Demonstration of the 1.53-&#x00B5;m coherent DIAL for simultaneous profiling of water vapor density and wind speed

Masaharu Imaki; Hisamichi Tanaka; Kenichi Hirosawa; Takayuki Yanagisawa; Shumpei Kameyama

doi:10.1364/OE.400331

1. Introduction

A light detection and ranging (lidar) system is an attractive instrument to measure the density of the tropospheric water vapor (H₂O), which affects the growth of cumulonimbus that causes localized heavy rainfall [1]. Especially, the range-resolved coherent differential absorption lidar (DIAL) has many advantages in (i) the high receiving sensitivity owing to the heterodyne-detection, (ii) suppression of the noise from solar background by narrowband spectral filtering, and (iii) the simultaneous profiling of the H₂O density and wind speed along the observation direction.

The first coherent DIAL observation of atmospheric molecules was proposed by Kobayasi and Inaba in 1975 [2]. Subsequently, Hardesty [3] reported the simultaneous profiling of H₂O density and wind speed. This work utilized the 10-µm wavelength with carbon dioxide (CO₂) lasers due to the maturity as compared with other lasers in those days. Kavaya et al. [4] discussed the capability of H₂O profiling for the ground-based and space-based coherent DIAL with the 2-µm wavelength region. After these pioneering works, the coherent DIAL systems using 2-µm solid state lasers have been demonstrated mainly for the profiling of CO₂ concentration [5–9]. The coherent DIAL for simultaneous profiling of CO₂ concentration, H₂O density, and wind speed has also been shown [9]. The 1.65-µm coherent DIAL for simultaneous profiling of methane concentration and wind speed has been demonstrated recently [10]. On the other hand, the de-facto standard wavelength of the coherent lidar has moved to the 1.5-µm region [11–21] because of eye-safety and the evolution of devices for optical fibers. Recently, we proposed the 1.53-µm coherent DIAL for the simultaneous profiling of H₂O density and wind speed, and showed its theoretical feasibility in ground-based measurements [22], with the motivation of future ground-based network stations using this DIAL.

In this paper, we show the experimental demonstration of the coherent DIAL which we found feasible in the above mentioned recent work. To the best of our knowledge, this paper shows the first demonstration of the DIAL which realizes the simultaneous profiling of H₂O density and wind speed using the1.5-µm wavelength region. Relative to our related conference papers [23,24], the present paper shows additional results and analysis for the demonstration. In the followings of this paper, we explain the configuration of the DIAL system. Next we show the wavelength locking circuit, which is the key component of the system, and its evaluation result. We also introduce the demonstration results of the validity of the measured H₂O density and the example of the simultaneous profiling of H₂O density and wind speed. The coherent DIAL of this paper does not have the function of beam scanning, therefore, the wind speed profiling is limited to the line-of-sight (LOS) direction. The wind speed and direction profiling using beam scanning (for example, conical) is the remaining future issue.

2. 1.53-µm coherent DIAL system

2.1. System configuration

The configuration of the 1.53-µm coherent DIAL is shown in Fig. 1. The system utilizes the commercially available polarization maintained optical fiber components for the optical communication systems. The laser sources are distributed feed-back laser diode (DFB-LD) modules for the wavelength region of 1.53-µm. The LD consists of gallium indium arsenide phosphide core layer grown on an indium phosphide substrate (GaInAsP/InP). The laser linewidth of the GaInAsP/InP DFB-LD is 1 MHz. The DFB-LD module has the function of automatic current control (ACC) and automatic temperature control (ATC). For the ON wavelength, the additional driving current control is performed using the wavelength locking circuit. The optical switch consists of electrically-controlled polarization rotator and a polarizer. The switching interval of the optical switch is 1.25 s. The pulse modulator is an acousto-optic modulator (AOM) with a double-pass configuration [15] which has an up-shift frequency of 160 MHz. This AOM is made of chalcogenide glass. The optical amplifier is an erbium doped fiber amplifier which is tuned for the 1.53-µm wavelength band. This amplifier has the output peak power of 29 W, 470 ns pulse width, and 8 kHz pulse repetition frequency. The optical signal-to-noise ratio (SNR), which corresponds to the amplified spontaneous emission (ASE) level, is 30 dB within the optical bandwidth of 0.2 nm. The influence of the ASE in the SNR for the received signal can be negligible by carefully designing the isolation level of the circulator. The self-phase modulation in the fiber amplifier causes an additional up-shift frequency of 2 MHz [16]. Consequently, the sum of this shift frequency and that of AOM is 162 MHz, and is the intermediate frequency of this DIAL system. The anti-aliasing filter has a bandwidth of about 100 MHz with the center frequency of the above mentioned intermediate frequency of 162 MHz. The balanced receiver has the bandwidth of 800 MHz and consists of two photo-detectors which are made of indium gallium arsenide (InGaAs). The other system parameters for the experimental setup are listed in Table 1. The receiving bandwidth of 4.5 MHz in the table is the equivalent receiving optical filter bandwidth since the system uses heterodyne-detection. The ON and OFF wavelengths are selected by referring our previous study and considering the height profile of the absorption coefficient [22]. Note that these wavelengths include the influence of the shift frequency of 162 MHz. The absorption coefficients of the wavelengths (in Table 1) are derived from the HITRAN 2004 database [25] at the ground level pressure of 1013 hPa and the temperature of 296 K. The selected absorption line has the center at 1531.374 nm.

