Abstract
Spectra, such as astrophysical spectra, can provide detailed diagnostics on the state of their emitting volume. Emission-line diagnostics are found by assuming a model for the spectral emission line and then fitting the model to the data. It is shown for Poisson noisy emission-line data, via the application of Cramer-Rao lower bounds, that there are limits to the precision that line fitting can achieve. The limits depend on the spectral line model and the noise properties of the data. A Cramer-Rao lower bound treatment introduces a framework in which questions of line fitting in particular and spectrometers in general may be posed. Some example applications are given and their implications for the design of spectrometric observations are discussed.
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