Simulation and optimization of Fe resonance fluorescence lidar performance for temperature-wind measurement

Cheng Li; Cheng Li; Cheng Li; Decheng Wu; Decheng Wu; Decheng Wu; Qian Deng; Qian Deng; Fei Cui; Zhiqing Zhong; Zhiqing Zhong; Dong Liu; Dong Liu; Dong Liu; Yingjian Wang; Yingjian Wang

doi:10.1364/OE.455189

1. Introduction

The neutral atmosphere in the mesosphere and lower thermosphere (MLT, ∼75-115 km) region is quite thin; thus, the Rayleigh backscattered signal is also very weak. The Rayleigh method can theoretically be used to measure temperature and wind velocity in this region, but it must employ a huge power-aperture lidar system to improve signal-to-noise ratio, which is difficult to implement [1]. Fortunately, the nature provides metal atoms, such as, Na, K, Fe, and Ca, to us as tracers [2]. When the emitted laser irradiates the MLT region and the wavelength is just on the characteristic absorption spectrum of the metal atom, it will absorb the photon and jump to the ground-state by spontaneous radiation to produce resonance fluorescence [3]. Although the density of metal atoms only accounts for one-tenth that of molecules at the same height, the resonance fluorescence backscatter cross section is about fifteen orders of magnitude larger than that of molecules [4,5]. The intensity of the signal is approximately equivalent to that of the Rayleigh signal at 30-40 km, where the measurement accuracy is already relatively high. Therefore, resonance fluorescence lidar is a powerful tool to study the complex atmospheric dynamics in the MLT region.

The first resonance fluorescence lidar was established in 1968 [6] and the first successful temperature measurement for Na lidar was studied in 1978 [7]. Sodium atoms became an ideal tracer due to their large density and backscatter cross section [1,8]. In 1994, She et al. proposed the three-frequency ratio technique [9], and from then on, Na lidar system began to develop rapidly. It mainly adopts an acousto-optic modulator (AOM) to adjust the narrowband laser central frequency to the opposite ends of the sodium atomic resonance line. Combined with the large-aperture telescope, high accuracy approaching 1 K and 1 m/s can be achieved at night with resolutions of a few ten minutes and a few thousand meters [10]. However, the Na lidar requires a relatively stable operating environment, which limits its development in harsh and remote areas, such as, the North and South Poles, airborne and shipboard, and even satellite-borne platforms in the future [1]. Compared with sodium atoms, the effective backscatter cross section of iron atoms (372 nm) is approximately 15 times smaller, but the density of iron atoms is 2-4 times higher than that of sodium. Therefore, there is no significant difference in the signal levels between iron and sodium layers [11]. More importantly, the operating wavelength is near-ultraviolet, therefore, the Rayleigh signal is greatly enhanced compared with sodium (589 nm) and potassium (770 nm) [8,12]. It is possible to use Fe lidar as a Rayleigh lidar below the MLT region. Next, the nuclear of ⁵⁶Fe is zero; thus, ⁵⁶Fe has no hyperfine splitting, and its absorption cross section is about 73 times smaller than that of sodium. Therefore, under the same saturation effects, Fe lidar can generate the laser of higher power density, and it can allow smaller field of view, which are especially crucial for daytime measurement [13]. Finally, the German Aerospace Center (DLR) successfully applied a diode-pumped Nd:YAG laser to ground-based Fe lidar and worked on airborne system research. Compared with common alexandrite lasers, the size is greatly reduced, the technology is mature, and it also has higher efficiency and stability at the same laser power [13]. This is especially suitable for airborne and shipboard environments. Based on the above points, Fe lidar is another ideal candidate for future “whole atmosphere lidar”.

In 1998, the University of Illinois at Urbana-Champaign, cooperating with the Aero-space Corporation and the National Center for Atmospheric Research, successfully developed a broadband Fe Boltzmann lidar using an injection-seeded, frequency-doubled, and flashlamp-pumped alexandrite laser. The power-aperture was 0.39 Wm². The wavelengths were 372 nm and 374 nm. The temperature accuracy was about 5 K with resolutions of 2 h and 1 km [1,14]. Chu Xinzhao’s research group from the University of Colorado at Boulder started to develop Fe lidar in 2007, using a flashlamp-pumped pulsed alexandrite ring Laser. The power-aperture was about 0.2 Wm², the receiver field of view (FOV) was 500 µrad, and the expected measurement accuracy was less than 1.1 K and 1.5 m/s with resolutions of 1 h and 1 km [12]. In addition, much progress has also been made in the design of high-efficiency lidar [15], innovations in wind discriminators [16], and data processing [17], which has been successfully applied to Fe lidar systems in recent years. In 2007, the Leibniz Institute (IAP) in Germany successfully developed a scanning alexandrite-laser-based Fe lidar system [18]. The wavelength was 386 nm. The power-aperture was reduced to 0.06 Wm² and the FOV was compressed to 54 µrad due to saturation effect. The daytime accuracy was 5 K and 1.4 m/s when the resolutions are 1 h and 1 km. In 2015, DLR started to generate 372 nm laser through the third harmonic generation of a Nd:YAG laser operating at 1116 nm wavelength. The power-aperture was about 0.065 Wm². The FOV was 0.4 mrad [13]. Subsequently, the maximum of power-aperture of this system was upgraded to 2.8 Wm², but the lidar would suffer from severe saturation effect, therefore, DLR chose the power-aperture as 0.6 Wm². The first flight experiment was conducted in 2019, however, it didn’t have temperature and wind results above 70 km. In China, only Wuhan University has developed a Fe Boltzmann lidar that is supported by dye lasers [19]. Till now, Fe lidar has acquired many desirable results and it even has some observations of neutral Fe layers from 110 km to 155 km with amazing system efficiency [15,20]. However, it is still hard to confirm what level of measurement performance can be achieved. We had better construct a theoretical model of Fe lidar to have a complete understanding of system performance before the system prototype is completed, and we can check whether the lidar system is completed according to the design specifications. This was previously defective.

In this paper, detailed description of the Fe lidar model is presented in the part of Simulation model. The relationship between temperature-wind and the lidar equation is obtained by the principle of Fe lidar, the impact factors of measurement are proposed and the night and daytime calibration curves are presented in Section 2.1. The expressions for the temperature-wind uncertainties and the signal-to-noise ratio of the lidar equation are derived and optimized using the error propagation method. The corresponding minimum signal-to-noise ratio is obtained according to the required accuracy in Section 2.2. In Section 2.3, according to the minimum signal-to-noise ratio and the impact factors, the index decomposition of the main parameters of the Fe lidar is carried out. In the part of Results and discussion, the performance of Fe lidar are simulated through the specific value after index decomposition, and some discussion and limitations are also conducted. In the end of the paper, conclusions and outlook are demonstrated.