Fig. 1. Schematic of 1.53-µm coherent DIAL.

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Table 1. System parameters.

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2.2. System operation process for simultaneous profiling of H₂O density and wind speed

The continuous-wave (CW) laser lights from the two laser sources are locked to the ON and OFF wavelengths which are absorption and non-absorption wavelengths. Either ON or OFF wavelength is selected by an optical switch, and fed to the optical pulse modulator and amplifier. In this process of the modulation and amplification, an intermediate frequency is used. The selected output is transmitted to the atmosphere through a telescope. A part of the CW light is tapped and used for a local signal light for heterodyne detection. The backscattered signal in each range bin is heterodyne-detected by a balanced receiver and converted to an electrical signal. After passing through the anti-aliasing filter and analog-to-digital (A/D) conversion, the detected signal at each bin is spectrally analyzed using a fast Fourier transform (FFT) and accumulated with a signal processor. The white noise component is subtracted from the accumulated spectrum with a known noise level after whitening the noise prior to performing this subtraction. The peak of the accumulated spectrum indicates the Doppler-shifted intermediate frequency. The mean frequency is estimated as the first moment around the peak in the spectrum, and the line-of-sight (LOS) wind speed is obtained as the difference between this mean frequency and the intermediate frequency. The schematic of the DIAL measurement is shown in Fig. 2. The hatched area below each peak designates the signal intensity employed in the DIAL measurement. This signal intensity (i.e., the hatched area in Fig. 2) is obtained by adding the intensities in all the spectral components around the peak. Then, the differential absorption optical depth (DAOD), the H₂O concentration (n), H₂O density (n’) and are calculated from the signal intensities for ON and OFF wavelengths in neighboring two ranges, P_{r_ON}(z), P_{r_ON}(z+Δz), P_{r_OFF}(z), and P_{r_OFF}(z+Δz) as

(1)$$DAOD(z )= \textrm{ln}\left[ {\frac{{{P_{r\_OFF}}({z + \Delta z} )}}{{{P_{r\_ON}}({z + \Delta z} )}} \cdot \frac{{{P_{r\_ON}}(z )}}{{{P_{r\_OFF}}(z )}}} \right], $$

(2)$$n(z )= \frac{1}{{2 \cdot \Delta z \cdot ({{k_{ON}} - {k_{OFF}}} )}} \cdot DAOD(z ), $$

(3)$$n^{\prime}(z )= \frac{{n(z )M}}{{{N_A}}}, $$

where z is the range (i.e., distance), Δz is the range resolution of the lidar, k_ON (k_OFF) is the absorption coefficient at the ON (OFF) wavelength, M is the molecular mass, and N_A is Avogadro’s number.

Fig. 2. Schematic of the spectrum obtained by applying FFT to two neighboring ranges.

