# Research on Compressed Sensing Spectrometry Based on Electro-Optical Transmittance Coding
## 1 Introduction  
Spectroscopy reveals the essential characteristics of atoms, molecules, and molecular structures of substances [1]. It plays an important role in various fields, such as nondestructive testing, food safety testing, meteorological monitoring, agricultural general survey, geological resource exploration, and military target reconnaissance. With the development of spectrometry, the snapshot, miniaturized, and integrated methods and instruments have been gradually expanded [2, 3, 4, 5]; however, they still face unprecedented challenges.  
A conventional spectrometer is realized primarily through light splitting, filtering or interference. Computational spectrometry based on compressed sensing theory promotes the development of a new method of integrated and snapshot spectrum measurement. [PERSON] et al. took the lead in using a two-dimensional coding template and dispersive optical element to study snapshot compressed sensing spectrometry [6, 7]. This method uses both a binary-valued aperture to realize transmittance coding and a dispersive element to mix signals arriving at the focal plane of detector arrays. The spectrum is further inverted through the compressed sensing reconstruction algorithm. The target spectral data can be obtained after several measurements, and the spectrometry is fast and efficient. However, this method requires transformation from the spectral to the spatial dimension; consequently, it uses spatial coding to realize spectral coding, which undoubtedly increases the complexity of instrument architecture, cost and volume. [PERSON] et al. placed a liquid crystal variable retarder (LCVR) between two orthogonal polarizers, and the regulation of incident spectral transmittance was flexibly realized by controlling LCVR's phase retardation [8]. Spectrum measurement with a high compressed ratio was demonstrated by coding the transmittance under different retardations. The method accomplished thecoding in the spectral dimension, thereby producing a simpler and smaller system structure. Furthermore, compressed spectrometry is proposed using a Fabry Perot (FP) resonator, and the piezoelectric driver was used to adjust the distance between the two mirrors of the FP resonator to obtain different spectral transmittance regulations [9]. LCVR and FP resonators can realize direct coding in the spectral dimension, which significantly reduces the volume of the system. Nevertheless, the time responses of the methods are both in the order of ms. This is not conducive for applications that require ultrafast spectrum measurements, such as the fluorescence spectrum, explosion radiation spectrum etc. In addition, LCVR and FP are significantly affected by ambient temperature; additionally, the FP resonator is also sensitive to vibration interference. Further, the methods have poor environmental adaptability and limited working stability.  
Recently, a new type of computational spectrometry combines recent progress in nanophotonics. Etalon arrays, etched thin films, and metasurfaces have been built on the focal plane of detector arrays for the development of micro spectrometers [10; 11; 12; 13; 14]. These methods are also coded in the spectral dimension, and their spectral resolutions are directly constrained by the number of coding arrays. The spectral resolution has exceeded 1 nm, but the fabrication of a large scale metasurface composed of hundreds different coding arrays is not only time-consuming but also costly.  
In summary, fast, snapshot, and integrated spectrometry based on compressed sensing with transmittance coding in the spectral dimension must be studied. In this study, compressed sensing spectrometry based on electro-optic transmittance coding is proposed as an alternative to LCVR, FP and film coding templates. The sinusoidal driven transmittance coding and uncorrelated discrete compression measurement mechanism are explored, and a precision reconstruction algorithm is established. Additionally, a fast hyperspectral compressed measurement method is developed.