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Abstract
What we believe to be a novel low-cost broadband continuous-wave water vapor differential absorption lidar (CW-DIAL) technique has been proposed and implemented by combing the Scheimpflug principle and the differential absorption method. The broadband CW-DIAL technique utilizes an 830-nm high-power multimode laser diode with 3-W output power as a tunable light source and a CMOS image sensor tilted at 45° as the detector. A retrieval algorithm dedicated for the broadband CW-DIAL technique has been developed to obtain range-resolved water vapor concentration from the DIAL signal. Atmospheric remote sensing of water vapor has been carried out on a near-horizontal water vapor path to validate the performance of the broadband CW-DIAL system. The retrieved water vapor concentration showed a good consistency with those measured by an air quality monitoring station, with a correlation coefficient of 0.9669. The fitting error of the water vapor concentration is found to be less than 10%. Numerical simulation studies have revealed that the aerosol-induced error on the water vapor concentration is below 5% with a background water vapor concentration of 5 g/m3 for most atmospheric conditions. The experimental results have successfully demonstrated the feasibility of the present broadband CW-DIAL technique for range-resolved water vapor remote sensing.
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1. Introduction
In recent decades, extreme meteorological disasters such as typhoons, droughts and floods occur frequently, which seriously threaten the sustainable development of human society. Atmospheric water vapor mainly originates from the evaporation of the ocean surface, but it is also influenced by evaporations from lakes, rivers, vegetation and localized sources. In the form of three-phase transformation, the water vapor will greatly affect the changes of precipitation, temperature and humidity along the way in the process of participating in the earth's water cycle [1]. Water vapor is also one of the most important greenhouse gases. When the earth absorbs the sunlight radiation, it will reflect or scatter unabsorbed energy mainly in the infrared region. Since the water vapor has many absorption bands in the infrared region, it will re-fix the energy radiated by the earth into the atmosphere, resulting in temperature rise in the atmosphere [2]. This warming effect will also continue to increase the accumulation of water vapor in the atmosphere and further contribute to the greenhouse effect [3]. Since the spatial-temporal distribution of water vapor can change rapidly, accurate profiling of water vapor content, which is of great significance for understanding atmospheric radiation/chemistry, predicting precipitation or extreme weather events, etc. [4,5], has attracted considerable interests in recent years.
Microwave radiometers, as a passive ground-based remote sensing equipment, can obtain atmospheric humidity from the ground to the altitude of 10 kilometers by measuring the attenuation of microwave radiation of water molecules at specific microwave frequencies [6–8]. Apart from relatively lower spatial resolution, microwave radiometers are also susceptible to clouds and rainfall. Sun photometer measures the solar radiation at different wavelengths to evaluate the optical characteristics of aerosol and column content of water vapor, etc. [9,10]. The Global Positioning System (GPS) method inverses the content of water vapor by analyzing the time-delay of GPS signals transmitted by GPS navigation satellites [11–13]. Besides, radiosonde can measure water vapor content at different altitudes through balloon-based sensors [14], but with limited temporal resolution and spatial resolution. Active remote sensing techniques, such as the Raman lidar technique and the Differential Absorption Lidar (DIAL) technique, are capable of detecting water vapor profile with high temporal and spatial resolution. The Raman lidar technique often transmits high-power laser pulses into the atmosphere and then detects the Raman scattering echoes of water vapor and nitrogen, from which the water vapor content can be evaluated. Since the first demonstration of water vapor Raman lidar by Melfi et al. in 1969 [15], the Raman lidar technique has been widely applied for water vapor profiling [16–24]. However, the Raman lidar signal is quite weak owing to the small cross section of Raman scattering, which may be seriously affected by the solar background light, making it challenging for daytime measurements.
