NanoCarb hyperspectral sensor: on performance optimization and analysis for greenhouse gas monitoring from a constellation of small satellites
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Abstract
NanoCarb is an innovative Fouriertransform imaging spectrometer dedicated to the measurement of CO_{2} and CH_{4}. Both its unusual optical principle and sampling strategy allow to reach a compact design, ideal for small satellite constellation as investigated by the European project SCARBO. The NanoCarb performance assessment as well as a proof of concept is required in this framework. We have developed a design strategy to optimize the performances. We demonstrate the potential of the concept through an estimation of the sensitivity, compliant with the space mission target. We also present a preliminary mitigation of the bias induced by water on CO_{2} and CH_{4} retrieval, illustrating the efficiency and the flexibility of the NanoCarb partial interferogram sampling technique. The presented design reaches a subppm random error for CO_{2} and sub10 ppb random error for CH_{4}, considering 128 km swath and 2 by 2 km^{2} ground resolution. Design optimization and more systematic performances are discussed.
Keywords
Hyperspectral sensor Anthropogenic GHG emissions Fouriertransform spectroscopy NearIR passive remote sensing1 Introduction
One of the issues of studying climate change is to reduce uncertainties in estimating emissions of the main greenhouse gasses (GHG)—CO_{2} and CH_{4} [1]—leading to a better distinction between anthropogenic and natural sources. The first challenge for dedicated space missions is to monitor the atmospheric total column and/or vertical profiles with both a drastically improved statistical error and smaller systematic bias. The second one is to provide an improved revisit frequency and spatial coverage of the monitoring.
LIDAR active technology (MERLIN European project [2] or ASCENDS project in the US [3]) achieves sensitive measurements independently to solar illumination conditions, in like manner dedicated spaceborne Thermal InfraRed (TIR) passive spectrometers (IASI [4]). Nevertheless, LIDAR are inherently limited to unidirectional sounding, while TIR spectrometers are less sensitive to the lowest atmospheric layers where anthropogenic activities are significant. By the opposite, Short Wave Infrared (SWIR or near IR) spectrometry only allows daytime monitoring, but with improved sensitivity to the lowest parts of the atmosphere. GOSAT [5] and GOSAT2,^{1} OCO2 (see footnote 1) or TANSAT (see footnote 1), are current space missions dedicated to CO_{2} and/or CH_{4} monitoring in this domain. GeoCARB (see footnote 1) in the US, or MicroCarb [6], CO2M (CarbonSat) [7], and TROPOMI (see footnote 1) in Europe are the future planned missions or spaceborne instruments.
Nevertheless, not all these missions can achieve sufficient spatial and temporal coverage, with a typical revisit frequency of 15 days for the majority of them, from a sunsynchronous orbit. In addition, individual costs of these missions are a real hurdle to put into orbit a constellation.
A way forward to increase the revisit frequency and spatial coverage is to complete these current reference missions with a constellation of low cost, small satellites, and calling for breakthroughs in compact hyperspectral sensing. The challenge is to adapt kilogramclass payload for typical 50 kgclass platforms, maintaining their performances compatible with current reference missions and the main science issues: kilometric ground resolution, sensitivity bellow 1 part per million (ppm) over the averaged dry column of CO_{2}, and bellow 10 parts per billion (ppb) for CH_{4}. Moreover, it is important to reach a 100 km swath to increase the spatial coverage and to contextualize some hotspots according to the background (e.g., plume).
In this framework, the Horizon 2020 project Space CARBon Observatory (SCARBO) [8] aims at assessing the feasibility of a lowcost constellation of small satellites onboarding dedicated GHG sensor. The SPEX [9] dedicated aerosols sensor is also provided in the platform. The project relies on small satellites to monitor CO_{2} and CH_{4} emissions, complementing the lowrevisit highperformance satellites.
Several orbital configurations are investigated in this scenario. One of the simplest consists to put 40 small satellites into the same sunsynchronous orbit at 600 km height. With a 128 km swath and a small recovering between consecutive footprints at ground for crosscalibration purposes, it is possible to ensure a daily revisit over emerged lands at midlatitudes.
The core miniature GHG sensor of this constellation is the NanoCarb concept, a static Fouriertransform imaging spectrometer, first introduced in sections III.B and III.C of [10]. In this concept, both the use of a low finesse Fabry–Perot array and a partial interferometric sampling strategy allow to achieve a large swath at high spectral resolution as well as to obtain an optimal use of the available pixels for a high sensitivity in a snapshot acquisition mode.
However, this uncommon instrumental concept enforces a shift of paradigm in atmospheric sounding domain. Indeed, the acquired data are quite different from classic dispersive or Fourierbased spaceborne systems: the information content of the data is very low (as defined in [11]), compared with a conventional radiance spectrum. Consequently, a careful upstream design of the instrument is required. The main issue is to maximize the sensitivity to the average column of CO_{2} and CH_{4}, while minimizing biases due to other geophysical parameters.
In this paper, we introduce a forward approach to design NanoCarb, and then we analyze its performances for CO_{2} and CH_{4} atmospheric total column measurement. We base this approach on an analytical model of the NanoCarb radiometric sensitivity coupled with considerations over information present in the Fourier domain. We present a preliminary design of the two main components of the instrument which are the narrowband filter and the interferometer, and we investigate some promising features of the concept.
In Sect. 2, we present the NanoCarb principle and sampling strategy. Then in Sect. 3, we describe our radiometric model (direct or forward model), which is used in Sect. 4 to select the optimal spectral band, and in Sect. 5 to select the optical path differences (OPD). We derive and discuss some considerations about performance capabilities of the concept.
2 Nanocarb concept principle
In this section, we describe the principle of the NanoCarb spectrometer: optical principle and sampling strategy. A description of the expected data products is also presented, to introduce some potential calibration or data processing issues, even though the purpose of this paper is only focused on theoretical description and preliminary design.
2.1 Optical principle
Current NanoCarb bands
Band  Region  Measurement 

