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Abstract
We report performance of a satellite-borne coherent Doppler wind lidar (SCDWL), which equips a planer waveguide amplifier (PWA) operating in a wavelength of 1.5 µm. The performance is defined by detection probability, measurement precision, and bias, and is characterized with a Doppler wind lidar (DWL) simulation that considers a realistic wind velocity profile, and instrumental and atmospheric parameters. Among the parameters, we carefully model those related to the PWA whose figure of merit has great impact on the performance of SCDWL and has shown rapid improvement in recent years. Moreover, we introduce three models for a backscattering coefficient (high, moderate, and low) to assess the influence from variation of atmospheric backscattering. Our simulation demonstrates that the SCDWL can work with reasonable performance for the target altitude of 6 km in the case of the high-backscattering model. The simulation also exhibits that the SCDWL can observe wind velocity at the altitude of 12 km if improved instrumental parameters or higher backscattering coefficients are considered. In addition, we reveal that non-uniform wind velocity distribution degrades the performance of the SCDWL and induces a bias between measured and real wind velocity.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. INTRODUCTION
A Doppler wind lidar (DWL) enables measurement of wind velocity in a distant region with fine spatial resolution and a high repetition rate. Owing to these advantages, DWLs have been employed in various fields [1–5]. Especially, implementation of a DWL on a satellite has been an active topic in the scientific community for several decades. A satellite-borne DWL (SDWL) is capable of observing three-dimensional global distribution of wind velocity from an orbit. Wind data obtained by an SDWL is expected to improve performance of numerical weather prediction (NWP) [6,7]. There have been several projects aiming to develop an SDWL (for example, WINDSAT [8], SPARCLE [9], ELISE [10], and Aeolus [11]). Among them Aeolus was successfully launched in 2018 and has demonstrated its ability to observe wind velocity profiles from a satellite. So far wind velocity profiling by Aeolus has been tested and utilized by various studies [12–15]. Aeolus has paved the way to implementing and operating an SDWL.
Aeolus equips a DWL called Atmospheric Laser Doppler Instrument (ALADIN). ALADIN has a high-power laser transmitter with a wavelength of 355 nm and has two (namely, Mie and Rayleigh) channels. The former and latter channels observe backscattered lights from atmospheric aerosols and molecules. Backscattering from molecules is not so sensitive to atmospheric conditions, altitudes, and locations; thus having the Rayleigh channel ensures a high detection probability of wind velocity profile. ALADIN is classified as an incoherent DWL, where a Doppler frequency shift of the backscattered light is measured by direct-detection with a double-edge technique using optical filters [13,15]. In such a configuration, the following two terms are required to retrieve wind velocity correctly. The first one is careful characteristic stabilization of optical components including the optical filters. The second is a priori information on spectral broadening of Rayleigh backscattered light, which depends on atmospheric conditions. Although great effort has been made for calibration to keep accurate wind velocity measurement, a survey of several validation campaigns of Aeolus showed that there is still a certain bias error in measured wind velocity [14]. On the other hand, most of DWLs operating on the ground are classified as a coherent DWL. A coherent DWL is usually operated with an infrared wavelength and measures backscattered light from atmospheric aerosols. The Doppler frequency shift is directly measured from heterodyne-detected signal of the received and the local lights [1,16]. Thanks to the direct measurement of the frequency shift, a coherent DWL is in principle free of bias error in measured wind velocity. Therefore, a satellite-borne coherent DWL (SCDWL) can contribute to improve performance of NWP and is also useful as complementary to Aeolus. However, the forementioned projects related to an SCDWL have not been launched yet owing to several technological difficulties. One of the most critical issues is a low aerosol (i.e., Mie) backscattering coefficient in the stratosphere, which severely limits the signal-to-noise ratio (SNR) of an SCDWL. Although a straightforward way to improve SNR is to transmit a laser pulse with a high energy, formerly it was not easy for a light transmitter used in a coherent DWL to achieve a sufficiently high pulse energy.
Recently a pulse energy of light transmitters for a coherent DWL has shown great improvement in a wavelength of 1.5 µm. The pulse energy was constrained mainly by a small mode area of an optical fiber amplifier, which induces unwanted nonlinear effects such as the simulated Brillouin scattering. Although use of a large-mode-area fiber can relax the above effects, it reduces beam quality. For addressing the above issue, Sakimura et al. [17] proposed a planer waveguide amplifier (PWA). Its large mode area and small difference of refractive index between the core and the clad suppress the nonlinear effects greatly and allow to output a high-energy laser pulse with good beam quality. The pulse energy was 3.2 mJ in 2019 [17], but it was increased to 45 mJ in 2023 [18]. In addition, the Safety Avionics (SafeAvio) project of the Japan Aerospace Exploration Agency (JAXA) [19] developed an airborne coherent DWL with a 1.5-µm PWA. The project has verified observation of wind velocity in a high altitude (${\gt} {12}\;{\rm km}$), where the backscattering coefficient is low. In addition, it has demonstrated a successful operation of the coherent DWL with an airborne platform, which is a harsh environment for an optical system. Considering the above discussion, we believe that it is now worth reconsidering the performance of an SCDWL with a 1.5-µm PWA with the up-to-date parameters.