The DIAL technique utilizes differential absorption of water vapor at two nearby wavelengths, often referred to as on-resonance wavelength (λon) and off-resonance wavelength (λoff) [25–27]. In water vapor DIAL techniques, high-energy narrowband laser pulses at λon and λoff wavelengths are alternately transmitted into atmosphere to acquire the corresponding lidar echoes based on the time-of-flight (TOF) principle, from the ratio between the lidar signals at λon and λoff wavelengths, the water vapor content can be accurately retrieved without auxiliary measurements. The pulsed DIAL technique put high requirements on the performance of pulsed tunable laser sources in the near infrared region (e.g., 828 nm, 937 nm), such as narrowband linewidth, high pulse energy, excellent frequency stability etc., which are also the main challenges for the implementation of a water vapor DIAL system [28]. Recently, a field deployable diode laser-based DIAL technique has also been developed, while the performance may be limited by the low pulse energy and the relatively longer pulse duration (∼1 µs) [29]. In 2020, Newsom et al. evaluated the performance of a water vapor broadband DIAL system developed by Vaisala, which utilizes a long-pulse laser diode (∼910 nm, 220 ns) as the light source [30]. The Vaisala prototype, based on the micro-pulse lidar technique, was designed to provide height-resolved measurements of humidity in the lower troposphere with a temporal resolution of 20 min. Atmospheric measurements revealed good agreements between the water vapor contents measured by the broadband DIAL and the radiosonde.
In 2014, a continuous-wave (CW) DIAL technique based on the Scheimpflug principle has been proposed and demonstrated by measuring O2 absorption as well as its absorption cross-section [31]. The CW-DIAL technique utilizes a narrowband continuous-wave semiconductor laser diode as the emission source and a tilted CCD/CMOS image sensor as the detector. The range-resolved atmospheric backscattering signals are obtained from pixel intensities. The lidar technique, also referred to as the Scheimpflug lidar (SLidar) technique, has been widely used in agriculture [32–40], air pollution monitoring [41–47], etc., owing to the robust system structure, high cost performance and short blind range. In 2019, Mei et al. has developed a SLidar-based NO2-DIAL technique using an 1.6-W 450-nm laser diode as the light source and a ppb-level measurement sensitivity has been achieved [48], which has demonstrated the great potential of the SLidar technique for atmospheric trace gas monitoring.
In this work, a novel low-cost broadband water vapor CW-DIAL technique has been proposed and implemented based on the Scheimpflug principle, which utilizes a low-cost high-power multimode 830-nm semiconductor laser diode as the light source. A retrieval algorithm has dedicated to the broadband DIAL technique has also been developed to obtain the water vapor profile. Differential absorption measurements on atmospheric water vapor content have been carried out. Comparison studies with the local monitoring station have been performed to validate the feasibility of the proposed DIAL technique for range-resolved atmospheric water vapor sensing.
2. Broadband continuous-wave water vapor DIAL
2.1 Principle of the water vapor DIAL technique
The broadband CW-DIAL technique for water vapor measurements is based on the Scheimpflug principle, which describes the relationship between the object and the image planes when the object plane is not parallel to the plane where the lens is located. When the laser beam plane (object plane), the image plane and the lens plane intersect, the imaging system can still form an in-focus image of the object plane with a theoretically infinite depth-of-field (DoF) [49,50], while employing a large aperture. As shown in Fig. 1(a), a high-power CW laser diode, often operating at modulation mode, transmits a collimated laser beam into the atmosphere. The corresponding backscattering light originating from molecules and aerosols are collected by a large-aperture telescope, which is then detected by a tilted CCD/CMOS camera, with the optical configuration satisfying the Scheimpflug principle. The atmospheric echoes at different distances are acquired by different pixels of the image sensor. According to the geometrical optics and the Scheimpflug principle, the relationship between different pixels and the measurement distance can be calculated [51]. The lidar echo measured by the SLidar technique can be obtained by
Here λ is the wavelength, z is the distance, Ks is the system constant, P0(λ) is the power spectral density, O(z) is the geometric overlap factor, β(λ, z) is the atmospheric total backscattering coefficient, αaer.(λ, z) and αmol.(λ, z) are extinction coefficients of atmospheric aerosols and molecules, respectively. In SLidar system, the value of O(z) is typically equal to 1 in the measurement range.
Fig. 1. Schematic of the Scheimpflug lidar technique. Ф is the observation angle of the receiving telescope, Θ is the tilt angle of the image plane in respect to the lens plane, LSep is the separation between the optical axis of the receiving telescope and the optical axis of the transmitting telescope (baseline).
