The availability of compact transmission grating spectrometers now allows an attractive and economical alternative to the more familiar Czerny-Turner configuration for many high-temperature plasma applications. Higher throughput is obtained with short focal length refractive optics and stigmatic imaging. Many more spectra can be obtained with a single spectrometer since smaller, more densely packed optical input fibers can be used. Multiple input slits, along with a bandpass filter, can be used to maximize the number of spectra per detector, providing further economy. Curved slits can correct for the strong image curvature of the short focal length optics. Presented here are the governing grating equations for both standard and high-dispersion transmission gratings, defining dispersion, image curvature, and desired slit curvature, that can be used in the design of improved plasma diagnostics.
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