In this paper, we report on the performance of an SCDWL with a 1.5-µm PWA. Our analysis is based on a DWL simulation that takes realistic atmospheric conditions and wind velocity profiles into account. The simulation evaluates the three performance measures of detection probability, measurement precision, and bias. In contrast to pioneering works for a DWL simulation [20–25], we put great importance on estimating the performance of a 1.5-µm PWA, which is the key device for future operation of the SCDWL. Recent progress of its performance is introduced into the simulation. Moreover, we carefully study the influence from wind velocity distribution within signal accumulation time. Non-uniform distribution of wind velocity results in a broadening and an asymmetric shape of a spectrum of the received light, which have a significant impact on the performance. In particular, the asymmetric shape of the spectrum induces a bias error in measured wind velocity, which does not exist in a coherent DWL in principle and has not been explicitly analyzed in the previous studies. The results of our simulation prove that the SCDWL with the up-to-date parameters can observe wind velocity with reasonable performance at the target altitude of 6 km in the case of the high-backscattering model. In addition, the observation at a target altitude of 12 km is revealed to be possible if further improvement of the parameters is assumed.
This paper is organized as follows. First, operation and the optical configuration of the SCDWL are described in Section 2. Next, Section 3 explains the model of DWL simulation. Then, Section 4 describes wind velocity profiles and atmospheric parameters considered in the DWL simulation. Section 5 shows the performance of a 1.5-µm PWA and other instrumental parameters employed for the simulation. Then, the simulation procedure and results are shown in Section 6. Finally, this paper is concluded in Section 7.
2. OPERATION AND OPTICAL CONFIGURATION OF SCDWL
A. Operation
Figure 1(a) shows the operation of the SCDWL. We assumed that the SCDWL is equipped on the Super Low Altitude Test Satellite (SLATS) [26]. Its flight altitude is 300 km and is assumed to move along a line of latitude. The SCDWL emits laser pulses to the ground and receives the pulses backscattered by aerosols in the atmosphere. The SCDWL has a single telescope. Although a DWL measures wind velocity in the same region at least along two lines of sight (LOSs) for estimating wind velocity vectors [27], it was reported that wind velocity measured by a single LOS is still effective for improving the performance of NWP [28]. The LOS of the SCDWL is inclined along roll direction with 35° for obtaining information on horizontal wind velocity.
Figure 1(b) is a schematic illustration of signal processing. First, the laser pulse scattered from the atmosphere is received. The received signal is almost continuous because aerosols are continuously spread along the LOS. After heterodyne detection with the local light, the received signal is split into short time bins with a width of 2 µs (corresponds to about 300 m along the LOS or 250 m along an altitude). Then, the Fourier spectrum is calculated for every bin. We call this spectrum “single-shot received spectrum (SSRS).” Next, SSRSs in four successive time bins are averaged (“ASSRS”). As a result, an ASSRS is obtained for every 1200 m range along the LOS and for every laser pulse. The SCDWL flies with a velocity of approximately 7.7 km/s while transmitting laser pulses with a repetition rate of 150 Hz. This means that every laser pulse hits different regions along the orbit of the satellite. As a result, the SCDWL can obtain ASSRSs two-dimensionally (along the LOS and the orbit). Then, ASSRSs at 1800 regions are accumulated [“accumulated received spectrum (ARS)”] for increasing the detectability at the expense of horizontal resolution. The accumulation results in horizontal resolution of approximately 92 km. Finally, wind velocity is estimated by analyzing the ARS with a combination of peak detection and centroid computation algorithms. By repeating the above procedure, the SCDWL measures two-dimensional wind velocity along the LOS and the orbit at intervals of 1200 m and 92 km, respectively.
B. Optical Configuration
Figure 2 illustrates the optical configuration of the SCDWL. It is composed of a seed laser (SL), a divider, an acousto-optic modulator (AOM), an optical fiber pre-amplifier (pre-FA), an optical fiber amplifier (FA), a PWA, a polarization beam splitter (PBS), a quarter waveplate (QWP), a telescope, a coupler, a balanced receiver (BR), and an analog-digital converter (ADC). Continuous 1.5-µm seed light is emitted by the SL and is split into a signal and local light by the divider. The AOM converts the signal light into a pulse and introduces a frequency shift. This frequency is determined by the dynamic range of measured wind velocity and the moving velocity of the satellite. Then, the signal light is amplified by the pre-FA, the FA, and the PWA in turn. The pre-FA and the FA are employed so that the signal light can have a high enough pulse energy to operate the PWA safely. The PWA is the main amplifier of the system and is described in detail later. The amplified signal light propagates through the PBS and the QWP, and then is transmitted to the atmosphere through the telescope. The laser pulse scattered by atmosphere is collected by the telescope and is directed to the receiving path, which is different from the transmitting path, after propagating through the QWP and the PBS. Although it is not explicitly shown in Fig. 2, introducing a wedge prim between the collimating optics and PBS is effective to suppress a lag-angle effect [29]. After the received and the local light is mixed and interfered, the mixed light is detected by the BR. The signal outputted from the BR corresponds to the heterodyne-detected signal described in Fig. 1(b).
