2.1

Sequential scanning

Some frequency agility is permitted by an Optical Parametric Oscillator (OPO) used in the emitter. This allows sounding of different species so as to eliminate the unknown content of H₂O when looking for CO₂ for instance [14]. But for each species the active wavelength is single.

One way to remedy this limitation is to multiply the emitted wavelengths along one absorption line [7]. A scan takes few ms to perform. The improvement of the spectral content allows a better retrieval of CO₂, with some information in the vertical profile [8] [11]. However in a space mission the reflectivity of the ground would not be the same for all wavelengths and the pointing of the telescope should be stabilized. Aerosol conditions may change too as sketched by Figure 1:

Figure 1.

Sequential wavelength scanning for a space borne lidar

Finally the wavelength of the master laser must be accurately stabilized or monitored during the scan, as for DIAL lidars.

2.2

Short frequency combs

Short frequency comb lidars are based on the principle of emitting a set of wavelengths similar to [11] but at the same time, and with an even and accurately known frequency step.

Figure 2.

Short frequency (or wavelength) comb used to sample one spectral line c.a. 6330 cm^-1

Even if the center frequency may shift, the absorption line is sampled at evenly spaced frequencies. Therefor the shape of the line is determined anyway. This relaxes the mastering of the central wavelength.

Finally all these wavelengths are detected by the same detector, as in a Michelson interferometer, with a reduced frequency bandwidth.

As a matter of fact the number of frequencies in a comb is a compromise between spectral richness, thus the quality of the concentration retrieval, and the energy of each one, hence the Signal to Noise Ratio in the spectrum, keeping in mind the limit of the available total energy onboard.

3.1

Dual (Short) Comb Spectroscopy

Dual Comb Spectroscopy (DCS) is now a well-known technique for fast, high resolution, large spectral domain spectroscopy [12] [13]. Since its debuts in the laboratory it was experienced to use it in open space (lidar mode) on the distance of few km [15]. DCS involves usually several hundreds of thousands teeth, spanning several nm spectral domains, and uses phase locked femtosecond (fs) lasers.

It involves two frequency combs, with a slightly different step. Thus the frequencies of comb #1 are υ_op+i.fr₁, and the frequencies of comb #2 are υ_op+i.fr₂. υ_op being the optical carrier frequency (in the order of 200 THz).

Complete frequency combs are a thrilling perspective for lidars, but their fitting to a space mission is beyond the state of the art of today’s short (fs) pulse optical amplifiers. In the case of short combs the feature is more modest, and the technique of comb generation is different, but the principles are the same for the spectroscopic point of view. Here 1 ≤ i ≤ 13. fr₁ ~ fr₂ are chosen to cover the molecule absorption line. Typically fr₁ ~ fr₂ ~ 1 GHz, and Δf_r = fr₁ – fr₂ ~ 1 MHz.

Both combs are amplified and sent through the atmosphere, are reflected back by a hard target, cross the atmosphere again, and are superimposed onto a detector. This generates a multi-heterodyne beat-note signal, at RF (Radio Frequency) frequencies i.Δf_r. Higher frequencies i.(fr₁+fr₂) and i.fr₁+j.fr₂ or i.fr₁+j.fr₂ are filtered out by a Low Pass Filter.

Figure 3.

General layout of a short comb lidar. EDFA: Erbium Doped Fiber Amplifier - PA: PreAmplifier – LPF: Low Pass Filter. Black: Polarization Maintaining (PM) fiber optics links – Red: open space optical path – Blue: electronic signal – υ: optical frequency – f: RF electronic frequency

3.2

Interferogram and spectrum

As both combs are generated from the same master monofrequency laser, the phase between them is stable and the beat-note builds up constructively. The optical total amplitude can be written as:

since we can neglect higher frequency terms thanks to the LPF. N is the number of frequency teeth.

