centered on three calibration sites: (a) CE-3, (b) MS-2, and (c) Apollo 16 highlands. The CE-3 calibration site zone is younger and has fewer craters than the other two frequently used sites. The width of each figure is 189.5 km.
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When the CE-3 in situ reflectance is used as a standard for comparison or for the calibration of Earth- or lunar-orbiting missions, two points should be kept in mind: (1) the view angle of VNIS is about 45°, which is unusual for orbital observation, and (2) the solar zenith angles and phase angles observed by the VNIS are large. Current missions, except for those using Earth-based instruments, usually observe at the nadir, and very few observe at 45°. We need to assess whether the orbital measurements with the 45° emission angle see more lithic fragments than those with a small emission angle. Moreover, there are few VNIS measurements at the CE-3 landing site. The multiple in situ measurements with variable viewing and illumination geometries with large range of angles are very important to understanding the bidirectional reflectance distribution function. Chang'E-4, which is scheduled to be landed on the far side of the Moon, has the potential of providing the opportunity for the in situ multi-angle measurements.

4. Conclusions

Measuring the reflectance spectra using a calibration panel on the surface of the Moon is crucial for obtaining the actual absolute reflectance. Such measurements were hampered due to the great difficulty in accessing the lunar surface until the end of 2013 when the first in situ spectra of the Moon were acquired by the CE-3 rover. The absolute reflectance of the CE-3 landing site is very low, consistent with a landing site rich in FeO and TiO₂. We compared the CE-3 in situ reflectance with several modern optical instruments orbiting the Moon. Although the comparison is only for the CE-3 landing site, it is consistent with other areas based on the stability of these instruments. The instrument data were derived from large amounts of comparison data in the literature (Ohtake et al. 2010; Besse et al. 2013b; Wu et al. 2016). The measurements of the LROC WAC and SP are higher and redder. The measurements of M³ OP2C and IIM are lower and bluer than those of LROC WAC and SP. The measurements of the VNIS fall between these two pairs. The laboratory reflectance of returned samples is much higher than the pristine regolith and is inappropriate for the calibration of orbital instruments. The VNIS reveals that in addition to roughness and compactness, lithic fragments and maturity also account for the laboratory reflectance of lunar samples that are much too high. There are some remaining issues for the measurements of in situ reflectance, e.g., the solar and view angles are limited, but CE-3 accomplished the first measurement with a calibration panel of reflectance on the surface of the Moon and extend the range of photometric geometry with large emission and phase angles, for a large range of wavelengths. Compared to other calibration sites previously suggested, the CE-3 site is much younger and less impacted and contaminated, and it has accurate in situ spectra measured on the lunar surface with a calibration panel and chemical compositions acquired by the APXS. Thus, we propose the CE-3 landing site and the in situ spectra as an optical standard for both radiance calibration and wavelength calibration for the lunar and Earth-orbital missions. Together with the elemental abundance measured by the CE-3 APXS, this site can also serve as a compositional calibration site for elemental mapping. For the convenience of application, the new site can be extensive to the area with the same spectra, which is easy to find because the last major phases of mare basalts have a homogeneous composition and cover large areas of western maria.

We thank the entire Chang'E-3 team for making the mission a success and providing the data, and Dongya Guo, Wenxi Peng, and Xingzhu Cui from the Institute of High Energy Physics, Chinese Academy of Sciences for providing the elemental abundances derived from APXS on board CE-3. This research was supported by the Macau Science and Technology Development Fund (103/2017/A, 119/2017/A3, 075/2014/A2), the Open Fund of Key Laboratory of Radiometric Calibration and Validation for Environmental Satellites, National Satellite Meteorological Center, China Meteorological Administration, Minor Planet Foundation of Purple Mountain Observatory and the National Natural Science Foundation of China (11773087, 41422110).

Appendix A: Definition of Reflectance Used in this Paper

1. Reflectance Factor (REFF): The ratio of the radiance reflected from the surface into a given direction to that of a standard panel and corrected with the REFF of the standard panel at the measurement geometry. The equation is:

$\begin{eqnarray*}\mathrm{REFF}(\lambda ,{\theta }_{i},{\varphi }_{i},{\theta }_{r},{\varphi }_{r}) & = & \displaystyle \frac{{I}_{\mathrm{sample}}(\lambda ,{\theta }_{i},{\varphi }_{i},{\theta }_{r},{\varphi }_{r})}{{I}_{\mathrm{std}}(\lambda ,{\theta }_{i},{\varphi }_{i},{\theta }_{r},{\varphi }_{r})}\\ & & \times {R}_{\mathrm{std}}(\lambda ,{\theta }_{i},{\varphi }_{i},{\theta }_{r},{\varphi }_{r})\end{eqnarray*}$

where λ, θ_i, _i, θ_r, and _r are the wavelength, Sun zenith angle, Sun azimuth angle, view zenith angle, and view azimuth angle, respectively. I_sample is the radiance of the target measured by the instrument, I_std is the radiance of the diffuser panel measured by the instrument, and R_std is the REFF of the diffuser panel.