The water vapor content is then obtained by measuring the differential absorption of water vapor at different wavelengths, as shown in Fig. 1(b). One wavelength (denoted as λon) is located at the absorption peak of the water vapor absorption line or positioned at the spectral region with relatively higher absorption if a broadband laser source is utilized. The other wavelength (denoted as λoff) slightly deviates from the absorption peak of the water vapor absorption line or located in the region with relatively lower absorption. As the two wavelengths of λon and λoff are very close to each other, the backscattering and extinction effects of aerosols and other air components could be assumed the same. Therefore, the major difference between the lidar signals at λon and λoff wavelengths is determined by the differential absorption of water vapor. By evaluating the ratio of the atmospheric lidar signals at λon and λoff wavelengths, the concentration of water vapor can be retrieved. When employing a high-power multimode laser diode as the light source, the spectral of the output laser beam is much wider comparing with the water vapor absorption lines, and the influence of the spectral width should be taken into account. The broadband DIAL ratio can be written as follows
Here σ(λ, z) is the absorption cross-section of water vapor, K is a ratio factor and N(z) is the water vapor concentration. In the case of vertical probing, σ(λ, z) will depend on the detection distance z due to the variation of atmospheric pressure and temperature at different altitudes. Thus, it is necessary to utilize the absorption cross-section at the specific temperature in the retrieval process. In general, the value of σ(λ, z) at various temperatures can be obtained from spectral database, e.g., HITRAN, which is sufficient for near horizontal DIAL measurements. In vertical DIAL measurements, the temperature/pressure profile can be obtained from the radiosonde measurements or evaluated according to the U.S. Standard Atmosphere Model [52,53]. Then, the water vapor absorption cross-section at different altitudes can be obtained for the retrieval of the water vapor concentration. Since the experiment was carried out on a near horizontal path in this work, the dependency of the absorption cross-section on the measurement distance is not considered in the following discussions. If the wavelength dependencies of the backscattering coefficient and the extinction coefficient of aerosols and molecules are ignored in the spectral range of the DIAL measurements, Eq. (2) can be simplified as follows
As can be seen from Eq. (3), the convolution is involved in the DIAL-ratio equation, from which it is difficult to mathematically derive the water vapor content. Thus, a retrieval algorithm dedicated to the broadband CW-DIAL technique is highly needed.
2.2 Water vapor DIAL system
The low-cost broadband CW-DIAL system mainly consists of a transmission unit, an optical receiver unit and a system controlling unit. The system structure and specifications of the CW-DIAL are shown in Fig. 2(a) and Table 1, respectively. In the transmission unit, a high-power (3-W) multimode semiconductor laser diode operating at around 820-830 nm, with a cost of about 400 USD, is used as a tunable light source. During experiments, the case temperature of the laser diode is controlled and the injection current of the laser diode is modulated through a driving circuit to adjust the emission wavelength. The operation wavelength of the laser diode is tuned by the case temperature and the injection current so that the operation wavelength can be switched between λon and λoff. As the pigtailed laser diode has a relatively larger divergence (25.4°), the output laser beam is collimated first by a cylindrical lens pair and then by a refractor telescope. The transmitted laser beam would be absorbed and scattered in the atmosphere, and the corresponding backscattering light will be collected and detected by the optical receiver unit, mainly consisting of a Newtonian telescope and a CMOS camera. The image of the transmitted laser beam is acquired by the CMOS camera and then transferred to a computer for analysis. The system controlling unit is mainly composed of a data acquisition card (DAQ), a computer, a spectrometer, etc. The DAQ card is utilized to synchronize the trigger signals between the camera and the driver of the laser diode, while the spectrometer is used to monitor and record the laser spectrum in real time. The whole lidar system is controlled by a C++ based software developed by our research group. It should be mentioned that the spectrometer used in the present DIAL system (Ocean Optics, HR4000CG) costs about 5,500 USD, which is cost-effective comparing with those wavelength meters used in conventional DIAL techniques. Besides, much cheaper spectrometer dedicated to the spectral region of 820-830 nm with a spectral resolution of 0.2 nm is also commercially available (OPTOSKY, ATP3334).
Fig. 2. (a) Schematic of the low-cost CW-DIAL based on the Scheimpflug principle; (b) Time sequences of the camera exposure, the spectrometer and the laser diode; (c) The pixel-distance relationship after calibration.
Table 1. Specifications of the low-cost broadband CW-DIAL system for water vapor measurements.