A₁(υ_op+k.fr₁) and A₂(υ_op+k.fr₂) are the amplitudes of the optical flux at optical frequencies υ_op+k.fr₁ and υ_op+k.f_r2, after crossing the atmosphere twice. “A” is closely related to the spectral transmission and is the parameter we are looking for. As fr₁ ~ fr₂, we can approximate and write: A₁(υ_op+k.fr₁) = A₂(υ_op+k.fr₂) = A_k in equation (1).

The intensity I_tot(t) = A_tot(t).A_tot(t)* can be derived from equation (1) as:

I_tot(t) constitutes an interferogram signal similar to the one of a Michelson interferometer like [4].

The electrical signal is proportional to I_tot(t) and equation (2) shows that it is the inverse Fourier Transform of A_k = A₁(υ_op+k.fr₁) = A₂(υ_op+k.fr₂) series. So the processing consists in digitalizing the signal and calculating its Fourier Transform. A(f) = TF[I_tot(t)] is the spectrum in the RF domain. It must be translated to the optical domain by as the amplitude of A_k appears at the RF frequency component k.Δf_r in equation (2).

One interesting feature of DSC is inferred from equation (2). As I_tot(t) is the superposition of harmonic phase locked components, it is periodical with a repetition rate of . This is illustrated by Figure 4 and can be demonstrated by:

Figure 4.

Superposition of harmonic phase locked components. Red: resulting total signal

This repetition makes it easy to average several acquisitions with no moving part in the instrument as long as the target is stable.

3.3

Spectral resolution and sampling

Each interferogram is monitored in the temporal interval. As with passive interferometer the spectral resolution is the Full Width at Half Maximum (FWHM) of the Fourier transform of the box-car truncation function of the interferogram. As a consequence, the FWHM of the instrument (sinc) function is 1.21.Δf_r in the RF domain, and 1.21.f_r1 ~ 1.21.f_r2 in the optical domain. But it must be outlined that the useful spectrum is empty between the very narrow comb teeth. Even if the final spectrum is the physical spectrum convoluted by the instrument function, no lateral component but of the solar background is aliased in the considered channel as zeros of the instrument function coincide with the adjacent teeth when , as shown by Figure 5:

Figure 5.

Inter-sample convolution. Comb teeth are symbolized by arrows. Red and blue: instrument functions of two adjacent samples

The samples of the spectrum can be considered as polluted only by the solar spectrum adjacent components, but these are of low level and independent one another. This is a peculiar property of DCS.

Each tooth of the comb is as narrow as few kHz, depending on the spectral purity of RF wave injected in the optical modulators. In the optical domain they are spaced by f_r1 ~ f_r2, of the order of 1 GHz here, i.e. 7.5 pm at 1.5 µm, i.e. 0.033 cm^-1 at 6600 cm^-1.

3.4

Generation of short frequency combs

Short frequency combs can be generated from a cw mono-wavelength laser using an Electro-Optic Modulator (EOM) for phase modulating of the master laser. When passing through an EOM driven by a voltage V = b.sin(ωt+φ), the laser phase i.ω₀.t becomes i.(ω₀.t + b.sin(ωt+φ)) as can be seen in Figure 6:

Figure 6.

Phase modulation of a Master Laser with an EOM

The building of short frequency combs from such a phase modulation is presented in § 5.1.

There are two positive technical consequences to the use of frequency combs. First the frequency step is highly stable, even, and mastered, being generated by RF ultra-stable oscillators. Secondly it spreads the total energy within several frequencies, lowering the level of each of them with respect to the Brillouin’s scattering threshold in the fiber amplifiers.

3.5

Emitter architecture

The instrument relies on two branches similar to Figure 6, branch #1 having F = fr₁ and branch #2 having F’ = fr₂. However one of the combs generated has to be shifted so as to avoid ambiguity of beat-notes i.Δf_r. and –i.Δf_r, around the central original frequency, as can be seen in Figure 7:

Figure 7.

Global frequency shift of one comb

At first order, D must be equal to so that no tooth of the two combs superimpose and give birth to the same beat note tone.