B1–O_{2}  760 nm  Surface pressure, aerosols 
B2–CO_{2}  1.6 µm  CO_{2} 
B3–CH_{4}  1.66 µm  CH_{4} 
B4–strong CO_{2}  2.06 µm  Aerosols 
The interferometric core is formed by the association of an interferometer array (6) with a microlens array (µlens—7). Each interferometer has a specific thickness. The focal plane array (FPA—8) is placed in the focal plane of the µlens array, to obtain a set of thumbnails, each one being associated to one thickness of the interferometric plate. In this configuration, the image formed in each thumbnail is a replication of the same FoV, modulated by the associated interferometer.
Each interferometer is a lowfinesse Fabry–Perot (FP), which modulates the spectrum of the incoming light in accordance with the interferometer optical path difference (OPD), which depends mainly on the Fabry–Perot thickness and slightly on the angle of incidence (this latter dependency creating the rings which modulate the image on each thumbnail, see Fig. 4). The currently investigated device is based on silicon, offering a natural reflection at the air–Si interface about 55%, which leads to twowavedominated interferences. This configuration is optimal to manage at the same time the compactness of the device and large FoV, as well as sensitivity as explained in [12] with more details. The device can be replicated, each one filling a part of the same FPA or using a dedicated FPA, to monitor synchronously several spectral bands.
Because interferential filter lies in the pupil plane in front of µFP array, a spectral band shift occurs in the field of view of each thumbnail. We integrate this shift in the NanoCarb numerical model and consider it in the design of the instrument.
This concept is compact and fully static. In the following, we will explain the partial interferometric sampling strategy of the NanoCarb concept, enabling snapshot acquisitions at high spectral resolution.
2.2 Partial sampling of the interferogram
The strategy we adopt to reach a high spectral resolution while keeping a large swath in snapshot mode is to target only the useful information in the Fourier space. Thus, the NanoCarb spectrometer acquires only partial interferograms.
The acquisition of partial interferograms was already developed in the 1970s by Kyle for temperature measurement in CO_{2} lines [13], then by Fortunato who applied this method to the measurement of SO_{2} concentration [14]. More recently, some studies can be found for the SIFTI instrument [15], and for IASI data processing [16], showing both a better geophysical bias mitigation, such as surface temperature, and an improvement of the signaltonoise ratio (SNR).

To obtain a measure of the Xspecie concentration, as independently of the interferants as possible (for example, water).

