Abstract

We present the recovery of excitation intensity dependence from spatially and temporally averaged data as an inversion problem. Thus cross sections and line shapes are obtained as a function of local instantaneous intensity rather than peak intensity or pulse energy. In the nonsaturated regime, actual and experimental cross sections are related by a Volterra integral equation. For exponential intensity profiles, the problem is solved by Abel inversion. For mildly nonlinear cross sections, inversion results are obtained from the moments of the excitation density function. For the most general case, inversion by collocation is discussed, in particular by the direct-inversion approach. In the saturation regime, the problem becomes nonlinear in the time coordinate and has to be reformulated so as to include a saturation parameter. It is shown how inversion results can be obtained under the constraint of the constant spectral area under the line profile, yielding also a value for the saturation parameter. Our treatment should allow the extension of such diagnostic schemes as two-photon laser-induced fluorescence into the saturation regime, maintaining calibration while enabling a higher SNR.

© 1988 Optical Society of America