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A Recalibration of the Diffraction Efficiency of the Transmission Grating Spectrometers on EXOSAT

We describe a recalibration of the diffraction efficiency of the transmission gratings on EXOSAT. This recalibration is required in order to quantitatively interpret the soft X-ray spectra obtained with these instruments on Sco X-1. Because this source is extremely bright, the spectra are sensitive enough to reveal residual systematic effects in the grating efficiency. Specifically, we observe short-wavelength radiation dispersed into high (m > 5) spectral orders, which is usually too weak to be detectable. We develop a simple model for the diffraction efficiency and briefly discuss some properties of the efficiency, applicable to X-ray transmission gratings in general. We explore the effect of a new degree of freedom, the cross-sectional shape of the grating bars. We then use a set of preflight calibration spectra to constrain the free parameters of the model. The new efficiency curves are in satisfactory agreement with the calibration data and quantitatively account for the anomalies seen in the spectrum of Sco X-1. We also briefly discuss an empirical zero-order profile shape, appropriate for the analysis of spectra of very bright sources.