2. Bidirectional Reflectance Factor (BRF): The ratio of the radiance reflected from the surface into a given direction to that of a perfectly diffuse surface under the same conditions of illumination. The equation is:

$\begin{eqnarray*}&&\mathrm{BRF}(\lambda ,{\theta }_{i},{\varphi }_{i},{\theta }_{r},{\varphi }_{r})=\displaystyle \frac{\pi \cdot I(\lambda ,{\theta }_{i},{\varphi }_{i},{\theta }_{r},{\varphi }_{r})\cdot {D}^{2}}{{E}_{0}(\lambda )\cdot \cos i}\end{eqnarray*}$

where λ, θ_i, _i, θ_r, and _r are the wavelength, Sun zenith angle, Sun azimuth angle, view zenith angle, and view azimuth angle, respectively. I is the radiance measured by the instrument and E₀ is the solar irradiance at 1 au. In this study, E₀ is taken from the New Synthetic Gueymard Spectra (Gueymard 2004) because it is used by the CE-3 team for the on-board calibration of VNIS. D is the Sun–Moon distance in kilometers at the observation time divided by the standard Sun–Moon distance (149, 597, 870 km).

3. Radiance Factor (RADF or IOF, I/F) (Hapke 2012): The ratio of the bidirectional reflectance of a surface to that of a perfectly diffuse surface illuminated at an incidence angle of zero. The equation is:

$\begin{eqnarray*}&&\mathrm{RADF}(\lambda ,{\theta }_{i},{\varphi }_{i},{\theta }_{r},{\varphi }_{r})=\displaystyle \frac{\pi \cdot I(\lambda ,{\theta }_{i},{\varphi }_{i},{\theta }_{r},{\varphi }_{r})\cdot {D}^{2}}{{E}_{0}(\lambda )}\end{eqnarray*}$

where the definitions are the same as for the BRF.

Appendix B: The in situ Radiance and REFF for the VNIS Measurements

Appendix B comprises Table 2.

