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What's wrong with the throughput-resolution product? A fiber-fed spectrograph forces a reevaluation of instrument design parameters

Fiber-fed spectrographs have now been employed in astronomy for several years. They offer the principle advantages of increasing the number of objects with which simultaneous spectra may be recorded, better stability, an improvement in versatility, and factors associated with the mode-scrambling properties of fibers. However, the nature of these spectrographs pose new questions of certain design parameters. A traditional figure of merit for spectrographs is the throughput-resolution product (A(Omega) R). It is shown that A(Omega) R is no longer a constant as the entrance `slit' is varied. Here, `slit' has a new meaning. In both the first and higher order optics sense, A(Omega) R is investigated and compared with a better figure of merit. This new figure of merit maximizes the potential information content at the spectrograph focal plane. At a minimum, it incorporates the oft neglected instrument response and transmission/efficiency parameters (such as with a grating). Other refinements are made as well. Comparisons may be made both across spectrometer types and as a design guide within a family, where options must be evaluated.