To obtain a measure of the interferants where appropriate, as independently as possible. The main atmospheric interferants are the aerosols and the water vapor. Temperature profile, pressure at ground, and albedo are also crucial in the retrieval process, and consequently require dedicated spectral or interferometric channels.
Figure 3 shows some partial derivative interferograms for a variation of concentration of CO_{2}, CH_{4}, and water, for the spectral band chosen as a example. The red dashed lines highlight the regions where the sensitivity of CO_{2} or CH_{4} is optimal, but biased by water, while the blue ones spot regions where the measurement of water is optimal with respect to CO_{2} or CH_{4}.
A particular attention must be paid to the choice of spectral bands and sampled OPDs when designing NanoCarb. These points will be detailed, respectively, in Sects. 4 and 5.
2.3 NanoCarb data products
The L0 data product of NanoCarb is the snapshot focal plane intensity acquired by the detector. For demonstration purpose, a noiseless simulation can be seen in Fig. 4—left, in the unrealistic case of a spatially and spectrally uniform scene.
The colored points spot an individual field of view (iFoV) imaged in all the thumbnails. The extraction of the intensity on a single exposure for this iFoV allows to retrieve the associated partial interferogram (Fig. 4right), assuming a lab calibration of the corresponding OPD (see [18] and [19]). This snapshot interferogram is the L1a data product of NanoCarb. For a given iFoV at this level, n_{FP}, the number of thumbnails—or FP—per spectral band, is the number of interferometric channels.
The L2 data product is the concentration value for a single iFoV, retrieved from this L1b concatenated partial interferogram. In the case of a multiband design, the measurement vector to be inversed is the concatenation of all the L1b concatenated partial interferograms from each one of these bands.
3 Analytical radiometric model of performances
We propose here a solution to estimate the sensitivity of NanoCarb as a function of the instrumental parameters. Model of intensity over the FPA at each level of data is introduced as well as derived analytical performance expression. In this model, the scene is assumed to be homogeneous at the scale of the spatial resolution.
3.1 NanoCarb instrumental model
Equations (1–4) allow to simulate 1Dinterferograms with NanoCarb radiometric properties on an arbitrary scale of OPD as presented in Fig. 3.
3.1.1 On NanoCarb data product models
We overlook, in this paper, the point spread function (PSF) of the microlens array, as it can be shown that at least 90% of the fringe visibility can be saved with a Nyquist sampling of the PSF. A convolution of the 2D NanoCarb image with the effective PSF could simulate this effect with a quite good accuracy.
Since we only consider homogeneous scene, this model can also be used to simulate NanoCarb L1a product, that is the partial 1Dinterferogram at a given iFoV (given \(\theta\)).
Noise is added on this interferogram, taking into account photon noise (Poisson distribution) and additive read out noise (RON), with normal distribution.
3.1.2 On thermal issues
The T dependency in Eq. (6) induced by temperature dependency of the optical index of silicon enables a thermal analysis of the system based on the model described above. This more advanced study is out of the scope of this paper, which focuses on the sensitivity of the concept for GHG measurement. However, preliminary investigations have shown that the interferometric envelope variation induced by a 0.1 K deltaT is one magnitude smaller than the one induced by a 1 ppm variation of CO_{2}. Such a thermal regulation over a 0.1 s exposure is fully achievable with current cooling devices.
3.2 Atmospheric model
Terrestrial radiance \(L_{\sigma }\) is simulated using the Standard US Model [20] for temperature and pressure profiles as well as atmospheric composition and concentration profiles. This model is implemented in the radiative transfer code LBLRTM [21], using the spectroscopic database HITRAN [22]. We simulate nadir terrestrial radiances with LBLRTM in the 1.6 µm and 1.66 µm band, taking into account fine spectroscopic effects such as line blending.
For this preliminary work, we assume a clear sky. CO_{2} and CH_{4} retrieval with input measurements of a joint aerosoldedicated instrument (SPEX [9]) will be implemented later in the framework of SCARBO. By focusing on the 1.6 µm and 1.66 µm band, we assume also that the atmospheric pressure is perfectly measured in the NanoCarb dedicated band.
3.3 Analytical noise model
We aim here at deriving an expression of the radiometric noise in ppm or ppb of the considered specie X over the detector, to deliver a preliminary design of the instrument. A solution is to compare the required sensitivity for a targeted concentration variation, to the effective SNR over the fringe visibility measurement.
The ratio \(S_{{{\text{ph}},X}} /S_{\partial \left[ X \right]}\) gives a good appreciation of the NanoCarb radiometric sensitivity for the given concentration variation \(\partial \left[ X \right]\). Indeed, \(\left( {S_{{{\text{ph}},X}} /S_{\partial \left[ X \right]} } \right)\partial \left[ X \right]\) is directly a noise over the concentration estimate in the same unit as \(\partial \left[ X \right]\). For example, a ratio of 0.5 for \(\partial \left[ {{\text{CO}}_{2} } \right]\) = 1 ppm means a noise over L1b data product equivalent to 0.5 ppm.

