1. The ROLO Lunar Calibration System Description and Current Status
Thomas C. Stone
U.S. Geological Survey, Flagstaff, AZ USA
GSICS Lunar Calibration Workshop
EUMETSAT
01 December 2014

2. Introduction and Background
Timeline of ROLO:
Studies at the USGS Astrogeology Center, supporting the NASA Moon landing program in the 1960s
lunar albedo mapping, for landing site selection
lunar cratering rates, which showed the stability of the lunar surface
feasibility to use the Moon as a calibrated light source
Funding from NASA to develop the lunar calibration method
for EOS instruments: SeaWiFS, MODIS, ASTER, MISR, Hyperion…
established the ROLO facility: telescopes and data collection system
Studies of lunar reflectance modeling, for developing the calibration reference
showed that the most useful quantity is spatially-integrated irradiance
showed that an analytic model is needed, to accommodate the various geometries of instruments’ Moon observations

3. ROLO Telescope Facility
Acquired an extensive set of lunar and stellar observations, used to characterize the brightness behavior of the Moon and provide the basis dataset for the lunar model.
Located at USGS in Flagstaff Arizona, 2143m altitude
Twin telescopes, 20cm dia.
23 VNIR bands, 350−950 nm
9 SWIR bands, 950−2450 nm
Imaging cameras — radiance
Operated more than 8 years
> Moon images
phases from eclipse to 90°
> star images
ROLO telescopes zenith-pointed at dusk

4. ROLO Data Processing for Modeling
The basis data for the lunar model are ROLO lunar irradiance measurements, processed similarly to Moon images from spacecraft instruments:
Radiance calibration developed from ROLO measurements of the star Vega, tied to published absolute stellar energy distribution data
absolute uncertainties for Vega: 1.0–1.5% VNIR, 3–4% SWIR
Corrections for atmospheric transmission developed for each observing night from many star measurements
Empirical correction for atmospheric scattering around the Moon disk

5. ROLO Lunar Model
The lunar model kernel describes the disk-equivalent reflectance (A).
Reflectance was chosen to take advantage of the smooth lunar spectrum, and eliminate the effects of the solar fine structure This introduces a dependence on the solar spectrum used!
Empirical formulation, a function of the geometric variables of phase angle (g) and librations (Φ, φ, θ)
equation designed to minimize residuals from fitting the ROLO dataset
Coefficients derived by fitting ~1200 observations in each band (k)
mean fit residual ≈ → a measure of the relative precision

6. Example Computation of ROLO Model
Lunar disk-equivalent reflectance at 865 nm
Spread shows the effect of libration, ~5%
Lambert sphere

7. Lunar Model Operation — Inputs Processing
User inputs:
Observation time
Spacecraft position (X,Y, Z)
Double-Precision Ephemeris DE421
SPICE Toolkit
Moon position
Phase angle (g)
Sun position
Librations (Φ, φ, θ)
Moon orientation

8. Lunar Model Operation — Output Processing
Computing the model equation gives the lunar disk reflectance (Ak) at the 32 ROLO wavelengths. A representative lunar reflectance spectrum is then fitted to these Ak values:
Symbols □ are Ak
from the lunar model computation
Solid line is the reference lunar reflectance spectrum, fitted to the Ak values.

9. Lunar Model Operation — Post-Processing
The fitted lunar reflectance spectrum is convolved with the instrument band spectral response functions and the solar spectrum to give the lunar irradiance (EM) at the band wavelengths:
Important: this step cancels the dependence on the solar spectrum. The only valid output of the ROLO model is the lunar irradiance.
It is an error to use directly the lunar reflectance computed by ROLO!

10. Lunar Model Operation — Post-Processing
The model computations (Afit) and ΩM are for standard Sun–Moon and Moon–Observer distances, i.e. the mean orbital radii of the Earth and the Moon, respectively.
Apply distance corrections:
The final output E′M is the lunar irradiance present at the instrument location at the time of the observation, in each sensor spectral band.
For comparisons to observations made by instruments, corrections for oversampling are applied to the irradiance measurement data.
For typical lunar calibration interactions, ROLO provides the computed geometry parameters: phase and libration angles, distance correction factors, Moon disk apparent size and orientation.

11. Current Status
Current model version (311g) is used in many different applications:
sensor response trending/on-orbit calibration stability
nighttime aerosol optical depth measurements with lunar photometers
photometric corrections for imaging instruments in orbit around the Moon
Uncertainty of the relative irradiance, i.e. changes in lunar brightness with phase angle and librations:
initially specified by residuals from fitting ROLO dataset: ~1%
comparisons made by new instruments (e.g. VIIRS, PLEIADES) show geometry dependencies up to several percent; analyses ongoing
the ROLO model is being revised with constraints developed from these comparisons, particularly PLEIADES (more about this on Thursday)
Uncertainty of the absolute irradiance: 5–10%
demonstrated by comparisons of multiple instruments
can be constrained by new, dedicated absolute lunar irradiance measurements

12. Thank You!