1.1

SCALE concept at CNES

Dual Comb Spectroscopy principle with short frequency combs (only a few teeth are generated by the phase modulation of a continuous wave laser) opens the path to a new generation of LIDAR instruments, potentially usable in airborne or space greenhouse gases sounding missions. Short frequency combs scan a whole absorption line of the target molecule with a near-perfect mastering of the spectral pattern. Thus, the main advantage of short combs is to relax the highly accurate frequency calibration needed in the case of DIAL LIDARS, especially for CO₂ sounding. More generally, it allows for a retrieval processing based on Bayesian optimal estimation that can deal with several technical or geophysical unknowns, thanks to the spectral richness and accuracy of the signal. After a series of R&D studies carried out by ONERA and CNES on frequency comb LIDARS^1,2, CNES has initiated the development of an Exploratory Project (also known as « PEX ») in CNES. Exploratory Projects are a new innovative category of projects set up in CNES a few years ago, which are limited in time and budget and specially designed to test innovative technologies. They are based on a pragmatic approach focused on the demonstration objective, and are designed and developed internally in CNES. SCALE Exploratory Project has been decided in July 2020 and started in September 2020, for an airborne demonstration planned in July 2023. It aims at demonstrating the feasibility and the performance of two innovations patented by CNES: the use of short frequency combs for atmospheric sounding, and the improvement of SNR obtained through Double Heterodyne Detection.

These two innovations have been studied and validated in lab environments through research activities performed between 2014 and 2019 with ONERA. The combination of these two innovations is believed to bring a breakthrough in atmospheric sounding, thanks to the improved richness of the information retrieved with short combs (compared to IPDA LIDARs), the relaxation of frequency knowledge constraints and the improvement of SNR. A system level Phase 0 Study has been conducted in CNES in 2019 and concluded that the performance budget shows a good balance between the contributors and would be compliant with the objective of 1ppm CO2 retrieval over 50km. However, theory and literature could not give answers to all the performance questions raised (impact of the Speckle effect, DHD mixing performance, turbulence for vertical shots…). Thus, confrontation with an airborne system experiment was necessary to test performances in a mode representative configuration before moving on to a Space Project. In parallel, a simplified Lab-POC (Proof Of Concept) has been developed in the Optics Lab from the beginning of the PEX. It is used to perform the validation of different set points for the Airborne-POC, the study of specific technical aspects such as speckle and to enable SCALE teams to generate the representative signals required to develop and optimize the signal processing algorithms, which are key to reaching the targeted performance.

1.2

SCALE airborne demonstrator

The Airborne POC of SCALE will fly in July 2023 on a Commercial ATR42 Aircraft from the SAFIRE fleet. This ATR42 has been specially modified for atmospheric measurements and is used regularly for scientific experiments. The SAFIRE fleet is located in Francazal near Toulouse, and is funded by CNES, Meteofrance and CNRS. SCALE Airborne Proof of Concept is currently under development in CNES, supervised by the project team and CNES experts from different subdirectorates. All subsystems are now contracted, and the first deliveries have been received and verified in the CNES Optics Laboratory, progressively building up the Airborne-POC. A series of scientific equipment will be present on board the aircraft, and scientific means set up on-ground and in balloons on the trajectory of the ATR42, to derive the reference CO2 mixing ratios to be compared with SCALE processed data.

In parallel to the PEX, a Phase 0 with Airbus Defense and Space has started early 2022 and is planned to end in 2023. Its aim is to study the feasibility and any instrument design improvement required to target a space mission with a SCALE instrument on-board for Greenhouse gases measurements. The results of this Phase0 study, combined with the results and lessons learned of the PEX, will open the way to a Spaceborne SCALE study.

