An analytic method for inversion problems of the Fredholm integral type is developed. The application of this formalism to error analysis and optimal experimental design is discussed. Finally, results from this method for a simulated experiment are compared with other commonly used inversion techniques.

An analytic method for inversion problems of the Fredholm type is developed. This method allows a quantitative discussion of the information content of various sets of experimental measurements. It is shown that if the solution is assumed to have a finite Fourier series representation then the solution may be separated into two independent parts, one given by the data and the other by constraints imposed on the solution.

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