Analysis and Validation of the Signal-to-Noise Ratio for an Atmospheric Humidity Profiling Spectrometer Based on 1D-Imaging Spatial Heterodyne Spectroscopy

Sub-kilometer spatial resolution humidity profiles from the stratosphere to the mesosphere are essential for investigating the function of atmospheric water vapor in the global water and energy cycles as well as in radiation transport. The significant variations in atmospheric radiation at low altitudes and the gradual changes at high altitudes pose challenges to the data acquisition and processing methods of limb imaging spectrometers that rely on atmospheric scattering and absorption mechanisms. In this paper, the effects of two binning techniques—interferogram binning and recovered spectrum binning—on improving the spectral signal-to-noise ratio (SNR) are examined through theoretical analysis and simulations, exemplified by a one-dimensional (1D) imaging spatial heterodyne spectrometer designed for measuring atmospheric humidity profiles. Rician random variables are employed to characterize the amplitude of the recovered spectral points under varying signal conditions, from which spectral SNR expressions are derived for both binning methods. The difference in both methods is evaluated through numerical simulations and experiments. Simulation results demonstrate that, with an integration time of 0.3 s and a spectral resolution of 0.03 nm, the input signal below 50 km is strong, with photon noise being the dominant factor, and both binning methods improve SNR proportionally to the square root of the number of binned rows. As the signal weakens above 50 km, additive noise gradually becomes dominant with increasing tangent altitude, and spectrum binning yields a higher SNR than interferogram binning. Experimental data obtained from a similar type of spectrometer further validate these simulation findings. The results indicate that spectrum binning provides greater advantages in improving the SNR for detecting water vapor in the mesosphere, paving the way for achieving a higher vertical resolution in subsequent retrievals.