3. EQUATIONS FOR DWL SIMULATION
A. Wideband SNR
Here we describe equations for a wideband signal-to-noise ratio (SNR), which is employed for the DWL simulation. According to Kameyama et al. [16,20], wideband SNR of a coherent DWL is given by the following equation with a few minor modifications:
B. Detection Probability, Measurement Precision, and Bias
Then, we describe the model computing detection probability (DP), measurement precision (MP), and bias, which are employed generally to evaluate the performance of a DWL [20–25]. Figure 3(a) is the flowchart of the model. It traces the operation of the SCDWL illustrated in Fig. 1(b). First, the value of the wideband SNR (${{\rm SNR}_{\rm w}}$) is set. Then, the indices ${i_{\rm A}}$, ${i_{\rm L}}$, and ${i_{\rm I}}$ are initialized. These indices are employed for expressing a target altitude, a target latitude, and an iteration, respectively. The list of wind velocity at the target attitudes and latitudes, ${V_{\rm w0}}({i_{\rm A}},\;{i_{\rm L}})$, is also prepared considering a realistic wind profile (described in Section 4.A. in detail). Next, the single-shot received spectrum ${\rm SSRS}(\nu ; {i_{\rm I}}, {i_{\rm A}}, {i_{\rm L}})$ is computed following the equation below:
Fig. 3. (a) Flowchart of the DWL simulation. (b) Schematic illustration of fitting of the histogram.
The above procedure enables us to calculate the DP, the MP, and the bias for a given value of ${{\rm SNR}_{\rm w}}$.
4. ATMOSPHERIC PARAMETERS
A. Wind Model
We describe the models of the wind profile that are required for the DWL simulation. The wind profiles were based on NWP data provided by the Japan Meteorological Agency [32]. The NWP data is a three-dimensional wind profile and has a horizontal grid of 0.1° and 0.125° along the directions of latitude and longitude, respectively. Its range for altitude spans from the ground to 16 km. We ignored a vertical component of wind velocity vector and regard that the wind velocity vector is inside a horizontal plane. The NWP data covers a wide area around Japan (22.4–47.6°N and 120–150°E). We assumed that the satellite flies along the line of longitude on 135°E and extracted a wind profile around two areas such as (I) (31.6°N–32.4°N, 135°E) and (II) (40.6°N–41.4°N, 135°E). This is because the wind velocity profiles in these areas show the strong dependency on the altitude and the latitude. The range of latitude of areas (I) and (II) corresponds approximately to the accumulation length.
Figures 4(a) and 4(b) demonstrate the LOS component of wind velocity in areas (1) and (II), respectively. We chose altitudes of 1, 2, 6, and 12 km. For convenience, we call, for example, altitude of 1 km in the area (II) “(II-1).” The lines with the same color are the wind velocity in adjacent time bins. Each line shows a characteristic trend. For example, wind velocity is very stable in (I-1) while it depends strongly on latitude and bins in (II-6).
Fig. 4. (a), (b) LOS component of the wind velocity in areas (I) and (II), respectively. The blue, orange, yellow, and violet lines represent the altitudes of 12, 6, 2, and 1 km, respectively. (c), (d) Calculated ARSs for areas (I) and (II), respectively. The blue, orange, yellow, and violet lines represent ARSs for the altitudes of 12, 6, 2, and 1 km, respectively. The green line represents ARS for no wind. Each line is offset along the vertical axis for clarity. The horizontal axes of (c) and (d) correspond to those of (a) and (b), respectively. The insets show the ARSs after aligning the center wind velocity.
To visualize the impact of the wind profile on the performance of the SCDWL, we simulate the accumulated received spectrum (ARS) in areas (I) and (II) as shown in Figs. 4(c) and 4(d). The noise in the ARS is ignored for emphasizing the influence purely from the wind profile. In addition, the case where the wind velocity is zero is also indicated in the figures as a reference (“no wind”). It is straightforward that the center of the ARS is shifted in coincidence with the average of the wind velocity in each condition. In addition to the shift, we pay attention to the width and peak value of the ARSs. The width is broadened in several conditions in comparison to the “no wind” condition [see also the insets of Figs. 4(c) and 4(d)]. This is mainly due to a change of wind velocity along latitude, in other words during the accumulation. If wind velocity is constant over latitude, the width of ARS is comparable to that in the “no wind” condition. However, if wind velocity is not constant, the center of SSRS is gradually shifted during accumulation, and then the width of ARS increases. If wind velocity changes linearly the broadening is symmetric as shown in (I-12). On the other hand, the broadening is asymmetric as indicated in (II-1) and (II-6) if wind velocity changes nonlinearly. The peak value of the ARSs drops if the width of ARS is broadened. Such broadening and the drop of peak value are very characteristic in an SCDWL where a long accumulation length is required for observation. The impact of the wind profile on the performance of the SCDWL is quantitatively discussed in Sections 4.B and 4.C.
In addition to the above-mentioned wind profile, Kolmogorov wind turbulence [20] is considered in the simulation. The energy dissipation coefficient in the Kolmogorov regime is set at ${0.032}\;{{\rm m}^2}/{{\rm s}^2}$, which corresponds to moderate turbulence [20]. This value is used for estimation of the width of the ${\rm SSRS}({\nu ;{i_{\rm I}},{i_{\rm A}},{i_{\rm L}}})$ in Eq. (4), and it influences ${\rm ARS}({\nu ;{i_{\rm I}},i_{\rm A}^{\prime}})$ in Eq. (6) and Figs. 4(c) and 4(d).
