Stray light in radiometric measurements is caused by internal scattering within the instrument that allows photons that emanate from one region of spectral/physical space to be detected as if they were from another. Stray light is particularly damaging for imagers that sample a large dynamic range such as the limb profiler (LP) from the Ozone Mapping and Profiler Suite (OMPS). In that case, even a very small fraction of photons from high-intensity sources can dominate measurements in a low intensity part of the image. Removing stray light contamination is analogous to performing a de-convolution. This process is both computationally expensive (if performed rigorously) and can lead to substantial error amplification.

We use a regression representation of the OMPS-LP in the forward model of the optimal estimation method to remove stray light. If properly trained, a regression exploits correlations between components of the radiative and measurement fields that allow us to efficiently reconstruct one field from incomplete knowledge of the other, reducing the computational cost and allowing us to overcome sub-sampling of the measurements. By incorporating the regression model into the forward model we obtain additional benefits. (1) Input to the regression is output from an idealized radiative transfer calculation (RT) and, therefore, the regression model does not amplify measurement error. (2) Output from the RT calculation can be, in principle, perfectly anticipated (unlike observations) and, so, the regression model is (again, in principle) perfectly trainable. (3) A regression model is essentially a tangent linear model for the instrument and, thus, adjusting the kernel to accommodate the instrument model requires only a single matrix multiplication of the RT kernel by a matrix of regression coefficients, which are pre-calculated.

In order for us to rigorously demonstrate the viability of our method, it is necessary to develop a training strategy, test it with independent validation data and develop a method for retraining the regression model to accommodate changes of the instrument after launch. Here, we describe our efforts to train and validate the regression model. All data is simulated with the Herman and Flittner radiative transfer model and a detailed instrument model. Training data (pair sets of radiance/measurement data) are constructed from basis vectors for atmospheric conditions in a ‘linear' sub-space of the radiative transfer model (i.e., a sub-space of the atmospheric state over which the radiative transfer calculation is approximately linear). Validation data is constructed from Markovian perturbations to standard atmospheric profiles of temperature and ozone number density.