In the CW-DIAL technique, accurate timing sequence is crucial to perform differential absorption measurements of water vapor. As shown in Fig. 2(b), a trigger signal from the CMOS camera, synchronized with the exposure of the camera, is sent to the DAQ card, which generates a modulation signal for the laser diode driver and a trigger signal for the spectrometer. Thus, the spectrometer can also alternately measure the laser spectra of λon and λoff wavelengths. In order to eliminate the influence of the background signal on the lidar echo signal, a dark frame is taken by turning the laser diode off. As a result, three exposures have been taken in a single measurement period for the measurements of the λon lidar signal, the λoff lidar signal and the background signal. By subtracting the background signal in each measurement cycle, the background signal can be effectively eliminated. However, it should be noted that the noise from the background signal and the image sensor cannot be subtracted. Thus, further signal processing is also required.
In order to obtain the lidar profile, it is necessary to calibrate the relationship between the pixel and the measurement distance. During atmospheric measurements, the laser beam is first directed to a building with a known distance and the corresponding beam spot is obtained by the image sensor, from which the pixel-distance relationship can be calibrated, as shown in Fig. 2(c). Besides, the laser beam can also be targeted on buildings with different distances to verify the accuracy of the pixel-distance relationship. As shown in Fig. 3(a), the distance calibration accuracy is generally about 1%, implying that the calibration uncertainty has little effect for the present DIAL measurements. The range resolution, which deteriorates with the increasing of the measurement distance, is shown in Fig. 3(b). As can be seen, the near-range resolution of the system is very high (in the order of cm), while the long-range resolution could be lower than the typical range resolution of the traditional pulsed atmospheric lidar (e.g., 15 m or so).
Fig. 3. (a) Verification of the pixel-distance relationship with objects located at different distances; (b)The relationship between the range resolution and the distance.
3. Methods
3.1 Signal acquisition and processing
In order to minimize the background signal and thus improve the signal-to-noise ratio (SNR), the region-of-interest (ROI) with 240 × 2048 pixels containing the full image of the transmitted laser beam is selected during image acquisition with an exposure time of 200-500 ms. Figure 4(a) shows the beam image obtained after subtracting the background image. By adding the pixel intensities of the beam image in one direction, the pixilated lidar signal can be obtained. As can be seen from Fig. 4(b), the intensity of the on-wavelength lidar signal is much lower than that of the off-wavelength lidar signal. The intensity difference of the two lidar signals is mainly attributed to the residual amplitude modulation (RAM) effect of the laser diode, which implies that both the wavelength and the output power increase with the increasing of the driving current. During DIAL measurements, the temperature of the laser diode is stabilized by a thermal electric cooler, while the central-wavelength of the laser spectrum can be precisely tuned by adjusting the current. Since the on-wavelength is smaller than the off-wavelength, the output power at the on-wavelength as well as the intensity of the corresponding lidar signal is lower.
Fig. 4. (a) The image of the transmitted laser beam; (b) The pixilated lidar signal obtained by binning pixels along one direction; (c) The lidar signal after pixel-distance calibration; (d) The DIAL ratio curve.
Although the background signal, including the sky background and the dark current of the image sensor, can be subtracted, the noise in the lidar signal does not decrease and is inevitably influenced by the noise originating from the sky background and the image sensor. The noise of the DIAL signal predominantly comprises the temporal noise and the fixed pattern noise (FPN). The temporal noise mainly includes the photon shot noise, the dark current noise and the image sensor readout noise, which can be reduced by signal averaging. The FPN is divided into the dark signal non-uniformity (DSNU) noise and the photon response non-uniformity (PRNU) noise. The DSNU noise can be removed during background subtraction. The PRNU noise, attributing to different responses for each pixel under the same illumination, has a nonlinear relationship with the incident light intensity for low light level conditions. Under high light level conditions, the PRNU noise will increase with the increasing of the incident light intensity. Thus, the noise for the background image is not the same with the case acquiring the lidar signal when the laser diode is turned on. Thus, the atmospheric background noise and the PRNU noise of the image sensor are the main noise source of the lidar signal.
During nighttime measurements, the photon shot noise is very small, allowing for noise reduction to levels negligible through signal averaging within a few minutes. Under this circumstance, the PRNU noise would be dominated. As shown in Fig. 4(b), the noise level (standard deviation) of the on-wavelength lidar signal is about 10 (digital numbers), while it is about 20 for the off-wavelength lidar signal. The primary reason for the discrepancy in noise between the two signals is due to the variance of the PRNU noise, which generally linearly increases with the light intensity illuminated on the CMOS sensor under high light level conditions. Since the intensity of the off-wavelength lidar signal is larger, it also has a higher noise level. However, the SNR between these two lidar curves are nearly the same (SNR≈150). During daytime measurements, the photon shot noise from sunlight background would become the dominant noise.
