ALBERT

Description: A standard problem in gamma-ray astronomy data analysis is the decomposition of a set of observed counts, described by Poisson statistics, according to a given multicomponent linear model, with underlying physical count rates or fluxes which are to be estimated from the data. Despite its conceptual simplicity, the linear least-squares (LLSQ) method for solving this problem has generally been limited to situations in which the number n(sub i) of counts in each bin i is not too small, conventionally more than 5-30. It seems to be widely believed that the failure of the LLSQ method for small counts is due to the failure of the Poisson distribution to be even approximately normal for small numbers. The cause is more accurately the strong anticorrelation between the data and the wieghts w(sub i) in the weighted LLSQ method when square root of n(sub i) instead of square root of bar-n(sub i) is used to approximate the uncertainties, sigma(sub i), in the data, where bar-n(sub i) = E(n(sub i)), the expected value of N(sub i). We show in an appendix that, avoiding this approximation, the correct equations for the Poisson LLSQ (PLLSQ) problems are actually identical to those for the maximum likelihood estimate using the exact Poisson distribution. We apply the method to solve a problem in high-resolution gamma-ray spectroscopy for the JPL High-Resolution Gamma-Ray Spectrometer flown on HEAO 3. Systematic error in subtracting the strong, highly variable background encountered in the low-energy gamma-ray region can be significantly reduced by closely pairing source and background data in short segments. Significant results can be built up by weighted averaging of the net fluxes obtained from the subtraction of many individual source/background pairs. Extension of the approach to complex situations, with multiple cosmic sources and realistic background parameterizations, requires a means of efficiently fitting to data from single scans in the narrow (approximately = 1.2 keV, HEAO 3) energy channels of a Ge spectrometer, where the expected number of counts obtained per scan may be very low. Such an analysis system is discussed and compared to the method previously used.

Description: Launched in February 2013, the Landsat-8 carries on-board the Thermal Infrared Sensor (TIRS), a two-band thermal pushbroom imager, to maintain the thermal imaging capability of the Landsat program. The TIRS bands are centered at roughly 10.9 and 12 micrometers (Bands 10 and 11 respectively). They have 100 m spatial resolution and image coincidently with the Operational Land Imager (OLI), also on-board Landsat-8. The TIRS instrument has an internal calibration system consisting of a variable temperature blackbody and a special viewport with which it can see deep space; a two point calibration can be performed twice an orbit. Immediately after launch, a rigorous vicarious calibration program was started to validate the absolute calibration of the system. The two vicarious calibration teams, NASA/Jet Propulsion Laboratory (JPL) and the Rochester Institute of Technology (RIT), both make use of buoys deployed on large water bodies as the primary monitoring technique. RIT took advantage of cross-calibration opportunity soon after launch when Landsat-8 and Landsat-7 were imaging the same targets within a few minutes of each other to perform a validation of the absolute calibration. Terra MODIS is also being used for regular monitoring of the TIRS absolute calibration. The buoy initial results showed a large error in both bands, 0.29 and 0.51 W/sq msrmicrometers or -2.1 K and -4.4 K at 300 K in Band 10 and 11 respectively, where TIRS data was too hot. A calibration update was recommended for both bands to correct for a bias error and was implemented on 3 February 2014 in the USGS/EROS processing system, but the residual variability is still larger than desired for both bands (0.12 and 0.2 W/sq msrmicrometers or 0.87 and 1.67 K at 300 K). Additional work has uncovered the source of the calibration error: out-of-field stray light. While analysis continues to characterize the stray light contribution, the vicarious calibration work proceeds. The additional data have not changed the statistical assessment but indicate that the correction (particularly in band 11) is probably only valid for a subset of data. While the stray light effect is small enough in Band 10 to make the data useful across a wide array of applications, the effect in Band 11 is larger and the vicarious results suggest that Band 11 data should not be used where absolute calibration is required.