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Determining Bandpass Of Spectrometric Instruments Which Use Concave Gratings

An algorithm for determining the bandpass of spectrometric instruments is presented. This algorithm makes use of the results of tracing rays through a concave holographic grating in order to obtain an irradiance distribution which is convolved with the exit slit of a monochromator or a detector element of a spectrograph. The resulting convolution may be interpreted as a function of irradiance vs. wavelength, which we call the instrumental profile. A finite number of rays alone is not enough to establish bandpass of a particular instrument configuration. Smoothing from the convolution and possibly additional filtering of the irradiance data are necessary in order to get a continuous irradiance function from which a single bandpass quantity is determined. Examples of one particular instrument design are used to compare the results of a computer program using this algorithm to actual instrument bandpass measurements.