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Signal-to-noise ratio prediction for spaceborne imaging spectrometers based on solar elevation angle and surface reflectivity
Background Introduction
Signal-to-noise ratio (SNR) is a crucial indicator of the detection performance of imaging spectrometers, directly impacting the quality of spectral information acquisition from ground objects. In spaceborne imaging spectrometers, SNR determines the effective identification capability of spectral features of targets such as vegetation, water bodies, and minerals. Because observation geometry and surface reflectance characteristics significantly influence entrance pupil radiance, the SNR of imaging spectrometers varies considerably under different solar altitude angles and surface reflectance conditions. Therefore, it is necessary to quantitatively predict the SNR based on typical observation conditions during the instrument design and performance evaluation phases.
Technical Principles
The signal-to-noise ratio (SNR) is defined as the ratio of the number of signal electrons Ns to the total system noise σ.
Given the solar elevation angle and surface reflectivity, the number of signal electrons in a single spectral band of the detector can be expressed as:
In the formula, Lλ is the entrance pupil spectral radiance, Δλ is the spectral bandwidth, A is the pixel area, Ω is the equivalent solid angle, t is the integration time, τ is the system transmittance, η is the quantum efficiency, h is Planck's constant, and c is the speed of light. The total system noise is obtained by superimposing multiple noise sources:
Where, σdarkFor dark current noise, σreadTo read out noise, σas toTo quantize noise, σ2shot=NsThis is photon noise. The entrance pupil spectral radiance can be simulated using the Modtran or 6S model of atmospheric radiative transfer, and based on this, a quantitative assessment of the signal-to-noise ratio for each band can be completed.
Simulation Experiment
Taking a certain type of dispersive spaceborne imaging spectrometer from Xiguang as an example, its signal-to-noise ratio performance was simulated and evaluated. The main parameters of the instrument are shown in Table 1.
Table 1. Partial parameters of a certain model of Xiguang imaging spectrometer
Under radiation conditions of a solar elevation angle of 70° and a surface reflectivity of 60%, the entrance pupil radiance in the visible light band was simulated using MODTRAN software. The main input parameters of the software and the inverted entrance pupil spectral radiance are shown in Table 2 and Figure 1.
Table 2. Main Input Parameters for the Software
Figure 1. Result of entrance pupil radiance inversion
Results and Data Analysis
The entrance pupil radiance curve is obtained by resampling the entrance pupil radiance curve at the center wavelength of the camera and removing the atmospheric absorption peak, as shown in Figure 2.
Figure 2. Resampled entrance pupil radiance curve
The signal-to-noise ratio (SNR) results for each band were further calculated, as shown in Figure 3. The results indicate that the overall SNR distribution across the spectral bands is relatively smooth, with an average SNR of approximately 42.18 dB. In most bands, the system exhibits a photon noise-dominated operating state; readout noise and dark current noise contribute relatively little to the total noise.
Figure 3. Calculation results of signal-to-noise ratio for each channel
A slight decrease in signal-to-noise ratio was observed in some bands, mainly related to the reduction in entrance pupil radiance at the spectral edges or near absorption features, which is a normal physical phenomenon caused by changes in spectral energy distribution. Overall, the imaging spectrometer exhibits good signal-to-noise ratio performance under the set typical observation conditions, and can meet the application requirements for spectral detection and quantitative inversion of ground objects in the visible light band.