A Methodology for Internal Light Sources Estimation

A reconstruction technique of bioluminescence sources in natural waters from in situ irradiance data is presented. The inverse problem is formulated as a nonlinear constrained optimization problem, assuming that the bioluminescence unknown profile can be represented by a sum of distributed Gaussian sources. The objective function is defined as the square Euclidean norm of the difference vector between experimental and computed data. The authors use the Hydrolight 3.0 code, which solves numerically the time-independent one-dimensional radiative transfer equation in natural water bodies using the invariant imbedding theory. The proposed inversion technique was tested with noise-corrupted synthetic data and yielded good numerical results. The influence of the number of Gaussian sources, as well as their standard deviations in the estimation, is analyzed. KEY WORDS—Inverse problem, bioluminescence sources, invariant imbedding method, radiative transfer equation