2.1

Heterodyne signal on the detector

Considering a k^th teeth in the first probe comb (comb A) and the LO comb, the current induced on the photodetector is

Where P_LOk is the power of the k^th tooth of the LO comb [W], P_Ak is the power of the k^th tooth of the 1^rst probe comb [W], S is the sensitivity of the detector [A/W], γ_H is the heterodyne mixing efficiency, ν_Ak is the frequency of the k^th tooth of the 1^rst probe comb [Hz], ν_LOk is the frequency of the k^th tooth of the local oscillator comb [Hz], and t is the time [s]. The DC part of this signal is filtered before digitizing. The total signal digitized, for order k, after proper filtering, is composed of the superposition of heterodyne beat notes of LO and comb A (noted ) and the beat note of LO and comb B (noted ):

Where and are the AC current:

As a result, the power spectral density of the total digitized signal is a comb composed of seven pair of peaks (k = -3,…3), each peak inside a pair corresponding to the probe comb A and B, respectively. As comb A and comb B have very close optical frequencies, (6 MHz difference), we can consider that each peak inside a pair is equally absorbed by the atmosphere.

2.2

Data processing for phase noise correction

Laser phase noise and phase noise induced by atmospheric turbulences limits the integration time of the signal. However, to obtain a good SNR, it is necessary to average a large number of temporal signals (with a random phase). To remove this frequency noise and coherently average a large number of interferograms, one solution is to choose a reference peak and extract the temporal evolution of its phase for the phase correction. As the probe combs come from the same laser source and cross the same atmospheric turbulences, their frequency noise is almost similar all along the spectrum, and the random phase cancels by correcting the whole signal by the phase of the reference peak⁷. However, in real condition, the Speckle could affect differently each order of the comb, making it impossible to phase-correct all the comb by only one of its line. To address this issue, we use two probe combs, and make a second heterodyne mixing between the two same order peaks of probe comb A and probe comb B. After numerical filtering of each pair of peaks, the principle of this data processing method called DHD is to calculate, at each time sample t, the square of :

For each comb, the frequency of a k-order tooth is affected by a frequency noise Δυ and a random phase φ. Numerical filtering keeps the lowest frequency of the last term of Equation 4 only. By replacing and by their expression given in Equation 3, the low frequency part of this last term can be written as:

Each peak of a pair comes from the same optical source, travel almost the same optical path, and have very close optical frequencies (6 MHz difference). Thus, Δν_Ak = Δν_Bk and υ_Ak = υ_Bk. The common phase and frequency noise on each probe comb cancels, and Equation 5 becomes:

The difference between optical frequencies ν_Ak and ν_Bk is determined by the frequency difference on the RF signals applied on AOM A and AOM B. In practice, this difference is few MHz, reducing the signal bandwidth ΔΒ from hundreds of MHz for the complete heterodyne spectrum (and several GHz for the optical spectrum) to only few MHz for the final useful electrical signal.

3.1

Time of flight measurement

For an accurate CO2 retrieval, the instrument must be able to measure precisely the optical path traveled by the probe combs. Measuring the time flight between the calibration pulse and the echo pulse gives this parameter. The accuracy on this dating is driven by the precision needed on the concentration of the gas studied. For carbon dioxide, the required accuracy is 1 ppm, or 0.25% in relative. It is thus estimated that an accuracy of 10 ns must be reached for the temporal location of a pulse, or 2.3 μs after averaging of 50,000 shots. The probe combs are pulsed with super-Gaussian shaped temporal envelope. These pulses are generated by modulating acousto-optical modulators (AOM) with a RF signal. In the SCALE concept, two acquisitions are made for each measurement. The first acquisition is the sampling of a leak on board the instrument and considered as the reference pulse. The second is an acquisition of a measurement pulse that travelled through the atmosphere. That pulse was affected byits reflection on the ground by the speckle. Normally used to obtain calibrate measurements, these two signals can be reused to determine the time of flight of photons.

