1. Introduction

Coherent heterodyne lidars have become important atmospheric analysis tools since their realization. The basic functionality of launching a laser pulse and recording a time trace of backscatter signal provides range resolved information of the scattering targets. Heterodyne mixing of backscattered light with a local oscillator generates radio frequency signal at determined heterodyne frequency and the doppler shifts in frequency are proportional to target speed. In atmospheric measurement context this translates into wind speed measurement from aerosol scattering. Advanced signal analysis techniques have been used to extract wind fields [1], windshear [2], turbulence [3], wake wortexes [4], low level jets [5], rain fall and rain drop size distributions [6,7] making the coherent heterodyne lidar versatile tool in aviation and weather applications. The doppler frequency shifts are absolute and easy to extract as long as the signal to noise ratio is sufficient. The signal amplitude has been used in estimation of planetary boundary layer height [8] and aerosol backscatter coefficient [9], and when combined with doppler data, revealing aerosol transport in atmosphere [10].

The signal amplitude is affected by aerosols backscatter coefficient and extinction coefficient which are specific for each aerosol type. Extinction from aerosol scattering attenuates the laser power creating an effect that low altitude scattering appears stronger when compared to high altitude scattering even if the aerosol content is identical. This attenuation problem has been circumvented with inversion algorithms which operate in an assumption that only the aerosol number density creates change in the signal amplitude. The algorithms assume either strong attenuation and solve extinction coeffiecient [11,12] or, in clean atmosphere, non-depleted laser power to solve backscatter coefficient [13]. Both algorithms and their combinations are widely used and succeed when aerosol optical properties remain constant meaning that the extinction to backscatter ratio does not change with altitude. Typical values for extinction to backscatter ratio range between 10 sr and 100 sr [14] and cause relative errors if the inversion calculations are applied in a measurement containing layers of different aerosols.

Direct detection lidars have solved the attenuation problem by measuring aerosol and molecular scattering simultaneously. The number density of molecules is dependent on atmospheric pressure and behaves in predictable way as function of altitude. The molecular signal can be compared to theoretical or measured model and the extinction of the laser power can be solved as function of altitude. The aerosol backscatter coefficients can then be extracted after the extinction is known [15] leading into a more accurate analysis of signal sources and atmospheric events such as pollen, dust or ash cloud identification and transport.

Molecular and aerosol backscatter are spectrally separable. Aerosol backscattering spectrum is almost identical to laser spectrum as the aerosols move primarily with the wind producing shifts in the order of few MHz without significant broadening. On the contrary, while the molecules move along with the wind, they show characteristic Cabannes lines triple peak backscattering spectrum [16] with 1.6 GHz full-width-half-maximum (FWHM) at laser wavelength of 1 µm. The Doppler broadening is caused by the temperature distribution of the molecules and the two side peaks appear because of spontaneous photon-phonon interaction between the laser light and air [16]. The triple peak spectrum is also widely known as Rayleigh-Brillouin spectrum. In addition, molecules produce two orders of magnitude weaker Raman scattering [16] where the frequency shift for $N_2$ is approximately 70 THz [17] making optical separation of aerosols and molecules easier. The state of the art techniques for detection of molecular scattering include Raman lidars and high spectral resolution lidars (HSRL) [18] which rely on detection of Raman scattering of nitrogen molecules and the Rayleigh-Brillouin scattering of air molecules, respectively.

The technical challenges of direct detection HSRL instruments lie in the accurate laser wavelength locking since the optical filtering systems must be able to separate aerosol and molecular scattering apart and additionally filter the background sunlight. The modern HSRL instruments are able to capture molecular scattering with wavelength locked lasers producing pulse energies up to to level of 10-100 mJ [19–21] while successful measurements have been carried out also with low energy micropulse instruments. The receiver bandwidth can be as low as 5.7 GHz [22], where stabilising the laser and the optical filters is a serious task. Coherent detection does not require complicated laser and filter stabilisation as the coherent mixing down-converts the received optical spectrum in to radio frequency spectrum centred around the laser wavelength. The complete Rayleigh-Brillouin spectrum can be measured without scanning the laser wavelength, which enables simultaneous scattering, extinction, wind speed and temperature analysis, given that proper signal-to-noise ratio is reached within the gigaherz-wide-bandwidth.