Practically speaking, a global shift is provided by an Acousto-Optic Modulator (AOM). As AOMs don’t work around D.C. but around 110 MHz, comb #1 is shifted by 110 MHz – D/2 and comb #2 is shifted by 110 MHz + D/2.

The complete diagram of the emitter gathers the above considerations in Figure 8:

Figure 8.

Complete emitter diagram for a short comb lidar

A pulse picker is introduced in each branch to allow a pulse emission mode according to allow time tagging of the echoed pulse.

The calibration channels measure the energy spectra actually emitted to correct the echo signal from emitter discrepancies.

3.6

Detection and processing

Detection of the interferogram is straightforward as a low bandwidth detector (few MHz) is sufficient. It must be followed by a LPF of which cut-off frequency is at maximum half of f_r to avoid aliasing in the spectrum. In our case f_r/2 is much higher than our maximum useful frequency N.Δf_r. This is why the LPF cut-off frequency is set just above N.Δf_r in order to limit the noise bandwidth.

The sampling of the interferogram is made at twice N.Δf_r, at least, with a resolution sufficient to generate negligible noise. Averaging of several interferograms can be made, then a Fourier Transform is performed to finally obtain up to 13 samples in the absorption line of the target molecule [17].

4.1

SCALE objectives

SCALE is viewed as a demonstration mission for CO₂ sounding with a short comb lidar, in the 1.57 µm or 2 µm region. The measurements are averaged along a cell on the ground of 50 km long. Its width should be few hundred meters. The number of spectral samples will be between 3 and 13, the optimum remains to be determined. The spectra should allow retrieving more independent elements in the vertical profile (Degree Of Freedom For Signal “DOFFS”) than a DIAL lidar.

4.2

SCALE key parameters

The spectral parameters of the combs were given in § 3.

The radiometric performances are driven by the following factors. The most important one is the energy of each laser pulse. Assuming that one third of the 150 W delivered by the platform is dedicated to one comb amplifier, assuming an electro-optic efficiency of 35% for the pump laser diode, and taking into account the opto-optical efficiency of 21% [19], we consider an optical power of 3.7 W for each comb. Given the repetition rate of F_rep=7.2 kHz (consistent with the non-ambiguous range of 40 km required for atmospheric sounding from space) this power yields to a E₀=0.5 mJ energy per pulse and per comb. Of course this energy is spread over the N teeth of a comb. The pulse duration is t_pulse=0.5 µs.

The altitude is lowered to R₀=400 km. The receiver telescope diameter is 0.7 m. We consider the ground reflectivity to be Ref=0.1 sr^-1. The total atmospheric optical depth is taken to 0.5 which leads to an atmospheric transmission of T_atm²=0.6, typical of the edge of a CO₂ transmission line in the near infrared. The optical transmission of the receiver is T_inst=0.7 and the one of the emitter T_emit=0.9. The background parasitic flux is determined by the Solar Zenithal Angle (SZA) of 60°.

The detector is granted a top of the art performance with a Noise Equivalent Power (NEP) of 5 fW/√Hz including the preamplifier. Its efficiency is η=0.8.

4.3

SNR in the interferogram and in the spectrum

Assuming that the noise in the interferogram is white and non-correlated, the Signal to Noise Ratio (SNR) in one channel (of width df) in the RF spectrum (which is the same as for the optical spectrum) is given from the SNR at the central sample of the interferogram by:

f_Max is the maximum frequency in the interferogram and S_TF(f) is the Fourier Transform of the interferogram.

Equation (4) can be simplified if we define as the average value of S_TF(f):

4.4

Signal

The central sample of the interferogram receives all the frequencies in phase, so only one frequency can be considered with energy E₀ when emitted. This sample is acquired during a time defined by the maximum RF frequency in the interferogram according to the Nyquist frequency as .

This allows the calculation of the number of detected photon-electrons, from one comb, in the central sample of the interferogram according to the “lidar formula”:

h.υL is the energy of the photon at frequency υL.

2.N(R₀) determines the “signal” of the SNR expression since two combs fall onto the detector.