A temporal dating based only on their super-Gaussian envelope would not allow to reach the need since the generated pulses have a 2 μs width at half height. To obtain the desired accuracy, a correlation method based on interferograms contained in reference and measurement pulses has been developed. This technique allows to determine the time of flight with the sufficient accuracy by detecting the maximum correlation between the two measurements. To verify this method, a reference pulse was measured on board the instrument, without free-space propagation as presented in Figure 4(a). At the same time, a series of pulses with controlled time spacing, propagating in free space and distorted by the speckle have been detected as shown in Figure 4(b). It was thus possible to compare the theoretical time spacing of the pulses with the results of the method, as illustrated Figure 4(c). These preliminary measurements showed that the correlation method led to errors at least four times lower than the theoretical need despite the presence of speckle

Figure 4:

(a) Reference pulse measured on board the instrument without free-space propagation. (b) Series of pulses after their propagation in free-space and degradation by speckle. (c) Filtered correlation between the reference pulse and the series of measurement pulses.

4.1

Useful Signal to Noise Ratio

We assume that the optical power coming back from the target is the same for the two probe combs, and we call it P_Sk:

Equation 6 becomes:

The useful Signal to Noise Ratio (SNR) is about P_Sk, i.e. the k^th component in the spectrum of the optical power coming from the target:

where var(P_Sk) is the variance of the measurement of P_Sk. As Equation 8 shows, P_Sk is proportional to . Thus, . The useful SNR will be half that of the k^th low frequency component of the heterodyne current signal as generated by the detector. Assuming that the noise is white and dominated by shot noise, and considering combs of N_teeth = 7 teeth, with an evenly distributed power on them, we can express the SNR as a function of the total heterodyne current at time t = 0, including all its spectral components:

4.2

Radiometric SNR on heterodyne current

The received signal power is close to:

as it is the sum of the two probe beams of equal powers. P_S is the power of each received combs, all spectral components included. At time t = 0, all the beat tones are in phase and the current has the value:

The different shot noise sources generate the signal variances:

with: q = electron charge [C]

ΔB = the final bandwidth of the signal, after DHD process is applied;

F = excess noise factor of the detector;

P_BG = optical power of sun radiance backscattered by the ground;

P_LO = optical power of the local oscillator onto the detector.

The detector dark current gives rise to the signal variance: 2. q. ΔB. F. I_dark where I_dark is the dark current generated by the detector. The main current noise after the detector is due to the first stage amplifier, a Resistor Trans Impedance Amplifier (RTIA). Back propagated to the output of the detector, the variance that the RTIA generates is:

Where G is the gain of the RTIA; and I_{b_RTIA} is the noise current generated at the output of the RTIA. Finally, the radiometric part of the SNR in the heterodyne current is thus:

In the case where the local oscillator power is larger than the other signals, this expression becomes:

Equation 14 depicts a photon noise limited, direct detection, situation, with the drawback of a γ_H < 1 heterodyne mixing efficiency. On the other hand, DHD allows a detection bandwidth as low as a few MHz.

4.3

Effect of speckle

Noise due speckle adds quadratically to radiometric noise:

As shown in ⁸, the speckle adds noise to the measurement, and the spectral components are uncorrelated provided that they are spaced by a sufficient frequency gap, and/or the roughness of the backscattering is bigger than a few mm. This is the case in SCALE as it uses the reflection on the ground onto a footprint of 2 m diameter. As is the case with coherent detection, the SNR due to Speckle, if one considers a single shot on a rough surface, is:

When N_shot shots, with a renewal rate of τ_renew are averaged, the total SNR, averaged in the spectrum, becomes:

τ_renew is given by: if V_sat < Φ_{pixel ground}. F_c ; = 1 otherwise; where V_sat is the velocity of the satellite, Φ_{pixel_ground} is the diameter of the laser footprint on ground, and F_c is the pulse repetition frequency, as illustrated in Figure 5:

Figure 5:

renewal rate of successive spots on ground

Because of Equation 16, the final SNR is limited by the worse of radiometric noise and speckle noise. The latter being equal to 1, there is no use having a radiometric SNR much better than 1 on a single shot. On the contrary if , the total SNR will be limited by this low value.