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2.3. Theoretical systematic error and requirement for wavelength stability

The absorption spectrum is shown in Fig. 3 under the model of the U.S. standard atmosphere 1976 and the H₂O density of AFGL atmospheric constituent profiles [26]. The Voigt model is used in the calculation of the absorption spectrum. In deriving the DIAL-measured H₂O density, the absorption coefficients in Table 1, which corresponds to the ground level case, are used for all results, and any compensation regarding the temperature and pressure change is not performed. This works well for practical ground-based measurements since any a priori atmospheric information (pressure, temperature, etc.) regarding the upper altitudes is not needed in the measurement. Therefore, there is systematic error in the DAOD measurement especially for the height profiling. The wavelength instability is also a source of DAOD error. Figure 4 shows the theoretical systematic DAOD error versus ON wavelength error for some altitudes. It is shown that the required wavelength stability corresponding to the DAOD error of 5% is 0.2 pm for the measurement altitude of up to 2 km. Regarding the OFF wavelength, a larger value of the stability, 2 pm (corresponding to the frequency of 256 MHz), is acceptable to achieve the same DAOD error of 5%.

Fig. 3. Absorption spectrum of 1531.374 nm absorption line.

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Fig. 4. Wavelength error versus DAOD error for each altitude.

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3. Wavelength locking circuit

3.1. Concept of wavelength locking

In general, wavelength locking is performed using a combination of wavelength locking to the absorption line center of H₂O and offset-locking. However, there is a difficulty for the laser wavelength in locking directly to the line center of H₂O, since the absorption coefficient is small. Concretely, the absorption line intensity for the selected absorption line (1531.374 nm) is 3.07 × 10⁻²⁴ cm⁻¹/mol and the self-broadening linewidth is 0.44 cm⁻¹. Consequently, the transmittance in the gas cell with the path length of 1 m is 0.9999 under the room temperature even in the saturated H₂O density condition (for the calculation of this value, see Appendix A). This means almost no absorption appears in the gas cell, and it is clear that precise wavelength locking to this line center is difficult.

To overcome this issue, we developed wavelength locking circuit using a hydrogen cyanide (HCN) gas cell, which has a large optical absorption near the ON wavelength of H₂O. Figure 5 shows the wavelength locking circuit for ON wavelength. The circuit consists of a line center locking unit on to the HCN absorption line and an offset locking unit for locking to the ON wavelength. Both of these units can be realized by the commercially available optical fiber-based components including the HCN gas cell (HCN-13-H(16.5)-20-FCPC, manufactured by Wavelength References, path length: 16.5 cm). This fiber-based configuration gives both compactness and stable operation (i.e., no need for the optical alignment).

Fig. 5. Schematic diagram of wavelength locking circuit.

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3.2. Line center locking unit

In the line center locking unit, the phase modulation method [27,28] is deployed, by considering the suitability for the fiber-based configuration and the good availability of the fiber-pigtailed phase modulator of the 1.5-µm wavelength band which is made of lithium niobate. The wavelength of CW laser light is tuned for the absorption line center of HCN R18 branch which is close to the ON wavelength. The center wavelength of the target absorption line is 1531.276 nm. The laser light is divided and one part of the divided light is used as the input to the offset locking unit. The other part of the divided light is modulated by the phase modulator and detected by an InGaAs photo-detector after passing through the HCN gas cell that has a path length is 0.8 m. For precise locking, the gas cell is used at the low pressure of 20 torr to make the absorption line width narrow. The linewidth of this absorption line is 38 MHz/Torr [29] and is 760 MHz for the pressure in the gas cell. The absorption line intensity is not known, but in the past literature [29], the transmittance in the gas cell have been shown as about 0.6 with a path length of 0.15 m under the pressure of 25 torr. It is obvious that the transmittance of the gas cell which we used has enough absorption for wavelength locking. The modulation frequency of the phase modulator is 842 MHz which is roughly equal to the absorption linewidth. The detected signal from the photo-detector is mixed with a modulation signal which has the same frequency as that of the phase modulation. The mixed signal is A/D converted and recognized as the error signal which corresponds to the wavelength difference from the center wavelength of the absorption line. Figure 6(a) shows the schematic of the modulated light for absorption line and error signal. If the laser wavelength is controlled to be at the center of the absorption line, the side-band optical signals, which are positive and negative amplitudes, are equally absorbed in the gas cell, and these signals are canceled in the detection by the photo-detector, and then, the amplitude of the error signal becomes zero. If the laser wavelength has an offset from the absorption line center, a difference appears between the positive and negative amplitude of the side-band optical signals, and then, the error signal has some amplitude. Therefore, the laser wavelength can be stabilized to the center wavelength of the absorption line by driving the amplitude of the error signal to zero using a central processing unit (CPU) and tuning the driving current of the DFB-LD through a digital to analogue (D/A) converter and a driver. The output resolution of the D/A converter corresponds to the wavelength control resolution of 7.6 MHz. The feed-back control frequency is 100 Hz.