B. Backscattering Coefficient
We investigate on the model for the backscattering coefficient $\beta$. Careful modeling of $\beta$ is essential for the performance analysis because the wideband SNR of the SCDWL depends strongly on $\beta$. Since there is a limited number of studies reporting direct measurement of $\beta$ in a high altitude in 1.5 µm, we converted $\beta$ measured in another wavelength into that in 1.5 µm. According to Srivastava et al. [33], $\beta$ in 1.54 µm (${\beta _{1.54}}$) can be converted into that in 2.1 µm (${\beta _{2.1}}$) with the following equation:
Fig. 5. Calculated backscattering coefficient in 1.5 µm. The blue, orange, and yellow lines represent HM, MM, and LM, respectively. The upper, middle, and lower panels represent the 10-, 50-, and 90-percentile models.
Table 1. Parameters for the DWL Simulation
Table 2. Descriptions of the Models of Backscattering Coefficient
C. Other Atmospheric Parameters
The round-trip transmittance $\tau (R)$ depends on the target distance (altitude) and was modeled by
Fig. 6. (a) Transmission per a unit distance $T({\rm ALT})$ and (b) refractive index structure constant ${\rm C}_{\rm n}^2$.
5. INSTRUMENTAL PARAMETERS
A. Performance of 1.5-µm PMA
We analyze the performance of a 1.5-µm planar waveguide amplifier (PWA). The 1.5-µm PWA, which is the main laser amplifier, is the key to implement the SCDWL. Figure 7(a) is a schematic illustration of the configuration of the 1.5-µm PWA [17,18]. It is characterized by its unique rectangular configuration where a planar core of a Er,Yb:glass is sandwiched by cladding layers. This configuration is bonded on a heat sink to waste heat generated by pumping. The left and right sides are covered with anti-reflection coatings and the pump light is injected from these sides. The other two sides are coated with high-reflection coatings except for the areas through which the light to be amplified is inputted and outputted. The inputted light propagates along a zig-zag path while being amplified as illustrated in Fig. 6(b). Then the amplified light is outputted from the outputting area. In contrast to large-mode-area Er-doped fiber amplifiers, which are another approach for obtaining a high pulse energy in 1.5 µm, the PWA is capable of suppressing unwanted nonlinear effects, which severely limit pulse energy, and obtaining good beam quality thanks to its unique planar configuration.
Here we quantitatively examine the performance of the PWA as the main laser amplifier of the SCDWL. Its performance can be evaluated comprehensively with the modified figure of merit (FoM) [18]. The modified FoM is the updated version of FoM and is determined by the pulse energy $E$, the pulse repetition rate, and the beam quality ${{\rm M}^2}$. These parameters impact the performance of the SCDWL. First, we discuss the value of the pulse energy $E$ that is feasible with the 1.5-µm PWA. According to Eq. (1), the laser pulse energy $E$ plays an important role for achieving a high SNR. A 1.5-µm PWA was reported for the first time by Sakimura et al. [35] in 2012 and emitted a pulse energy of 1.9 mJ at that time. Then the pulse energy was gradually improved to 9 mJ until 2018 [36–38]. In 2023, the pulse energy jumped to 45 mJ thanks to introduction of a novel symmetric double-cladding structure and a large-mode-area (LMA) erbium-doped fiber amplifier (EDFA) as a preamplifier [18]. The former increases a mode field diameter of the PWA and the latter enables to strongly amplify the signal light incident to the PWA. We assumed the pulse energy $E$ of 45 mJ, which is from the latest report [18], for the DWL simulation in this study.
Next, the influence of the beam quality ${{\rm M}^2}$ is investigated. ${{\rm M}^2}$ impacts the system efficiency since a low ${{\rm M}^2}$ results in spilling over of transmitted energy from the receiving field-of-view, which is diffraction-limited. The reported value of ${{\rm M}^2}$ in the latest report [18] is 1.84, and this is worse than the value demonstrated in the earlier report [17] ($= \;{1.29}$). We calculate the drop of system efficiency that is attributed to ${{\rm M}^2}$ of 1.84 by utilizing the model described in Eq. 28 in [39]. In this calculation, we express the transmitted beam with a certain ${{\rm M}^2}$ by a diffraction-limited beam with smaller (${{1/M}^2}$) beam size. This can simulate the influence of the above-mentioned spilling over of transmitted energy. The estimated value is approximately ${-}{2.2}\;{\rm dB}$ and was considered for calculation of the system efficiency as described in Section 5.B.
Then, the pulse repetition rate of 150 Hz was employed. This value is from the latest report [18] and has already been mentioned in Sections 2.A and 3.B.
In addition to the parameters considered in the modified FoM, an optical SNR (OSNR) of the 1.5-µm PWA is also important. OSNR is defined as the ratio of the peak of the signal and the noise in the spectrum of the amplified light. The noise is continuous and is leaked from the transmitting path to the receiving path with unwanted reflection or scattering by optical components (for instance, PBS, QWP, and the telescope). This implies that a low OSNR reduces the system efficiency ${\eta _{\rm s}}$. The OSNR of 18 dB is reported in [18], and this may drop system efficiency. However, the reference proposes a solution to improve OSNR, which is an introduction of an additional small-sized PWA as the preamplifier. In addition, the noise leaked to the receiver can be suppressed by employing high-grade optical components that have a good anti-reflection coating and a smooth surface. Considering the above, we ignored the influence from OSNR on the system efficiency in this study.