2. Simulation model

In the early stage of development, we should preliminarily determine the theoretical parameters of each part of the lidar components. Therefore, parameter simulation is an indispensable part of the lidar system design and research. Figure 1 shows a parameter simulation model of Fe lidar. Section 2 will discuss the process and key point of this simulation model, mainly including, principle, uncertainty caused by photon noise error, simulation and optimization of parameters, and potential temperature-wind measurement performance.

Fig. 1. Simulation model of Fe lidar.

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2.1 Principle and the impact factors of measurement

It is assumed that the iron atoms are in the thermal equilibrium state and they undergo random thermal motion. Due to the Doppler shift effect, when the central frequency f₀ of the fluorescence photon is moving with velocity V_R relative to the observer, the observed fluorescence photon frequency is shown as Eq. (1) [3]

(1)$$f = {f_0} \pm {V_R}/{\lambda _{Fe}}.$$

In the detection direction, various groups of atoms with different velocities will have different jump frequencies. The velocity distribution of iron atoms obeys the Maxwell-Boltzmann distribution law, and the average absorption cross section of the detected absorption spectral lines will be the single-atom absorption cross section to integrate the velocity distribution. Therefore, the average absorption cross section can be expressed as Eq. (2) [12]

(2)$${\sigma _{abs}}({{f_0},T,{V_R}} )= \frac{1}{{\sqrt {2\pi } {\sigma _{Fe}}}}\frac{{{e^2}{f_{ik}}}}{{4{\varepsilon _0}{m_e}c}}\exp \left[ { - \frac{{{{({{f_{Fe}} - f} )}^2}}}{{2\sigma_{Fe}^2}}} \right],$$

(3)$${\sigma _{Fe}} = \sqrt {{k_\textrm{B}}T/{M_{Fe}}{\lambda _{Fe}}^2} = \sqrt {\gamma T} ,$$

where σ_Fe is the Doppler broadening; k_B is the Boltzmann constant; M_Fe is the Fe mass; T is the atmospheric temperature; λ_Fe is the laser emitting wavelength of Fe lidar; e is the electron charge; f_ik is the oscillator strength; ε₀ is the permittivity of free space; m_e is the electron mass; and f_Fe is the central frequency of the iron resonance absorption line. Taking into account the natural broadening mechanism of the laser, the total scattering cross section should be the convolution of the average absorption cross section and laser linewidth. Therefore, the effective scattering cross section can be shown as Eq. (4)

(4)$${\sigma _{eff}}({{f_0},T,{V_R}} )= \frac{1}{{\sqrt {2\pi } {\sigma _e}}}\frac{{{e^2}{f_{ik}}}}{{4{\varepsilon _0}{m_e}c}}\exp \left[ { - \frac{{{{({{f_{Fe}} - f} )}^2}}}{{2\sigma_e^2}}} \right],$$

(5)$${\sigma _e} = \sqrt {\sigma _{Fe}^2 + \sigma _\textrm{L}^2} ,$$

where σ_L is the laser linewidth. Since iron atoms have four stable isotopes in nature, ⁵⁴Fe, ⁵⁶Fe, ⁵⁷Fe and ⁵⁸Fe, they will cause different degrees of drift in the central frequency of the absorption spectrum. As the Table 1 shows, after considering Fe isotopes, the effective scattering cross section is Eq. (6), and Eq. (7) is the concrete form

(6)$${\sigma _{eff}}({{f_0},{f_{Fe}},T,{V_R}} )= \sum\limits_{n = 1}^4 {{\sigma _{eff,n}}} (isotope) \times {A_n},$$

(7)$${\sigma _{eff}}({{f_0},T,{V_R}} )= \frac{1}{{\sqrt {2\pi } {\sigma _e}}}\frac{{{e^2}{f_{ik}}}}{{4{\varepsilon _0}{m_e}c}}\sum\limits_{n = 1}^4 {{A_n}} \exp \left[ { - \frac{{{{({{f_{Fe}} - f} )}^2}}}{{2\sigma_e^2}}} \right],$$

where A_n is the relative abundance of stable isotopes. Figure 2 shows that the effective scattering cross section is very sensitive to the changes in temperature and wind velocity, which can be measured based on this feature. If the experiment ignored the isotope effects and considered ⁵⁶Fe only, it would lead to a larger effective scattering cross section and an increase in spectral width, eventually resulting in a 20 K temperature bias [12].

Fig. 2. (a) The effective scattering cross section considering the isotopes (solid line), ⁵⁶Fe effective scattering cross section (dashed line) for different wind velocity at T = 200K; (b) The effective scattering cross section considering the isotopes (solid line), ⁵⁶Fe effective scattering cross section (dashed line) for different temperature at V_R= 0m/s.

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Table 1. Isotopic Data of Fe Atoms [10]

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To measure temperature and wind velocity simultaneously, Fe lidar utilizes the classical three-frequency ratio technique, whose advantage is that fast switching between the three frequencies eliminates errors caused by Fe density fluctuations during data collection. According to the three frequencies (f₀, f₊, f_-), the temperature response function R_T and the wind velocity response function R_V can be defined as Eqs. (9) and (10) [8,12]

(8)$${f_ + } = {f_0} + \delta f, {f_ - } = {f_0} - \delta f,$$

(9)$${R_T} = \frac{{{N_{Fe}}({{f_ + }} ){N_{Fe}}({{f_ - }} )}}{{N_{Fe}^2({{f_0}} )}},$$

(10)$${R_V} = \frac{{\ln [{{N_{Fe}}({{f_ - }} )/{N_{Fe}}({{f_ + }} )} ]}}{{\ln [{{N_{Fe}}({{f_ + }} ){N_{Fe}}({{f_ - }} )/N_{Fe}^2({{f_0}} )} ]}}.$$

These ratios are sensitive functions of temperature and wind, and they obey the Maxwell–Boltzmann distribution law under thermodynamic equilibrium. Where, δf is the central frequency shift, and N_Fe is the expected photon count at different frequencies. The lidar equation for f₀ can be expressed as Eq. (11) [3]

(11)$${N_{Fe}}({f_0}) = (\eta G)\left( {\frac{{{P_L}\tau }}{{hc/{\lambda_{Fe}}}}} \right)\left( {\frac{A}{{4\pi {z^2}}}} \right)\mathrm{\Delta }z[{{\sigma_{eff,\pi }}({f_0}){n_{Fe}}} ]({T_{a,m}^2T_{Fe}^2} ),$$