Typical fiber based coherent heterodyne lidars are designed primarily for long range wind speed measurements. The signal-to-noise ratio is often limited by the pulse peak power since fiber laser systems are limited by stimulated Brillouin scattering (SBS). Modern lidar laser sources rely on advanced SBS mitigation techniques in large mode area fibers producing pulse energy up to 110 µJ and peak power up to 1.1 kW making wind speed measurement possible up to 16 km [23]. While the best coherent heterodyne lidars are on par or produce higher pulse energies than micropulse HSRL systems [22,24], they lack the detection bandwidth to reliably record the Rayleigh-Brilouin scattering spectrum.

The heterodyne receivers work as mixers and down-convert the optical frequencies to electrical domain. Essentially, the heterodyne receiver is a spectrometer with its electrical bandwidth corresponding to the optical bandwidth the used laser wavelength. Typical lidar receivers are optimised for wind speed measurement limiting the electrical bandwidth to few hundred megahertz as larger bandwidth would produce unnecessary amount of data for windspeed measurement. The limited bandwidth alone makes it impossible to record molecular spectrum with a heterodyne receiver. However, recently a coherent heterodyne lidar based on a solid state laser source at the wavelength of 2 µm was shown capable of molecular scattering measurement [25]. The pulse energy of the lidar was 2 mJ and the receiver bandwidth was 500 MHz closely matching the width of molecular spectrum at the measurement wavelength. Furthermore, Rayleigh-Brillouin scattering measurement has been demonstrated using a fiber based system at the wavelength of 1.5 µm [26] with a limited spectral bandwidth of 400 MHz. The measurements show the potential for coherent heterodyne lidar being able to calibrate the aerosol amplitude data with simultaneous molecular scattering measurement when the pulse energy and receiver bandwidth are upscaled correctly.

In this work, a fiber based coherent heterodyne lidar capable of simultaneous aerosol and molecular scattering measurement is demonstrated. The design is based on traditional coherent lidars, while a novel laser system and receiver are designed for molecular scattering measurement. Wavelength of 1 µm was chosen for higher backscatter coefficient in Rayleigh regime. Additionally the laser source utilises tapered fiber amplifier technology to create peak power of 2.2 kW with pulse energy of 288 µJ and excellent beam quality as demonstrated previously by authors [27]. This is also the first demonstration of tapered fiber laser source in atmospheric lidar measurement to our knowledge. The heterodyne receiver has been designed for molecular scattering with electrical bandwidth of 1.5 GHz making a simple high spectral resolution receiver with high tolerance to sunlight and removing the need of additional optical filtering or precise laser stabilisation. The molecular spectra is presented in multiple altitudes together with integrated molecular backscattering up to 1 km altitude.

2. Lidar instrument

Coherent heterodyne lidar produces high spectral resolution measurement by design. The two major challenges to measure molecular scattering are orders of magnitude lower backscatter coefficient when compared to aerosols [16] and the required bandwidth of 3 GHz if the full scattering spectrum is considered. In terms of technology this led to design of novel laser source for high peak power and application of high sample rate digitisation and pre-processing electronics for signal capture.

2.1 Laser source

Fiber based laser sources have proven reliable and robust for lidar use. Typical coherent lidars operate at the wavelength of 1.5 µm where eye safety power limits are high and cost of telecom fiber components is low. Molecular scattering measurements are typically carried out at wavelength of 532 nm or 355 nm as the scattering in Rayleigh regime is proportional to $\lambda ^{-4}$, $\lambda$ being laser wavelength. For this prototype 1- µm-region was chosen for increased scattering efficiency and available laser power from advanced tapered fiber technology. The laser source with wavelength of 1053 nm used in this work has been published previously in Ref. [27]. The main characteristics include pulse energy of 288 µJ with 130-ns-pulse-length reaching peak power of 2.2 kW and beam quality parameter of $M^2 < 1.2$ making the source ideal for coherent lidar application [28]. The essential components of the laser source are presented in Fig. 1.

 

Fig. 1. Laser source for the lidar. The design includes a seed laser diode, single mode pre-ampifier and tapered power amplifier. The first acousto-optic modulator is used to create pulses from seed laser and the second modulator acts as additional filter to remove constant seed leakage to transceiver optics.