B. Other Instrumental Parameters
Table 1 summarizes parameters employed for the DWL simulation. The target range $R$ ranges from approximately 348 to 366 km, which corresponds to target altitudes of 15 and 0 km. The focal distance of the telescope $F$ is approximately 366 km, which means that the telescope is focusing on the ground. The number of the time bins to be averaged ${N_{\rm b}}$ is set to four or two for the target altitude of upper or lower than 2 km, respectively. The number of accumulations ${N_{\rm L}}$ is set to 1800. Note that ${N_{\rm L}}$ of 1800 corresponds to the accumulation time of 12 s. The system efficiency ${\eta _{\rm S}}$ and the far-field system efficiency in the case of negligible atmospheric refractive turbulence ${\eta _{\rm F}}$ are set to ${-}{7.9}$ and ${-}{4}\;{\rm dB}$. ${\eta _{\rm S}}$ is determined considering transmission and aberration of optical components, quantum efficiency, power penalty, optical SNR, beam quality ${{\rm M}^2}$, and other minor losses. ${A_{\rm c}}$ is set to 0.71 [40]. The width of the single-shot received spectrum (SSRS) $\sigma$ is set to 1.87 MHz, which considers laser pulse width (2 µs), effect of wind turbulence within a single time bin, and laser linewidth. The wideband receiving bandwidth ${B_{w}}$ is set to 180 MHz, which means that the dynamic range of detectable Doppler frequency is $\pm {90}\;{\rm MHz}$. This value of ${B_{w}}$ is determined by the range of horizontal wind velocity. We assumed the horizontal wind velocity of $\pm {100}\;{\rm m/s}$ considering the maximum velocity of a westerly jet stream [41]. The LOS component of the range of $\pm {100}\;{\rm m/s}$ is about $\pm {57}\;{\rm m/s}$, and corresponds to the Doppler frequency of approximately $\pm {74}\;{\rm MHz}$. This range is sufficiently covered by ${B_{w}}$ of 180 MHz. Note that we consider the two cases where the SCDWL observes the jet stream from ascending and descending orbits. In addition, we ignore the Doppler shift induced by the moving velocity of the satellite platform since the LOS direction is perpendicular to the moving direction as shown in Fig. 1(a). We can improve the performance of the SCDWL if we limit the signal search range for the Doppler frequency (i.e., $\pm {90}\;{\rm MHz}$) by employing a priori information of wind velocity at the target site. However, we assumed the worst case where a priori information is not available. The value for the pulse energy $E$ is 45 mJ as discussed in Section 5.A. The effective diameter of the telescope $D$ is set to 0.7 m. We determined this value considering mountability of the telescope on the assumed satellite platform. The laser wavelength $\lambda$ and the Planck coefficient $h$ are 1.55 µm and ${6.63} \times {{10}^{- 34\:}}{\rm J}\;{\rm s}$, respectively. The laser linewidth is not shown in Table 1 and is assumed to be negligible. This assumption is reasonable if a distributed feedback erbium-doped fiber laser with a linewidth of a few tens of kHz is used [16]. The backscattering coefficient $\beta$, the round-trop transmission $\tau$, and the refractive index structure constant $C_{n}^2$ were shown in Section 4. The energy dissipation coefficient is ${0.032}\;{{\rm m}^2}/{{\rm s}^2}$.
Fig. 7. Schematic illustrations of the (a) configuration of the 1.5-µm PWA and (b) zig-zag path of the signal beam in the core layer [17,18].
6. SIMULATION PROCEDURE AND RESULTS
A. Simulation Procedure
The procedure of the DWL simulation is described. First, the wideband SNR was estimated for given instrumental and atmospheric parameters (see Section 3.A). Then, the detection probability (DP), the measurement precision (MP), and the bias as a function of the wideband SNR were computed through the DWL simulation (see Section 3.B). Finally, the DP, the MP, and the bias for the estimated wideband SNR were calculated.
Fig. 8. Calculated wideband SNR for different target altitudes. The blue circles, orange rectangles, and yellow diamonds are calculated with the 50-percentile backscattering models of HM, MM, and LM, respectively.
B. Wideband SNR
First, we calculated the wideband SNR for different target altitudes as shown in Fig. 8. We employed the 50-pecentail models shown in the middle panel of Fig. 5. The wideband SNR curves differ greatly depending on the model of the backscattering coefficient. For instance, the wideband SNR at 6 km for high- (HM), moderate- (MM), and low-backscattering models (LM) are ${-}{26.7}$, ${-}{30.4}$, and ${-}{37.4}\;{\rm dB}$, respectively. Such a behavior suggests that the backscattering coefficient, which strongly depends on atmospheric conditions, plays an important role for the detection. In addition, the wideband SNR decreases in a high altitude regardless of the backscattering models, which prevents the SCDWL from observing wind velocity in a high altitude.