Fig. 6. Error signal of the wavelength locking circuit.

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3.3. Offset locking unit

Figure 6(b) shows a schematic of the operation of the offset locking technique. The wavelength of CW laser light is tuned for the ON wavelength of H₂O. The CW laser light and the stabilized laser light for HCN absorption line are mixed, and the beat signal is detected by the photo-detector. The frequency of the detected beat signal has a frequency around the target offset frequency of 13.663 GHz, which is the difference between the target wavelength of 1531.383 nm and the HCN absorption line at 1531.276 nm. Note that the target wavelength is not same as the ON wavelength since the output of the laser source is frequency shifted by the AOM and fiber amplifier. The frequency of the beat signal is down-converted to around 1.663 GHz with a reference signal with a frequency of 12 GHz. The down-converted signal is then divided and the power of a part of the divided signal is detected and A/D converted after passing through an electrical filter and a power detector. The other part of the divided signal is also A/D converted directly. The ratio of the two A/D converted values corresponds to the transmittance of the filter, and also to the frequency of the beat signal which is determined by the characteristics of the electrical filter edge. The CPU recognizes the frequency of the beat signal with the transmittance change of the filter. The driving current of the DFB-LD is precisely controlled to make the filter transmittance constant using a CPU, D/A converter, and a driver. Consequently, the frequency of the beat signal is tuned for the target offset frequency of 13.663 GHz. Note that the down-conversion of the beat signal makes the filter cut-off frequency low, and can make the filter edges sharp. This contributes to making the sensitivity of the error signal higher, and to precise offset locking.

3.4. Evaluation result of wavelength stability

The wavelength stabilities of the line center locking and offset locking circuits are evaluated using the following procedure. First, the curve of wavelength versus the error signal is calibrated by using the wavelength meter and plotting the amplitude of the error signal. In this calibration, the wavelength locking operation is not performed and the wavelength is changed over a wide range on purpose by changing the driving current. The slope relating the wavelength error and the error signal amplitude is obtained. Then, the wavelength locking operation is performed by sampling the error signal, and the wavelength error is predicted from the error signal amplitude and the above mentioned slope. Figure 7 shows the results of wavelength stabilities of the line center locking and offset locking under the air-conditioned room temperature. The sampling interval of the measured wavelength is about 0.01 s. It can be seen that the wavelength locking for both circuits worked well without any wavelength drifting. The wavelength stability for HCN R18 absorption line attains 0.07 pm which corresponds to 9.05 MHz, and the wavelength stabilities for the offset wavelength attain 0.102 pm which corresponds to 13.0 MHz. This satisfies the requirement which is shown in section 2.3. The stability of the offset wavelength can be kept also for the ON wavelength since the stability of the frequency shift in the AOM and fiber amplifier is almost ideal in principle. The limitation factors for the ON wavelength stability are (i) the laser linewidth of the LD, (ii) the wavelength control resolution of the D/A converter, (iii) white noise in the driving signal for the LD, (iv) the feed-back control frequency, and (v) noise of the photo-detector. The laser linewidth of the LD of 1 MHz (as denoted in the section 2.1) is much smaller than the above mentioned stability. The wavelength control resolution of 7.6 MHz (as denoted in the section 3.2) is considered to be the dominant limitation factor. The impacts of the remaining factors (iii) – (v) have not been investigated but it is reasonable to consider that they are not dominant. Figure 8 shows the Allan deviation plot of the result of Fig. 7. The deviation (the vertical axis) in Fig. 8 is simply decreased inversely proportional to the square root of the averaging time. This means the sampled error signal is random, and implies that the improvements regarding (i) – (v) contribute to the wavelength stability improvement (especially, (ii)). The OFF wavelength is stabilized only with the ACC and ATC. The stability has been evaluated using the wavelength meter and is 0.56 pm which corresponds to 72.2 MHz.

