Although of great interest for science and resource utilization, the Moon's permanently shadowed regions (PSRs) near each pole present difficult targets for remote sensing. The Lyman Alpha Mapping Project (LAMP) instrument on the Lunar Reconnaissance Orbiter (LRO) mission is able to map PSRs at far-ultraviolet (FUV) wavelengths using two faint sources of illumination from the night sky: the all-sky Ly α glow produced as interplanetary medium (IPM) H atoms scatter the Sun's Ly α emissions, and the much fainter source from UV-bright stars. The reflected light from these two sources produces only a few hundred events per second in the photon-counting LAMP instrument, so building maps with useful signal-to-noise (SNR) ratios requires the careful accumulation of the observations from thousands of individual LRO orbits. In this paper we present the first FUV albedo maps obtained by LAMP of the Moon's southern and northern polar regions. The results show that (1) most PSR regions are darker at all FUV wavelengths, consistent with their surface soils having much larger porosities than non-PSR regions (e.g., ∼70% compared to ∼40% or so), and (2) most PSRs are somewhat “redder” (i.e., more reflective at the longer FUV wavelengths) than non-PSR regions, consistent with the presence of ∼1–2% water frost at the surface.
 A new method for observing PSRs is used by the Lyman Alpha Mapping Project (LAMP) on NASA's Lunar Reconnaissance Orbiter (LRO) mission, involving passive remote sensing at night using reflected light from the interplanetary medium (IPM) and from stars. LAMP is a far-ultraviolet (FUV) imaging spectrograph [Gladstone et al., 2010a] on LRO [Chin et al., 2007; Vondrak et al., 2010]. During LRO's nominal mission for NASA's Exploration Systems Mission Directorate (ESMD), the LAMP instrument observed FUV emissions from the nightside of the Moon to search for indications of water frost and other surface volatiles in permanently shadowed regions (PSRs) near each pole. LAMP accomplished this by recording the reflected signal from the nightside lunar surface (and PSRs) due to IPM Ly α and FUV starlight. Both these light sources provide roughly uniform (although very faint) illumination across the sky and were estimated using model fits [Pryor et al., 2008] to SOHO/SWAN data [Bertaux et al., 1997] for the IPM Ly α illumination and IUE data [Nichols and Linsky, 1996] for stellar fluxes (plus LOLA topography [Mazarico et al., 2011] for sky visibility) in order to convert the LAMP-observed brightnesses into albedos. Figure 1 shows how these sources vary over the sky. Because of the Moon's peculiar spin pole, which is never >1.54° from the ecliptic normal, the illumination of the south and north pole PSRs is essentially given by the lower and upper hemispheres, respectively, as shown in Figure 1. From the Moon, the IPM Ly α is generally brightest in the upstream direction (ecliptic longitude λ = 74.4°, ecliptic latitude β = −5.2° [Witte, 2004]) and faintest in the downstream direction. The IPM Ly α illumination varies seasonally due to the Earth's location in the interstellar wind, and on shorter timescales due to the variation in the solar Ly α flux. The latter are accounted for using TIMED/SEE data [Woods et al., 2005]. The stellar illumination is approximately constant, but with an integrated brightness considerably less than the IPM Ly α source and much less uniformly distributed. For example, at the south pole the integrated flux of FUV starlight over the LAMP bandpass is 3.1 × 107 photons/cm2/s, about 6× less than the average IPM Ly α flux of 1.8 × 108 photons/cm2/s there, or about 14% of the total night side illumination. About 10% of the total FUV flux of starlight at the south pole comes from the single brightest star, α Crucis. In contrast, at the north pole the integrated flux of FUV starlight over the LAMP bandpass is 4.2 × 106 photons/cm2/s, about 55× less than the average IPM Ly α flux of 2.3 × 108 photons/cm2/s there, or about 1.8% of the total night side illumination. The reason for the large difference in stellar illumination between the north and south poles (which is very important for LAMP's SNR) is that since the galactic center is in the southern ecliptic hemisphere, most UV-bright stars are also located there (as can be easily seen in the SWAN data); the FUV stellar illumination is ∼9× to ∼5× larger for south pole PSRs than for north pole PSRs over the spectral range 110–190 nm.