(12)$${T_{Fe}} = \exp \left[ { - \int_{{z_{\textrm{bottom }}}}^z {{\sigma_{eff,\pi }}{n_{Fe}}} (z)\textrm{d}z} \right],$$

where η is the total system efficiency, which includes the laser transmitting system efficiency, receiving system efficiency and detector quantum efficiency. G is the geometric factor; P_L is the laser power; τ is the integration time; h is Planck’s constant; A is the telescope aperture area; z ranges from the scatter to the lidar receiver; n_Fe(z) is the Fe density; T_a,m is the one-way atmosphere transmittance, which considered the extinction of aerosols and molecules; T_Fe is the additional iron layer transmittance. It is assumed that Fe density remains constant during a short period of time, combined with the Eq. (11), R_T and R_V can be simplified as follows

(13)$${R_T} = \frac{{\sigma _{eff}^{}({{f_ + },T,{V_R}} )\sigma _{eff}^{}({{f_ - },T,{V_R}} )}}{{\sigma _{eff}^2({{f_0},T,{V_R}} )}} = \exp ({ - \delta {f^2}/\sigma_e^2} )= {e^{ - \alpha }},$$

(14)$${R_V} = \frac{{\ln [{\sigma_{eff}^{}({{f_ - },T,{V_R}} )/\sigma_{eff}^{}({{f_ + },T,{V_R}} )} ]}}{{\ln [{\sigma_{eff}^{}({{f_ + },T,{V_R}} )\sigma_{eff}^{}({{f_ - },T,{V_R}} )/\sigma_{eff}^2({{f_0},T,{V_R}} )} ]}} = \frac{{ - 2{V_R}}}{{{\lambda _{Fe}}\delta f}}.$$

Based on the Eqs. (13), and (14), the calibration curves are theoretically calculated from a range of temperatures and wind velocities. Night curve and daytime curve differs because of different optimum frequency shifts of AOM (As section 2.2 shows.). Considering the influence of Fe isotopes, a decrease of the peak and a broadening of the spectral line leads to a deviation of pure Gaussian line shape, which results in a calibration curve rather than a straight curve. As Fig. 3 shows, the calibration curves have homogeneous sensitivity for different temperatures and wind velocities, which illustrate that Eqs. (9) and (10) are the appropriate choice. During the data processing, we put what we got in the experiment R_T and R_V into the curve to find the corresponding temperatures and wind velocities. In addition, the Hanle effect can be overlooked [21]. It only changes the intensity of the atomic spectrum without changing the spectral line shape and frequency; thus, there is no influence on R_T and R_V.

Fig. 3. The calibration curves. (a). Night; (b). Daytime

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Resonance fluorescence backscattered signals are generally selected as 40-50 km Rayleigh signals for system calibration. According to the Eq. (11), increasing the laser power, iron resonance fluorescence and Rayleigh photons should have increased linearly. However, due to the saturation effect, a resonance fluorescence photon stimulates a particle without a hundred percent of probability, but the Rayleigh photon can stimulate it. Therefore, the laser power increases to a certain extent, resonance fluorescence photons are no longer linearly increasing. The calibration results will become larger than the actual results, which leads to temperature and wind velocity larger than the actual values [3]. As for iron atoms, it has no hyperfine structure, the saturation effect can be calculated quantitatively by defining the saturation time [22,23]. The saturation time can be expressed as Eq. (15)

(15)$${t_\textrm{S}} = \frac{{{z^2}\Omega \Delta {t_\textrm{L}}}}{{2{\sigma _{eff,\pi }}{N_\textrm{L}}T_{a,m}^{}T_{Fe}^{}}},$$

(16)$$\Omega = \frac{\pi }{4}\theta _\textrm{L}^2,{N_\textrm{L}} = \frac{E}{{hc/{\lambda _{Fe}}}},$$

where Ω is the solid angle; θ_L is the beam divergence (full angle); Δt_L is the laser pulse duration; N_L is the total number of emitted photons related to single pulse energy. From Eq. (15), we can see that t_s is related to laser parameters, such as, the beam divergence, laser pulse duration, laser pulse energy, and t_s is also related to atomic physical parameters, such as, effective scattering cross section and atmosphere transmittance. The larger t_s is, the less likely the atoms will be saturated, which means that the larger the beam divergence is, the longer the pulse duration is, and the smaller the laser pulse energy is, the easier suppressing saturation effects will be. The saturation effects limit the usage of very high laser power densities to improve the signal-to-noise ratio (SNR) for daytime measurement. Therefore, it requires being traded off in the simulation. A method for determining saturation effects was proposed by G. MEGIE et al. [23], as early as 1978. The calculation formula is shown as Eq. (17)

(17)$${R_s} = \frac{{N_\textrm{S}^{\textrm{Sat}}(\lambda ,z)}}{{N_\textrm{S}^{}(\lambda ,z)}} = \frac{1}{{1 + ({{\xi_\textrm{R}}/{t_\textrm{S}}} )}}\left\{ {1 - \frac{{{\xi_\textrm{R}}}}{{\Delta {t_\textrm{L}}}}\frac{{({{\xi_\textrm{R}}/{t_\textrm{S}}} )}}{{1 + ({{\xi_\textrm{R}}/{t_\textrm{S}}} )}}} \right.\left. { \times \left[ {\exp \left( { - \frac{{\Delta {t_\textrm{L}}}}{{{\xi_\textrm{R}}}}\left( {1 + \frac{{{\xi_\textrm{R}}}}{{{t_\textrm{S}}}}} \right)} \right) - 1} \right]} \right\},$$

(18)$$P_{Fe}^{\textrm{Sat}} = ({1 - {R_s}} )\times \mathrm{100\%,}$$

where ξ_R is the radiative lifetime of the atoms. If ξ_R is zero for instantaneous scattering, such as Rayleigh and Mie, R_s will be one, which means there is no saturation effect. P_Fe^Sa^t is the saturation rate. It is assumed that R_s is equal to 0.99, and the metal layer in the MLT region will have one percent of atoms saturated.