The left term shows as expected a statistical error improvement with the total number of photoelectrons as a function of the photon noise. Moreover, this term highlights the evolution of the NanoCarb sensitivity as a function of the contrast variation over the targeted interferometric regions. It requires a maximization of the interferometric Jacobian contrast, e.g., in the 5.6 mm OPD region for the CO_{2} (Fig. 3). Only the spectral filtering performed by the interferential filter permits such an optimization.

The right term is a second order (\(\sim 10^{  3}\) compared to \(\sim 10^{1}\) for the left term in the worst case). Nevertheless, it illustrates a potential downgrading of the sensitivity when an optimization of the Jacobian contrast decreases the total number of electrons in the targeted region. Thus, a joint tradeoff must be carefully achieved to not degrade the fringe visibility when optimizing the spectral bandwidth.
On the maximum sensitivity interferometric area of the CO_{2} band, the expected \(\partial V_{{X{\text{CO}}_{ 2} }} /\left( {\partial \left[ {{\text{C0}}_{2} } \right] = 1 {\text{ppm}}} \right)\) is ranged around \(10^{  4}\), calling for \(\sim 10^{8}\) electron per iFoV for a target random error of 1 ppm in a snapshot acquisition.
3.3.1 Assumption over intensity level

On L1a snapshot partial interferogram: \(\bar{N}_{\text{ph}} = \bar{N}_{\text{snap}} n_{\text{FP}}\) is the mean total level of photoelectron contributing to the signal for a given iFoV in a single snapshot frame, with \(n_{\text{FP}}\) the number of Fabry–Perot for the considered spectral band.
 On L1b concatenated partial interferogram: As explained previously, the L1b data product is the coregistration of snapshot acquisitions while the iFoV shifts across the thumbnail during the orbit. Given \(n_{ \exp }\) the number of coregistered exposures for a given iFoV, we can express the total number of photoelectrons in L1b data products as:$$\bar{N}_{\text{ph}} = \bar{N}_{\text{snap}} n_{\text{FP}} n_{ \exp } ; \left[ {\text{e/ifov}} \right],$$(12)\(n_{ \exp }\) depends on both the number of pixels per thumbnail side \(N_{\text{S}}\) and on acquisition frame rate. To permit signal coregistration, the minimum frame rate must be set to achieve an orbital brooming of one pixel between two exposures. Thus, the maximum number of coregistered exposures for one single iFoV is:where \({\text{broom}}_{\text{pix}}\) is the orbital brooming expressed in pixel.$${ \hbox{max} }\left\{ {n_{ \exp } } \right\} = N_{\text{S}} \times {\text{broom}}_{\text{pix}} ,$$(13)
4 Optimization of the spectral bands
This section aims to illustrate the design strategy of the NanoCarb spectral bands, for SNR purposes. We expect to demonstrate the radiometric performances of NanoCarb and its potential for the SCARBO mission, expressed in terms of statistical error over the total column of CO_{2} or CH_{4} measurement, with our forward model.
4.1 Investigated NanoCarb design
FPA characteristics used in NanoCarb radiometric study, based on NGP features [24]
FPA format  1024 × 1024 
QE  0.9 
Sensitivity range  0.5–2.5 µm 
Pixel pitch  15 µm 
Readout noise  170 e^{−} 
Operating temperature  170 K 
Saturation level  590 ke^{−} 
Nominal NanoCarb band configuration for performance estimation
Altitude  600 km 
Frame rate  1pixel brooming 
Dedicated FPA size  1024 × 1024 
Pixel per thumbnail side \(N_{\text{S}}\)  128 
Number of FabryPerot and thumbnails \(n_{\text{FP}}\)  64 
Pixel sampling at ground (iFoV)  1 km 
Swath (fov)  128 km 
Maximum exposure time  144.46 ms 
4.2 Parametric optimization of the SNR
With the basic design above, we present here an optimization of the NanoCarb CO_{2} and CH_{4} spectral bands, using synthetic interferograms, coupled with our radiometric performance model, and a model of 4cavities narrowband filter. The optical transmission of the device is in range about 80%. We assume a linear evolution of the absorbed power with the concentration. This last point is well suited on the unsaturated 1.6 µm and 1.66 µm bands we consider here.
We vary the filter central wavenumber σ_{0} over the spectral regions of interest, as well as its full width at half maximum (FWHM) from 1 to 100 cm^{−1}. For each couple {σ_{0}; FWHM}, we compute the singleiFoV snapshot radiometric sensitivity from a differential interferometric envelope ∂V/∂X, with ∂X a finite variation of concentration for the specie X. On this envelope, we search where the fringe visibility is maximum in the range of OPD corresponding to the Fourier signature of absorption line mean periodicity over the related spectral band.

