1. Dr. Douglas Hope Research Scientist U.S. Air Force Academy Distribution A. Approved for public release, distribution unlimited

2.  Imaging SOI  spatial information on object from resolved imagery  Non-resolved SOI  Infer physical information about object, i.e. materials, orbital parameters, shape and morphology from observed light curves  NRSOI for a geosynchronous satellite  Nadir-pointing attitude is fixed  The pose of the satellite essentially does not change  Information in a GEO light curve depends on  Object shape  Surface materials  The illumination geometry between the Sun, object and observer Distribution A. Approved for public release, distribution unlimited

3.  NRSOI is an estimation problem  Ill-posed problem  Extraction of information about the object depends on both measurements and a priori information on the object  Statistical information as a priori information on an object  Estimate symbol value from the channel output (in the presence of noise)  Characterize any a priori information on the symbol by a probability distribution  A measure of information (entropy) is assigned to this symbol probability distribution Example: Let X denote the symbol for the FA abundance of solar cell material on a GEO Gaussian distribution with mean value = 0.70 5.01 bits6.04 bits Symbol distribution on the right has a greater potential to convey information about the FA Distribution A. Approved for public release, distribution unlimited

4.  Mutual information  Measures information between the symbol distribution and measurement distribution  Marginal measurement probability function  Computed via Bayes Theorem  Evaluate integral using Metropolis-Hastings Monte-Carlo algorithm and compute MI  NRSOI Task: Measure and Estimate the abundance of surface materials on a GEO satellite  Objective #1 Assess an observation strategy for completing the NROSI task Compute the MI in data obtained using different FTN observation modalities Use this metric to compare the information on materials obtained using different observational/measurement scenarios Consider Broadband ( Johnson B,V and R filters) vs. spectroscopic measurements Distribution A. Approved for public release, distribution unlimited

5.  Single site vs. simultaneous observations from multiple sites in the Northern and Southern hemispheres (Spring Equinox 2014) Scenario #1: Single site in La Junta (southwest) Colorado Scenario #2: observations from Chile and Colorado Distribution A. Approved for public release, distribution unlimited

6.  Model the GEO as a single rectangular facet with appropriate dimensions GEO model (5) Surface materials Area is equivalent to the fractional abundance of the material MaterialMaterial Description Fractional Abundance Mean value 1TASAT BRDF# MB 0023 Solar Cell, Silicon, Sun Side0.80 2TASAT BRDF# MB 0001 Aluminum Alloy, 2024-T3, Polished 0.07 +/- 0.007 3TASAT BRDF# MB 0026 Kapton, Aluminized 1 Mil0.05 +/- 0.005 4TASAT BRDF# MB 0029 Mylar, Aluminized, Mylar Side0.05 +/- 0.005 5TASAT BRDF# MB 0061 Paint, Chemglaze Z202, White0.05 +/- 0.005 Assess MI on the fractional abundances of materials from broadband measurements and spectroscopic measurements a priori statistical information Distribution A. Approved for public release, distribution unlimited

7. Increasing spectral resolution MI = 3.8 bits broadband measurements from Colorado Distribution A. Approved for public release, distribution unlimited Maximum MI possible is 9 bits

8. MI in spectroscopic measurements from La Junta, CO Increasing spectral resolution MI = 3.8 bits broadband measurements from Colorado Distribution A. Approved for public release, distribution unlimited Maximum MI possible is 9 bits

9. Increasing spectral resolution MI in spectroscopic measurements from Colorado and Chile MI = 3.8 bits broadband measurements from Colorado MI=4.8 bits broadband measurements from Colorado and Chile MI in spectroscopic measurements from La Junta, CO Δλ = 80 nm Distribution A. Approved for public release, distribution unlimited Maximum MI possible is 9 bits

10.  Applied mutual information to an NRSOI task (abundances of materials)  Use the MI to assess the performance of the FTN when acquiring information on the surface materials of a GEO using broadband and spectroscopic measurement modes from multiple sites (Colorado and Chile)  Next, evaluate MI in the estimated fractional abundances  Compare different mutual information quantities to assess the performance of algorithm when extracting information from the data Information in the data Information in the estimates Distribution A. Approved for public release, distribution unlimited

11. Fractional abundances estimated using non-negative least squares algorithm ( Lawson, 1974) Solves This approach requires the probability distribution be computed empirically Distribution A. Approved for public release, distribution unlimited

12. Distribution of estimated solar cell abundances for single object Truth FA Distribution A. Approved for public release, distribution unlimited