# Dual-Gratings Imaging Spectrometer
###### Abstract  
Common dispersive-type spectroscopic instruments include prism-type and grating-type, usually using a single dispersive element. The continuous imaging band is always limited by the dispersion angle. When it is necessary to image two wavebands with an ultra-spectral resolution that are far apart, the imaging is difficult due to the large diffraction angle. To broaden the spectral coverage of the imaging spectrometer, in this paper, we propose a dual-gratings imaging spectrometer with two independently rotating gratings. In this proposed system, two very far apart wavelength bands can be imaged in the adjacent areas by adjusting the angle of the dual gratings. This greatly expands the spectral coverage of the imaging spectrometer. Currently, the only application area considered for this instrument is solar applications. In this article, we present the optical system of the dual-gratings imaging spectrometer, illustrate several advantages of the new structure, and discuss new problems caused by the dual-gratings, which are referred to as overlap between two spectra and double image offset. We deduced the calculation process of the dual grating rotation angle, the relationship between the final acquired image and the slit, the relationship between the angle change between the dual gratings and the double image offset, and the relationship between the MTF upper limit reduction and the spatial frequency. This article also summarizes the shortcomings of this structure and studies the applicable fields under these shortcomings. At last, we simulate a dual-gratings imaging spectrometer system, compare this scheme with two traditional schemes, and conclude that this instrument has certain practical significance. spectrometer; spectral range; double gratings +
Footnote †: journal: Medical Imaging  
10 October 2021  
**Sublinear optics**  
**Problems**  
+++ ==WARNING: Truncated because of repetitions==
**  
++  
Sometimes, people are more concerned about the spectral images of discrete bands with ultra-spectral resolution. For example, in the process of flare outbreak, the most obvious visible bands are H\(\alpha\) (656.281 nm), H-line (396.8 nm), and K-line (393.4 nm) of ionized calcium. People often use the ultra-spectral solar surface images of these three bands for research. The traditional observation method uses filters. This scheme pays more attention to the spatial change of the monochromatic sun surface, and ignores the real-time subtle spectral changes in the waveband. If ultra-spectral observations in these three bands are required, according to the design method of the traditional planar grating imaging spectrometer, the spectral coverage is too large, and the diffraction angle is too large, which leads to difficulty in imaging and greatly reduces the image quality. Therefore, only two imaging spectrometers can be used to image the dual-band spectrum, which will increase the volume of the system. However, the dual-gratings imaging spectrometer can easily solve this problem. The dual-gratings is an innovative structure that has been successfully used in many cases to improve the spectral resolution or spectral range of the system. In 2011, [PERSON] et al. studied a double-concave grating imaging spectrometer, which successfully improved the spectral resolution of the system [13]. In 2018, [PERSON] studied a multi-grating spatial heterodyne spectrometer. By changing a single grating to multi-grating, interference images with high spectral resolution and large spectral range were successfully obtained [14]. In 2018, [PERSON] researched a dual-grating dual-band imaging spectrometer, which divided the field of view into two and imaged different bands respectively [15]. As mentioned above, the dual gratings structure was used to improve the performance of the concave grating imaging spectrometer and the heterodyne interference imaging spectrometer. However, very few studies have applied it to planar grating imaging spectrometers.