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The seed laser and local oscillator was chosen at the wavelength of 1053 nm for favourable gain characteristics in ytterbium fibers and to avoid water vapour absorption in atmosphere. Innolume DFB-1053-PM-50 has linewidth less than 5 MHz and power of 50 mW. While the linewidth creates a limitation for windspeed measurement accuracy, 5 MHz is narrow when compared to molecular spectrum width.

The pulse generation, shaping and seed isolation is implemented with acousto-optic modulators (AOM). The first AOM operates in combined analogue-digital mode shaping 160-ns-long pulses at repetition rate of 10 kHz. The second AOM operates as digital On-Off switch in sync with the first AOM for additional seed isolation. The lidar transmitter and receiver share the same optical path leading into multiple optical surfaces causing back reflection into receiver despite antireflection coatings. While the optical isolation of a single AOM was enough, the AOM driver On-Off ratio was not sufficient and constant leakage signal from seed laser could be seen when the second AOM was not installed. The leakage appeared at the same frequency with the expected aerosol signal rendering the data false. The acousto-optic modulators create in total 300 MHz frequency shift in passing light for the heterodyne measurement.

The pulse amplification is divided into two sections for precise power control. The pre-amplifier is built with single-mode polarization maintaining active fibers doped with ytterbium. The power scaling in the pre-amplifier is ultimately limited by SBS but in practical terms the power is tuned based on the optimal performance. The power amplifier is built with a tapered polarization maintaining ytterbium doped fiber. The core diameter of taper in the narrow end is 17 µm and in the output it reaches 50 µJ. The single-mode pre-amplifier fiber is carefully spliced to the tapered fiber so that only the fundamental mode is excited. The tapering is relatively slow and preserves near single mode beam quality with $M^2 = 1.2$ at the output. The tapering has been shown beneficial as the amplifier reaches peak power of 2.2 kW before being limited by SBS. In atmospheric lidar measurements the amplifier generates approximately 1.9-kW-peak-power with pulse energy of 300 µJ and pulse length of 160 ns.

2.2 Transceiver

The monostatic transceiver is built with free space optical components. The setup is shown in Fig. 2. Transmitter and receiver paths are combined with a polarizing beam splitter (CCM1-PBS25-1064-HP/M, Thorlabs). Beam is aligned to the beam expander telescope with two dielectric mirrors. To minimize back reflection into the receiver, the quarter waveplate is placed after the first lens in the beam expander, and together with the beam splitter they form a free space circulator. The beam is expanded with two aspherical lenses to diameter of 60 mm while the output lens diameter is 75 mm.

 

Fig. 2. The transmitter-receiver optics and electronics. A polarisation beam splitter cube is used to combine the transmitted laser beam and receiver field-of-view. Together with quarter wave plate (QWP) they form a free space circulator. The beam expander is built with aspheric lenses and the beam reaches diameter of 60 mm at the output lens. The acousto-optic modulator is used to filter the back reflection of the laser pulse. Local oscillator and the received backscatter light are mixed in 50:50 beam splitter and coupled to balanced detector. The analogue-to-digital converter (ADC) and field-programmable-gate-array (FPGA) are used for digitisation and pre-processing of the received signal.

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The received light is coupled to a single mode fiber for heterodyne detection. The receiver was aligned by coupling the local oscillator in the receiver fiber from the 50:50 fiber coupler generating output into free space optics. The laser source beam and the local oscillator beam were aligned on top of each other precisely with the spiricon beam profiler camera at the polarizer and at distance of 1.5 m. The collimation of the telescope was adjusted with a shearing interferometer.

The fiber coupled received light is gated by an acousto-optic modulator. The peak power of 1.9 kW generates detector saturating back reflection even with anti-reflection coated optics. The pulse saturates the internal transimpedance amplifier as well the photodiodes rendering the low altitude signals useless. The recovery process from the saturation is in the order of five microseconds and creates changes in measured signal frequency spectra making molecular scattering measurement impossible. The acousto-optic modulator is off when the laser pulse is launched and turned on after the pulse has left the optics. The modulator adds additional 80 MHz frequency shift to the received light making total frequency shift 380 MHz.