4.5

Solar background

The number of photon-electrons from the Sun through the atmosphere is

with: L_sun=radiance of the Sun, Ω_sun=Sun solid angle, Δλ=width of the Narrow Optical Filter (NOF).

A NOF is inserted in front of the detector to limit the optical bandwidth of the sun flux. Its transmission is included in T_inst.

We consider Δλ=2 nm.

The larger the field of view θ_c, the larger the background flux, hence the noise. In reality the field of view of the receiver is somewhat bigger than the divergence of the laser to get some margins for misalignments. We consider a margin of 50%: θ_c = θ_L×1.5. A compromise was found against speckle noise around θ_L = 40 µrd.

4.6

Noises

Addressing the limits of the SCALE concept, we do not take into account the electronics noises in this preliminary budget.

As for natural noises, we take into account the following variances:

4.7

Turbulences

Turbulences affect both combs the same way. Therefore their superimposition in the pupil of the instrument should keep a high efficiency close to 1.

4.8

Polarization

As long as the optical fibers and elements of the instrument are of the Polarization Maintaining (PM) type, theory and experience show that polarization is not an issue for the stability of the signal. And the effect of the atmosphere on the optical beam polarization will be the same for the two combs, if any, so no perturbation in the heterodyne beat notes is to be feared.

4.9

Averaging

In this first evaluation we consider that the target is constant over D_av=50 km, so averaging of . F_rep measurements (with V_sat=7.5 km/s velocity of the satellite) will increase the SNR by a factor

4.10

Preliminary radiometric budget

The simple model above gives the preliminary estimate of the SNR, in each channel of the spectrum. Figure 10 summarizes the results of SNR calculation with the above assumptions, as a function of optical power of one comb, for several numbers of teeth.

Figure 10.

SNR in the SCALE spectrum, for an average along 50 km, as a function of optical power of one comb, for several numbers of teeth. See text for the parameters of the radiometric budget.

As expected the SNR increases with the optical power and decreases with the number of teeth.

Interestingly enough the influence of the solar background is weak with a SZA of 60°: day-time SNR is 6% lower than night-time SNR.

4.11

Discussion and ways forward

This work estimates the first order SNR one can reasonably hope for a short comb lidar fitted to a microsatellite bus. If we assume that the optimum number of teeth would settle at nine and the optical power, all loss taken into account, at 3 W per comb, the SNR would be 250 in day-time, after a 50 km averaging.

With these parameters the distribution of variances of equation (8) is shown by Figure 11:

Figure 11.

Distribution of noises in the interferogram with 3 W optical power and 9 teeth per comb.

The speckle noise is negligible and the background noise is low, but Figure 11 shows that the instrument is not yet photon-limited. Some progress should be envisaged there.

With key parameters consistent and in line with a microsatellite bus size, SCALE appears to be an instrument with performance perspectives interesting enough for an exploratory mission in the future, to demonstrate a new type of atmospheric active sounding.

5.1

9 and 13 teeth combs

We conducted calculations to optimize the generation of 9 and 13-tooth combs using an EOM driven by a wave consisting of a fundamental frequency and its harmonics. Decomposed into Bessel functions the spectrum of such a phase is given by:

where J_k(b) are the Bessel functions of the first kind.

Equation (9) gives the result for a simple harmonic modulation that produces a spectrum of ω-pitch lines. In this case, only parameter b (the modulation index) is available to act on the distribution of the lines in the optical spectrum. If we add a second harmonic in the modulating signal, we have a total of 3 parameters (2 amplitudes and a relative phase), and so on for 3 harmonic components.

In this case, the aim is to optimize the 5 parameters b1, b2, b3, φ2,φ3 in equation (10), with the help of a in-house optimization software, in order to optimize an overall criterion taking into account i) the dispersion of the levels on the useful lines, ii) the relative power in the useful lines compared to the other lines. In the case of the 9-tooth comb (Figure 12) a very good result is achieved with only the fundamental frequency and its harmonic 3. In the case of the 13-tooth comb, it is necessary to use in addition the harmonic 2 [16] to obtain a maximum deviation of 0.45 dB between the useful lines (Figure 13). It can be noted that other optimization criteria could be applied, for example to have the same signal to noise ratio for each tooth of the comb when analyzing an absorption line. In this case it would be necessary to emit more energy on the central lines.