2. LAMP Observations
 LRO's polar orbit provides for repeated observations of PSRs, enabling accumulation of the faint reflected UV signal with the photon-counting LAMP instrument. The LAMP instrument covers an FUV passband of 57–196 nm (in 760 elements of ∼0.18 nm each), and its 6° × 0.3° slit is nominally pointed at the nadir. LAMP spatial pixels are 0.3° in size (so there are ∼20 of them along the slit). At LAMP's sensitivity, which is monitored monthly and is traceable to IUE observations of the stars γ Gruis and ρ Leo (with an absolute accuracy of ∼15%), the nightside count rate due to reflected IPM Ly α and starlight is 200–300 counts/s over the entire slit. The background count rate is very low (∼20 counts/s) but is comparable to the signal from reflected starlight, resulting in a much lower SNR for the On (130–155 nm) and Off (155–190 nm) band albedo maps than for the Ly α (119–125 nm) band albedo maps (“On” and “Off” refer to our chosen adjacent wavelength bands covering regions of strong absorption by water frost and very little absorption by water frost, respectively).
 LAMP albedo maps created using the first 18 months of data for the Ly α (119–125 nm), On (130–155 nm), and Off (155–190 nm) wavelength bands are presented in Figures 2, 3, and 4, respectively. Notable craters are indicated (taken from a USGS gazetteer; some of the positions had to be adjusted to better match LOLA topography). These maps are created by combining monthly maps, which are produced as follows: (1) Using pointing solutions and ephemerides provided by the LRO project, count maps are created by projecting the time-tagged photons in a given band onto a lunar grid which oversamples the projected size of individual spatial pixels at the lunar surface; (2) exposure maps are created likewise, using the projected boundaries of each pixel and valid LAMP observation times; (3) a photon map is then produced in a similar way to the count map using events corrected for LAMP's effective area; (4) a brightness map is produced by dividing the photon map by the exposure map and by the solid angle of each LAMP spatial pixel; (5) an illumination map is created using model fits to the observed IPM Ly α sky brightness and appropriate stellar fluxes (using the 1000 brightest stars in the LAMP passband, as determined from IUE data), with accounting for the fraction of the sky visible from each location on the surface (using LOLA-generated topographic data); and, finally, (6) an albedo map is produced by dividing the brightness map by the illumination map. In producing the nightside albedo maps, valid observations have been restricted to surface locations where the solar zenith angle is SZA > 91°, in order to minimize any contribution from scattered FUV sunlight in locations near the terminator. We tested this restriction by producing maps with more stringent solar zenith angle requirements (e.g., only accepting observations with SZA > 92° or SZA > 93°). These changes had no substantial affect on the albedo maps, even for Shackleton PSR, which is always located at or near the terminator, and would be most sensitive to scattered sunlight. The SNR of the nightside albedo maps in this and other regions of near-permanent illumination are low and should be used with caution. More details on LAMP map production will be provided by K. D. Retherford et al. (manuscript in preparation, 2011). The SNR contours shown in Figures 2, 3, and 4 have been smoothed and are based solely on Poisson statistics (for each ∼240-m pixel) and thus do not account for any systematic errors (such as possible errors in background subtraction). To estimate the effect that a background subtraction error would have on the albedo maps, we produced a cumulative south pole “On” map with a 10% lower background than used in the standard map shown in Figure 3. The albedo differences in the reduced-background map compared with the standard map were everywhere <2%.
 Using PSR-region masks produced using LOLA elevation maps, as described by Mazarico et al. , we present in Figures 5, 6, and 7 shaded relief maps with the FUV albedos of the Ly α (119–125 nm), On (130–155 nm), and Off (155–190 nm) wavelength bands shown, respectively, for just the PSR regions. Table 1 presents basic information about selected PSRs, and Tables 2 and 3 list their LAMP-determined FUV albedos in the south and north, respectively. The albedos and errors listed in Tables 2 and 3 are for each entire region (i.e., they take into account all valid 240-m pixels within each region, for which areas are provided in Table 1). The north pole On band and Off band values in Table 3 are included for completeness, but should be used with caution, as it is clear from Figures 3 and 4 that the SNR per 0.06-km2 map cell of these data is marginal, and the large area averages (Table 3) do not include estimated systematic errors. Overall, these maps and tables demonstrate how diverse the PSRs are at each pole, even given the relatively low SNR of the LAMP non–Ly α data. Two main results stand out in the LAMP measurements. First, most PSRs (e.g., Haworth, Shoemaker, Faustini near the south pole) are considerably less reflective at FUV wavelengths (e.g., at Ly α the typical PSR plane albedo is ∼0.028, while the typical plane albedo in the non-PSR area of the crater or an equal-area ring outside the crater is ∼0.036). Notable exceptions to this rule include Shackleton and a similar-sized crater on the poleward rim of Nobile in the south, and Whipple and Sylvester N in the north. Second, even though the Off band results have low SNR, it appears that PSRs are redder than their surroundings (i.e., from Table 2 it is found that in all the PSR regions listed, except for Shoemaker, the (Off band)/(On band) albedo ratio is largest in the PSRs, low in the non-PSR regions, and lower still in an equal-area ring around the crater). Also noteworthy is that the non-PSR regions within some craters are brighter than their surroundings (e.g., Shoemaker, Wiechert J, Idel'son L in the south). The lower Ly α albedo regions are roughly correlated with the coldest regions reported in Diviner temperature maps [Paige et al., 2010]. As the LRO mission continues, the SNRs of the accumulated LAMP albedo maps should continue to improve, although those for the north pole On and Off band maps are likely to remain disappointingly low (as mentioned above, the stellar flux above north pole is much less than the stellar flux above the south pole). This situation may be improved when higher-SNR dayside albedo maps, currently in preparation, become available for comparison (in non-PSR regions) with the nightside maps presented here.
