2.1

Architecture

The amplification chain is shown in Figure 1. The source architecture is based on a Polarization Maintaining (PM) Master Oscillator Fiber Power Amplifier (MOFPA) made of four Thulium Doped Fiber Amplifiers (TDFA) pumped by laser diodes at 793 nm. The MOFPA is alternatively seeded by two narrow-linewidth Distributed Feed-Back Laser Diodes (DFB-LD) using an Optical Switch (OS) with a rate up to 20 kHz. The pre-amplifier (TDFA1) delivers a continuous signal. The optical power at its output is split in two parts, one delivering the Local Oscillator (LO) power used to generate the beat note signal for heterodyne detection and one seeding the second amplifier. TDFA1 has been design to preserve as much as possible the optical properties of the seeders to ensure optimal detection performance¹³. An Acousto-Optic Modulator (AOM) shapes the signal into pulses and adds an optical frequency offset of 80 MHz for heterodyne detection. At the TDFA2 output, a Mach-Zehnder Electro Optic amplitude Modulator (EOM) is used as a time-gated attenuator to filter amplified AOM parasitic spikes and the inter-pulse Amplified Spontaneous Emission (ASE). TDFA3 output peak power is limited by Stimulated Brillouin Scattering (SBS). Its output is filtered by a High Reflectivity Fiber Bragg Grating (HR-FBG) centered on 2051.2 nm with a width of 1 nm. It permits to remove the large ASE component that can degrade the amplification efficiency at the signal wavelength in last amplifier. The last amplifier (TDFA4) is made with Large Mode Area (LMA) fiber that is longitudinally stretched to overcome the SBS limit. The laser output is spliced to a pigtail which made easier the collimation. For more details on the fiber laser source, see^11,14.

Figure 1:

All-fiber MOPA architecture. DFB-LD: Distributed Feedback Laser Diode, OS: Optical Switch, LO: Local Oscillator, TDFA: Thulium Doped Fiber Amplifier, AOM: Acousto-Optic Modulator, EOM: Electro-Optic Modulator, ASE: Amplified Spontaneous Emission, HR-FBG: High Reflectivity Fiber Bragg Grating, SBS: Stimulated Brillouin Scattering

2.2

Laser performance

In this part, we summarized the most important feature of the fiber laser presented in section 2.1 for DIAL/Doppler application. In Table 1, main optical feature are shown

Table 1:

Main laser optical features

The laser wavelength is center on 2051.2 nm and tunable over 1 nm (i.e. 70 GHz) using the temperature setting of the seeder. The tuning range is limited by the HR-FBG width. It fully covers the R30 absorption line allowing the use of the side band for DIAL operations. In this study, the Pulse repetition Rate (PRF) and the pulse duration are set to 20 kHz and 200 ns respectively. The laser energy is 120 μJ which corresponds to 600 W/2.4W peak/average power. This working point is slightly under the SBS threshold in order to limit the warming of the pump diodes. The switching rate between the ON-line and OFF-line wavelengths is up to 20 kHz for pulse-to-pulse switching. Fast wavelength switching is required to keep high atmospheric correlation between ON and OFF signals. For the atmosphere to be considered as ‘frozen’, a switching rate of 1kHz or more is typically required¹⁵ (for space-borne operation, the requirement is higher since the satellite is moving very fast. In current solid-state lidar designs, the inter-pulse time between ON and OFF laser shots is typically 250 μs, which sets at 4 kHz the ON-OFF switching rate requirement¹⁶). In Table 2, the main features for lidar operations are summarized.

Table 2:

Laser features for DIAL operation

Heterodyne detection required a LO with low RIN. In our scheme, the noise is limited by the shot noise (quantum limit) at RIN=-170 dB/Hz. In this study, we reach -160 dB/Hz which leads to less than 1 dB loss on the Carrier-to-Noise Ratio (CNR). The spectral linewidth represents another critical issue to reduce the integrated noise. Indeed, narrower is the signal spectrum, lower is the integrated noise and higher is the CNR. In our case, the spectral linewidth is lower than 5 MHz. It represents a loss on the CNR of 1 dB compared to a pure Fourier-transform limited pulse (considering also the DFB-LDlinewidth of 2 MHz). The Signal-LO (S-LO) beat frequency stability can involve a broadening of the signal spectrum when averaging shots, and for the reason explained before, it could degrades the CNR. The RMS S-LO stability is 100 kHz at 10 ms averaging time and follows a root-time decrease up to 10 s. It implies negligible broadening of the averaged signal spectrum. The beam quality (M²) denotes the beam divergence and is crucial to maximize the CNR. In our case it represents a loss of 0.5 dB on the CNR. Last three features in Table 2 play a role on the CO₂ measurement bias. The seeder is working in free-running mode and we measured a frequency shift lower than 50 MHz on 10 minutes. It leads to less than 0.2% bias on the CO₂ VMR (at R30 center), but anyway it will be necessary in the futur to lock the DFB-LD frequency^17,18 to ensure optimal performance. The transmission of the switched off wavelength is called the cross-talk (or spectral purity) and is crucial for DIAL measurement. In heterodyne detection, this feature is relaxed compared to the direct detection. In our case, the cross talk is -23 dB on both the LO and the emitted signal which leads to a bias lower the 0.1% up to 3km of propagation in the atmosphere. The SMSR is also an important issue in the same way as the cross-talk. Our SMSR is higher than 45 dB and involve negligible VMR bias.

2.3

Expected lidar performance

In the perspective of a global monitoring of the CO₂ from space, the use of direct detection appears as much more performant to reach space mission goal of 0.1% VMR relative error. This study being in its first phase and for a reason of simplicity of implementation, we performed a heterodyne detection. It also presents the advantage to allow simultaneous wind monitoring for autonomous CO₂ flux rate measurement. However, in this part, we investigate the VMR error for both, heterodyne and direct detection.

The DIAL equation writes¹⁹:

Where WF is the Weighting Function (in ppm^-1.m^-1), Δz is the range resolution (distance to hard target for IP-DIAL measurement) and P_ON/OFF is the returned signal power. The log expression represents the slope of the optical depth i.e. the absorption coefficient. The VMR error can be expressed as:

Where N_avg is the number of VMR values averaged, σ is the standard deviation and ρ is the correlation coefficient, p_{X Y} = cov(X, Y) / (σ_X.σ_Y) with cov the covariance function. In this equation, we can identify the Signal-to-noise Ratio as SNR_p=P/σ(P). In heterodyne detection, the SNR can be written³:

Where N_pulses is the number of shots averaged to calculate a single returned power P, M_t is the number of independent speckle patterns and CNR is the Carrier-to-Noise Ratio. In practice, M_t is close to unity when the range gate equals to the laser coherence length. For a single shot (N_pulses = 1), the SNRpulse is close to the unity in heterodyne detection. For this reason, it is better to use heterodyne detection with high PRF (>1 kHz) as it allows a fast accumulation to increase the SNR and then reduce the VMR error. Regarding the energy of the fiber laser of 120 μJ, the CNR will be usually lower than 0 dB for atmospheric signal and higher than 10 dB up to 5 km on a hard target.

In direct detection, the SNR for a single shot can be higher than 1 as the speckle noise can be largely averaged by the detector area²⁰. For space-borne measurement, as the number of averaged shot is limited, the use of direct detection appears preferable. In Killinger et al.²¹, the inter-comparison between heterodyne and direct detection shows, in same conditions, a SNR five times higher in direct detection.

On Figure 2 is plotted the VMR standard deviation assuming SNR_ON=SNR_OFF (case where the distance of propagation is not sufficient to involve important absorption or case where ON-line and OFF-line signals energy are chosen to compensate the absorption), WF=1.6.10^-6 ppm^-1.m^-1 (On-line signal at the R30 centre and no pressure/temperature variation on the line of sight) and the correlation degree equals to 0 function of the SNR for a single pulse (SNRpulse, horizontal axis) and the product ν_avg^1/2.Δz (vertical axis) which is representative to the space-time resolution.

Figure 2:

VMR error as function of the single pulse SNR and the product N_avg^1/2.Δz

The CO₂ concentration in the atmosphere is around 400 ppm. Plotted blue lines stand for the relative errors of 100%, 10%, 1% and 0.1% (precision goal for spatial mission). For 1 km integrated path and 100 pairs of shot averaged, an heterodyne measurement can reach 10% relative error while a direct detection can reach 2% in the same condition regarding the performance reported in²¹. Moreover, if there is no relative displacement between hard target and the emitter, the speckle pattern is unchanged and the statistical error decrease slower in time. In the assessment for the A-Scope mission², some feasibility studies are detailed.