Table 2. In Situ Radiance and REFF for the VNIS Measurements

Wavelength (nm)	Radiance (W m⁻² Sr⁻¹ μm⁻¹)				Reflectance
	5	6	7	8	5	6	7	8
450	15.524	10.983	8.416	11.985	0.044	0.041	0.035	0.029
455	15.937	10.856	8.158	11.512	0.046	0.041	0.034	0.029
460	16.533	11.120	8.494	12.494	0.048	0.042	0.035	0.031
465	16.910	11.020	8.011	12.322	0.049	0.042	0.034	0.031
470	17.640	10.533	8.442	12.297	0.053	0.041	0.036	0.031
475	17.947	11.534	8.823	12.989	0.052	0.044	0.037	0.032
480	18.381	11.517	8.426	11.991	0.053	0.043	0.035	0.030
485	16.487	11.264	8.704	11.608	0.052	0.046	0.040	0.031
490	16.806	11.368	8.568	12.282	0.051	0.045	0.037	0.032
495	16.862	11.288	8.576	12.512	0.051	0.045	0.037	0.032
500	16.808	11.681	8.486	12.495	0.053	0.048	0.038	0.034
505	17.059	11.901	8.659	13.350	0.053	0.048	0.039	0.035
510	16.779	11.434	8.864	12.193	0.053	0.047	0.040	0.033
515	15.798	10.749	8.273	11.480	0.053	0.047	0.040	0.033
520	16.754	10.796	8.459	11.946	0.056	0.047	0.041	0.034
525	17.311	11.694	9.501	12.586	0.056	0.049	0.044	0.035
530	17.553	11.671	9.213	12.769	0.055	0.048	0.042	0.035
535	17.648	12.278	9.374	13.053	0.056	0.051	0.043	0.036
540	17.256	12.454	9.698	12.626	0.056	0.053	0.046	0.035
545	17.927	12.534	9.711	12.856	0.057	0.053	0.045	0.035
550	17.934	12.474	9.537	12.981	0.058	0.052	0.044	0.036
555	18.418	12.520	9.372	13.283	0.060	0.053	0.044	0.037
560	17.768	12.804	9.343	12.976	0.059	0.056	0.045	0.037
565	18.603	12.920	10.159	13.364	0.062	0.056	0.049	0.038
570	18.099	12.969	9.828	13.160	0.061	0.057	0.048	0.038
575	18.824	12.642	9.847	13.371	0.062	0.055	0.047	0.038
580	18.517	12.609	9.777	13.088	0.062	0.055	0.047	0.037
585	18.401	13.202	10.092	13.488	0.062	0.058	0.049	0.039
590	18.238	12.839	9.781	12.716	0.063	0.058	0.049	0.038
595	18.529	12.724	9.711	13.061	0.064	0.057	0.048	0.038
600	18.513	12.845	9.767	13.298	0.065	0.059	0.049	0.040
605	18.722	13.071	10.209	13.268	0.066	0.060	0.052	0.040
610	18.027	12.799	10.151	13.162	0.064	0.059	0.052	0.040
615	17.790	12.644	9.865	13.099	0.065	0.060	0.052	0.041
620	17.718	12.597	9.431	12.760	0.065	0.060	0.050	0.040
625	17.540	12.087	9.402	12.774	0.065	0.058	0.050	0.040
630	18.266	12.838	9.866	12.947	0.068	0.062	0.053	0.041
635	17.304	12.247	9.828	12.312	0.065	0.060	0.053	0.040
640	16.805	11.981	9.479	12.732	0.064	0.060	0.052	0.041
645	16.545	11.946	9.072	12.547	0.063	0.060	0.050	0.041
650	16.107	11.532	8.789	11.959	0.063	0.059	0.050	0.040
655	15.625	10.873	8.370	11.867	0.065	0.059	0.050	0.042
660	16.380	10.751	8.376	12.212	0.066	0.056	0.048	0.042
665	16.385	11.307	8.975	12.578	0.066	0.060	0.052	0.043
670	16.031	11.501	9.008	12.328	0.065	0.061	0.052	0.043
675	16.260	11.573	9.188	12.055	0.066	0.061	0.054	0.042
680	16.491	11.048	8.810	11.946	0.068	0.060	0.053	0.042
685	16.029	11.108	8.898	12.023	0.067	0.060	0.054	0.043
690	16.454	11.065	8.743	11.713	0.069	0.061	0.053	0.042
695	16.150	11.282	8.877	11.713	0.069	0.063	0.055	0.043
700	15.952	11.104	8.868	11.921	0.068	0.062	0.055	0.044
705	15.752	11.271	8.949	11.807	0.068	0.063	0.055	0.043
710	15.836	11.038	8.869	11.448	0.069	0.063	0.056	0.043
715	15.724	10.796	8.674	11.623	0.070	0.063	0.056	0.044
720	15.550	11.002	8.510	11.252	0.070	0.065	0.055	0.043
725	15.428	11.106	8.526	11.519	0.070	0.066	0.056	0.045
730	14.937	10.981	8.613	11.434	0.069	0.066	0.057	0.045
735	14.572	11.289	8.719	11.628	0.067	0.068	0.058	0.046
740	14.319	11.000	8.539	11.128	0.068	0.068	0.059	0.045
745	14.269	10.827	8.368	11.081	0.067	0.067	0.057	0.045
750	14.295	10.596	8.199	11.075	0.068	0.066	0.057	0.045