 In this section we investigate some possible causes of the PSR albedo variations at LAMP wavelengths, which could result from the presence of FUV-absorbing (or FUV-reflective) volatiles at the surface or from changes in surface properties (e.g., porosity) at these interesting locations.
 Following Goguen et al. , we use the FORTRAN codes spher.f and refl.f written and described by Mishchenko et al.  and provided at http://www.giss.nasa.gov/staff/mmishchenko/brf/ to calculate the expected reflectivity of the lunar surface as a function of wavelength. For a point-like source of illumination, the reflectivity R is defined through the following relation between the observed intensity I (at zenith angle cos−1μ and azimuth angle φ) and the incident flux πF (at zenith angle cos−1μ0 and azimuth angle φ0):
 For many problems, the point-like source of illumination is the Sun. For instance, the FUV albedo determined by Henry et al.  using Hopkins Ultraviolet Telescope (HUT) observations of the subsolar region of the full Moon is R(1, 1). In contrast, for the LAMP nightside observations the diffuse illumination from the IPM Ly α covers the entire sky. Assuming that the IPM Ly α illumination is completely uniform, we may replace πF with IIPMdμ0dφ0 and integrate over μ0 and φ0 to obtain
 The LAMP surface albedos can be related to intrinsic properties of the surface soil particles, e.g., their single-scattering albedo (ϖ°) [Hapke, 1993; Mishchenko et al., 1999]. An approximate solution to the radiative transfer equation [Hovenier and Hage, 1989] yields an estimate of AS that can be expressed as
and 〈cos Θ〉 is the asymmetry parameter of the phase function.
 Using optical constants estimated for the average Moon (based on terrestrial basalt measurements) from Shkuratov et al. , we show in Figure 8 the variation in wavelength expected for plane albedo, spherical albedo, subsolar reflectivity (and ϖ°) over the LAMP bandpass. These curves were calculated using the Mishchenko et al.  radiative transfer codes, using the particle size distribution determined by Goguen et al.  to provide a good fit to visible photometric observations over a considerable portion of the Earth-facing lunar surface. It will be seen that the Shkuratov et al.  average Moon optical constants do not provide an especially good fit to the observed lunar FUV albedo, which is slightly blue but essentially flat (likely due to extensive space weathering of the lunar soils), but they are useful for showing how the different albedos compare with each other. It is seen that, all else being equal, the LAMP albedo (AP(1)) is expected to be ∼10–15% larger than the subsolar albedo (R(1, 1)) measured by HUT, and both are considerably less than the Bond albedos.
Figure 9 shows how the plane albedo would vary with wavelength if the surface particles had the same size distribution, but were composed of water ice or mercury. While mercury (observed by LAMP at surprising abundances in the LCROSS plume [Gladstone et al., 2010b]) has a modest increase in reflectivity at wavelengths >160 nm, it is minor compared to the ∼100× increase in the reflectivity of water frost over the same wavelength range. We thus expect that, of the important PSR volatiles, LAMP is most sensitive to the presence of water frost (as originally expected).
 Porosity (P) has an important effect on the albedo, which cannot be addressed by the semi-infinite radiative transfer code of Mishchenko et al. , but which has been considered by Hapke . Considering the regime where coherence between particles is negligible, but shadowing of deeper particles by overlying monolayers is important, Hapke  derives an approximate expression for the plane albedo
Figure 10 shows how porosity affects the plane albedo, other factors being equal. The porosity for the upper few centimeters of low-latitude lunar soils has been found to be ∼0.4–0.5 [e.g., Colwell et al., 2007]. However, even larger porosities may be possible in PSRs due to charging effects (i.e., leading to the formation of “fairy castle” structures). Results from the LCROSS impact indicate high porosities in the Cabeus PSR [Schultz et al., 2010; Hayne et al., 2010].