Fig. 7. Time dependence of offset locking and line center locking wavelength.

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Fig. 8. Allan deviation plot of Fig. 7.

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4. Atmospheric measurement results

4.1 SNR performance

Figure 9 shows the range dependence of the SNR for the horizontal path measurement regarding both ON and OFF wavelengths. The calculated SNR of OFF wavelength and random error (standard deviation) of the measured H₂O density are also shown. The equations for the SNR calculation are derived in Appendix B. The beam focusing range is 350 m, the range bin size (i.e., the time gate width in the signal processing) is 100 m, and the number of accumulation N is 3 × 10⁶ corresponding to 6.25 min for each wavelength. In the signal processing, (i) the spectral accumulation for one of the wavelength is performed for 1.25 s, then (ii) it is switched for the other wavelength by using the optical switch, and then (iii) the process of steps (i) and (ii) are iterated until reaching at the total accumulation time for each wavelength becomes 6.25 min. The aerosol backscatter coefficient is roughly estimated using a particle counter and is 5.41 × 10⁻⁸ m⁻¹sr⁻¹. The aerosol extinction coefficient is calculated by assuming the lidar ratio of 50 sr. The molecule attenuation is negligible because the value is smaller than that of aerosol attenuation at the wavelength of 1.5-µm region. The refractive index structure constant is assumed to be 1.7 × 10⁻¹⁴ m^−2/3, which is the SLC daytime model [30] under the condition of 18.5 m height. For the measured results, detector-noise related SNR is derived as the ratio of the peak intensity and the standard deviation of the noise intensity within the noise region of the received spectrum. The speckle-noise-related SNR is solely derived based on the number of accumulation. The total SNR is calculated using these two SNRs (see, Eqs. (14)–(16) in Appendix B). It is seen that the calculated SNR for OFF wavelength is in good agreement with the experimental one. Further, the difference of SNR between ON and OFF wavelength becomes larger for the longer range. This is due to the absorption of H₂O for the ON wavelength. The random error of the measured H₂O density is derived using the SNR and shown for the second vertical axis. This derivation is performed as follows. The range resolution for the DIAL measurement (Δz in Eq. (2)) is set to 300 m. This means that the SNRs at two ranges with an interval of 300 m are picked up for both of the ON and OFF wavelengths. Consequently, the first center range for the H₂O density profiling is 250 m (first picked up range bin set: 100 m and 400 m), and the calculation step is 100 m. Note that there is a trade-off between the smaller differential absorption with the shorter range resolution and the longer accumulation time, and further, it is assumed that the SNR and H₂O density are constant within the range gate. The H₂O density is calculated using the Eqs. (1)–(3), and then the random error is derived as

(4)$$E(z )= n^{\prime}(z )\cdot \frac{{\mathrm{\Delta }n(z )}}{n}, $$

where the relative random error Δn/n, is expressed using the SNR of ON and OFF wavelengths as

(5)$$\frac{{\Delta n}}{n}(z )= \frac{1}{{DAOD(z )}}\cdot \sqrt {{{\left( {\frac{1}{{SN{R_{ON}}(z )}}} \right)}^2} + {{\left( {\frac{1}{{SN{R_{OFF}}(z )}}} \right)}^2} + {{\left( {\frac{1}{{SN{R_{ON}}({z + \Delta z} )}}} \right)}^2} + {{\left( {\frac{1}{{SN{R_{OFF}}({z + \Delta z} )}}} \right)}^2}} . $$

In Fig. 9, the random error of less than 1 g/m³ is derived for the range of up to 500 m. For wind sensing, the required SNR is about 7 dB [22] and the measurable range is more than 1 km, but in this case, the measurable range for the simultaneous profiling is limited to a shorter range because of the higher SNR requirement for the precise DIAL measurement. In general, the SNR for the ON wavelength becomes low because of the higher absorption, as demonstrated in Fig. 9. This implies that there is a potential for the optimization of the DIAL measurement performance by setting un-equal accumulation times between the wavelengths, although the same accumulation time is used in this experiment. This should be discussed in future research.

Fig. 9. Range dependence of SNR for horizontal path measurement.