The received light is combined in 50:50 fiber coupler with the local oscillator light for balanced detection. To measure high bandwidth molecular signals, a balanced photodetector with bandwidth of 2.5 GHz (PDB482C-AC, Thorlabs) is used. Additionally a high speed amplifier (HSA-Y-2-20, Femto) together with passive attenuators is used to split the signal for oscilloscope monitoring and to optimise voltage level for analogue-to-digital converter.

2.3 Heterodyne spectrum measurement

The heterodyne receiver acts as a downconversion spectrometer by design. The electric fields of the local oscillator and received light are mixed creating a beating signal on the photodiode with the frequency corresponding the difference in the frequency of the mixed fields. In case of heterodyne one of two fields has been purposefully frequency shifted, as is in this work by 380 MHz. By default, if the scattering target is not moving towards or away from the laser pulse travel direction, the amplitude signal will appear at the heterodyne frequency $\nu _h =$ 380 MHz. A moving target causes a doppler frequency shift to the received electric field and the identical shift will be recorder relative to the heterodyne frequency. Fourier analysis can then be applied to reveal the signal spectral content. The non-shifted signal will appear at the heterodyne frequency and doppler shifted signals appear accordingly. The heterodyne receivers electrical bandwidth together with discrete Fourier transform parameters determine the receivers total bandwidth and resolution while the measurement wavelength is bound by the local oscillator.

The beating oscillations measured by the photodiode are described by the Eq. (1)

The heterodyne receiver measures the absolute value of the difference frequency $|\nu _s-\nu _{lo}|=|\nu _h+\Delta \nu _{d}|$. For example, in the instrument receiver if the target causes either a doppler shift of $\Delta \nu _{d}=$-160 MHz or $\Delta \nu _{d} =$-600 MHz the oscillations will appear at the frequency of 220 MHz in both cases. In case of large bandwidth signals, spectral features will fold and overlap each other. The folding happens for beating amplitude components and has to be treated properly when spectral fitting is applied for signal power. As Eq. (1) shows the beating oscillation amplitude is proportional to the square root of received of power and scattering power can be acquired by calculating the power spectral density from the recorder beating signal with discrete Fourier transform algorithm.

The expected scattering spectrum is a combination of aerosol and molecular scattering. The aerosol scattering spectrum mimics the laser spectrum only shifting in the order of tens of megaherz when the wind causes movement towards or away from laser pulse travel direction. The molecules in air, mainly nitrogen and oxygen, are in constant movement and can be well described by kinetic gas theory. The movement is proportional to the pressure and temperature of the gas and the molecule velocities follow the Maxwell-Bolzmann distribution. The velocity distribution causes the molecular scattering spectrum to broaden and additionally the natural density fluctuations moving in the air alters the refractive index periodically creating stokes and anti-stokes peaks to the scattering spectrum. These peaks are called Cabannes-lines according to their first observer and the triple peak spectrum is commonly referred as Rayleigh-Brillouin scattering as a reference to Rayleigh scattering from smaller than wavelength targets and Brillouin scattering induced by the density fluctuations in the medium [16].

The simulated backscatter spectrum is presented in Fig. 3(a) as the spectrum appears relative to the local oscillator and b) as the spectrum appears when recorder with the heterodyne receiver. The aerosol spectrum has been simulated with no Doppler shift as linear response to the laser spectrum. The laser spectrum is approximated with Lorentzian spectrum and a linewidth of 3 MHz. The molecular scattering spectrum has been simulated with Tenti S6 model [29] in 1 atm pressure and −3 °C temperature. The amplitudes in simulation were normalized with 1:200 ratio to represent the magnitude difference and width of the aerosol scattering spectrum at the base of peak.

 

Fig. 3. a) Spectral content of atmospheric scattering relative to $\nu _{lo}$ in normal pressure and −3 $^{\circ }$ C temperature. The black line presents pure Rayleigh-Brillouin scattering (RBS) from molecules and the dashed gray line presents total signal spectrum with aerosols with maximum values normalized to 1:200 ratio. b) Spectrum after heterodyne detection with $\nu _h=$ 380 MHz frequency. The spectral features with negative frequencies relative to $\nu _{lo}$ are folded and added to the positive side.

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The heterodyne receiver requires electrical bandwidth of at least 1.5 GHz to record the molecular scattering spectrum. The simulation of the folded spectrum in Fig. 3(b) indicates that the most recognisable features appear as the folded peak at 220 MHz, followed by the slope until the knee shape is formed at 900 MHz. The slope decays fast from 1000 MHz and $3{\% }$ of the maximum value is left at 1500 MHz setting a feasible limit for the receiver to capture the meaningful portion of the folded spectrum.

