# Research on Compressed Sensing Spectrometry Based on Electro-Optical Transmittance Coding
## 4 Discussion  
The experimental results of LED light sources demonstrate that the reconstruction relative error does not decrease for \(M\) = 35 measurements. The compressed sensing spectrometry method was manipulated in the visible light band of 0.38-0.78 \(\upmu\)m for spectral  
Figure 8: Laser spectrum measurement experiment: (**a**) Laser light spot; (**b**) Results of compressed sensing spectrum measurements.  
Figure 9: Fluorescent lamp spectrum measurement experiment: (**a**) Laboratory lighting fluorescent lamp source; (**b**) Compressed sensing spectrum measurement result.  
\(N=1024\) channels; thus, the compressed ratio is \(M/N=1\):29, which indicates that the spectrometry achieves a high compressed ratio measurement. The compressed spectral measurement results exhibit good agreement with the results of the commercial spectrometer HR4000. The reconstruction relative error of LED light source is less than 3.79%, whereas the reconstruction relative errors of laser and fluorescent lamp spectrums are slightly more than double. This difference is primarily because laser and fluorescent lamp spectrums have narrower spectral bands compared with the LED light spectrum. Nevertheless, the relative errors are maintained in the order of \(10^{-2}\); thus, their reconstruction accuracy is high.  
The FWHM of the spectral measurement is as high as 1.2 nm, which is slightly more than 0.8 nm of the HR4000 measurement. Furthermore, the spectral resolution can reach approximately 0.4 nm in the visible light band range (0.38\(\sim\)0.78 \(\upmu\)m) with 1024 spectral channels. For comparison, performance of several reported methods were listed in Table 2. Hence, the proposed scheme can achieve more hyperspectral resolution measurements with less measurements. In addition, there are no moving elements in our optical system, and the LiNbO\({}_{3}\) electro-optic crystal has good temperature stability, thus the spectrometry method is not affected by the temperature change and vibration interference.  
The LiNbO\({}_{3}\) electro-optical transmittance coding modulator has a wide allowable light transmission range of 0.35-5 \(\upmu\)m, the detection spectral range can be prolonged to near infrared or shortwave infrared regions. Moreover, the measurement of the compressed spectral signal is completed within 1/4 cycles of the driving voltage of the electro-optic modulator, and the signal measurement time does not exceed 0.25 ms, which is better than the minimum integration time of 4 ms of HR4000. Thus, the proposed method realizes fast and wide spectral range hyperspectral resolution measurements. The size of the LiNbO\({}_{3}\) electro-optic crystal (\(L_{X}\), \(Ly\), \(L_{Z}\)) was selected as 2 mm \(\times\) 4 mm \(\times\) 40 mm in this paper. To ensure sufficient beam aperture and the uniformity of the driving electric field, it is best to set the light passing area (\(xoy\) plane) to 2 mm \(\times\) 4 mm. It is appropriate to set the length of crystal (\(L_{Z}\)) to 20 mm to 60 mm. Significantly, the shorter the length is, the easier it is to align the optical path. While a higher driving voltage needs to be provided to obtain the irrelevant transmittance elements for the coding measurement matrix \(\Phi\) according to Equations (2) and (5).