 Interestingly, the Off (155–190 nm) band albedos of several south pole PSRs are larger than the Ly α (119–125 nm) band and On (130–155 nm) band albedos. In Figures 11, 12, 13, and 14 we present LAMP-determined albedos for Faustini, Shoemaker, Haworth, and Shackleton craters, respectively, compared with the HUT-observed subsolar region albedo and the LAMP albedos for the entire south pole region from 80°S to 90°S (both of which are rather flat throughout the FUV). While Shoemaker crater shows only minor reddening, the other three craters have substantially larger Off band albedos. Shoemaker crater also stands out from the other south pole PSRs in terms of its large epithermal neutron deficit [Mitrofanov et al., 2010], which is a possible indicator of a large subsurface concentration of water ice. However, in some models of neutron transport, a surface frost layer can result in epithermal neutron enhancements [Lawrence et al., 2011]. Thus, it may be that the lack of a water frost signature for Shoemaker in the LAMP data is consistent with a strong deficit in the epithermal neutron data. In other words, the LEND results for Shoemaker may be unobscured by surface frost and indicate a buried layer of ice, while in other PSRs surface frost may result in an increase in epithermal counts, masking the presence of ice at depth. A more detailed knowledge of the depth distribution of ice is likely needed to correctly relate neutron data to the LAMP results.
 Assuming that these higher Off band albedos are due to water frost mixed into the soil at their surface, to obtain the increase of the Off band albedo compared to the On band albedo requires ∼1–2% H2O frost (by area). Note that adding this small amount of water frost does not significantly decrease the albedos at shorter FUV wavelengths. Since water frost is expected to be the most abundant volatile in the PSRs [Colaprete et al., 2010], it is unlikely that the low PSR Ly α albedos could be due to the presence of other, very FUV-dark volatiles. Instead, a likely explanation for the FUV darkness of the PSRs is that they are regions of higher porosity in the surface soil. Using the Hapke  approximation illustrated in Figure 10, it seems that decreasing the Ly α albedo by a factor of 0.028/0.036 ∼ 0.78 is consistent with an increase in porosity from ∼0.4 outside the PSRs to ∼0.7 in the PSRs.
 While not conclusive, the LAMP results indicate that high porosity and the presence of ∼1–2% water frost in the PSR soil of several south polar craters is consistent with their observed FUV albedos. This second result is unexpected, since it was pointed out by Morgan and Shemansky  that IPM Ly α should destroy any water frost at the surface faster than it can accumulate. These authors estimated a desorption rate of 7 × 106 cm−2 s−1, based on an IPM Ly α brightness of 500 R and assuming the loss process to be similar to that of gas-phase H2O photolysis. However, laboratory measurements of the photodesorption of 35-K water ice by Ly α indicate a steady state yield of 0.0035 H2O molecules photon−1 [Westley et al., 1995; Öberg et al., 2009]. In combination with the flux at the surface from a uniform sky brightness of 500 R (πF = πI = 500 × 106/4 = 1.25 × 108 photons cm−2 s−1), this yield results in a desorption rate of 4.4 × 105 cm−2 s−1, or ∼16× less than the rate estimated by Morgan and Shemansky . The conclusions reached by these authors are thus considerably less severe for the long-term existence of water frost at the surfaces of PSRs than originally thought. At this reduced desorption rate the loss of water from IPM Ly α photolysis is comparable to the steady source of water due to micrometeoroids and the episodic source due to comets (i.e., 1.9 × 105 cm−2 s−1 and 3.4 × 105 cm−2 s−1, respectively, from Morgan and Shemansky [1991, Table 3]). The fact that the sources and sinks of water are roughly equal may explain the observed heterogeneity in the FUV albedos of the PSRs, since it would make the retention of frost very dependent on local conditions and their history. Over the billion-year history of the PSRs some frost migration (vertically and horizontally) is expected. At the lowest PSR temperatures measured by Diviner, thermal diffusion is extremely slow [Schorghofer and Taylor, 2007]. However, in warmer PSRs, thermal cycling can increase diffusion rates considerably [Siegler et al., 2011]. Thus, some heterogeneity may be caused by temperature differences. Even in the coldest regions, impact gardening is expected to substantially redistribute volatiles with depth [e.g., Crider and Vondrak, 2003].
 We thank the LRO project for support of the LAMP observations reported here. In particular we thank C. Tooley, D. Everett, M. Houghton, A. Bartels, C. Baker, R. Saylor, R. Vondrak, G. Chin, J. Keller, T. Johnson, and S. Odendahl for making LRO work so well. LAMP is funded by NASA under contract NNG05EC87C, whose financial support we gratefully acknowledge.