The power spectral density is calculated in intervals of 25 m up to altitude of 5400 m. The time trace signal is recorded for 43 µs of which the first 6.72 µs the receiver AOM is closed and only shot noise from local oscillator and electrical noise of the detector are present. The recorded time trace is divided in range gates of 166 ns and the power spectral density is calculated for each range gate with fast Fourier transform algorithm. Averaging is performed for each range gate spectrum separately by summing the range gate spectra together. The end product is a sum of 8192 spectra for each range gate. Averaged spectra are saved after 0.82 s for post processing. Analogue-to-digital conversion, fast Fourier transforms, and averaging are performed with the Zync UltraScale+ RFSoC ZCU111 Evaluation Kit (Xilinx), which integrates 12-bit analogue-to-digital converters and field-programmable-gate-array (FPGA) on chip for real-time pre-processing. The analogue-to-digital converter runs at the sample rate of 3.072 GS/s for the measurements. The FPGA design and programming was made by Xiphera Ltd. based on the algorithm provided by authors.

2.4 Spectral analysis

The aerosol and molecular scattering powers are extracted in post-processing. The power spectral densities produced by the FPGA algorithm include at least thermal noise from components, shot noise from photons hitting the photodiodes and the beating produced by received photons mixed with the local oscillator while detector frequency response shapes the spectrum. The frequency response of the detector is extracted for each measurement set from range gates between 2 µs and 4 µs when the receiver AOM is off. The shot noise spectral shape is first analysed by subtracting prerecorded detector noise curve without local oscillator. The shot noise by nature is white noise and the shape of measured shot noise spectrum is used as the detector frequency response curve. All spectra are then normalised with the frequency response data to gain comparable power on all frequencies. The noise power is subtracted from all the spectra by selecting a far distance range gates with no aerosol or molecular signal. The far-distance range gates include all noise sources and any possible level variations that might happen during different measurement times making the noise subtraction stable. The end result is frequency corrected and noise power subtracted set of power spectral densities starting at altitude of 50 m and reaching 5400 m in increments of 25 m. In general, the aerosol data can be extracted without additional averaging and the molecular features become visible after averaging 10 minutes of the real-time data in post-processing.

The frequency corrected spectra are fitted with aerosol and molecular scattering models for further analysis. Aerosol peaks are fitted with Lorentzian line profile function by fixing the linewidth to 3 MHz and using the center frequency and peak amplitude as free parameters. Lorentzian function fits the laser lineshape especially at peak base and is relatively light for computing resources. The fitting results an accurate estimation of peak center and amplitude, from which the wind speed and the scattering power can be calculated. The folded molecular spectrum is fitted with Tenti S6 model by calculating the full spectrum and folding it in electric field amplitude domain for correct shape. The measured temperature of −3 °C and pressure of 1 atm at ground level were used as input parameters. The temperature dependent gas transport coefficients collected by Witschas et al. [30] were used for the calculations. The scattering power from molecules is calculated from the power spectral density curves by first subtracting the fitted aerosol peak and integrating the data up to 900 MHz. The aerosol peak frequency interval from 240 MHz to 520 MHz as well as known artefact peaks from the instrument are left out from the integration interval additionally.

3. Results

We setup the lidar for proof of concept measurements on February 2nd, 2023, at 12:00 AM, in Tampere, Finland. The weather was cloudy with temperature of −3 °C. The visibility was more than 59 km according to Finnish meteorology institute open database from Tampere-Pirkkala airport, 14 km away from the place of measurement. The lidar beam was set to point vertically. We were able to record aerosol backscatter from the ground up to 1100 m where the laser beam hit a cloud. The result of aerosol scattering measurements can be seen in Fig. 4 where we have averaged the signal for 0.82 s for each column. The signals do not have any range or overlap corrections applied as the dynamic range is better presented without range correction and the overlap function between the transmitter and receiver has not been measured. Defining those corrections is out the scope of this work.

 

Fig. 4. Aerosol backscatter signal. Each data point corresponds to detected total power from aerosol scattering on each time and distance.

