Optical optimization of a dual-band sun-as-a-star extreme ultraviolet spectrograph for measuring the line-of-sight velocity of coronal mass ejections

The detection of Line-of-sight (LOS) velocity of coronal mass ejections (CMEs) is crucial for understanding and forecasting their propagation. The LOS velocity can be derived from the Sun-as-a-star extreme ultraviolet spectrograph based on the Doppler effect. However, the poor spectral resolution of existing instruments is not sufficient for detection. In the paper, we propose a dual-band Sun-as-a-star spectrograph with high spectral resolution for measuring the LOS velocity of CMEs. Based on a multilayer concave grating operating in a normal incident mode, we optimized the parameters of the spectrograph for the wavelength ranges of 18.3\( \sim \)21.3 nm and 49.6\( \sim \)52.9 nm. The spectral resolving power for these two ranges exceeds 1000 and 2000, respectively, which is about three times higher than that of the Extreme ultraviolet Variability Experiment onboard the Solar Dynamics Observatory. B\(_4\)C/Al and B\(_4\)C/Mo/Al multilayer structures were optimized to improve the diffraction efficiency across both bands simultaneously. We also evaluated the instrument performance by calculating the photon numbers. Additionally, we discussed the degradation of spectral resolution caused by the stability of satellite platform, determining that the stability should be better than ±7.2\(^{\prime \prime }\)(\( \pm \)0.002\(^\circ \)) within the exposure time of 60 s. Our investigation provides a new way to observe Sun-as-a-star extreme ultraviolet spectrum.