Uncertainties in Absolute Quantum Efficiency

In this section we attempt to enumerate error sources and, to the extent possible, to quantify the errors in the best-fit model quantum efficiency. It is useful to distinguish at the outset errors arising from the limited precision with which the parameters of the adopted model are constrained by the available data, on the one hand, from those arising from inadequacies in the quantum efficiency model, on the other hand. At the risk of creating some confusion, we choose to say that the former type arise from ``measurement errors'' since their ultimate origin is the uncertainty in the measured quantities used to constrain the model. Thus we shall sometimes use the phrase ``measurement errors'' as an abbreviation for ``errors in predicted quantum efficiency resulting from errors in measurement.'' We label the latter error type ``modelling errors,'' intending an analogous ellipsis.

In general, effects of modelling errors are difficult to quantify, and, in any event, not particularly well-bounded at this writing. In contrast, the effects of measurement errors can be quantified using well-known techniques, though it must be emphasized that even these errors must be interpreted carefully. In particular, measurement errors produce quantum efficiency errors which are NOT statistically independent from energy to energy. For many purposes it is therefore much more useful to conceive of the quantum efficiency vs. energy function itself, rather than the quantum efficiency at any particular energy, to be the random variable whose value is constrained by the model fitting.

In this section we first present a straightforward (though incomplete) quantitative analysis of the effects of measurement errors. We then discuss modelling errors. While an effort has been made to quantify modelling errors, more work remains to be done on this problem. As a result, our discussion serves mainly to guide future work.