2.2 Temperature-wind uncertainty

There are many factors that cause temperature and wind velocity measurement errors, such as, photon noise, random fluctuations in the laser frequency and linewidth, and fluctuations in iron layer temperature, wind, and density [10]. For the theoretical simulation of the lidar system, the random errors caused by the photon noise are important issues to be considered. The temperature and wind velocity can be obtained from Eqs. (3), (5), (13) and (14), respectively

(19)$$T ={-} \frac{{\delta {f^2}}}{{\gamma \ln {R_T}}} - \sigma _L^2/\gamma ,$$

(20)$${V_R} ={-} \frac{{{\lambda _{Fe}}\delta f}}{2}{R_V}.$$

According to the error propagation method [24], the specific formula derivation process is shown in the Appendix, and the respective uncertainties are derived as follows

(21)$$\Delta T = \frac{{\sigma _e^4}}{{\gamma \cdot \delta {f^2}}}\frac{{\Delta {R_T}}}{{{\textrm{R}_T}}} = \frac{2}{\alpha }{\left[ {\frac{{{e^\alpha }({1 + \beta {e^{ - \alpha /2}}} )}}{{(1 - \psi )(1 + \beta )}} + \frac{1}{\psi }} \right]^{1/2}} \cdot \frac{{(T + \sigma _L^2/\gamma )}}{{SN{{R}_0}}},$$

(22)$$\Delta {V_R} = {V_R}\sqrt {{{(\frac{{\Delta {\textrm{R}_V}}}{{{\textrm{R}_V}}})}^2}} = {\left[ {\frac{{{e^\alpha }({1 + \beta {e^{ - \alpha /2}}} )}}{{\alpha (1 - \psi )(1 + \beta )}}} \right]^{1/2}} \cdot \frac{{{\lambda _{Fe}}\sqrt {\sigma _{Fe}^2 + \sigma _\textrm{L}^2} }}{{SN{{R}_0}}},$$

where

(23)$$SN{{R}_0} = \sqrt {N_{Fe}^2({{f_0}} )/[{N_{Fe}^{}({{f_0}} )+ {N_B}} ]} = \sqrt {N_{Fe}^{}({{f_0}} )/(1 + {\beta ^{ - 1}})} ,$$

(24)$$\beta = N_{Fe}^{}({{f_0}} )/{N_B},$$

Ψ is the dwell time of the lidar works in the f₀ state, which can be set by the AOM as required; N_B is mainly influenced by sunlight background noise counts, and β is the ratio of expected photon counts at central frequency and background noise counts, which β is much larger than one at night and smaller than one during the day, theoretically. To obtain much smaller errors caused by photon noise, the dwell time, central frequency shift and laser linewidth should be optimized. Since linewidth is an important parameter of lasers, which limited by frequency chirp, we set it to 35 MHz similarly based on the level of spectral properties of existing lasers [10,16]. The coefficients of uncertainty are set to A and B. It can be expressed as

(25)$$A = \frac{{2(T + \sigma _L^2/\gamma )}}{\alpha }{\left[ {\frac{{{e^\alpha }({1 + \beta {e^{ - \alpha /2}}} )}}{{(1 - \psi )(1 + \beta )}} + \frac{1}{\psi }} \right]^{1/2}},$$

(26)$$B = {\lambda _{Fe}}\sqrt {\sigma _{Fe}^2 + \sigma _\textrm{L}^2} {\left[ {\frac{{{e^\alpha }({1 + \beta {e^{ - \alpha /2}}} )}}{{\alpha (1 - \psi )(1 + \beta )}}} \right]^{1/2}},$$

(27)$$C = {({A^2} + {B^2})^{1/2}}.$$

The effects of the dwell time and central frequency shift on A and B are shown in the Fig. 4, and the values are the minimum results after optimization. It is clear from the color change that the temperature is more sensitive to the change of the parameter than the wind velocity. Interestingly, when the dwell time is set to zero, the wind error is minimum. Of course, in this case, it would not be possible to measure temperature, but most of the time, we need to measure temperature and wind simultaneously, which is weighted equally. Therefore, the same method as Gardner is adopted [10]. The method combines the optimum results from temperature and wind, but differently, this simulation model considers the performance at night and daytime precisely. The optimization function to C is set in Eq. (27). Table 2 shows minimum error and corresponding dwell time and frequency in the left column. And it shows the optimum error after considering temperature and wind velocity at daytime and night and corresponding dwell time and frequency in the right column. The results are different from Gardner’s, because some additional factors have been taken into account. Therefore, the calibration curves are different for daytime and night, as Fig. 3 shows.

Fig. 4. Optimization of the dwell time and central frequency shift to obtain minimum values of A and B. (a). Temperature optimization at night; (b). Temperature optimization at daytime; (c). Wind velocity optimization at night; (d). Wind velocity optimization at daytime.

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Table 2. Temperature-wind uncertainty after dwell time and central frequency shift optimization

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To obtain a high accuracy of 1 K and 1 m/s at night, SNR_night must be larger than 378, and the expected accuracy is 3 K and 3 m/s at day due to the strong sunlight background noise, SNR_day should also be larger than 246. If the above accuracy is to be met, the methods to improve SNR of conventional lidar is increasing the transmitting power and reducing the FOV. However, the saturation effects limit the usage of high laser power densities to detect iron atoms in the MLT region. If the power density is reduced by increasing beam divergence, it would be bound to cause some problems. To ensure the reception efficiency, it is inevitable to increase the FOV. The direct way of improving SNR is to increase the aperture of the receiving telescope, but we should consider the difficulties of consequent processing, limitations of the airborne and shipboard space, and problems of achieving daytime measurement. Therefore, the saturation effects have put forward stringent requirements for Fe lidar design. Next section, we will carefully analyze the impact of saturation effects and decompose the parameters of lidar and atmosphere.

2.3 Index decomposition

To describe the effect of each parameter clearly on the backscattered photon counts, the Eq. (11) is written in the form of the product of two terms as Eq. (28)

(28)$${N_{Fe}}({f_0}) = X \cdot Y,$$

(29)$$X = ({\sigma _{eff,\pi }}{n_{Fe}})({T_{a,m}^2T_{Fe}^2} ),Y = (\eta G)\left( {\frac{{{P_L}\tau }}{{hc/{\lambda_{Fe}}}}} \right)\left( {\frac{A}{{4\pi {z^2}}}} \right)\mathrm{\Delta }z,$$

where X is related to atmospheric parameters only. X is called the atmospheric term. Y is related to lidar parameters only, which is called the lidar term.

In the atmospheric term, the main influencing parameters are Fe density and atmospheric transmittance at the iron layer. Fe density varies with seasons and latitudes, it is also affected by waves [25,26]. Thus, we use the mean density data detected by the Fe Boltzmann lidar of Wuhan University as a representative [27]. Most research has focused on the primary iron layer between 80 and 100 km, where the metal densities can exceed 10⁴ cm^-3 [10]. In addition, the WACCM-Fe model [28] has been proposed by the University of Leeds, which is also a reliable data source for simulation. Atmospheric transmittance from the ground to 100 km takes account of the extinction of aerosols and molecules and the extinction of iron atoms above 80 km

(30)$${${T_{\textrm{total}}} = T_a^{}T_m^{}T_{Fe}^{} = \exp \left( { - \int_{0km}^{30km} {{\alpha_a}_\textrm{ }} \textrm{d}z} \right) \cdot \exp \left( { - \int_{0km}^{1\textrm{0}0km} {{\alpha_m}_\textrm{ }} \textrm{d}z} \right) \cdot \exp \left[ { - \int_{80km}^{1\textrm{0}0km} {({\sigma_{eff,\pi \textrm{ }}}{n_{Fe}})\textrm{d}z} } \right]$},$$

where α_a is the extinction coefficient of aerosol, and the data [29] were measured by the local lidar in Hefei, China. α_m is the extinction coefficient of molecules, which can be described by Eq. (31)

(31)$${\alpha _m} = \frac{{8\pi }}{3} \times 1.54 \times {10^{ - 3}}\exp ( - z/7){\left( {\frac{{532}}{{{\lambda_{Fe}}}}} \right)^4}.$$

The simulation results are shown in Fig. 5(b), and the two-way atmosphere transmission T²_total at the peak altitude is 0.292.