The red squares in the maps spot the optimal filter in terms of SNR.

The contours highlight regions as a percentage of the optimal sensitivity.

The partial derivatives in radiance for ∂[CO_{2}] = 1 ppm and ∂[CH_{4}] = 10 ppb are superimposed to the σ_{0} scale, illustrating the evolution of the sensitivity with the periodic spectroscopic pattern.

Some regions in the maps are aberrant, and set to zero. On the CO_{2} map: some parts of the region around σ_{0} = 6280 cm^{−1} enclosed by the 25% contour; on the CH_{4} map: the region around σ_{0} = 6000 cm^{−1}. On these regions, the algorithm fails to find a signature on the targeted interferometric range. In the case of CO_{2}, there are no CO_{2} absorption lines, and the interferogram is dominated by residual continuum shape. Concerning CH_{4}, the band is dominated by saturated line group around 6000 cm^{−1}.
CO_{2}: the line periodicity is small (~ 2 cm^{−1}) and presents some quite important jitters along the σ_{0}axis. As a consequence, the maximal sensitivity evolves rapidly with a shift of spectral band, which is responsible for unstabilities of the relative CO_{2}/H_{2}O sensitivity in the FoV for the optimal red point {σ_{0}= 6216 cm^{−1}; FWHM = 17 cm^{−1}}. The symmetric optimal filter {σ_{0}= 6336.3 cm^{−1}; FWHM = 17 cm^{−1}} is also rejected due to a huge amount of water on this region. The finally chosen filter {σ_{0}= 6213 cm^{−1}; FWHM = 24 cm^{−1}} is a tradeoff between CO_{2}/H_{2}O sensitivity, SNR, and stability in the FoV.
CH_{4}: the periodicity of the CH_{4} absorption line is large (~ 12 cm^{−1}). Consequently, the optimal filter {σ_{0}= 6078 cm^{−1}; FWHM = 69 cm^{−1}} is wide, and the sensitivity slowly revolves around this optimal point, which is convenient to design the narrowband filter. Hence, despite of the large amount of water on this band, some interesting interferometric waterfree regions, stable in the FoV, can be found as we will see in next section. Thus, the red spotted filter parameters are chosen for B3.
Selected filter for B2 and B3 bands and relevant snapshot sensitivity, given a solar zenithal angle of 55° and an albedo of 0.2
Band  Filter  Max. snapshot sensitivity/iFoV  

σ_{0} (cm^{−1})  FWHM (cm^{−1})  
B2—CO_{2}—1.60 µm  6213  24  3.10 ppm 
B3—CH_{4}—1.66 µm  6079  69  27.02 ppb 
4.3 Extrapolation of the noise over CO_{2} and CH_{4} measurements on L1b data product
The last subsection illustrated the strategy to design the spectral bands of NanoCarb. Given the two retained B2 and B3 bands, we aim at extrapolating here the intrinsic radiometric sensitivity of the instrument at L1b level.
4.3.1 Statistical error on CO_{2} measurement
The exploitation of all the available snapshot acquisitions largely fulfills subppm noise on CO_{2} measurement, in all the considered configurations, and observation conditions. The performances are even below 0.5 ppm in the more favorable observation conditions (albedo > 0.2). Hence, the use of only 50% of the available snapshot acquisitions allows again to reach a subppm noise. This is a benefit to mitigate interpolation issues between the different frames caused, for example, by platform dispointing or jitter, as well as cloud effects.
4.3.2 Statistical error on CH4 measurement
The 10ppb sensitivity target is reached too in all observation conditions, with the coregistration of at least 50% of the available frames. We can expect a noise around 5 ppb in the worst observation conditions (albedo = 0.05), by coregistering all the available frames.

