X-ray flux from filtered arrays of detectors without unfolding

A simple computational method is proposed for estimating the time-dependent flux F[ΔE](t) of an x-ray spectrum S(E,t) over domain [ΔE] from data Dk(t)(k=1,…,N) obtained by an N-channel array of filtered detectors. It is assumed that the data are related to the spectrum by a discrete, inhomogeneous, first-kind Fredholm integral equation Dk=∫S(E,t)Rk(E)dE, where Rk(E) is the known response function for each detector channel of the diagnostic. The proposed method constructs a spectral sensitivity HLS(E) for the diagnostic array as a linear combination ∑k=1NakRk(E) of the responses, where the coefficients ak are obtained by a least-squares criterion plus a constraint. The ak values, once determined, apply as long as the responses are valid. The flux estimate is then simply FLS(t)=∑k=1NakDk(t), without a spectral unfold of the data. The method is useful for quick analyses of time-dependent data, for comparisons with other flux-measuring diagnostics, and for the experimental design of filtered-detector arrays. ...

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