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The Fig. 4 shows typical attenuated backscatter data. The boundary layer can be clearly seen between 0 m and 200 m with strong scattering features appearing from 600 s to 1800 s. The strong signal from 1000 m to 1200 m is due to a cloud hit.

To demonstrate the molecular scattering detection capabilities, for Fig. 5 and Fig. 6 we have time averaged the data by including columns without low-altitude clouds at 200 m altitude. In total the time average contains 884 columns corresponding to 724 s. The strong backscatter signal from low-altitude clouds create transient processes in the detector altering the baseline level and frequency response temporarily. By excluding the columns with transient processes, the molecular scattering data is available up to 800 m.

 

Fig. 5. Integrated scattering power of specific frequencies at each range gate. a) aerosol scattering, (b) molecular scattering and (c) instrument background. The aerosol scattering power in a) has been acquired by fitting a Lorentzian lineshape to aerosol signal and integrating the fitted shape. The molecular scattering power in (b) has been calculated by integrating the spectra up to 900 MHz and ignoring the aerosol peak frequencies and known instrument artefacts. The instrument background in c) is calculated by integrating the same frequencies as for molecular scattering but in the measurement the instrument was covered blocking the laser beam after the beam expander.

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Fig. 6. Signal spectrum on different range gates. a) is the lowest range gate free of initial bang from optics at 75 m. b) is from 150 m, c) is from 300 m and d) is from 950 m.

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The time averaged total power of aerosol and molecular scattering together with system noise power has been presented in Fig. 5 as a function of measurement distance. To estimate aerosol scattering power presented in Fig. 5(a)), we have fitted a Lorentzian spectrum and use the area of the fit as the aerosol scattering power. The aerosol signal is typically strong and robust fit is possible without modifying the fitting parameters. The molecular scattering power in Fig. 5(b)) is acquired by integrating frequencies from 6 MHz to 240 MHz and 540 MHz to 900 MHz. The signal to noise ratio of molecular scattering decreases with larger frequencies and the signal practically vanishes into noise in high altitudes at frequencies over 900 MHz. To avoid cross-talk with aerosol scattering, the Lorentzian fit of aerosol peak has been subtracted from data before integration and the frequencies from 240 MHz to 536 MHz are not included to avoid fitting artefacts due to aerosol scattering residues. The background power presented in Fig. 5(c)) has been acquired by replicating the measurement with the beam blocked after the beam expander so that no laser light enters to or from the atmosphere.

The power spectral densities in Fig. 6 present features from aerosol scattering, molecular scattering and system noise sources. The aerosol signal is present at 380 MHz and does not show meaningful shift implying no vertical wind during the measurement. The sharp peaks at 162 MHz, 936 MHz and 1206 MHz are interference from acousto-optic modulator drivers. The molecular scattering features can be seen clearly in Fig. 6(a), (b) and (c) ranging from 0 MHz to 1536 MHz. The aerosol peak does not significantly leak to molecular scattering frequencies as can be seen by comparing Fig. 6(a) and (d) from 75 m and 950 m altitudes, respectively. The aerosol peaks have the same order of magnitude but the spectral features around the peak are visibly different. Additional confirmation for successful molecular measurement is provided by the baseline shape following the simulated folded molecular spectrum especially at 75 m and 150 m altitudes in Fig. 6(a) and 6(b).

4. Discussion

Coherent heterodyne lidars are actually high spectral resolution spectrometers by design. The measurement wavelength is defined by the seed laser, also acting as the local oscillator for the receiver. The configuration eliminates the need of optical and atomic vapour chamber filters, both of which require precise wavelength stabilization of the laser. The local oscillator has to be stable and the laser has to be temperature and current controlled with typical drivers, but no additional locking or stabilization is required. Slow wavelength drifting in few second timescale is not a problem as the local oscillator and the laser output drift simultaneously. The spectral resolution in this work is mainly limited by the sampling time in the Fourier analysis providing interval of 6 MHz in frequency domain, which is more than sufficient in for molecular scattering studies. The receiver bandwidth is limited by the receiver electronics to 1.5 GHz, which is wide enough for folded molecular scattering spectrum while blocking background light effectively and the instrument shows identical performance in daylight as in the dark conditions.