After pixel-distance calibration, the range-resolved lidar signal is obtained, as shown in Fig. 4(c). Besides, raw lidar profiles have also been averaged for about 6 minutes to suppress background and dark current noises, etc. The Savitzky-Golay (S-G) filter has been employed to process the lidar signal to further reduce the noise of the image sensor [54]. The SNR of the signal is typically 150 before S-G filtering and increases to about 220 after S-G filtering. Finally, the DIAL ratio curve can be obtained by dividing the λon-wavelength lidar signal by the λoff-wavelength lidar signal, as shown in Fig. 4(d), which is related to the differential absorption of water vapor. In the present broadband CW-DIAL technique, the pixel-distance relationship is a non-linear function. Thus, the range resolution decreases with the increasing of the measurement distance, and equidistant interpolation on the lidar profiles has also been performed to facilitate subsequent concentration retrieval.
3.2 Spectral recording and the differential absorption cross-section
When the image sensor acquires lidar signals, the spectrometer also periodically records spectra, including the λon-wavelength spectrum, the λoff-wavelength spectrum and the background spectrum. By taking the median value of the laser spectra and subtracting the background spectra, the λon and λoff -wavelength spectra can be obtained. Figure 5(a) shows typical spectra of the laser diode, where the laser spectrum, determined by the case temperature and the injection current, is tuned to around 823.7-nm for the λon-wavelength and 824.6-nm for the λoff-wavelength. In principle, the on/off wavelengths can be tuned in a large region by tuning the driving current, which, however, can also lead to a much lower output power especially for the on-wavelength and thus deteriorate the signal intensity. The present wavelength pair is determined by optimizing the differential absorption cross section and the intensity of the lidar signal. It should be noted that wavelength optimization should be carried out for each laser diode used in the DIAL system.
Fig. 5. (a) λon and λoff spectra of the 830-nm laser diode, as well as the water vapor absorption cross-section with a standard atmospheric pressure and an ambient temperature of 23°C, the λon spectrum is located at the water vapor absorption peak, while the λoff spectrum is slightly deviated from the water vapor absorption peak; (b) Temporal variation of the equivalent differential absorption cross-section (Δσ) recorded on April 24, 2023.
Besides, the absorption cross-section of water vapor can be obtained from HITRAN database. The λon and λoff spectra are then used to calculate the real-time equivalent differential absorption cross-section (Δσ), which is given by
Here ${G_{{\lambda _{\textrm{on}}}}}(\lambda )$ and ${G_{{\lambda _{\textrm{off}}}}}(\lambda )$ are the normalized laser spectrum centered at λon and λoff wavelengths, respectively. From the value of Δσ, the spectral stability of the output laser beam can be evaluated. However, it should be noted that the value of Δσ cannot be directly used for the retrieval of the water vapor content. In DIAL measurements, by evaluating the value of Δσ, the spectral stability of the laser diode can be monitored, which is of great value for achieving high-performance water vapor DIAL measurements. The temporal variation of Δσ, which is calculated for fixed pressure and temperature, has been evaluated on April 24, 2023, as shown in Fig. 5(b). As can be seen, the variation of Δσ is quite large during measurements, implying that the laser spectra should be recorded and analyzed in real-time. Besides, the laser spectra are also important input parameters for the concentration retrieval, as shown by Eq. (3).
3.3 Retrieval algorithm for the water vapor concentration
As shown in Eq. (3), the DIAL ratio is an integration function, which is difficult to directly derive the mathematical expression of the water vapor content. In this work, piecewise least-square nonlinear curve fitting on the DIAL ratio curve has been performed to retrieve the water vapor concentration. According to Eq. (3), the λon and λoff spectra recorded by the spectrometer are used as input parameters, and the segmented DIAL ratio curve is fitted to obtain the water vapor concentration for each segment. It should be noted that when retrieving the concentration of water vapor at each segment, the absorption effect of water vapor in previous range, which can change the spectra of the transmitted laser beams (λon and λoff), should be considered. In other words, when retrieving the water vapor concentration for the broadband CW-DIAL, the water vapor concentration in previous range could affect the result of the present fitting.