Fig. 5. (a). Fe density; (b).one-way atmospheric transmission including aerosols, molecules, and iron atoms.

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The main influencing parameters of the lidar term include laser wavelength, beam divergence, laser pulse duration, laser power, telescope aperture and total system efficiency. The value of the power-aperture product has been widely used as an index to compare the performance and to assess the figures of merit of atmospheric lidar [5]. During daytime measurement, how to suppress strong background noise should also be considered. The atmospheric term parameters have their own physical properties and they cannot be changed artificially, while the lidar term parameters are stable and controllable. To achieve the expected accuracy, optimizing lidar term parameters becomes the core content of the simulation within the permissible range of the saturation effect.

The absorption lines of iron atoms in the ultraviolet region are mainly located in the bands of 372 nm, 374 nm, and 386 nm. The 372 nm wavelength, which is generated by the transition from the ground state a⁵D₄ to the excited state z⁵F₅. It has the largest intensity, which is approximately twice that of the 386 nm line [12,13]. It means that Fe lidar with a 372 nm wavelength can obtain a backscattered signal twice as strong as 386 nm, which is beneficial to improve SNR, at the same laser power.

In general, the saturation rate must be less than one percent to ensure the measurement accuracy of temperature and wind velocity. When beam divergence is compressed to 0.2 mrad, the laser power density can be kept constant by reducing the pulse energy or increasing the pulse duration. It ensures that the saturation rate does not increase. But the laser reduces the pulse energy, and correspondingly, backscattered signal also decreases. Therefore, SNR cannot be improved. In contrast, increasing the pulse duration is a more reasonable method. As it shown in Fig. 6, when laser pulse energy is 30 mJ and pulse duration is 50 ns, the saturation rate was less than one percent. The wider the pulse duration is, the greater the allowed laser pulse energy will be. It helped to further improve SNR.

Fig. 6. Effect of laser energy and pulse duration on the saturation rate.

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According to Eqs. (11) and (23), the night SNR and the total system efficiency are shown as

(32)$$SN{{R}_{night}} \approx \sqrt {N_{Fe}^{}({{f_0}} )} ,$$

(33)$${\eta _{night}} = SNR_{night}^2/\left[ {G\left( {\frac{{{P_L}\tau }}{{hc/{\lambda_{Fe}}}}} \right)\left( {\frac{A}{{4\pi {z^2}}}} \right)\mathrm{\Delta }z[{{\sigma_{eff}}({f_0}){n_{Fe}}} ]({T_{a,m}^2T_{Fe}^2} )} \right].$$

It is assumed that Fe lidar system can achieve measurement accuracy of 1 K and 1 m/s at resolutions of 10 min and 1000 m, the system efficiency should be at least 12.5 percent when the power-aperture is 1.41Wm². To realize lidar observations in full daylight, it is also essential to reduce the solar background to improve SNR. Since there is no suitable atomic absorption spectrum at 372 nm, unlike the Faraday atomic filter widely use on Na and K lidar systems, Fe lidar utilizes a single-channel Fabry-Perot etalon to achieve narrow-band filtering [18]. The daytime SNR and the background noise counts [8] are expressed as

(34)$$SN{{R}_{day}} = \sqrt {N_{Fe}^2({{f_0}} )/N_{Fe}^{}({{f_0}} )+ {N_B}} \approx \sqrt {SNR_{night}^4/{N_B}} ,$$

(35)$${N_B} = \frac{{{\lambda _{Fe}}}}{{hc}}{P_b}\pi {({\theta _{FOV}}/2)^2}{d_{FP}}A{\eta _r}(2\Delta z/c) \cdot \tau {r_L},$$

(36)$${\eta _{day}} = \frac{{{\psi _{opt - night}}}}{{{\psi _{opt - day}}}}{\eta _{night}},$$

where P_b is the background sky spectral radiance, which depends on many factors, including the elevation angle of the Sun, the pointing direction of the lidar relative to the Sun, the altitude of the lidar, and the laser wavelength [8]. We estimate its value by MODTRAN, and the results are presented in Fig. 7. θ_FOV is the FOV (full angle); d_FP is the optical bandwidth of the Fabry-Perot etalon; η_r is the optical efficiency of the telescope including detector quantum efficiency; r_L is the laser repetition rate. Assuming that the temporal and spatial resolutions are still 10 min and 1000 m during the day, and suppressing the N_B below 376⁴/244² from Eq. (34), an additional 5.5 pm optical bandwidth of the Fabry-Perot etalon is needed on the base of the interference filter, at the same time, the total efficiency of the daytime system should be at least 12.09 percent.

Fig. 7. Background sky spectral radiance at moon for zenith observations at sea level under conditions of excellent visibility with the Sun at an elevation of 75°

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The transmittance of Fabry-Perot etalon affects the total efficiency of the system, so it is only moved into the optical path during the day. Therefore, to obtain a peak transmittance, a high fineness of the Fabry-Perot etalon is required unlike the ultrahigh fineness of IAP system [18]. According to design theory [30], if the optical bandwidth is 5.5 pm and the fineness requirement is 15, the peak transmittance is 71 percent in this situation. In other words, only when the total efficiency at night reaches 17.03 percent, can the accuracy of 3 K and 3 m/s during the day be met after moving into the Fabry-Perot etalon for the resolutions of 10 min and 1 000 m. This is not the major challenge. Because the current quantum efficiency of the detector working in photon-counting mode at 372 nm can reach 40 percent [16], and optical system devices have relatively high transmittance, such as, receiver mirrors and interference filters.

3. Results and discussion

Our analysis is derived from the uncertainties of temperature and wind velocity in Section 2, which is based on the derivation of the error propagation method. To achieve measurement accuracy of 1 K and 1 m/s at night and 3 K and 3 m/s during the daytime, and to ensure the saturation rate of Fe lidar system is less than one percent, the lidar parameters are simulated and optimized in detail. The results are listed in Table 3.