C. Detection Probability and Measurement Precision
Figures 9(a) and 9(b) demonstrate the calculated detection probability (DP) for different wideband SNR (${{\rm SNR}_{\rm w}}$) values. Both figures indicate that all the DP curves are increasing functions of ${{\rm SNR}_{\rm w}}$ and reach unity at ${{\rm SNR}_{\rm w}}$ of over ${-}{27}\;{\rm dB}$ regardless of altitudes and areas. This is intuitive since a higher ${{\rm SNR}_{\rm w}}$ leads to a higher probability to correctly recognize the peak in the accumulated received spectrum (ARS). In addition, the DP curves can be classified into upper and lower groups by the value of DP. The upper group includes (I-1), (I-2), (II-2), and (II-12), and the lower one includes (I-6), (I-12), (II-1), and (II-6). This classification can be understood by the difference of the shape of ARS. As described in Figs. 4(c) and 4(d), the shape of the ARSs for the upper group is approximately coincident with that of the “no wind” case. On the other hand, the ARSs for the lower group show wider widths and lower peak values than the “no wind” case. Figures 9(c) and 9(d) plot the measurement precision (MP) as a function of ${{\rm SNR}_{\rm w}}$ for different target altitudes. The MP curves show a similar trend to the DP curves in that they improve as ${{\rm SNR}_{\rm w}}$ increases and can be classified into the same two groups. The fact that DP and MP curves can be classified by the shape of ARS suggests that detailed analysis on the influence from it is essential to assess the performance of the SCDWL.
Fig. 9. Simulated (a), (b) DPs and (c), (d) MPs for different wideband SNRs in area (I) and area (II). The blue circles, orange rectangles, yellow diamonds, and violet triangles represent target altitudes of 12, 6, 2, and 1 km, respectively. Note that the number of accumulations ${N_{\rm L}}$ is 1800. The number of time bins to be averaged ${N_{\rm b}}$ is two or four for the target altitude of ${\lt} {2}\;{\rm km}$ or ${\gt}= {2}\;{\rm km}$, respectively.
We analyze the influence from the shape of ARS in detail from the viewpoint of its width. Figures 10(a) and 10(b) show the dependency of DP and MP on the full width of half maximum (FWHM) of ARS (${\Delta _{\rm{ARS}}}$). We choose the wideband SNRs of ${-}{31}$, ${-}{33}$, and ${-}{35}\;{\rm dB}$ and extract the values of DP and MP at the chosen wideband SNR. The FWHM of the ARS (${\Delta _{\rm{ARS}}}$) can be obtained from the ARS shown in Figs. 4(a) and 4(b). Figures 10(a) and 10(b) demonstrate a clear dependency of DP and MP on ${\Delta _{\rm{ARS}}}$, which can be smoothly fitted with second order polynomials shown as the broken lines. Such a dependency suggests that the wind profile within the accumulation length plays an important role for detection. Broadening of ${\Delta _{\rm{ARS}}}$ is attributed to a spatial change of wind velocity within the accumulation length. This means that ${\Delta _{\rm{ARS}}}$ is more likely to be large as the accumulation length gets longer. However, SCDWL requires a long accumulation length (time) for achieving sufficiently high detectability, and thus gets sensitive to a spatial change of wind velocity. Therefore, considering the influence from ${\Delta _{\rm{ARS}}}$ is crucial for characterizing the performance of an SCDWL. Note that a dependency of MP on ${\Delta _{\rm{ARS}}}$ is examined also in the previous study [21], and the analogous trend to our analysis is obtained.
Fig. 10. Dependency of (a) DP and (b) MP on FWHM of ARS (${\Delta _{\rm{ARS}}}$). The blue circles, orange rectangles, and yellow diamonds are for the wideband SNRs of ${-}{35}$, ${-}{33}$, and ${-}{31}\;{\rm dB}$, respectively. The black broken lines are the polynomial fit of the plots. Note that MP and DP curves that are not included in Fig. 9 are considered for increasing the number of the plots.
D. Bias
Here we analyze the bias of measured wind velocity. As mentioned in Section 1, there is in principle no bias in wind velocity measured by a coherent DWL thanks to its measurement principle. However, our simulation revealed that there should be a bias between measured and real wind velocities if the shape of the accumulated received spectrum (ARS) is asymmetric. Figures 11(a) and 11(b) show the simulated bias as a function of the wideband SNR in areas (I) and (II), respectively. In the figures, a large bias appears especially in (II-1) and (II-6), where the shape of the ARS is asymmetric [see the inset of Fig. 4(d)]. Their dependency on the wideband SNR is resulting from the process for fitting the histogram of measured wind velocity. Figure 11(c) illustrates how the bias is induced. The figure assumes that the real wind velocity ${V_{\rm w0}}$ changes nonlinearly along the accumulation length and takes stationary values of ${V_{{\rm w}0,\min}}$ and ${V_{{\rm w}0,\max}}$ at the beginning and the end. Such a ${V_{\rm w0}}$ curve results in the ARS with an asymmetric shape. In this case, ${V_{{\rm w}0,\mu}}$ is between ${V_{{\rm w}0,\min}}$ and ${V_{{\rm w}0,\max}}$. On the other hand, the measured wind velocity ${V_{\rm e}}$ is likely to be close to ${V_{{\rm w}0,\min}}$. This is because the ARS has its peak around ${V_{{\rm w}0,\min}}$ and the wind velocity close to the peak is extracted with a high probability by a peak detection algorithm. As a result, the bias between measured (${V_{\rm e}}$) and real (${V_{{\rm w}0,\mu}}$) wind velocity is induced. It should be noted that the bias can be cancelled with a signal processing if the shape of ARS can be obtained perfectly (e.g., noiseless condition). However, such a situation is unrealistic. The result shown above indicates that the bias should be considered even for an SCDWL if the wind profile is complex. The bias induced by the asymmetric ARS has not been explicitly reported in previous studies.