As the broadband CW-DIAL system is designed based on the Scheimpflug principle, the detection blind range of the DIAL system is about 80 meters. Therefore, the initial distance selected for the retrieval can be set to e.g., 100 m, and the DIAL curve is divided into different segments with a certain length (e.g., 300 m in this work). As the absorbance of the water vapor is generally proportional to the product between the absorption path and the water vapor concentration, a smaller segmentation range can be used for a relatively higher water vapor content. On the other hand, a short segmentation range could lead to larger uncertainties on the retrieved water vapor concentration, owing to noise and atmospheric inhomogeneity, etc. If it is assumed that the water vapor concentration within a certain range is constant, the retrieval algorithm of the water vapor content is summarized as below.
Step 1: Obtain the DIAL ratio curve (Ratio(z)) and the laser spectra (λon and λoff) from the DIAL measurements.
Step 2: Dividing the DIAL ratio curve into m segments, [z0, z1], [z1, z2], … [zi-1, zi], … [zm-1, zm] (i = 1, 2, …, m). The water vapor concentration is assumed to be identical in each segment with a length of Lseg. A short segment length will lead to a large fitting error in the nonlinear fitting process, while a longer segment length means a lower spatial resolution. The segment length used in this work (300 m) is determined based on simulation studies on lidar signals with a SNR of 100∼200. Nevertheless, the segment length can be adjusted according to measurement conditions, etc. The initial retrieval distance (z0) is mainly determined by the blind range of the DIAL system.
Step 3: Set the initial values of the parameters to be fitted based on a first guess, namely the initial water vapor concentration (C0) and the initial ratio factor (K0). It should be noted that C0 represents the initial value of the parameter to be fitted in the nonlinear fitting, but not the retrieved/practical water vapor concentration (N0) in the region of [0, z0]. The inversion algorithm iterates from these initial values and then obtains the best fitting result after a number of iterations based on the principle of least squares. Therefore, the initial value (C0) of the water vapor concentration can be set in combination with the humidity of the monitoring site or specified within a reasonable water vapor concentration range (e.g. 1∼20 g/m3). The initial value of the ratio factor (K0) is generally set to 1.
Step 4: Retrieve the water vapor concentration N1 in the first segment ([z0, z1]), and assume the regions of [0, z0] and [z0, z1] have the same water vapor concentrations (N0 = N1). The DIAL ratio function in this fitting segment can be written as
According to Eq. (5), Ratio1(z) is subjected to a nonlinear curve fitting. The water vapor concentration (N1) and the ratio factor (K) for the first segment ([z0, z1]) can be obtained based on the principle of least squares. The evaluation parameters, such as the Jacobian matrix and residuals, are obtained to evaluate the fitting uncertainty.
Step 5: Retrieve the water vapor concentration Ni in the i-th (2 ≤ i ≤ m) segment. The DIAL ratio function in the i-th fitting segment can be written as
In Eq. (6), the water vapor concentration before the initial inversion distance ([0, z0]) is considered to be the same as that of the first segment ([z0, z1]). According to Eq. (6), the water vapor concentration Ni and the ratio factor (K) for the i-th segment (zi-1, zi) can also be obtained.
4. Measurements and results
Atmospheric measurements have been carried out in Dalian, China, in April, 2023. The DIAL system was located in the Graduate Education Building of Dalian University of Technology. A micro-air monitoring station was located on the top of the building to record the ambient water vapor concentration. A tall building in Dalian High-Tech Zone, located at 2.29 km away from the DIAL system, was utilized as the calibration target to evaluate the pixel-distance relationship. Near-horizontal atmospheric measurements, limited by the field of view of the laboratory, have been carried out to measure range-resolved water vapor concentration.
4.1 Range-resolved water vapor measurements
In order to validate the feasibility of the broadband CW-DIAL system, atmospheric measurements have been conducted in a near-horizontal direction from April 24 to April 25, 2023. During the measurements, the exposure time of the image sensor was set to 500 ms with an analog gain of 2. The lidar profiles have also been averaged for 240 times, corresponding to about 6 minutes for a single DIAL measurement. Typical DIAL signal and the corresponding curve fitting results are shown in Fig. 6(a). As can be seen, the fitting curves are generally in good agreement with the original DIAL signals. The uncertainty of the nonlinear fitting can be characterized by the upper and lower limits within the 95% confidence interval of the retrieved water vapor concentration, which can be calculated by combining the Jacobian matrix and the residuals of the nonlinear fitting. The error bars shown in Fig. 6(b) demonstrate the fitting errors of the water vapor concentration. It can be seen that the fitting error for the water vapor concentration is generally below 10%.