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4.2 Simultaneous H₂O/wind measurement and verification of measured H₂O density

In this section, the simultaneous measurement of H₂O density and wind speed is demonstrated. The experiment was performed from 18:00 of February 3rd to 6:00 of February 6^th, 2017, at Mitsubishi Electric Corporation, Information Technology R&D center in Kamakura city, Japan. Figures 10 and 11 show the time history of measured results for the horizontal path, regarding SNR, LOS wind speed, and H₂O density. Both of the range bin size and the nearest range are 300 m. The SNR and LOS wind speed data in the figures is for the OFF wavelength at the nearest range (i.e. 300 m) and is almost the same value as that of the ON wavelength. For the verification of the H₂O measurement, the measured data of the H₂O density of the DIAL was compared with that of the in-situ sensor (T&D Corporation, RTR-53) which was located about 20 m away from the DIAL. The in-situ sensor is a humidity and temperature sensor, therefore, the H₂O density of this sensor is obtained using such two parameters. The two range data of 300 m and 600 m for the horizontal path was used in the DIAL measurement (i.e., the range resolution of 300 m and the center range is 450 m). The data accumulation time for each wavelength is 6.25 min and 12.5 min for the total in Fig. 10. This means the data refresh interval for the DIAL measurement is 12.5 min. Figure 11 shows the comparison result between the DIAL-measured and in-situ-sensor-measured results. The rainfall had started at 16:00 of February 5th. The measured H₂O density of each sensor increased from 4 g/m³ to 7 g/m³ just before the rainfall. In this experiment, we are not able to discuss on the measurement accuracy of less than 1 g/m³, since the specification of the accuracy of the in-situ sensor is 1.2 g/m³. However, it can be seen that there is a qualitatively good agreement in trending between the DIAL-measured and in-situ-sensor-measured results. Figure 12 shows the random error (i.e. precision) of the DIAL-measured result. This is derived by the standard deviation in the time window of 12.5 min and the time history is obtained by sliding this window. The blue line in Fig. 12 is the predicted result from the SNR data of Fig. 10 (by assuming the SNR for ON and OFF wavelength and neighboring ranges are approximately the same). The equations for this prediction are shown in Eqs. (4)–(5). The two results on the random error are basically in agreement. Figure 13 shows the frequency spectrum of the H₂O density which is calculated by the Fourier transform of the time history data in Fig. 11. Such analysis (i.e. using the Fourier transform of the measured time history data) is an authentic method for the analysis of the random measurement error regarding the naturally changing phenomena (for example, see [31] in the case of the wind sensing lidar). There are two components in the spectrum. The first one is the fluctuation of the real H₂O density which is in the low frequency region. The second one is the component of the random error which is white. The random error in the whole measurement period can be derived from the integration of average level of the white component in the spectrum (in Fig. 13, frequency region of > 1 × 10⁻⁴ Hz). The derived random error is 0.56 g/m³. Figure 14 shows the correlation plot of the H₂O density measured by the DIAL and in-situ sensor. The scatter in the correlation plot seems larger for the horizontal direction in the figure. This is due to the larger random error of the DIAL-measured result. The three-parameter regression is performed. The coefficient of determination is 0.73, the slope is 1.14, and the offset is 0.38 g/m³.

Fig. 10. Time history of SNR and LOS wind speed.

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Fig. 11. Comparison with DIAL and in-situ sensor H₂O data.

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Fig. 12. Predicted and measured random error of H₂O density of DIAL data.

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Fig. 13. Spectrum of H₂O density measured by DIAL and in-situ sensor.

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Fig. 14. Correlation plot of H₂O density measured by DIAL and in-situ sensor.

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4.3 Vertical profiling of H₂O and wind

The time history of the vertical profile of H₂O density and wind speed were simultaneously measured from 16:00 November 1st to 14:00 November 4th, 2019. The laser beam was transmitted to the atmosphere with the zenith angle of 35.4 degrees, and the data accumulation condition is same as in section 4.2. Both of the range bin size and DIAL measurement resolution are 100 m, which corresponds to the height resolution of 82 m with consideration of the beam angle. Figures 15(a) and 15(b) show the height profile of SNRs for ON and OFF wavelengths, respectively, (c) H₂O density, and (d) LOS wind speed. The measurable height is basically up to 1 km which corresponds to the measurable range of 1.2 km. The measurable arrange is in the same range as that of Fig. 9, even though the range resolution is higher (Fig. 15: 100 m, Fig. 9: 300m). This is due to the higher SNR in Fig. 15, which, in turn, is because of the higher aerosol backscattering condition. Such data has potential for employing in the data-assimilation models (for example, the grid analysis and display system [32]), as the additional information, to improve the rainfall prediction accuracy.