Table 3. Key lidar parameters from simulation and optimization

View Table | View all tables in this article

We can refer to the value in Table 3 to simulate the measurement performance of Fe lidar at night and day under different spatial and temporal resolutions, and then estimate the approximate accuracy, which can be achieved at a specific resolution, as shown in Table 4. No matter the time is day or night, when the resolutions are 10 min and 1000 m, the accuracy set in Section 2 has long been met. The most influential factor of the index decomposition is power-aperture. If the telescope aperture is limited by environmental conditions, the long-pulse-duration and high-power laser operating at 372 nm wavelength is particularly important. the maximum power of DLR’s system has reached to 6W, but saturation effect limits the application of such high power. Considering the saturation rate of Fe lidar can be quantified, more research should be invested in algorithms to correct it. If the method is well-founded, the measurement performance can be further improved. Of course, if we need to explore the structure of static and dynamic instabilities in the MLT region and its seasonal variations, it is essential to obtain high accuracy results with ultrahigh spatial and temporal resolutions. In this case, we must change the power-aperture. For example, we use a 3.5 m receiving telescope that is similar to Zhao’s system [31]. In addition, for Na and K lidar utilizing the three-frequency ratio technique, the system parameters can be further optimized based on the simulation model proposed here. It is useful to create a performance table, which helps us understand the optimal performance more clearly in different situations.

Table 4. Estimation of accuracy at night and day under different spatial and temporal resolutions

View Table | View all tables in this article

We also simulate the uncertainties at different heights of the iron layer when the resolutions are 10 min and 1000 m. As is shown in Fig. 8, at the peak height (about 88 km), Fe lidar shows excellent performance when the density is greater than 8000 cm^-3. In other words, even in spring and summer, when Fe density is the lowest in the year, it can also achieve good performance. The accuracy can be less than 3.8 K and 2.7 m/s between 80 km to 100 km at night, and it can be less than 7.4 K and 5.8 m/s between 82 km to 95 km at day, corresponding to a density requirement greater than 500 cm^-3 and 3000 cm^-3 approximately. Apparently, the accuracy differences between night and daytime are large. The Fabry-Perot etalon with 5.5 pm (about 12 GHz) bandwidth is used for simulation. if the frequency stabilization of the emitting laser can be stabilized within a few megahertz, taking into account the temperature broadening (more than 2 GHz), the bandwidth of Fabry-Perot etalon can be further reduced to several two gigahertz. It is very critical to enhance the measurement accuracy during the day.

Fig. 8. Simulation of lidar performance based on the obtained key parameters. The red lines come from the NRLMSISE-00 temperature mode [32] and HWM93 radial wind velocity mode, the blue line is the Fe density and the shaded area are measurement errors caused by photon noise derived from Section 2. (a). Temperature at night; (b). Temperature at daytime; (c). Wind velocity at night; (d). Wind velocity at daytime.

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These simulation results show that a reasonable index decomposition can lead to high performance of Fe lidar and the lidar parameters list in Table 3 are justifiable and achievable under the current technology level. However, the simulation is an ideal result. In actual applications, how to ensure the stability of the laser frequency, such as, jitter, linewidth variations, how to ensure the confinement of the optical path, and how to improve efficiency are the critical issues we should focus on. These issues will affect the final Fe lidar performance.

4. Conclusions and outlook

In this paper, we have built a complete simulation model of Fe lidar, including principle, uncertainty caused by photon noise error, simulation and optimization of parameters, and potential temperature-wind measurement performance. The results obtained from the model are summarized into two points. One, the night and daytime calibration curves are acquired after considering the Fe isotopes and optimizing the frequency shift. The curves show homogeneous sensitivity for different temperatures and wind velocities and it will be used as our standard in future experiments. Two, it is helpful for the design of Fe lidar and it allows us to deepen the understanding of the existed system. For example, what is the influence degree of the saturation effect when the laser power is increased; and when the simulation parameters and the system operating parameters are equal, but there is a huge difference in measurement performance, what parameters can be changed to reduce it.

Besides the simulation model, 372 nm wavelength laser with high efficiency and robustness, frequency stabilization module and filtering devices during the daytime are also key technologies, and we are working on these technologies. It is very meaningful to make some contributions to the development of high-performance Fe lidar in the world.

Appendix: derivation of temperature-wind uncertainty

The atmospheric temperature response function R_T and the wind velocity response function R_V have been defined as Eqs. (9) and (10). we take the logarithm of them and then use the standard error propagation method with Eq. (37) and (38) to obtain the uncertainty of R_T and R_V

(37)$$\ln {{R}_T} = \ln {N_{Fe}}({{f_ + }} )+ \ln {N_{Fe}}({{f_ - }} )- 2\ln N_{Fe}^{}({{f_0}} ),$$

(38)$$\ln {{R}_V} = \ln [{\ln (N_{Fe}^{}({{f_ - }} )/N_{Fe}^{}({{f_ + }} ))} ]- \ln [{\ln ({N_{Fe}}({{f_ + }} ){N_{Fe}}({{f_ - }} )/N_{Fe}^2({{f_0}} ))} ]= \ln P - \ln Q.$$

(39)$$\begin{aligned} \frac{{\Delta {{R}_T}}}{{{{R}_T}}} &= \sqrt {{{\left[ {\frac{{\partial \ln {{R}_T}}}{{\partial N_{Fe}^{}({{f_ + }} )}}\Delta N_{Fe}^{}({{f_ + }} )} \right]}^2} + {{\left[ {\frac{{\partial \ln {{R}_T}}}{{\partial N_{Fe}^{}({{f_ - }} )}}\Delta N_{Fe}^{}({{f_ - }} )} \right]}^2} + {{\left[ {\frac{{\partial \ln {{R}_T}}}{{\partial N_{Fe}^{}({{f_0}} )}}\Delta N_{Fe}^{}({{f_0}} )} \right]}^2}} \\& = \sqrt {{{\left[ {\frac{{\Delta N_{Fe}^{}({{f_ + }} )}}{{N_{Fe}^{}({{f_ + }} )}}} \right]}^2} + {{\left[ {\frac{{\Delta N_{Fe}^{}({{f_ - }} )}}{{N_{Fe}^{}({{f_ - }} )}}} \right]}^2} + {{\left[ { - \frac{{2\Delta N_{Fe}^{}({{f_0}} )}}{{N_{Fe}^{}({{f_0}} )}}} \right]}^2}} \\& = \sqrt {\frac{2}{{(1 - \psi )SNR_ + ^2}} + \frac{2}{{(1 - \psi )SNR_ - ^2}} + \frac{4}{{\psi SNR_0^2}}} \\& = \sqrt {\frac{4}{{\psi SNR_0^2}} + \frac{4}{{(1 - \psi )SNR_ \pm ^2}}} = \frac{2}{{SN{{R}_0}}}\sqrt {\frac{1}{\psi } + \frac{1}{{(1 - \psi )}} \cdot \frac{{SNR_0^2}}{{SNR_ \pm ^2}}} , \end{aligned}$$