0.2–1 ppm target for CO_{2} noise is reached with a nominal allocation of one NGP for the 1.6 µm band.

1–5 ppb for CH_{4} noise is reached in the same conditions.

These good intrinsic performances enable (1) a decrease of the exposure time up to a factor 4 to mitigate pointing blurring effects, (2) the allocation of samples to other dedicated areas of the interferogram, for example, to jointly measure water.
This optimization of the NanoCarb radiometric performances is done with a very faint evolution of the instrumental complexity. As the number of pixels increases for the totality of the spectrometer, we are confident to a linear increase of the volume of the optical part of NanoCarb (from the objective to the FPA), driven by the size of the sensitive area on the detector. As an example, if we evaluate a volume of ~ 250 cm^{3} with one NGP, the volume with a next generation 2 k 2 k NGPlike [26] will be approximately increased by a factor of eight. Weight and full thermal regulation must be treated as such, which is a real advantage compared to dispersive spectrometry techniques and scanning Fouriertransform spectrometers.
We demonstrated here the intrinsic radiometric capabilities of the NanoCarb concept for CO_{2} and CH_{4}, in a forward approach. Nevertheless, this study does not study any impact of the instrumental or geophysical biases, and does not allow consequently to accurately choose the interferometric samples.
5 Design of the Fabry–Perot microinterferometer array
Previous section focused on band optimization for SNR purposes. We develop and illustrate here a proper strategy to mitigate bias impacts over CO_{2} or CH_{4} measurement, by designing the microFP interferometer array and choosing the OPDs to sample. We mainly present waterrelated issues as justified in a first subsection. A second subsection presents a forward exploration of the information content of the interferogram, as the last one introduces an inverse approach to estimate the performances and generalize this optimization.
5.1 Biases over B2 and B3 bands and geophysical variables
Geophysical variables to be retrieved from NanoCarb measurement, and impact over the different bands. In green—the dedicated spectral bands when occurred

Clouds and aerosols issues, monitored on B1 and B4 bands, are consequently not considered despite their huge impact over CO_{2} and CH_{4} measurement. We assume a perfect joint measurement by SPEX, similar to clear sky assumption. An upcoming study will be led to assess the unbias capability of the SPEX instrument over NanoCarb measurement, with a realistic model of performances.

We assume a perfect joint estimation of surface pressure from B1 band.

The albedo estimation accuracy relies on the radiometric calibration capability of the device, and has not been yet studied. Works based on experimental characterization are in progress to evaluate FPA miscalibration impact over our signal knowledge. A discussion about it is proposed in paragraph 5.4.