Fig. 15. Time history of vertical profile regarding (a) SNR for ON wavelength, (b) SNR for OFF wavelength, (c) H₂O density, and (d) LOS wind speed.

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5. Conclusions

We experimentally demonstrated performance of the 1.53-µm coherent DIAL and showed the simultaneous profiling of H₂O density and wind speed. The optical setup, including the wavelength locking part, has the fiber-based configuration, which is utilized with the commercially available components for the optical communication systems. The wavelength locking circuit has a unique feature in the combination of the line center locking to the HCN absorption line and offset locking to the target wavelength for the H₂O absorption. The stability of the ON wavelength was 16.2 MHz and satisfied our requirement. We also presented the results of the simultaneous profiling of H₂O density and wind speed. The measurable range for simultaneous profiling is up to 1.2 km. The validity of the DIAL-measured H₂O density was confirmed using the in-situ sensor and there was a good agreement in the diurnal change. The random error was in the reasonable value in the comparison with the predicted value from the SNR. The random error which was derived from the spectrum of the measured H₂O density was 0.56 g/m³. The vertical profiles of the measured H₂O/wind were also shown with a resolution of 100 m. Few studies on H₂O sensing DIAL [33–35] revealed better H₂O profiling performance (for example, the measurable range (altitude) of up to 6 km in [35]). However, the data of this paper shows the potential in contributing to the further accuracy improvement of the data assimilation for the rainfall prediction, thanks to the function of the simultaneous profiling of H₂O density and wind speed. The wind speed profiling in the present paper is limited for the LOS direction. The wind speed and direction profiling with a beam scanner is a remaining task for future development. The longer range or higher altitude profiling is also needed for enhanced data assimilation (in [1], it has been stated that the required profiling altitude is 0.2–2 km for the forecasting heavy rainfall in Japan). For such a profiling, the higher power laser transmitter is needed. We also developed the Er, Yb: glass planar waveguide amplifier for this purpose [36] and started the demonstration using this amplifier [24].

Appendix A: Equations for calculation of transmittance in the gas cell

The transmittance in the gas cell is calculated as

(6)$${T_C} = exp\left( {\frac{{ - {\kappa_C}L}}{{\pi \gamma }}} \right), $$

where L is the path length in the cell, γ is the absorption linewidth. In the saturated pressure condition in the H₂O cell, γ is the self-broadening linewidth. κ_C is the absorption coefficient at the absorption line center and is calculated as

(7)$${\kappa _C} = S \cdot \rho , $$

where S is the line intensity of the absorption line. ρ is the molecular density. In the case of H₂O gas cell, ρ is the saturated density and is obtained by

(8)$$\rho = \frac{{217e(T )}}{{T + 273.15}} \cdot \frac{{{N_A}}}{M}, $$

where T is the Celsius temperature. e(T) is the saturated pressure of H₂O and is expressed by

(9)$$e(T )= 6.1078 \cdot {10^{\frac{{7.5T}}{{T + 273.3}}}}. $$

Appendix B: Equations for calculation of the received power and SNR

The equations for the received signal power and SNR calculation are shown below. Such equations are derived in [22]. The received optical power is given by

(10)$${P_r}(z )= \frac{{{P_0}{\beta _a}(z )\cdot \pi {D_r}^2 \cdot c\tau {\eta _O}{\eta _d}(z )T(z )}}{{8{z^2}}}, $$

where P₀ is the peak power of the emitted laser beam, τ is the full pulse width, D_r is received aperture, β_a is the aerosol backscatter coefficient, η_O (η_d) is the is the efficiency corresponding to the optical loss of components (heterodyne detection, see below); T is the round-trip atmospheric transmittance given by

