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2 August 2002 Oblique projection retrieval of the atmosphere (OPRA)
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Space Computer Corporation has developed an innovative atmospheric retrieval algorithm called OPRA (Oblique Projection Retrieval of the Atmosphere). This algorithm is designed to retrieve both path radiance and atmospheric transmissivity directly from calibrated LWIR radiance spectra through a two-stage application of oblique projection operators. The OPRA method assumes the surface in the pixel field of view has an emissivity close to unity. Under this condition, the sensed radiance can be accurately modeled as the blackbody ground radiance attenuated by a multiplicative transmissivity and enhanced by an additive path radiance. The oblique projection operator is defined in terms of a range space H and a null space S. The subspaces H and S are independent, although not necessarily orthogonal. The properties of the operator are such that when it is applied to a measured signal all components spanned by the null space S are eliminated, while those spanned by the range space H are preserved. Stage 1 of OPRA nullifies the surface radiance multiplied by the transmissivity and retrieves the path radiance. Stage 2 is applied to the logarithm of the measured signal minus the retrieved path radiance to nullify the log of the Planck function and thereby retrieve the log of the transmissivity. The OPRA algorithm has been applied to both model data and SEBASS LWIR data and initial results indicate that atmospheric retrieval errors are sensitive to instrument artifacts not included in the various subspace definitions.
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Pierre V. Villeneuve and Alan D. Stocker "Oblique projection retrieval of the atmosphere (OPRA)", Proc. SPIE 4725, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery VIII, (2 August 2002);

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