Fig. 11. (a), (b) Simulated bias between measured and real wind velocities in areas (I) and (II) for different target altitudes and ${{\rm SNR}_{\rm w}}$ values. Outliers are excluded. (c) Schematic illustration explaining the cause of the bias.
E. Summary of Performance
Finally, we combined the calculated detection probability (DP), measurement precision (MP), and bias with the wideband SNR to characterize the performance of the SCDWL. Figures 12(a) and 12(b) summarize the DP, the MP, and the bias values at the estimated wideband SNR. These figures are obtained as follows. First, the wideband SNR at the target altitudes of 1, 2, 6, and 12 km for the high- (HM), moderate- (MM), and low-backscattering models (LM) are estimated from Fig. 8. Then, the DP, the MP, and the bias at the estimated wideband SNR are read from Figs. 9 and Fig. 11. Finally, the read DP, MP, and bias are summarized in Fig. 12. In the figures the mission requirements for Aeolus [28] are indicated as the black broken lines for quantitative comparison. The requirement for the DP is over 0.95 and that for the MP is below 1.43 (${\gt}{2}\;{\rm km}$) or 0.57 m/s rms (${\lt}{2}\;{\rm km}$). It should be noted that the requirement for the MP is converted to the LOS direction. In addition, Fig. 12(c) shows the accumulated received spectrum (ARS), which corresponds to the plots in Figs. 4(c) and 4(d), for clarifying the influence from the shape of the ARS.
Fig. 12. (a), (b) Summary of (a) DP (orange bars), and (b) MP (blue bars) and bias (yellow bars) of the SCDWL. The upper, middle, and lower panels represent the backscattering model of HM, MM, and LM, respectively. The broken lines correspond to the requirement for Aeolus. The blank areas [(LM/I-12) and (MM/II-12)] are attributed to the limited altitude range of the backscattering model shown in Fig. 5. Note that blank conditions [for example, (MM/I-12) and (LM/II-12)] correspond to the case where the estimated ${{\rm SNR}_{\rm w}}$ value is out of range of Figs. 9(a)–9(d). (c) Summary of the noiseless ARS of the SCDWL. The plots are identical to those in the insets to Figs. 4(c) and 4(d). The black broken lines represent the case of “no wind.”
Figure 12(a) describes the estimated DP values. The figure shows a clear dependency of the DP on an altitude and the backscattering model. The DPs are comparable to the requirement at the altitude of up to 6 km for the HM. As for the MM and LM, the requirement cannot be satisfied at the same altitude. On the other hand, the influence from the width of the ARS (${\Delta _{\rm{ARS}}}$) is not significant in the DP. For instance, the DP of (HM/II-12) is lower than that of (HM/II-6) although ${\Delta _{\rm{ARS}}}$ of the former is narrower than that of the latter [see Fig. 12(c)]. This indicates that the dependency on the backscattering coefficient is dominant for the DP.
Figure 12(b) exhibits the estimated MP and bias. The MP depends mainly on ${\Delta _{\rm{ARS}}}$. This is clear from that the MP meets the requirement in (HM/II-12) where ${\Delta _{\rm{ARS}}}$ is narrow but the backscattering coefficient is very low. Figure 12(b) also indicates that the bias is not dependent strongly on the backscattering coefficient and ${\Delta _{\rm{ARS}}}$ but on the asymmetry of ARS. For example, the bias is well below the requirement in (LM/II-6) where both the DP and the MP fail to satisfy the requirement due to its low backscattering coefficient and a large ${\Delta _{\rm{ARS}}}$. On the other hand, the bias exceeds the requirement in (HM/II-1) owing to the severe asymmetric shape of the ARS [see Fig. 12(c)]. Even though the simulation results indicate that the bias is not negligible, the bias is basically smaller than that of Aeolus [14].
In summary, Figs. 12(a) and 12(b) demonstrate the performance of the SCDWL. The SCDWL is estimated to have comparable performance to the mission requirement of Aeolus at the target altitude of up to 6 km if the HM and small variation of wind velocity within the accumulation length are assumed. In addition, the MP is comparable to or better than the requirement even in the altitude of 12 km if the broadening of the ARS is small. The bias is much better than the requirement if the shape of the ARS is approximately symmetric.