Water is one of the main interferants affecting B2 and B3 bands, and is consequently treated in this preliminary design of microinterferometer array.
We present below a simple study of the impact of a misestimation of the total column of H_{2}O over the averaged column of CO_{2} retrieval. The goal is to derive an estimation of the required accuracy we have to reach, for illustrative purposes. The retrieval algorithm is a simple least mean square method based on a Levenberg–Marquardt algorithm. Its specificity is to work with partial concatenated L1b interferograms, without intermediate radiance spectrum retrieval.
This observation was well expected if we consider the CO_{2} interferogram as in Fig. 3—left: the partial derivative for 1 ppm of CO_{2} is comparable in flux to the one for 10% of water in the 5.6 mm region. Therefore, both H_{2}O and CO_{2} have a significant and comparable impact over the fringe intensity. With similar considerations, the impact of water over CH_{4} band is greater by a factor 10 at least.
This result justifies the need to refine the NanoCarb design to mitigate the water impact on B2 and B3 bands. Especially, we will consider in the next subsection the selection of several dedicated interferometric regions in a forward approach.
5.2 Design for water mitigation with forward model
The forward model of NanoCarb is implemented here to search for interferometric regions in B2 and B3 bands where sensitivity to CO_{2} and CH_{4} is optimal related to water and instrumental issues, especially the spectral band shift in the FoV of the filter, responsible for interferometric signature variabilities and instabilities.
On Figs. 12 and 13, the superimposed blue curves show the evolution of the water interferometric signature along the longitudinal axis, while the brown–white–green curves state for CO_{2} on B2 on Fig. 12 and CH_{4} on B3 on Fig. 13. Each graph (a–d) on both Figs. 12 and 13 represents one among the four selected iFoV on the swath.
CO_{2}on B2 Fig. 12: The maximum of sensitivity for CO_{2} at 5.6 mm seems stable in the FoV even for the most extreme iFoV of the swath. Nevertheless, this interferometric region is also sensitive to water in quite important proportions (typically 50% of CO_{2} visibility), calling for dedicated H_{2}O disjoint region. The 1.2 mm water region is rejected due to huge sensitivity variations in the FoV. On the contrary, the 2.4 mm waterdominated region is stable in the FoV while the sensitivity to CO_{2} is almost null. As a conclusion, the CO_{2} waterbiased 5.6 mm region and the water CO_{2}free 2.4 mm region are selected to guarantee an unbiased measurement of CO_{2} concentration.
CO_{2} on B2 has a harmonic signature at 11.2 mm of OPD that we did not consider here. Indeed, such a high OPD induces high frequency FP ring pattern and consequently potential pixel sampling issue. This consideration is related to the interferometric transposition of the Jacquinot criterion about spectral resolution and sampling.
CH_{4}on B3 Fig. 13: The CH_{4} signature presents several harmonic regions every 1.05 mm of OPD, and thus as many sensitive areas. Nevertheless, only the first two have fringes in a favorable proportion of sensitivity CH_{4}/H_{2}O, and we limit the study to the 2.5 mmwide plotted regions. CH_{4} signature is very stable in the FoV, as well as several water areas such as at 0.9 mm, 1.25 mm, and 2.35 mm. The maximum sensitivity of CH_{4} at 1.05 mm seems to be free of water. Additional samples placed on the second CH_{4} harmonic could provide also a measurement of a more varied kind of information, for instance about vertical profile.
5.3 Illustration of CO_{2} and water retrieval with two OPD areas
Despite a slow convergence of the water estimation, this very interesting result shows a quick convergence of the CO_{2} column retrieval toward a numerically limited fraction of the real value. It seems that the chosen partial sampling of the interferogram permits in this case a robust degeneracy removing of water over the CO_{2} retrieval.
The next subsection introduces some leads to improve this design as well as assess its performances.
5.4 Discussion about design optimization and performances assessment

Generalization of the approach to all the geophysical variables described in Table 5, as well as instrumental biases.

Number of allocated FPs (samples) per identified region.

Sampling strategy: (1) multipoint sampling of the interferometric envelope, calling for multiple disjoint regions, or (2) concentration of all the samples on some regions illustrated in the previous subsection. While the concentration of samples at maximum sensitivity areas ensures a maximum SNR, the variety of measured information is very poor, potentially responsible for important sensitivity to other geophysical biases or verticalinduced profile effects.

Validation of the chosen interferometric samples in terms of reached absolute accuracy on L2 data product (systematic biases).
5.4.1 Generalized bias mitigation strategy for OPD choice
 1.
Fix the NanoCarb key features, for instance number of pixels, number of Fabry–Perot, FoV, etc.
 2.
Fix the spectral bands by SNR forward analysis as presented in the previous section.
 3.
Forward analysis of sensitivity of the interference domain as presented in subSect. 5.2. The aim is to identify consistent interferometric regions and consequently restrain OPD range of analysis, for both all bands and geophysical parameters. A Bayesian approach of the information could be also considered as described in Sect. 2.5 of [11].
 4.
Multivariable retrieval on L1b data for n sets of n_{FP} samples chosen by Monte Carlo in the restrained parameter space.
This method potentially enables to derive performance trends as a function of the number of allocated samples per identified region as well as the distribution of regions along the interferometric envelope.
5.4.2 Instrumental issues
Main considered instrumental issues for a NanoCarbbased payload, related impact over the performances, and assumed criticality for the final data quality considering knowing solutions
Impact  Solution  Criticality  

