Tandem gratings of double-dispersion mount make it possible to design an imaging spectrometer for the weak light observation with high spatial resolution, high spectral resolution, and high optical transmission efficiency. The traditional tandem Wadsworth mounting is originally designed to match the coaxial telescope and large-scale imaging spectrometer. When it is used to connect the off-axis telescope such as off-axis parabolic mirror, it presents lower imaging quality than to connect the coaxial telescope. It may also introduce interference among the detector and the optical elements as it is applied to the short focal length and small-scale spectrometer in a close volume by satellite. An advanced tandem Wadsworth mounting has been investigated to deal with the situation. The Wadsworth astigmatism-corrected mounting condition for which is expressed as the distance between the second concave grating and the imaging plane is calculated. Then the optimum arrangement for the first plane grating and the second concave grating, which make the anterior Wadsworth condition fulfilling each wavelength, is analyzed by the geometric and first order differential calculation. These two arrangements comprise the advanced Wadsworth mounting condition. The spectral resolution has also been calculated by these conditions. An example designed by the optimum theory proves that the advanced tandem Wadsworth mounting performs excellently in spectral broadband.
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