F. Performance with Improved Instrumental Parameters or Higher Backscattering Coefficient
Finally, we examine the performance of the SCDWL if improved parameters or higher backscattering coefficients are assumed. We focus on the condition of (HM/I-12) where both the DP and the MP fail to meet the mission requirement of Aeolus. We estimated the DP, MP, and bias for improved diameter of telescope $D$ and higher backscattering coefficient $\beta$. We assumed the $D$ of 0.7, 1.1, and 1.5 m for the analysis. The current value of 0.7 m was set considering the mountability of the telescope on the assumed satellite platform. On the other hand, Aeolus equips a telescope with a diameter of 1.5 m [13], which indicates that a telescope with a diameter of over 1.5 m is possible in principle. In addition, we assumed $\beta$ from ${{10}^{- 7}}$ to ${{10}^{- 9}}\;{{\rm m}^{- 1}}\;{{\rm sr}^{- 1}}$ for the following analysis. Although the backscattering coefficient is ${1.2} \times {{10}^{- 8}}\;{{\rm m}^{- 1}}\;{{\rm sr}^{- 1}}$ in the case of (HM/I-12), the value of $\beta$ ranges within a few orders of magnitudes in reality. For instance, Fig. 5 shows that $\beta$ of the high-backscattering model (HM) at the altitude of 6 km is ${5.1} \times {{10}^{- 7}}\;{{\rm m}^{- 1}}\;{{\rm sr}^{- 1}}$ in the 90-pecentile while it is ${4.0} \times {{10}^{- 9}}\;{{\rm m}^{- 1}}\;{{\rm sr}^{- 1}}$ in the 10-pecentile. In addition, $\beta$ is estimated to ${5 \!-\! 9} \times {{10}^{- 8}}\;{{\rm m}^{- 1}}\;{{\rm sr}^{- 1}}$ if we calculate $\beta$ from that measured in 532 nm by CALIPSO [42] from January 2018 to December 2018 with the procedure described in Section 4.B. Moreover, $\beta$ is increased significantly due to clouds. Although our calculation assumed a clear sky, a part of the sky is often covered with clouds, which exhibits a few orders higher backscattering coefficient than that of a clear sky [21]. Considering the above points, it is worth estimating the performance of the SCDWL with the improved $D$ and higher $\beta$.
Figures 13(a) and 13(b) show the DP, MP, and bias for higher backscattering coefficient $\beta$ and larger diameter of telescope $D$. Both figures demonstrate dramatic improvement of the DP and MP values. Even with $D$ of 0.7 m (the initial value), the DP and MP reach the requirement value for Aeolus at the $\beta$ of ${3.4} \times {{10}^{- 8}}$ and ${2.6} \times {{10}^{- 8}}\;{{\rm m}^{- 1}}\;{{\rm sr}^{- 1}}$, respectively. These values of $\beta$ are realistic since these are much lower than that of 90-percentile HM. In the case of $\beta$ of ${1.2} \times {{10}^{- 8}}\;{{\rm m}^{- 1}}\;{{\rm sr}^{- 1}}$ (the initial value), the MP meets the requirement at the $D$ of 1.1 m and the DP approaches the requirement at the $D$ of 1.5 m. These results suggest that improvement of $\beta$ and $D$ has a great impact on the DP and the MP values and enables the SCDWL to observe wind velocity at a high altitude.
Fig. 13. Calculated (a) DP and (b) MP and bias for different $\beta$ and $D$ values. The blue, orange, and yellow lines represent $D$ of 0.7, 1.1, and 1.5 m, respectively. The black broken horizontal lines represent the mission requirement of Aeolus. The gray vertical lines represent the value of $\beta$ corresponding to the aforementioned backscattering models.
On the other hand, the bias is nearly constant with $\beta$ and $D$ values. This is because the bias is mainly attributed to an asymmetric shape of the accumulated received spectrum (ARS), which means that increasing $\beta$ and $D$ is not effective. An alternative method is, for instance, the adaptive accumulation, which is reported by Kotake et al. [43]. The adaptive accumulation is a technique to adaptively change the accumulation length in response to real-time wideband SNR. The accumulation length is usually constrained by the SNR. However, the SNR is not constant since aerosols are not uniformly distributed and strong backscatter, for instance, clouds, sometimes exists. This means that a short accumulation length is sometimes enough for detection. A shorter accumulation length results in a lower probability of significant change of wind velocity within the length, which suppresses the asymmetric shape of ARS.
7. CONCLUSION
In this paper, we demonstrated an analysis on performance of an SCDWL with a 1.5-µm PWA. We developed the DWL simulator for estimating the performance considering realistic wind profiles. We carefully analyzed the latest performances of a 1.5-µm PWA, which is the key device to implement the SCDWL with an operation wavelength of 1.5 µm. We analyzed the modified FoM of the PWA and proved that pulse energy of 45 mJ is reasonable for the simulation and the system efficiency should be modified taking its beam quality into account. The DWL simulation demonstrated that the performance of the SCDWL is comparable to or better than mission requirements for Aeolus at the target altitude of up to 6 km in the case of the high-backscattering model and negligible broadening of the received spectrum. In addition, it was shown that further enhancement of the performance is possible with a higher backscattering coefficient and an improved diameter of the telescope. We characterized the influence on the performance from wind velocity distribution along the accumulation length. A non-uniform wind velocity distribution creates the broadened and asymmetric shape of the spectrum of received signal and induces degradation of performance and the bias, which can be usually ignored in a coherent DWL. Even though the simulation results of the bias are not negligible, they are basically smaller than the values in the Aeolus mission, which has been reported in the literature [14]. We believe that our analysis on the SCDWL with the 1.5-µm PWA deepens insight on the potential of an SCDWL and contributes to implementation of it. For developing future SCDWL, it is necessary to consider a detailed comparison with simulation assuming other wavelengths (for instance, 2 µm) [21,23,25], the strategy of laser scanning (for instance, conical scanning [25]), cooperation with a satellite-borne incoherent DWL [11–13], and hardware design ensuring operation in a space environment.
Funding
Japan Aerospace Exploration Agency.
Acknowledgment
The authors thank Mr. J. Nomura of Mitsubishi Electric Corporation for fruitful discussions on the performance of a 1.5-µm planar waveguide amplifier.
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, after the permission in the affiliations of the authors based on their data delivering policy.
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