Fig. 6. (a) The DIAL ratio curve and the corresponding fitting result for lidar signals measured at 21:42 on Apr. 24 and 3:56 on Apr. 25, 2023; the fitted concentration and the corresponding uncertainty for each segment of the DIAL ratio curve measured at 21:42 on Apr. 24, 2023(b) and 3:56 on Apr. 25, 2023(c).
The temporal evolution of the water vapor concentration measured in the whole night is shown in Fig. 7. The atmospheric relative humidity (RH: %) and temperature (T: °C) are monitored by the micro-air monitoring station for comparison studies, as shown in Fig. 7(a). The relative humidity is converted to the absolute concentration (g/m3) of water vapor. As can be seen from Fig. 7(b), the water vapor concentrations measured by the DIAL system are generally in good agreement with the water vapor concentration monitored by the micro-air monitoring station. Figure 8 shows the relationship between the one-hour averaged water vapor concentration measured by the broadband CW-DIAL technique and the water vapor concentration measured by the air monitoring station, where a correlation coefficient of 0.9669 can be achieved. Besides, the spatial and temporal distribution of the water vapor content during the measurement period has also been evaluated, as shown in Fig. 7(c).
Fig. 7. (a) Atmospheric humidity and temperature changes monitored by the micro-air monitoring station; (b) Comparison between the water vapor concentration measured by the DIAL system at the range interval of 0.1 ∼ 0.4 km and the water vapor concentration measured by the monitoring stations; (c) The spatial and temporal distribution of the water vapor (WV) concentration measured by the DIAL system.
Fig. 8. Water vapor concentrations measured by the micro-air monitoring station and the water vapor CW-DIAL system. (a) water vapor concentration with a temporal resolution of 6 minutes and (b) one-hour averaged water vapor concentration.
4.2 Systematic error due to aerosol
In the retrieval algorithm discussed above, the water vapor concentration is obtained from the DIAL ratio curve between the measured lidar signals at λon and λoff wavelengths, by assuming that the aerosol extinction/backscattering coefficients are the same at the λon and λoff wavelengths and no differential absorption is generated by other gases. Although the influence of other interfering molecules could be ignored in the 820-830 nm region, the wavelength dependency of the aerosol extinction/backscattering coefficients should be carefully considered for complex and dynamic atmospheric conditions, especially when the separation between the λon and λoff wavelengths is in the order of nanometer (about 2-nm in this case). However, it is difficult to directly evaluate the systematic error introduced by aerosols owing to the sophisticated broadband DIAL equation and a number of unknown parameters such as the aerosol extinction coefficient, the backscattering coefficient and the Angstrom exponent. Thus, simulation studies have been carried out to investigate the potential influence of the aerosol extinction/backscattering coefficients on the retrieved water vapor concentration.
The first step for simulation studies is to determine a number of parameters in the DIAL equation. The water vapor concentration is set to 5 g/m3 (Nset = 5 g/m3) in the simulation studies, by taking the present measurement result as a reference. From the present DIAL measurements, the aerosol extinction coefficient and the aerosol backscattering coefficient at λoff (824.6-nm) can be retrieved according to the Fernald method with a lidar ratio of 40 Sr, namely 1.7 × 10−4 m-1 and 4.25 × 10−6 m-1 respectively, which are then utilized as input parameters for the simulation. The λon spectrum and λoff spectrum, which are measured in actual experiments, are used as input parameters in this simulation calculation, as shown in Fig. 9(a). The wavelength dependency of the aerosol extinction and backscattering coefficients can be given by
Fig. 9. (a) Laser spectra used in the simulation studies, center wavelengths are λon0 = 823.7 nm and λoff0 = 824.6 nm; (b) Simulated DIAL ratio curves with different Angstrom exponents; (c) Retrieved water vapor concentration with different Angstrom exponents; (d) The relative retrieval error of the water vapor concentration with different Angstrom exponents.
Here η is the Angstrom exponent, varying between 0 and 2 in most atmospheric conditions. The backscattering Angstrom exponent and the absorption Angstrom exponent are assumed the same for simplification.