755	14.101	10.539	7.849	10.659	0.068	0.066	0.054	0.044
760	14.337	10.581	7.864	10.619	0.070	0.067	0.055	0.044
765	14.121	10.412	7.882	10.600	0.070	0.068	0.057	0.045
770	13.921	10.228	7.982	10.609	0.070	0.067	0.058	0.046
775	13.466	10.327	7.750	10.506	0.069	0.069	0.057	0.046
780	13.193	9.993	7.907	10.481	0.068	0.067	0.059	0.046
785	12.966	10.123	7.684	10.352	0.068	0.069	0.058	0.046
790	13.264	9.888	7.818	10.146	0.070	0.068	0.059	0.046
795	12.865	9.784	7.261	9.996	0.069	0.069	0.056	0.046
800	12.922	9.770	7.346	9.992	0.069	0.069	0.057	0.046
805	12.788	9.454	7.071	9.897	0.070	0.067	0.056	0.046
810	12.837	9.490	7.095	9.648	0.070	0.068	0.056	0.045
815	12.581	9.681	7.302	10.132	0.069	0.070	0.058	0.048
820	12.150	9.399	6.998	9.608	0.069	0.070	0.057	0.047
825	12.265	9.299	7.065	9.506	0.069	0.069	0.058	0.046
830	12.030	8.988	6.897	9.446	0.069	0.067	0.057	0.046
835	11.889	9.035	6.888	9.278	0.069	0.069	0.058	0.046
840	11.882	8.884	6.722	9.173	0.070	0.068	0.057	0.046
845	11.694	8.653	6.324	9.045	0.070	0.068	0.055	0.046
850	11.075	8.570	6.367	8.746	0.069	0.070	0.058	0.047
855	10.287	8.038	6.206	8.512	0.067	0.068	0.058	0.047
860	11.064	8.568	6.585	8.832	0.068	0.069	0.059	0.046
865	10.284	8.412	6.432	8.457	0.065	0.070	0.059	0.046
870	10.273	8.449	6.266	8.504	0.065	0.070	0.057	0.046
875	10.106	8.152	6.300	8.449	0.064	0.068	0.058	0.046
880	9.956	8.155	6.295	8.126	0.064	0.069	0.059	0.045
885	9.765	7.810	6.130	8.196	0.064	0.066	0.058	0.046
890	9.657	7.876	5.964	8.055	0.063	0.067	0.056	0.045
895	9.624	7.463	5.737	7.907	0.064	0.065	0.055	0.045
900	9.152	7.460	5.756	7.956	0.063	0.066	0.057	0.046
905	9.305	7.520	5.703	7.939	0.063	0.067	0.057	0.046
910	8.799	7.315	5.594	7.804	0.062	0.066	0.057	0.046
915	9.111	7.214	5.491	7.781	0.063	0.065	0.056	0.046
920	8.501	7.119	5.483	7.741	0.061	0.066	0.057	0.047
925	8.416	7.086	5.254	7.558	0.060	0.067	0.056	0.047
930	8.468	7.032	5.369	7.644	0.061	0.066	0.056	0.047
935	8.083	6.889	5.146	7.495	0.061	0.065	0.055	0.046
940	8.221	6.827	5.189	7.439	0.061	0.066	0.056	0.047
945	8.223	6.670	5.110	7.158	0.061	0.065	0.055	0.046
950	8.132	6.582	5.034	7.294	0.061	0.064	0.054	0.047
955	7.825	6.196	5.001	6.954	0.061	0.063	0.056	0.046
960	7.839	6.440	4.937	7.083	0.060	0.064	0.055	0.046
965	7.774	6.293	4.861	6.823	0.061	0.064	0.055	0.046
970	7.710	6.234	4.789	6.735	0.060	0.064	0.054	0.045
975	7.700	6.236	4.782	6.490	0.061	0.065	0.055	0.044
980	7.485	6.220	4.676	6.670	0.060	0.065	0.054	0.046
985	7.634	6.251	4.781	6.607	0.062	0.066	0.056	0.046
990	7.388	6.180	4.691	6.587	0.061	0.066	0.056	0.046
995	7.466	6.181	4.735	6.635	0.061	0.066	0.056	0.047
1000	7.406	6.032	4.682	6.354	0.061	0.065	0.056	0.045
1005	7.171	5.900	4.533	6.211	0.062	0.066	0.056	0.046
1010	7.377	5.954	4.660	6.260	0.062	0.066	0.057	0.045
1015	7.252	5.820	4.623	6.398	0.062	0.065	0.058	0.047
1020	7.038	5.915	4.464	6.201	0.061	0.068	0.056	0.046
1025	7.159	5.657	4.439	6.276	0.062	0.065	0.056	0.047
1030	6.932	5.736	4.329	6.282	0.061	0.066	0.055	0.048
1035	6.955	5.722	4.438	6.104	0.063	0.067	0.058	0.047
1040	6.901	5.688	4.370	6.168	0.063	0.067	0.057	0.048
1045	6.853	5.699	4.338	6.072	0.063	0.068	0.058	0.048
1050	6.959	5.492	4.237	6.025	0.064	0.066	0.057	0.048
1055	6.732	5.510	4.094	5.995	0.063	0.067	0.055	0.048
1060	6.663	5.483	4.218	5.868	0.063	0.068	0.058	0.048
1065	6.879	5.479	4.256	5.974	0.066	0.068	0.059	0.049
1070	6.666	5.298	4.123	5.854	0.065	0.068	0.058	0.049
1075	6.720	5.394	3.994	5.794	0.066	0.069	0.056	0.048
1080	6.677	5.497	4.138	5.793	0.066	0.071	0.059	0.049