Figure 12.

Theoretical optimized 9-teeth mini-comb using a single EOM driven by a fundamental frequency and its third harmonic

Figure 13.

Theoretical optimized 13-teeth mini-comb using a single EOM driven by a fundamental frequency, its second and its third harmonic

The experimental results obtained with a high-resolution optical spectrum analyzer correspond substantially to the theoretical results as shown in Figure 14 and Figure 15. The amplitude and phase settings must be accurate and compensate for the transmission characteristics of the power amplifier. This is facilitated by the use of an AWG sampled at 8 GHz, which performs a digital synthesis of the modulating signal. However, high frequency AWG generators has the drawback of producing unwanted lines and the EOM frequency choices must be adjusted so that these stray lines do not interfere with the measurements.

Figure 14.

Optical spectrum obtained for the optimized mini comb with 9 teeth. The blue and red tracks correspond to the 2 optical polarizations.

Figure 15.

Optical spectrum obtained for the optimized mini comb with 13 teeth. The blue and red tracks correspond to the 2 optical polarizations

It should be noted that depending on the temperature of the components (RF power amplifiers deliver about 1 watt) the settings change and so the level of the lines, by about 1 dB, if no temperature regulation is used.

5.2

Experimental setup

The experimental set-up in the laboratory is shown in Figure 16 and Figure 17. The two combs generated are added in a coupler, amplified in an EDFA and then sent in two reception channels: on one side the “measurement” channel which contains the HCN cell and a 10 km non PM fiber which simulates propagation, and on the other side the “reference” channel. The latter keeps in memory the levels actually emitted on each line, which may vary according to time, temperature and the characteristics of the EDFA. However, the transfer functions of the “measurement” and “reference” channels are not exactly identical since they use different components (photo detectors, RF amplifiers, filters). This has been calibrated.

Figure 16.

Laboratory set-up: general block diagram.

Figure 17.

Laboratory set-up

The beats of the homologous lines of both combs show an RF comb centered at the frequency AOM2-AOM1 (here 11.4 MHz) and with an EOM2-EOM1 step (here 0.1 MHz), as shown in Figure 18. We can notice that these lines are extremely stable because the optical waves that generate them have very close frequencies, travel identical paths at the same time, and have identical polarizations, even if part of the path uses non-PM fibers. Experimentally, stability identical to that of the RF and microwave signals used for the AOM and EOM modulators is observed. This property opens up the possibility of spectral analysis over very long observation times, thus improving the signal-to-noise ratio.

Figure 18.

Spectrum at the output of the “reference” channel

5.3

HCN spectra

The general appearance of the spectral transmission of the H₁₃C₁₄N cell (15 cm long, 25 Torr) is shown in Figure 19.

Figure 19.

NIST measurements for a H₁₃C₁₄N 15cm long, 25 Torr pressure cell. Red boxes indicate the actually measured absorption lines

These data are derived from measurements made by the NIST [20].

It should be noted that for our experiment, the two optical waves that beat (at practically the same frequency) are attenuated in the cell, which means that the sensitivity is doubled.

The measurement procedure is as follows: after tuning the source laser to the line to be analyzed, the spectra of the “measurement” and “reference” channels are recorded and the levels extracted from the 13 lines. The difference is then made to compensate for changes in the levels of emitted optical lines.

To facilitate comparison with the NIST results, the measurement points are adjusted with a global level offset that compensates for measurement channel losses and gain differences, as well as a global frequency offset to compensate for source laser drift (typically 100 to 200 MHz).

The results obtained for three lines at 1535.540 nm, 1555.436 nm and 1563.498 nm are shown in Figure 20, Figure 21 and Figure 22. For this last measurement, the pitch of the optical combs was reduced from 903 MHz to 303 MHz in order to better sample this absorption line.