Combining the simulated laser spectra and the water vapor absorption cross-section, the DIAL ratio can be simulated according to Eq. (2). As a result, the water vapor concentration at each segment can be obtained by fitting the simulated differential absorption curve according to the retrieval algorithm discussed above. As shown in Fig. 9(c), the retrieved water vapor concentration (NRe.) does not only increase with the increasing of η, but also increases with the retrieval distance. This is mainly attributed to the broadband characteristics of the laser spectra and the retrieval algorithm. When the water vapor concentration at a specific region is retrieved, the water vapor concentrations obtained from previous segments have to be used, leading to the accumulation of the retrieval error.
In the retrieval of the water vapor concentration, the aerosol extinction and backscattering coefficients, which are very difficult to obtain in practical DIAL measurements, have been ignored. On the other hand, the aerosol extinction coefficient and backscattering coefficient can be taken into account when simulating the DIAL Ratio curve with a known water vapor concentration, as shown in Fig. 9(b). Thus, the aerosol-induced error can be obtained by retrieving the water vapor concentration according to the algorithm mentioned above from the simulated DIAL curve. The relative error introduced by aerosols is defined by
Here NRe. is the water vapor concentration calculated by the inversion algorithm from the simulated DIAL curve taking the aerosol effect into account, Nset is the water vapor concentration set in the simulation studies. As can be seen from Fig. 9(d), the error introduced by aerosols increases with the increasing of the Angstrom exponent. Under the same Angstrom exponent, due to the inversion algorithm, the error will gradually add up with the increasing of the inversion distance, thus limiting the inversion distance. Nevertheless, the aerosol-induced relative error at each segment with different Angstrom exponents is generally less than 5% with an Angstrom exponent varying between 0∼2, as shown in Fig. 9(d).
5. Conclusion
In this work, combing the Scheimpflug principle and the differential absorption method, a novel low-cost broadband CW-DIAL technique has been proposed and developed for atmospheric remote sensing of water vapor. A low-cost 830-nm multimode laser diode is employed as the tunable light source for differential absorption measurements. The atmospheric backscattering signals are first collected by a telescope and then detected by a 45° tilted camera satisfying the Scheimpflug principle. The exposure of the camera is synchronized with the intensity/spectral modulation of the laser diode. The spectra of the emitted laser beams, alternately switching between λon (823-nm) and λoff (825-nm) wavelengths, are recorded by a spectrometer for real-time spectral analysis. A signal acquisition method and a retrieval algorithm dedicated to the broadband CW-DIAL technique have been developed to obtain the water vapor concentration from lidar profiles. Compared to traditional pulsed DIAL systems, the proposed broadband CW-DIAL system features low cost, compact structure, small blind zone and ease of maintenances.
Near horizontal atmospheric measurements have been carried out to verify the performance of the broadband water vapor CW-DIAL system. A good consistency between the water vapor concentration variations obtained by the water vapor DIAL system and the water vapor concentration reported by a micro-air monitoring station has been found out with a correlation coefficient of 0.9669. The overall fitting error of the retrieved water vapor concentration was below 10%. Simulation studies have also been carried out to evaluate the influence of the aerosol backscattering and extinction coefficients on the retrieval of the water vapor concentration. It has been found out that the aerosol-induced concentration errors were below 5% with a water vapor concentration of 5 g/m3, when the Angstrom exponent varied within the range of 0 to 2. The experimental results have successfully demonstrated the feasibility of the present broadband DIAL system for water vapor concentration measurements.
On the other hand, the performance of the present broadband CW-DIAL system can be further improved by increasing the laser power, employing a high-sensitivity image sensor in the infrared region and installing a proper narrowband optical filter for daytime measurements, etc. Besides, an ultra-high-resolution spectrometer dedicated to the wavelength region of 820-830 nm could be used, which can further improve the accuracy of the recorded laser spectra and thus the retrieved water vapor concentration. Moreover, since the exposure time of the camera is in the scale of 100 ms, the requirement on the acquisition speed of the spectrometer is not so high. Cheaper spectrometer equipment can be used to further reduce the system cost.
Funding
National Natural Science Foundation of China (62075025); Fundamental Research Funds for the Central Universities (DUT22JC17, DUT22QN246).
Acknowledgment
The authors greatly acknowledge the valuable help of Ruonan Fei during experiments.
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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