1085	6.575	5.169	4.085	5.742	0.066	0.068	0.059	0.049
1090	6.586	5.299	3.896	5.759	0.067	0.070	0.057	0.050
1095	6.397	5.240	3.972	5.533	0.067	0.072	0.060	0.050
1100	6.586	5.106	3.886	5.668	0.068	0.069	0.058	0.050
1105	6.458	5.216	3.862	5.712	0.067	0.071	0.058	0.051
1110	6.554	5.351	4.025	5.630	0.069	0.073	0.061	0.051
1115	6.464	5.236	4.088	5.659	0.068	0.072	0.063	0.051
1120	6.403	5.109	4.038	5.619	0.069	0.072	0.063	0.052
1125	6.386	5.198	3.930	5.452	0.070	0.074	0.062	0.051
1130	6.350	5.105	3.916	5.669	0.070	0.073	0.062	0.053
1135	6.537	5.202	3.907	5.572	0.073	0.075	0.063	0.053
1140	6.288	5.141	3.860	5.493	0.071	0.076	0.063	0.053
1145	6.443	5.246	4.030	5.671	0.073	0.077	0.066	0.055
1150	6.208	5.215	3.962	5.464	0.070	0.077	0.065	0.053
1155	6.369	5.207	3.933	5.480	0.073	0.078	0.065	0.054
1160	6.234	4.988	3.848	5.464	0.073	0.076	0.065	0.055
1165	6.277	5.107	3.888	5.532	0.074	0.079	0.066	0.056
1170	6.365	5.196	3.866	5.608	0.075	0.080	0.066	0.057
1175	6.130	5.177	3.933	5.504	0.073	0.081	0.068	0.056
1180	6.321	5.132	3.841	5.382	0.076	0.081	0.067	0.056
1185	6.262	5.135	3.842	5.409	0.076	0.082	0.068	0.056
1190	6.164	5.032	3.735	5.175	0.076	0.081	0.066	0.054
1195	6.234	5.012	3.762	5.261	0.077	0.081	0.067	0.056
1200	5.919	5.033	3.818	5.356	0.075	0.083	0.070	0.058
1205	6.066	4.888	3.753	5.222	0.077	0.081	0.069	0.057
1210	6.006	4.833	3.770	5.228	0.077	0.081	0.070	0.057
1215	6.044	4.912	3.731	5.220	0.077	0.082	0.069	0.057
1220	6.128	4.957	3.725	5.038	0.079	0.083	0.069	0.055
1225	5.965	4.849	3.671	5.217	0.078	0.083	0.069	0.058
1230	5.994	4.924	3.525	5.186	0.079	0.085	0.067	0.058
1235	5.964	4.838	3.677	5.191	0.079	0.084	0.071	0.059
1240	5.868	4.881	3.676	5.142	0.079	0.086	0.071	0.059
1245	5.852	4.813	3.651	5.177	0.079	0.085	0.071	0.060
1250	5.853	4.847	3.605	5.139	0.080	0.086	0.071	0.060
1255	5.745	4.804	3.630	5.123	0.079	0.086	0.072	0.060
1260	5.820	4.769	3.640	5.092	0.081	0.086	0.073	0.060
1265	5.817	4.761	3.589	5.103	0.081	0.087	0.072	0.061
1270	5.822	4.696	3.562	5.010	0.082	0.086	0.072	0.060
1275	5.742	4.801	3.662	5.205	0.081	0.089	0.075	0.063
1280	5.576	4.612	3.472	4.901	0.082	0.088	0.074	0.061
1285	5.599	4.539	3.435	4.881	0.082	0.087	0.073	0.062
1290	5.683	4.588	3.427	4.948	0.083	0.087	0.072	0.062
1295	5.690	4.634	3.521	4.995	0.083	0.089	0.074	0.062
1300	5.675	4.623	3.497	4.762	0.084	0.089	0.075	0.060
1305	5.653	4.579	3.457	4.831	0.084	0.089	0.074	0.062
1310	5.628	4.509	3.441	4.843	0.085	0.089	0.075	0.063
1315	5.513	4.535	3.396	4.875	0.084	0.091	0.075	0.064
1320	5.564	4.477	3.385	4.822	0.085	0.090	0.075	0.063
1325	5.587	4.475	3.439	4.897	0.086	0.090	0.077	0.065
1330	5.462	4.479	3.396	4.810	0.085	0.091	0.077	0.064
1335	5.374	4.475	3.364	4.851	0.084	0.092	0.076	0.065
1340	5.411	4.479	3.369	4.850	0.086	0.093	0.077	0.066
1345	5.477	4.460	3.376	4.804	0.087	0.093	0.078	0.066
1350	5.475	4.446	3.351	4.820	0.088	0.093	0.078	0.066
1355	5.379	4.223	3.287	4.666	0.087	0.090	0.077	0.065
1360	5.331	4.343	3.292	4.686	0.087	0.093	0.078	0.066
1365	5.302	4.314	3.253	4.546	0.088	0.093	0.078	0.064
1370	5.299	4.306	3.252	4.623	0.088	0.094	0.078	0.066
1375	5.301	4.328	3.264	4.667	0.089	0.095	0.079	0.067
1380	5.234	4.191	3.176	4.444	0.088	0.093	0.078	0.064
1385	5.215	4.238	3.155	4.486	0.089	0.094	0.078	0.065
1390	5.196	4.137	3.144	4.444	0.089	0.093	0.078	0.065
1395	5.121	4.148	3.114	4.448	0.089	0.094	0.078	0.066
1400	5.136	4.210	3.098	4.420	0.090	0.096	0.078	0.066
1405	5.115	4.093	3.046	4.378	0.090	0.094	0.078	0.066
1410	5.044	4.176	3.031	4.398	0.090	0.097	0.078	0.067
