A nonlinear optimization technique for ground-based atmospheric emission tomography

Solar-terrestrial interactions produce a rich variety of optical emissions in the Earth’s upper atmosphere (100–1000 km). While ground based brightness measurements (i.e., column integrated photon density) provide an important diagnostic of these processes, the more interesting physics is in the associated volume emission rate distribution (i.e., photon production/cm s versus altitude). This work examines a new technique for remote sensing of the Earths’ radiative environment. Brightness measurements from a network of ground-based imaging systems are used to define a limited angle emission tomography problem, from which two-dimensional (2-D) (latitude versus altitude) volume emission rate profiles are reconstructed. The incomplete angular coverage imposed by this viewing geometry leads to an ill-posed and ill-conditioned inverse problem. The problem is regularized by initially constraining the vertical profiles to be Chapman functions. Such a parameterization captures the mean features of a large class of emission structures. A weighted Euclidean distance between the measured and estimated data is then minimized, subject to side constraints that define the feasibility region for the Chapman parameters. The side constraints are implemented as barrier functions, resulting in an unconstrained nonlinear optimization problem. Minimization is performed using the Broyden–Fletcher–Goldfarb–Shanno variant of the Davidon–Fletcher–Powell (DFP) method. The resulting volume emission rate elements are then used as an initial guess to a multiplicative algebraic reconstruction (MART) algorithm. In addition to regularizing the problem, this technique exposes important geometrical limitations to this class of inverse problem.