3.1

Signal processing

The ON-line and OFF-line signals are handled separately for the power estimations. A sliding square gate of 200 ns (i.e. the coherence time of the pulse) is applied to the time-domain signal. The Power Spectral Density (PSD) is calculated for each distance-gate using a Fast Fourrier Transform (FFT). To smooth the spectrum we average N_pulses PSDs. The last sample of each shot is used as the noise PSD (called PSD_noise) and is subtracted to previous samples. Then the noise-subtracted PSD, called PSDhet, is numerically filtered around the peak signal with a 20 MHz square gate and integrated to estimate the return signal power P. The CNR is calculated by dividing the power P by the noise using the same numerical filter. The procedure is the same as the one detailed in²².

3.2

Absolute spectral reference system and ON-line/OFF-line energy difference monitoring for DIAL operation

The spectral reference system is shown on Figure 3 (Spectral ref.). The residual beam from the Brewster plate is used to determine the energy difference between ON-line and OFF-line pulses and to estimate the absolute frequency of the laser. The light is fiber-coupled and separated in two parts. The first part goes directly to a DC-coupled detector and allows the determination of ON/OFF energy difference (value K in Eq.(4)). The second path goes through a gas cell filled with pure CO₂. Then, it is possible to calculate the differential absorption of the cell as the ON and OFF-line pulses are consecutive.

Once digitized, each signal is averaged to improve the SNR. To calculate the transmission, we set the OFF-line signal at - 18.8 GHz apart from R30 absorption line center. The tuning precision of our current and temperature drivers gives a resolution of +/- 250 MHz considering the measured DFB-LD wavelength sensitivity. It involves a potential bias on the ON-line frequency of 50 MHz. The relative error on the WF is then lower than 0.2%. We used the HITRAN database and a local temperature sensor to compute the cell transmission. In a future phase, a frequency locking unit will be added to the system.

In the preliminary test presented in the following sub-section, WF and K are calculated by averaging 1000 pairs of shots. The K value is given with a relative random error lower than 1% over the averaging time of 10 ms to 10 s. The ON-line frequency is given with a random error of 25 MHz which represents a relative random error on the WF lower than 0.1%.

3.3

IP-DIAL

To perform an IP-DIAL measurement, we pointed the lidar on a static target located at 426 m. The IP-DIAL equation writes:

This equation is the same as Eq.(1) using z=0 and Δz=L where L is the distance to the hard target and K the energy difference between the ON and OFF signals (K=P_ON(0)/P_OFF(0)) determined using the spectral reference system. The WF for this measurements is 1,57.10^-6 ppm^-1.m^-1 slightly detuned from the R30 absorption line center. As a reference, we had a Picarro probe close to the lidar giving the VMR with a sub-ppm precision.

The Figure 4 (a) represents the VMR Allan deviation performed with a VMR time series where N_pulses = 100 shots and N_avg = 1. The minimum time-resolution is then 10 ms. On Figure 4 (b), the time series VMR (doted, red) is plotted with a time averaging of 2s i.e. 2.10⁴ pairs of shots (N_pulses=100 and N_avg= 200). The blue line is the Picarro probe data.

Figure 4:

(a) Allan deviation on the VMR (red) and -1/2 slope representing the stationary behavior (dashed, black), (b) VMR measurement of the Picarro probe (blue) and measured VMR by the lidar (doted, red)

The Allan deviation follows a τ^-1/2 slope i.e. a stationary behavior over the measurement time of 5 minutes. The average value of the VMR is 414 ppm and the value given by the Picarro probe is 422.5 ppm. As the measurements are not co-located, we are not able (currently) to determine the absolute precision of our instrument. However, it suggests that there is no major instrumental default. The statistical features calculated and observed for this measurement are summarized in Table 3.

Table 3:

IP-DIAL error analysis

The SNR of P_ON and P_OFF are similar as the distance of propagation does not significantly absorb the ON-line signal. Furthermore, the hard target signal is strong enough to limit the SNR by the speckle noise. The observed correlation degree of 0.64 is a consequence of high PRF and high switching rate which keep ‘frozen’ the atmosphere and the target reflectivity between ON-line and OFF-line signals. The observed IP-DIAL error is in good agreement with the calculations.