1415	5.045	4.080	3.031	4.336	0.090	0.095	0.078	0.066
1420	5.083	4.037	3.018	4.379	0.092	0.096	0.079	0.068
1425	5.033	3.959	3.000	4.203	0.093	0.095	0.080	0.066
1430	4.950	3.985	2.992	4.242	0.091	0.096	0.080	0.067
1435	5.048	4.023	2.985	4.313	0.093	0.097	0.079	0.068
1440	4.948	3.945	2.876	4.241	0.093	0.097	0.078	0.068
1445	4.943	3.923	2.872	4.203	0.093	0.097	0.078	0.068
1450	4.917	3.907	2.898	4.246	0.093	0.097	0.080	0.069
1455	4.892	3.893	2.945	4.180	0.094	0.098	0.082	0.069
1460	4.893	3.892	2.907	4.191	0.094	0.098	0.081	0.069
1465	4.877	3.877	2.938	4.125	0.095	0.098	0.083	0.069
1470	4.806	3.894	2.872	4.170	0.094	0.100	0.082	0.070
1475	4.737	3.797	2.827	4.099	0.095	0.099	0.082	0.070
1480	4.750	3.783	2.832	4.161	0.095	0.099	0.082	0.071
1485	4.716	3.689	2.785	3.987	0.095	0.098	0.081	0.069
1490	4.718	3.733	2.784	4.082	0.096	0.099	0.082	0.071
1495	4.715	3.737	2.790	4.074	0.096	0.099	0.082	0.071
1500	4.682	3.734	2.759	4.066	0.097	0.101	0.083	0.072
1505	4.460	3.601	2.720	3.889	0.096	0.101	0.085	0.072
1510	4.654	3.718	2.712	4.042	0.098	0.102	0.082	0.073
1515	4.653	3.622	2.713	3.952	0.098	0.100	0.083	0.072
1520	4.611	3.673	2.707	3.945	0.098	0.103	0.084	0.072
1525	4.565	3.565	2.683	3.938	0.098	0.100	0.083	0.072
1530	4.453	3.593	2.680	3.919	0.097	0.102	0.084	0.073
1535	4.503	3.559	2.611	3.863	0.099	0.102	0.083	0.073
1540	4.470	3.571	2.629	3.856	0.099	0.104	0.085	0.073
1545	4.488	3.553	2.611	3.820	0.100	0.103	0.084	0.073
1550	4.449	3.505	2.610	3.800	0.101	0.104	0.085	0.074
1555	4.360	3.499	2.586	3.778	0.100	0.105	0.085	0.074
1560	4.338	3.505	2.551	3.779	0.099	0.105	0.084	0.074
1565	4.328	3.461	2.541	3.762	0.100	0.104	0.085	0.074
1570	4.291	3.440	2.537	3.736	0.100	0.105	0.085	0.075
1575	4.190	3.375	2.489	3.642	0.101	0.106	0.086	0.075
1580	4.229	3.358	2.426	3.662	0.101	0.105	0.084	0.075
1585	4.180	3.357	2.464	3.632	0.101	0.106	0.086	0.075
1590	4.013	3.272	2.435	3.523	0.100	0.107	0.088	0.075
1595	4.244	3.358	2.468	3.652	0.103	0.107	0.087	0.076
1600	4.216	3.316	2.467	3.613	0.103	0.106	0.087	0.076
1605	4.170	3.316	2.447	3.604	0.104	0.108	0.088	0.077
1610	4.067	3.267	2.400	3.512	0.103	0.108	0.088	0.076
1615	4.018	3.236	2.430	3.518	0.103	0.108	0.090	0.077
1620	4.036	3.187	2.397	3.456	0.104	0.107	0.089	0.076
1625	4.101	3.248	2.412	3.547	0.105	0.108	0.089	0.077
1630	4.006	3.254	2.446	3.571	0.103	0.109	0.091	0.079
1635	3.957	3.166	2.358	3.416	0.105	0.109	0.090	0.077
1640	3.807	3.035	2.264	3.317	0.104	0.108	0.090	0.078
1645	3.857	3.051	2.288	3.338	0.105	0.108	0.090	0.078
1650	3.907	3.074	2.276	3.402	0.106	0.109	0.089	0.079
1655	3.909	3.055	2.316	3.366	0.106	0.108	0.091	0.078
1660	3.879	3.114	2.290	3.398	0.105	0.111	0.090	0.079
1665	3.845	3.068	2.275	3.284	0.106	0.111	0.091	0.078
1670	3.717	3.025	2.252	3.321	0.105	0.111	0.092	0.080
1675	3.703	2.956	2.215	3.252	0.106	0.111	0.092	0.080
1680	3.596	2.819	2.138	3.155	0.107	0.109	0.092	0.080
1685	3.660	2.893	2.170	3.173	0.107	0.111	0.092	0.080
1690	3.690	2.951	2.186	3.231	0.107	0.112	0.092	0.080
1695	3.656	2.927	2.180	3.134	0.107	0.111	0.092	0.078
1700	3.601	2.901	2.165	3.168	0.107	0.112	0.093	0.080
1705	3.580	2.884	2.141	3.166	0.107	0.113	0.093	0.081
1710	3.546	2.821	2.068	3.104	0.108	0.112	0.091	0.081
1715	3.524	2.819	2.075	3.087	0.108	0.113	0.092	0.081
1720	3.468	2.757	2.082	3.019	0.108	0.112	0.093	0.080
1725	3.429	2.685	2.035	3.020	0.108	0.110	0.092	0.081
1730	3.346	2.678	2.020	2.975	0.107	0.112	0.093	0.081
1735	3.192	2.622	1.944	2.882	0.106	0.114	0.093	0.082
1740	3.211	2.638	1.955	2.919	0.106	0.114	0.093	0.082