The selected laser wavelength and achieved peak power are advantageous for molecular scattering. The wavelength of 1.053 µm laser increases the molecular scattering coefficient by a factor of 5 when compared to 1.55 µm instruments as the the molecular scattering coefficient is proportional to $1/\lambda ^4$. The peak power of 1.9 kW enables the range resolution of 25 m for the measurement as the lidar signal is proportional to laser pulse energy and range gate length. If the peak power and laser wavelength are considered as scalable variables, then similar results should be achievable with peak power of 9.5 kW at 1.55 µm wavelength. Considering the power limitations in optical fibers and reported peak powers around 1 kW [23,31], the 1.55 µm instruments may struggle if applied for molecular detection. However, the total system noise has to be considered in the evaluation.

The dynamic range of the measured signal is more than four orders of magnitude. Even stronger signals have been measured from fog or rain saturating the detector signal when monitored with oscilloscope. The molecular scattering signal has to be averaged on the scale of minutes to resolve and 10 minutes to resolve the spectral features properly. Additionally, the weather has to be relatively clear as strong signals create recovery oscillations in the transimpedance amplifier as can be seen on Fig. 5(b) at the altitude of 1000 m. The instrument takes advantage of an additional acousto-optic modulator in the receiver to filter the reflection from the transceiver optics. Without the AOM the transimpedance amplifier and the photodiodes saturate making molecular scattering measurement impossible below altitude of 500 m. In high aerosol load conditions resolving either shape or total magnitude of molecular scattering may be compromised due to recovery oscillations caused by strong aerosol backscatter signal.

The noise sources of the measurement are well known. The main background is generated by electrical noise from the detector and shot noise generated by the local oscillator hitting the photodiodes. The background light from atmosphere is negligible to the point that noise levels are near identical when comparing measurements performed in sunlight and after sunset. The sunlight in theory increases the baseline level and in optical bandwidth of 1.5 GHz the sunlight can be assumed spectrally flat and constant intensity during the single shot measurement time making it easy to subtract in post processing. However, the fiber amplifier generates additional noise to the measurement. The fiber amplifier generates amplified spontaneous emission (ASE) at wavelengths from 1000 nm to 1100 nm. The ASE is proportional on the excited $Yb^{+3}$ ions which are used for laser pulse amplification. When the pulse is launched from the lidar, the number of excited ions reduces temporarily and with continuous pumping the ions will re-excite before the next laser pulse. The behaviour can be seen in Fig. 5(c), where the integrated magnitudes are presented. The background level through the measurement bandwidth increases rapidly after the pulse as the fiber amplifier recovers from the laser pulse. Similar ASE noise limitations were reported in Ref. [23]. The averaging time of the analysed signals corresponds 12 minutes and while being relatively long it is comparable to other similar instruments [25,26]. The 12 minutes averaging time produces excellent signal-to-noise ratio for integrated molecular scattering power as seen in Fig. 5(b), which enables shortening of the averaging time down to few minutes.

The high speed heterodyne receiver together with high peak power laser enables simultaneous wind speed, aerosol and molecular scattering measurements. The current instrument combines the wind lidar and high spectral resolution lidar in the same hardware without complicated laser stabilisation techniques. The calibrated extinction and backscatter calculations are possible when the telescope overlap is corrected from the data. The evident drawback comes from the polarisation dependency of the detector. In case of depolarisation from aerosols, the calculated backscatter coefficient will possess proportional error to the depolarisation factor. However, the analysis of depolarisation is left for future studies.

5. Conclusion

We have shown that a fiber based coherent heterodyne lidar can be used for detection of molecular scattering. The molecular scattering by its nature is orders of magnitude weaker than aerosol scattering and requires higher bandwidth. The fiber based coherent heterodyne lidars are often limited by their peak power capabilities to generate enough signal for detection of molecular scattering. The tapered fiber technology performs well in the coherent lidar application producing peak power of 1.9 kW as demonstrated. The tapered design enables high peak power within robust package and excellent beam quality. The wavelength of 1053 nm enhances the molecular scattering coefficient by factor of 5 when compared to typical coherent lidars operating at the wavelength of 1.55 µJ. The receiver bandwidth of 1.5 GHz and fast preprocessing electronics enable the capturing entire meaningful molecular scattering spectrum for further analysis. Coherent heterodyne lidars have potential to extend their capabilities from wind speed and attenuated backscatter measurements to calibrated backscattering and extinction analysis.