## Appendix: Details of SNR and Error Calculations for the IPDALLS System
Rayleigh scattering cross sections have been roughly estimated using [78]:  
\[\sigma^{R}=\frac{128\pi^{5}\alpha_{0}^{2}\left(6+3\rho_{n}\right)}{3\lambda^{4} \left(6-7\rho_{n}\right)}, \tag{5}\]  
with a depolarization factor \(\rho_{n}\) [-] for naturally polarized light and a volume polarizability \(\alpha_{0}\) [cm\({}^{3}\)] for standard air, giving \(\sigma_{532}^{R}=4.937e^{-31}\) m\({}^{2}\), \(\sigma_{935}^{R}=5.175e^{-32}\) m\({}^{2}\) and \(\sigma_{1064}^{R}=3.086e^{-32}\) m\({}^{2}\). The molecular scattering coefficients \(\gamma_{s}\) [m\({}^{-1}\)] follow by multiplying the cross sections by the molecular number densities in the standard atmosphere as a function of height. The atmospheric optical thickness \(\tau_{s}\) for limb sounding has then been calculated by integrating  
\[\tau_{s}\cong\sqrt{2R_{E}}\int_{h_{0}}^{\infty}\frac{\gamma_{s}\left(h\right) }{\sqrt{h-h_{0}}}dh, \tag{6}\]  
from the tangent height of the limb sounding \(h_{0}\) to an altitude of 90 km at which scattering is assumed to be negligible, where \(R_{E}\) denotes the radius of the Earth [79]. More detailed radiative transfer modelling studies, beyond the scope of this preliminary analysis, would be required to take into account Mie scattering and different atmospheric conditions, as well as a more realistic limb sounding geometry, scintillation, and related effects. Since we hypothesize that the use of optimally designed retroreflectors should limit interference and therefore target-generated speckle noise, and since we do not have a fully designed detection electronic circuit with given elements and measured statistical fluctuations, we limit the modelling of the SNR to the carrier-to-noise ratio CNR [33, 80]:  
\[SNR\cong CNR\cong P_{r}MR_{0}/\sqrt{B_{W}2q\left[\left(M^{2}FR_{0}\left(P_{r} +P_{\text{bkgrd}}\right)\right)+\left(I_{ds}+I_{db}M^{2}F\right)\right]}, \tag{7}\]  
where \(M\) [-] is the detector internal gain factor, \(R_{0}\) [A/W] the detector's unit gain responsivity, \(B_{W}\) [Hz] the amplifier bandwidth, \(q\) [C] the elementary charge, \(F\) [-] the detector's excess noise factor, \(P_{\text{bkgrd}}\) [W] the background radiance and \(I_{ds,b}\) [A] the detector's surface and bulk dark currents, respectively. In this expression, the numerator corresponds to the signal photocurrent [A], and the denominator to the total noise current in a Si avalanche photodiode (Si APD). Apart from external noise, we limited the analysis to detector noise and have disregarded contributions from the electrical amplification process, _i.e._, amplifier input noise current, input voltage noise current and thermal noise from the feedback resistor. Noise originating from outside the receiver is referred to as external noise (Equation 7, first term in the square brackets). External noise will mainly include signal shot noise (proportional to \(P_{r}\)), as well as high-frequency emission of radiation from outside sources within the receiver FOV, predominantly from auroras (not considered), and sunlight reaching the telescope, either by single and multiple scattering, or by direct irradiation (\(P_{\text{bkgrd}}\)). The scattering of sunlight depends mainly on solar elevation and azimuth, as well as measurement height. Here, a rough estimate for Rayleigh-only scattering of solar radiation into a receiver in occultation geometry is calculated after a simplified model presented in [81]. We calculated a profile of directional Rayleigh scattering coefficients \(\gamma_{R}(z,\lambda)\) [km\({}^{-1}\)sr\({}^{-1}\)] in the 1976 US Standard Atmosphere with a MIPAS daytime standard water vapour profile, using the modified-Edlen formula for the refractive index, and under the baseline assumption of a scattering normalized phase function corresponding to a \(0^{\circ}\) solar azimuth angle relative to the occultation plane and a 60\({}^{\circ}\) solar zenith angle at the tangent point.