1745	3.271	2.653	1.960	2.933	0.107	0.114	0.093	0.082
1750	3.289	2.644	1.968	2.905	0.108	0.114	0.094	0.082
1755	3.264	2.643	1.961	2.909	0.108	0.114	0.094	0.082
1760	3.202	2.624	1.947	2.888	0.107	0.115	0.094	0.083
1765	3.174	2.580	1.911	2.847	0.107	0.114	0.093	0.082
1770	3.188	2.510	1.890	2.828	0.109	0.112	0.093	0.083
1775	3.148	2.495	1.853	2.712	0.109	0.113	0.093	0.080
1780	3.140	2.520	1.855	2.715	0.110	0.115	0.094	0.081
1785	3.105	2.494	1.814	2.735	0.109	0.115	0.092	0.082
1790	3.140	2.507	1.827	2.755	0.111	0.116	0.093	0.083
1795	3.053	2.436	1.809	2.709	0.109	0.114	0.093	0.083
1800	3.007	2.372	1.789	2.684	0.109	0.112	0.093	0.083
1805	3.034	2.405	1.784	2.591	0.111	0.115	0.094	0.081
1810	2.999	2.383	1.680	2.623	0.111	0.115	0.090	0.083
1815	2.850	2.305	1.690	2.545	0.109	0.115	0.093	0.083
1820	2.834	2.209	1.662	2.506	0.110	0.112	0.093	0.083
1825	2.875	2.297	1.641	2.547	0.110	0.115	0.091	0.083
1830	2.876	2.301	1.688	2.557	0.110	0.115	0.093	0.084
1835	2.829	2.251	1.675	2.467	0.109	0.113	0.093	0.081
1840	2.820	2.250	1.596	2.476	0.110	0.115	0.090	0.083
1845	2.707	2.255	1.640	2.479	0.107	0.117	0.094	0.084
1850	2.782	2.233	1.627	2.461	0.110	0.116	0.093	0.084
1855	2.771	2.221	1.624	2.466	0.111	0.116	0.094	0.084
1860	2.738	2.200	1.615	2.346	0.111	0.116	0.095	0.081
1865	2.725	2.173	1.582	2.386	0.112	0.117	0.094	0.084
1870	2.636	2.116	1.568	2.284	0.111	0.117	0.096	0.082
1875	2.543	2.037	1.489	2.233	0.112	0.117	0.095	0.084
1880	2.608	2.049	1.500	2.251	0.112	0.115	0.093	0.083
1885	2.599	2.085	1.517	2.304	0.111	0.116	0.094	0.084
1890	2.558	2.040	1.460	2.279	0.110	0.115	0.091	0.084
1895	2.498	1.984	1.482	2.263	0.110	0.114	0.094	0.085
1900	2.522	2.016	1.465	2.244	0.111	0.116	0.093	0.084
1905	2.515	2.022	1.474	2.196	0.111	0.116	0.094	0.083
1910	2.461	2.021	1.469	2.239	0.109	0.117	0.094	0.085
1915	2.467	1.988	1.427	2.199	0.111	0.116	0.092	0.084
1920	2.468	1.969	1.458	2.145	0.112	0.116	0.095	0.083
1925	2.385	1.989	1.442	2.197	0.109	0.119	0.095	0.086
1930	2.408	1.918	1.409	2.133	0.112	0.116	0.095	0.085
1935	2.376	1.903	1.369	2.087	0.111	0.117	0.093	0.084
1940	2.309	1.841	1.364	2.061	0.111	0.116	0.095	0.085
1945	2.233	1.764	1.322	1.999	0.111	0.114	0.095	0.085
1950	2.304	1.836	1.332	2.056	0.113	0.117	0.094	0.086
1955	2.322	1.851	1.321	2.057	0.112	0.117	0.092	0.085
1960	2.322	1.848	1.360	2.033	0.113	0.117	0.096	0.085
1965	2.259	1.795	1.322	2.037	0.111	0.116	0.094	0.086
1970	2.220	1.764	1.320	2.031	0.110	0.115	0.095	0.086
1975	2.244	1.795	1.296	1.992	0.113	0.118	0.094	0.086
1980	2.226	1.789	1.287	1.977	0.113	0.119	0.095	0.086
1985	2.187	1.764	1.270	1.953	0.112	0.118	0.094	0.086
1990	2.186	1.750	1.251	1.934	0.113	0.118	0.093	0.085
1995	2.157	1.728	1.222	1.922	0.112	0.118	0.092	0.086
2000	2.156	1.729	1.223	1.912	0.113	0.119	0.093	0.086
2005	2.140	1.731	1.225	1.886	0.113	0.120	0.094	0.085
2010	2.124	1.717	1.232	1.868	0.113	0.119	0.095	0.085
2015	2.117	1.699	1.219	1.864	0.114	0.119	0.095	0.086
2020	2.087	1.677	1.211	1.855	0.114	0.119	0.095	0.086
2025	2.060	1.667	1.196	1.840	0.113	0.120	0.095	0.087
2030	2.025	1.648	1.181	1.828	0.113	0.120	0.095	0.087
2035	2.017	1.632	1.179	1.807	0.113	0.120	0.096	0.087
2040	2.017	1.627	1.172	1.805	0.114	0.120	0.096	0.087
2045	2.010	1.620	1.175	1.791	0.114	0.120	0.096	0.087
2050	2.002	1.633	1.176	1.786	0.114	0.122	0.097	0.087
2055	1.974	1.608	1.160	1.782	0.114	0.121	0.097	0.088
2060	1.903	1.555	1.156	1.760	0.111	0.119	0.098	0.088
2065	1.941	1.573	1.139	1.736	0.115	0.121	0.097	0.088
2070	1.930	1.558	1.124	1.680	0.115	0.121	0.096	0.085