(40)$${$\begin{aligned} \frac{{\Delta {{R}_V}}}{{{{R}_V}}} &= \sqrt {{{\left[ {\frac{{\partial \ln {{R}_V}}}{{\partial N_{Fe}^{}({{f_ + }} )}}\Delta N_{Fe}^{}({{f_ + }} )} \right]}^2} + {{\left[ {\frac{{\partial \ln {{R}_V}}}{{\partial N_{Fe}^{}({{f_ - }} )}}\Delta N_{Fe}^{}({{f_ - }} )} \right]}^2} + {{\left[ {\frac{{\partial \ln {{R}_V}}}{{\partial N_{Fe}^{}({{f_0}} )}}\Delta N_{Fe}^{}({{f_0}} )} \right]}^2}} \\& = \sqrt {{{\left[ { - \frac{1}{P}\frac{{\Delta N_{Fe}^{}({{f_ + }} )}}{{N_{Fe}^{}({{f_ + }} )}} - \frac{1}{Q}\frac{{\Delta N_{Fe}^{}({{f_ + }} )}}{{N_{Fe}^{}({{f_ + }} )}}} \right]}^2} + {{\left[ {\frac{1}{P}\frac{{\Delta N_{Fe}^{}({{f_ - }} )}}{{N_{Fe}^{}({{f_ - }} )}} - \frac{1}{Q}\frac{{\Delta N_{Fe}^{}({{f_ - }} )}}{{N_{Fe}^{}({{f_ - }} )}}} \right]}^2} + {{\left[ {\frac{2}{Q}\frac{{\Delta N_{Fe}^{}({{f_0}} )}}{{N_{Fe}^{}({{f_0}} )}}} \right]}^2}} \\& = \sqrt {{{\left[ {(\frac{1}{P} + \frac{1}{Q})\frac{{\Delta N_{Fe}^{}({{f_ + }} )}}{{N_{Fe}^{}({{f_ + }} )}}} \right]}^2} + {{\left[ {(\frac{1}{P} - \frac{1}{Q})\frac{{\Delta N_{Fe}^{}({{f_ - }} )}}{{N_{Fe}^{}({{f_ - }} )}}} \right]}^2} + {{\left[ {\frac{2}{Q}\frac{{\Delta N_{Fe}^{}({{f_0}} )}}{{N_{Fe}^{}({{f_0}} )}}} \right]}^2}} \\& = \sqrt {(\frac{1}{{{P^2}}} + \frac{1}{{{Q^2}}})\frac{4}{{(1 - \psi )SNR_ \pm ^2}} + \frac{1}{{{Q^2}}}\frac{4}{{\psi SNR_0^2}}} = \frac{2}{{SN{{R}_0}}}\sqrt {(\frac{1}{{{P^2}}} + \frac{1}{{{Q^2}}})\frac{1}{{(1 - \psi )}} \cdot \frac{{SNR_0^2}}{{SNR_ \pm ^2}} + \frac{1}{{{Q^2}}}\frac{1}{\psi }} , \end{aligned}$}$$

where

(41)$$P = \frac{{2\delta f \cdot {V_R}}}{{{\lambda _{Fe}}\sigma _e^2}},Q = \frac{{ - \delta {f^2}}}{{\sigma _e^2}},$$

(42)$$\frac{{SN{{R}_0}}}{{SN{{R}_ \pm }}} = \sqrt {\frac{{N_{Fe}^2({{f_0}} )/[{N_{Fe}^{}({{f_0}} )+ N_B^{}} ]}}{{N_{Fe}^{}({{f_ + }} )N_{Fe}^{}({{f_ - }} )/[{N_{Fe}^{}({{f_ + }} )N_{Fe}^{}({{f_ - }} )+ N_B^{}} ]}}} = {\left( {\frac{{{e^\alpha } + \beta {e^{\alpha /2}}}}{{1 + \beta }}} \right)^{1/2}}.$$

The expressions for temperature and wind velocity have been given in Eq. (19) and (20), and we can obtain their uncertainties using the same method as Eqs. (39) and (40)

(43)$$\frac{{\Delta T}}{T} = \left|{\frac{{\partial \ln T}}{{\partial {{\rm R}_T}}}\Delta {{\rm R}_T}} \right|= \left|{\frac{1}{T}\frac{{ - \delta {f^2}}}{{\gamma {{\rm R}_T}{{({\textrm{ln}}{{\rm R}_T})}^2}}}\Delta {{\rm R}_T}} \right|,$$

(44)$$\Delta T = \frac{{\sigma _e^4}}{{\gamma \cdot \delta {f^2}}}\frac{{\Delta {{\rm R}_T}}}{{{{\rm R}_T}}} = \frac{2}{\alpha }{\left[ {\frac{{{e^\alpha }({1 + \beta {e^{ - \alpha /2}}} )}}{{(1 - \psi )(1 + \beta )}} + \frac{1}{\psi }} \right]^{1/2}} \cdot \frac{{(T + \sigma _L^2/\gamma )}}{{SN{{\rm R}_0}}},$$

(45)$$\frac{{\Delta {V_R}}}{{{V_R}}} = \left|{\frac{{\partial \ln {V_R}}}{{\partial {{\rm R}_V}}}\Delta {{\rm R}_V}} \right|= \left|{\frac{{\Delta {{\rm R}_V}}}{{{{\rm R}_V}}}} \right|,$$

(46)$$\Delta {V_R} = {V_R}\sqrt {{{(\frac{{\Delta {{\rm R}_V}}}{{{{\rm R}_V}}})}^2}} = \frac{2}{{SN{{\rm R}_0}}}\sqrt {(\frac{{V_R^2}}{{{P^2}}} + \frac{{V_R^2}}{{{Q^2}}})\frac{1}{{(1 - \psi )}} \cdot \frac{{SNR_0^2}}{{SNR_ \pm ^2}} + \frac{{V_R^2}}{{{Q^2}}}\frac{1}{\psi }} .$$

We assume wind velocity to zero, which causes little error and allows us to further simplify Eq. (46), but it should be noted that Fig. 8 still utilizes Eq. (46) to obtain wind uncertainties

(47)$$\Delta {V_R} = \frac{2}{{SN{{\rm R}_0}}}\frac{{{\lambda _{Fe}}\sigma _e^2}}{{2\delta f}}\sqrt {\frac{1}{{(1 - \psi )}} \cdot \frac{{SNR_0^2}}{{SNR_ \pm ^2}}} = {\left[ {\frac{{{e^\alpha }({1 + \beta {e^{ - \alpha /2}}} )}}{{\alpha (1 - \psi )(1 + \beta )}}} \right]^{1/2}} \cdot \frac{{{\lambda _{Fe}}\sqrt {\sigma _{Fe}^2 + \sigma _\textrm{L}^2} }}{{SN{{\rm R}_0}}}.$$