(11)$$T(z )= \textrm{exp}\left[ { - 2\mathop \smallint \nolimits_0^R ({{\alpha_a}(z )+ {\alpha_m}(z )+ {\alpha_{{\textrm{H}_2}\textrm{O}}}(z )} )dz} \right], $$

where α_a (α_m) is the extinction coefficient of aerosol (atmospheric molecule) and α_H2O is the absorption coefficient of water vapor. The heterodyne-detection efficiency, η_d is expressed as

(12)$${\eta _d}(z )= \frac{{{\eta _F}}}{{1 + {{\left( {1 - \frac{z}{{{z_F}}}} \right)}^2} \cdot {{\left( {\frac{{\pi {{({A{D_r}} )}^2}}}{{4\lambda z}}} \right)}^2} + {{\left( {\frac{{A{D_r}}}{{2{S_0}(z )}}} \right)}^2}}}, $$

where η_F is the far-field heterodyne detection efficiency, D_t is the beam diameter of the nearest Gaussian beam, Z_F is the beam focusing range of the transmitted beam, and A is the correction factor describing the beam truncation of the telescope when the nearest Gaussian approximation is adopted. In this paper, the optimized condition of the far-field heterodyne detection efficiency η_F of −4dB and correction factor A of 0.71 has been used (the same condition as in [22]). S₀ is the transverse coherent length written as

(13)$${S_0}(z )= {\left[ {2.91{k^2}\mathop \smallint \nolimits_0^z C_n^2(R ){{\left( {1 - \frac{R}{z}} \right)}^{5/3}}dR} \right]^{ - 3/5}}, $$

where k is the wavenumber and $C_n^2(R )$ is the refractive index structure function at a certain range. This parameter has the dependence on the altitude, and represents the influence of the atmospheric refractive turbulence on laser beam propagation. Note that this equation is correct (see, [37]), and there was an unreported error in the corresponding equation of our past paper (Eq. (8) in [22]).

When the detection is shot-noise limited, and no correlation is seen between the signals of the ON and OFF wavelengths and those from different ranges, the SNR at each range is expressed as

(14)$$SNR(z )= \frac{1}{{\sqrt {{{\left( {\frac{1}{{SN{R_{det}}(z )}}} \right)}^2} + {{\left( {\frac{1}{{SN{R_{speckle}}(z )}}} \right)}^2}} }}. $$

The denominator includes the contributions om both the detector noise and speckle noise. These SNRs are given by

(15)$$SN{R_{det}}(z )= \frac{{\sqrt N {P_r}(z )}}{{Bh\nu }}, $$

(16)$$SN{R_{speckle}} = \sqrt N , $$

where h is the Plank constant, ν is the optical frequency, B is the spectral bandwidth of the received signal, and N is the accumulation number. Note that the Eq. (15) is slightly different from the corresponding equation of our past paper (Eq. (13) in [22]). The system efficiency (ηS in Eq. (13) of [22]) is included in η0 of Eq. (10) in this paper. These SNRs refer to the ratio between the signal intensity and its standard deviation. The value of SNR_det(z) in Eq. (15) expresses the detection ability of the wind measurement. The refractive turbulence impacts the detector-noise-related SNR (Eq. (15)). The turbulence-induced signal fluctuation also impacts the coherent DIAL performance especially in the case of the moderate-to-strong turbulence [38]. Although such impact is not expressed in the equations here, the calculated random error in Fig. 12 shows a good agreement with the experimental one. It is inferred that the degree of turbulence impact on the experiment of Fig. 12 was qualitatively small.

Disclosures

The authors declare no conflicts of interest.

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Item	Value
ON wavelength	1531.3814 nm
OFF wavelength	1531.5537 nm
Absorption coefficient for ON wavelength at the ground level	8.63 × 10⁻²⁴ cm⁻¹/mol
Absorption coefficient for OFF wavelength at the ground level	1.33 × 10⁻²⁵ cm⁻¹/mol
Peak power	29 W
Pulse width	470 ns (corresponding to 71 m)
Pulse repetition frequency	8 kHz
Aperture diameter	70 mm
Beam correction factor	0.71
Optical loss	4.6 dB
Receiving signal bandwidth	1.5 MHz

Demonstration of the 1.53-µm coherent DIAL for simultaneous profiling of water vapor density and wind speed

Abstract

1. Introduction