2075	1.907	1.546	1.111	1.693	0.114	0.121	0.096	0.087
2080	1.906	1.529	1.106	1.694	0.115	0.121	0.096	0.087
2085	1.870	1.512	1.093	1.696	0.114	0.120	0.096	0.089
2090	1.854	1.488	1.094	1.677	0.114	0.120	0.097	0.088
2095	1.850	1.479	1.048	1.625	0.115	0.120	0.094	0.087
2100	1.845	1.487	1.071	1.644	0.115	0.121	0.097	0.088
2105	1.851	1.472	1.069	1.659	0.116	0.121	0.097	0.089
2110	1.809	1.459	1.062	1.629	0.115	0.121	0.097	0.088
2115	1.798	1.452	1.023	1.614	0.115	0.122	0.095	0.089
2120	1.790	1.441	1.038	1.607	0.116	0.122	0.097	0.089
2125	1.753	1.407	1.039	1.609	0.114	0.120	0.098	0.090
2130	1.762	1.428	1.007	1.577	0.116	0.123	0.096	0.089
2135	1.756	1.415	1.022	1.587	0.116	0.122	0.098	0.090
2140	1.723	1.401	1.023	1.590	0.115	0.122	0.098	0.091
2145	1.739	1.396	0.995	1.570	0.117	0.122	0.096	0.090
2150	1.743	1.402	1.015	1.571	0.118	0.124	0.099	0.091
2155	1.729	1.384	0.994	1.561	0.118	0.124	0.098	0.091
2160	1.679	1.343	0.970	1.500	0.117	0.123	0.098	0.090
2165	1.604	1.287	0.961	1.485	0.115	0.121	0.100	0.091
2170	1.642	1.309	0.930	1.468	0.118	0.123	0.096	0.090
2175	1.655	1.328	0.952	1.497	0.118	0.124	0.098	0.091
2180	1.639	1.321	0.918	1.449	0.117	0.123	0.095	0.089
2185	1.621	1.307	0.933	1.475	0.117	0.123	0.097	0.091
2190	1.616	1.299	0.919	1.425	0.117	0.123	0.096	0.089
2195	1.616	1.289	0.928	1.459	0.118	0.123	0.098	0.091
2200	1.594	1.268	0.914	1.400	0.118	0.122	0.098	0.089
2205	1.581	1.270	0.913	1.443	0.118	0.124	0.099	0.093
2210	1.565	1.246	0.883	1.383	0.118	0.123	0.096	0.089
2215	1.562	1.242	0.901	1.414	0.119	0.123	0.099	0.092
2220	1.548	1.235	0.865	1.394	0.118	0.123	0.096	0.091
2225	1.533	1.184	0.889	1.398	0.118	0.119	0.099	0.092
2230	1.526	1.222	0.872	1.389	0.119	0.124	0.098	0.092
2235	1.498	1.227	0.888	1.398	0.117	0.126	0.101	0.094
2240	1.518	1.198	0.865	1.372	0.120	0.124	0.099	0.093
2245	1.494	1.187	0.842	1.342	0.119	0.124	0.097	0.092
2250	1.507	1.186	0.847	1.370	0.122	0.125	0.099	0.095
2255	1.475	1.174	0.848	1.341	0.120	0.125	0.100	0.093
2260	1.450	1.184	0.847	1.356	0.119	0.127	0.100	0.095
2265	1.466	1.153	0.827	1.328	0.121	0.125	0.099	0.094
2270	1.446	1.146	0.814	1.298	0.120	0.124	0.098	0.092
2275	1.405	1.148	0.829	1.331	0.118	0.126	0.100	0.096
2280	1.426	1.142	0.806	1.293	0.121	0.127	0.099	0.094
2285	1.420	1.125	0.790	1.285	0.121	0.126	0.098	0.094
2290	1.396	1.112	0.795	1.288	0.121	0.126	0.099	0.095
2295	1.401	1.091	0.782	1.287	0.122	0.125	0.099	0.096
2300	1.407	1.091	0.779	1.259	0.124	0.125	0.099	0.095
2305	1.393	1.101	0.787	1.284	0.123	0.127	0.100	0.097
2310	1.405	1.078	0.776	1.276	0.125	0.125	0.100	0.097
2315	1.372	1.070	0.760	1.243	0.123	0.126	0.099	0.096
2320	1.352	1.059	0.720	1.183	0.123	0.126	0.095	0.092
2325	1.304	1.054	0.736	1.250	0.120	0.127	0.098	0.099
2330	1.341	1.037	0.730	1.228	0.125	0.126	0.098	0.098
2335	1.343	1.041	0.732	1.219	0.125	0.127	0.099	0.097
2340	1.332	1.037	0.715	1.176	0.125	0.127	0.097	0.094
2345	1.294	1.054	0.750	1.217	0.122	0.130	0.102	0.098
2350	1.311	1.021	0.738	1.203	0.126	0.128	0.102	0.099
2355	1.301	1.006	0.728	1.203	0.126	0.127	0.102	0.100
2360	1.284	1.006	0.720	1.174	0.125	0.128	0.101	0.098
2365	1.296	1.007	0.706	1.181	0.127	0.129	0.100	0.099
2370	1.256	1.015	0.714	1.197	0.124	0.131	0.102	0.101
2375	1.300	0.980	0.709	1.188	0.130	0.128	0.102	0.101
2380	1.266	0.969	0.692	1.154	0.128	0.128	0.101	0.100
2385	1.240	0.963	0.684	1.144	0.127	0.129	0.101	0.100
2390	1.242	0.963	0.658	1.102	0.128	0.130	0.098	0.097
2395	1.245	0.944	0.662	1.131	0.129	0.128	0.099	0.100

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