Since β is much larger than one at night and much larger than one during the day, we can theoretically obtain the most simplified uncertainty expressions for temperature and wind velocity at night and day

(48)$$\Delta {T_{night}} = \frac{2}{\alpha }{\left[ {\frac{{{e^{\alpha /2}}}}{{(1 - \psi )}} + \frac{1}{\psi }} \right]^{1/2}} \cdot \frac{{(T + \sigma _L^2/\gamma )}}{{SN{{\rm R}_0}}},$$

(49)$$\Delta {T_{day}} = \frac{2}{\alpha }{\left[ {\frac{{{e^\alpha }}}{{(1 - \psi )}} + \frac{1}{\psi }} \right]^{1/2}} \cdot \frac{{(T + \sigma _L^2/\gamma )}}{{SN{{\rm R}_0}}},$$

(50)$$\Delta {V_{{\rm R} - night}} = {\left[ {\frac{{{e^{\alpha /2}}}}{{\alpha (1 - \psi )}}} \right]^{1/2}} \cdot \frac{{{\lambda _{Fe}}\sqrt {\sigma _{Fe}^2 + \sigma _\textrm{L}^2} }}{{SN{{\rm R}_0}}},$$

(51)$$\Delta {V_{{\rm R} - day}} = {\left[ {\frac{{{e^\alpha }}}{{\alpha (1 - \psi )}}} \right]^{1/2}} \cdot \frac{{{\lambda _{Fe}}\sqrt {\sigma _{Fe}^2 + \sigma _\textrm{L}^2} }}{{SN{{\rm R}_0}}}.$$

Funding

National Natural Science Foundation of China (41875033); Chinese Academy of Sciences President’s International Fellowship Initiative (2021VEA0006); Director Fund of Advanced Laser Technology Laboratory of Anhui Province (AHL2020ZR01).

Acknowledgment

The authors thank Professor Yi Fan of Wuhan University for providing the data of Fe density.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Fe isotope lines	Frequency offset/MHz	Relative abundance/%	Nuclear spin
⁵⁴Fe	-726.5	5.845	0
⁵⁶Fe	0	91.754	0
⁵⁷Fe	365	2.119	1/2
⁵⁸Fe	689.9	0.282	0

Parameter	Ψ	δf	Minimum Error	Ψ_opt	δf_opt	Optimum Error
ΔT_night	0.218	1050	$361 K / SN R_{0}$	0.205	932	$378 K / SN R_{0}$
ΔT_day	0.218	743	$722 K / SN R_{0}$	0.212	687	$737 K / SN R_{0}$
ΔV_R-night	0	657	$201 m s^{- 1} / SN R_{0}$	0.205	932	$264 m s^{- 1} / SN R_{0}$
V_R-day	0	464	$285 m s^{- 1} / SN R_{0}$	0.212	687	$393 m s^{- 1} / SN R_{0}$

Parameters	P_L (W)	A (m²)	θ_L (mrad)	Δt_L (ns)	σ_L (MHz)	δf_opt (MHz)	Ψ_opt (%)	η (%)	T²_total (%)	θ_FOV (mrad)	d_FP (pm)
Night	1.8	0.25π	0.2	50	35	932	20.5	17.03	29.2	0.4	/
Daytime	1.8	0.25π	0.2	50	35	687	21.2	12.09	29.2	0.4	5.5

Night	1 min	3 min	5 min	8 min	10 min	15 min
100 m	7.05 K, 5.4 m/s.	4.07 K, 3.12 m/s.	3.15 K, 2.41 m/s.	2.49 K, 1.91 m/s.	2.23 K, 1.71 m/s.	1.82 K, 1.39 m/s.
200 m	5.03 K, 3.85 m/s.	2.9 K, 2.23 m/s.	2.25 K, 1.72 m/s.	1.78 K, 1.36 m/s.	1.59 K, 1.22 m/s.	1.3 K, 1 m/s.
500 m	3.27 K, 2.5 m/s.	1.89 K, 1.45 m/s.	1.46 K, 1.12 m/s.	1.16 K, 0.89 m/s.	1.03 K, 0.79 m/s.	0.84 K, 0.65 m/s.
1000 m	2.44 K, 1.89 m/s.	1.41 K, 1.09 m/s.	1.09 K, 0.85 m/s.	0.86 K, 0.67 m/s.	0.77 K, 0.6 m/s.	0.63 K, 0.49 m/s.
2000m	1.96 K, 1.49 m/s.	1.13 K, 0.86 m/s.	0.88 K, 0.67 m/s.	0.69 K, 0.53 m/s.	0.62 K, 0.47 m/s.	0.51 k, 0.34 m/s.
Daytime	1 min	3 min	5 min	8 min	10 min	15 min
100 m	15.93 K, 13.13 m/s.	9.2 K, 7.58 m/s.	7.13 K, 5.87 m/s.	5.63 K, 4.64 m/s.	5.03 K, 4.15 m/s.	4.11 K, 3.39 m/s.
200 m	11.48 K, 9.47 m/s.	6.63 K, 5.47 m/s.	5.14 K, 4.24 m/s.	4.06 K, 3.35 m/s.	3.63 K, 3 m/s.	2.96 K, 2.45 m/s.
500 m	7.67 K, 6.32 m/s.	4.43 K, 3.65 m/s.	3.43 K, 2.83 m/s.	2.71 K, 2.24 m/s.	2.43 K, 2 m/s.	1.98 K, 1.63 m/s.
1000 m	6.11 K, 5.09 m/s.	3.53 K, 2.94 m/s.	2.73 K, 2.28 m/s.	2.15 K, 1.8 m/s.	1.93 K, 1.61 m/s.	1.58 K, 1.31 m/s.
2000m	5.49 K, 4.51 m/s.	3.17 K, 2.6 m/s.	2.46 K, 2.01 m/s.	1.94 K, 1.59 m/s.	1.74 K, 1.42 m/s.	1.42 K, 1.16 m/s.

Fe isotope lines	Frequency offset/MHz	Relative abundance/%	Nuclear spin
⁵⁴Fe	-726.5	5.845	0
⁵⁶Fe	0	91.754	0
⁵⁷Fe	365	2.119	1/2
⁵⁸Fe	689.9	0.282	0

Simulation and optimization of Fe resonance fluorescence lidar performance for temperature-wind measurement

Abstract

1. Introduction

2. Simulation model

2.1 Principle and the impact factors of measurement

2.2 Temperature-wind uncertainty

2.3 Index decomposition

3. Results and discussion

4. Conclusions and outlook

Appendix: derivation of temperature-wind uncertainty

Funding

Acknowledgment

Disclosures

Data availability

References

Data availability

Cited By

Figures (8)

Tables (4)

Equations (51)

Optics Express