The presence and distribution of hydrogen in the lunar sub-surface is a matter of considerable scientific and economic interest. This ancient surface, like that of Mercury, encapsulates a barely adulterated record of the history of the terrestrial planets, and the likely association of hydrogen with water molecules can provide insights into the past few billion years.

This presentation contains a detailed comparison of maps of the hydrogen distribution near the lunar south pole made by the Lunar Prospector Neutron Spectrometer (LPNS) and the Lunar Exploration Neutron Detector Collimated Sensors for EpiThermal Neutrons (LEND CSETN). Epithermal neutrons reflect the hydrogen abundance in the top metre of the regolith, such that lower neutron count rate corresponds to higher hydrogen abundance.

There are three important ways in which measured maps of epithermal neutron count will be degraded representations of what actually leaves the lunar surface:

1) the instrumental footprint resulting from neutron detectors not solely counting neutrons from the nadir direction,

2) the local background due to neutrons produced when cosmic rays strike the spacecraft itself, and

3) the inevitable stochastic noise associated with the finite measurement periods.

Each of these observational artifacts leaves an imprint upon the measured map. With a suitable choice of statistical estimators it is possible to infer empirically the importance of each of these factors for each of the LPNS and LEND CSETN.

The two widely-used statistical estimators that will be employed are: i) the autocorrelation function, and ii) the power spectrum. The autocorrelation function of a map is a measure of the similarity between values in pixels at different relative position. This function depends not only on the intrinsic clustering properties of the count rate, but also on both the smoothing length imposed on the data by the instrumental spatial resolution and the amount of uniform background that is introduced. Qualitatively, on scales smaller than the instrumental footprint the correlation function will be approximately flat. The power spectrum is just the Fourier transform of the autocorrelation function and represents an alternative way of showing which spatial scales contain information.

Results.

Using the autocorrelation functions and power spectra of the polar count rate maps, it is shown that the LEND CSETN has a footprint that it is least as big as would be expected for an omni-directional detector at an orbital altitude of 50 km. The collimated flux into the field of view of the collimator is negligible. The maps of lunar polar hydrogen with the highest contrast, i.e. resolution, are those resulting from pixon image reconstruction of the LPNS data (Teodoro, 2010). These typically provide weight percentages of water equivalent hydrogen that are accurate to 30% within the polar craters.

The LEND CSETN commissioning orbit data showed that the count rate decreases with increasing altitude. This trend is the opposite of that from counts generated by cosmic rays striking the spacecraft itself, because the Moon provides less shielding at higher altitudes. The collimated count rate should be approximately independent of altitude, because it only depends upon the collimator field of view as the lunar neutron emission is almost constant surface brightness. The only component of neutron counts into the LEND CSETN that decreases with increasing altitude is that which depends upon the angle subtended by the Moon, ie the omni-directional lunar counts. These will have higher energies to penetrate into the detector while not coming through the small collimator field of view, and constitute a significant, spatially-varying background.

The low count rate in the vicinity of Shoemaker crater determined from the LEND CSETN data was found to be consistent with a statistical fluctuation superimposed on a broad suppression in count rate of the sort produced by an omni-directional, spatially-varying high energy epithermal neutron background. If the lunar neutron count rate measured by the LEND CSETN was predominantly collimated, then there should be large count rate fluctuations present across the polar regions. That these are not observed in the autocorrelation function or power spectrum for the LEND CSETN map is evidence that the collimated fraction of the count rate is very low, and the effective footprint of the LEND CSETN is significantly larger than the collimator field of view.