## 4 Preliminary Performance Considerations for IPDALLS
### First Order Estimation of the Link Budget and Measurement Accuracy
\begin{table}
\begin{tabular}{l l l l} \hline
**Instrument key parameter** & **Unit** & **Value** & **Comment/Origin** \\ \hline Transmitter & & & \\ Pulse energy @ 935 nm & [mJ] & 75 & aligned with [4] \\ Effective pulse length (\(\tau_{L}\)) & [ns] & 75 & aligned with [33] \\ Laser beam divergence (\(\theta_{l}\)) & [\(\mu\)rad] & 15 & system preliminary design (minimize beam broadening) \\ \hline Receiver & & & \\ Telescope diameter (\(D_{\text{rec}}\)) & [m] & 0.50 & system preliminary design \\ Telescope field-of-view (FOV\({}_{\text{rec}}\)) & [\(\mu\)rad] & 280 & system preliminary design, aligned with [33] \\ System optical efficiency (\(\eta_{\text{sys}}\)) & [-] & 0.40 & estimate, aligned with [33] \\ \hline Detector (Excelitas/PerkinElmer Si APD C30954E-DTC) & & \\ Nominal gain (\(M\)) & [-] & 120 & product specification \\ Responsivity @ 900 nm (\(R\)) & [A/W] & 75 & spec, unit gain responsivity estimated as \(R_{0}=R/M\) \\ Maximum peak rating & [mA] & 10 & product specification \\ Surface dark current @ 22 \({}^{\circ}\)C (\(I_{ds}\)) & [nA] & 50 & value obtained from manufacturer \\ Bulk dark current @ 22 \({}^{\circ}\)C (\(I_{db}\)) & [pA] & 200 & value obtained from manufacturer (range 1–200) \\ \hline Retroreflector & & & \\ Effective reflector area (\(A_{\text{ref}}\)) & [m\({}^{2}\)] & 0.20 & system preliminary design \\ Reflector efficiency (\(\eta_{\text{ref}}\)) & [-] & 0.80 & estimate \\ Reflector beam divergence (\(\theta_{r}\)) & [\(\mu\)rad] & 40 & estimate, larger than twice the laser beam divergence \\ \hline \end{tabular}
\end{table} 
Table 1: Specification of instrument components used in the preliminary performance calculations. widely spaced wavelengths. Figure 6(b) shows that below 10 km, very little signal is received from the 532 nm harmonic when considering molecular scattering alone (_i.e._, before considering the effect of aerosol), so synergistic limb-nadir aerosol retrieval would likely be constrained to the stratosphere, where ozone absorption will need to be accounted for. Also plotted is the refractive dilution factor (see, e.g., [PERSON] _et al._[54]), which becomes increasingly relevant for signal attenuation within the UTLS and below. The kink at around 10 km is due to the strong refractive index change at the level of the tropopause. The irregularities and increase of the factor below about 5 km are related to a refractivity decrease in the moist lower troposphere, due to high water vapour contents, and this region is excluded from our performance simulations. A simplified power budget is used to estimate the returned signal energy for the limb sounding measurements, and corresponding profiles are shown in Figure 6(c). Losses are assumed to be mainly due to geometric beam broadening, molecular absorption and scattering, retroreflector and receiver efficiency, continuous as well as turbulent refractive effects and aerosol extinction, the last two of which we have not considered in this study. In practice, many further noise and error sources have to be considered, and a good account of key issues affecting the SNR of a nadir IPDA LiDAR is given in [33]. In this paper, we will for simplicity only consider the carrier-to-noise ratio (CNR) as a means to estimate measurement sensitivity with respect to the water vapour optical depth and expected random errors. To achieve a high CNR, we need to maximize the light throughput of the transmitted beam, by using a high power source with small beam divergence. We simultaneously need to minimize scattered light, by using a high focal number telescope to reduce the field-of-view (FOV). The solar background radiance, the standard limb passive DOAS signal, will be considerable for any daytime measurements in the near-infrared and at visible wavelengths. If scattered sunlight were on the same order of magnitude as the received laser signal, this would considerably limit our observation capabilities.