Figure 20.

Comparison of our measurements (red dots) and NIST (black continuous line) results for the 1534.540 nm line

Figure 21.

Comparison of our measurements (red dots) and NIST (black continuous line) results for the 1555.436 nm line

Figure 22.

Comparison of our measurements (red dots) and NIST (black continuous line) results for the 1563.498 nm line

We can see on these figures that the obtained results are quite good since we have deviations lower than 0.1 dB. A thorough analysis of these residual or bias errors shows that they can be explained by the parasitic lines generated by the microwave AWG mentioned above.

These results validate the concept of spectroscopy with two short frequency combs for the first time.

5.4

Future works: open space measurements

After these experiments on an HCN fiber absorption cell, it is scheduled to test in open space a lidar based on dual short frequency combs. The functional diagram of the instrument is the one of Figure 16, but the distance to the retroreflector will be 1 km, horizontal. Moreover we will sound water vapor at 1528.75 nm as there is no CO₂ absorption line strong enough in the C band of our tunable master laser. We expect a transmission of around 45 % as per Figure 24:

Figure 23.

Absorption coefficient of water vapor at the edge of the laser C band

Figure 24.

Instrument and processing model

The comparison of the measured spectra to those simulated from in-situ measurements will validate the accuracy of the short comb lidar.

These experiments will shortly take place in the ONERA’s facilities of Le Fauga, France.

6.1

Accuracy and DOFFS

The accuracy on the CO₂ retrieved concentration and the DOFFS are calculated for several numbers of teeth in the combs, and for several optical powers per comb: nominal (3.7 W), 2×nominal (5.4 W) etc… This will give perspectives for improving the retrieval. The first results are summarized in Figure 25:

Figure 25.

DOFFS in the total column and accuracy for 3 to 13 teeth in the combs (x axis), different optical powers, at 1.57 µm and 2 µm.

It can be seen that performances are slightly better at 2 µm than 1.57 µm. The loss of SNR with higher number of teeth seems balanced by the spectral information content at 1.57 µm. This is no more the case for the accuracy at 2 µm when N > 9. Performances are somewhat better with 3 teeth but some phenomena are neglected like [H₂O] uncertainty. However other calculations show that there is less correlation between atmosphere layers in the estimation of [CO₂] with 13 teeth.

The improvement of retrieval for higher optical power impels to search for better radiometric budget, either by improving detection or by increasing the power of the lasers. It is obvious that an operational mission should be photon limited in the future to reach the ultimate performance of DOFFS > 2 as pointed out by our study.

6.2

Spectral self-calibration

The Bayesian retrieval of [CO₂], from spectra affected by the above noise and a 0.001 cm^-1 mismatch of the central wavelength of the comb, was simulated for combs of 3 and 13 teeth, at 6356 cm^-1, i.e. 1.57 µm. The error on the retrieved wavelength is given by Figure 26 to be 5.10^-4 cm^-1 with 3 teeth and 2.10^-4 cm^-1 with 13 teeth (this occurs when the comb is centered on the absorption line):

Figure 26.

Comb central wavelength retrieval from SCALE spectra. Left: 3 tooth comb, right: 13 tooth com. ΔWN = frequency step, WN₀ = central frequency.

This is not as good as the A-SCOPE requirement (70 kHz) [9] but it allows to limit the [CO₂] error to 0.5% (2 ppm for 400ppm CO₂ column mixing ratio), thanks to the spectral richness of the comb, as inferred from Figure 27:

Figure 27.

Impact of a wavelength calibration error of 10^-3 cm^-1 on [CO₂] error. Left: 3 tooth comb, right: 13 tooth com. ΔWN = frequency step, WN₀ = central frequency.

It is worth noting that the 2 ppm error include the effect of the radiometric noise. The weight of the spectral calibration is only 1.2 ppm in the total error budget. The spectral calibration retrieval can be thus considered as efficient.