Spectral response calibration  High  OCT scan or spectral scan of each narrowband  Low 
Radiometric calibration  High  To be established  High 
Detector PRNU  High  Inflight calibration protocol has to be addressed  Low/high 
Parasitic/stray light  High  High criticality known for many space instruments with a similar performance aim but a different concept (e.g., dispersive spectrometer).  High 
Filter thermal stability  High  ~0.1–1 K thermal regulation  Low 
Interferometer thermal stability  
Platform stability  Low  Specification to be determined  Low 
Component behavior in space  Unknown  Radiation resistance of siliconbased components, multilayer processed surfaces, detector aging, etc., has to be addressed  Unknown 
Both spectral response and radiometric calibration of the instrument are critical to retrieve radiometrically calibrated L1a, and then L1b interferograms from L0 raw images. Even if the spectral response characterization of the instrument does not constitute a stumbling block by using either interferometric techniques such as optical coherence tomography [18, 19] or a spectral scan, efforts have to be provided to ensure a radiometrically calibrated device, with an accuracy to be determined. This latter may have a critical impact to disentangle between albedo variations over the scene and aerosolinduced extinction. Moreover, questions remain about calibration stability in time and inflight capabilities of recalibration with the considered 50 kgclass platform.
The PhotoResponse NonUniformity (PRNU) of the detector and more exactly the residual fixedpattern noise (RFPN) is related to the radiometric issue and must be treated as relevant, and its impact may be very significant with a Fouriertransform spectrometer [27].
Also related to radiometric calibration, and with a potential huge impact, is the issue of parasitic and stray light. Indeed, it has been observed in another FPbased space instrument such as GHGsatD “CLAIRE” [28] that stray light may be a critical point for the performances. A snapshot static Fouriertransform spectrometer such as NanoCarb is potentially more sensitive to temporal stray light variation compared with push broom or scanning spectrometers, because each interferometric channel and iFoV are associated with one different pixel of the detector.
On the other hand, as introduced previously in this paper (subSect. 3.1), thermal issue does not seem to be a hurdle to the instrument operability, since a 0.1–1 K thermal stability enables to avoid impacts over the measurement.
Platform stability and component behavior in space will be addressed later, as the efforts are currently focused on the demonstration of the NanoCarb concept feasibility at a quite early level.
Laboratory prototypes are being integrated to address some of these issues, as well as an airborne prototype is also planned for inflight demonstration of the NanoCarb performances in a relevant environment.
5.4.3 Systematic performances assessment
The performance assessment of NanoCarb is an iterative work in progress in the H2020 SCARBO framework. A Bayesian optimal estimation of CO_{2} and CH_{4} averaged dry column is assessed from the presented model of NanoCarb for a complete set of atmospheres and many observation scenarios. The followed methodology has been applied for CO_{2} M error parametrization [29]. This study, done with the Laboratoire de Météorologie Dynamique (LMD),^{2} will provide both expected random error of NanoCarb for CO_{2} and CH_{4} at L2 (to be compared with the noise at L1b presented in this paper), and systematic error. The latter will enable to validate the presented OPD choice and geophysical bias mitigation, or to refine it if relevant.
6 Conclusion
NanoCarb is an original concept of imaging spectrometer combining the use of innovative interferometric components and an unusual partial interferogram sampling technique. These two combined features are investigated in the SCARBO project to assess the feasibility of a constellation based on such miniaturized payloads to monitor the anthropogenic GHG emissions with a daily revisit and a global coverage.
In a forward approach, we showed the radiometric capabilities of this concept to measure CO_{2} and CH_{4} in the nearinfrared, through an optimal design of the narrowband filters. The expected theoretical and intrinsic performances, in terms of statistical error over measurement of the averaged column of CO_{2} and CH_{4}, are comparable to other dedicated space missions. Then we addressed the design of the interferometer, to manage geophysical biases. The design strategy has been illustrated for water mitigation. For instance, a significant theoretical decrease in waterinduced bias compared to CO_{2} measurement can be expected using an 8 × 8 interferometer array with 8 waterdedicated and 54 CO_{2}dedicated Fabry–Perot.
The study must now be completed to assess the performances of the concept in terms of systematic bias, taking into account all relevant geophysical interferants, and then validating or refining the interferometer design. Therefore, operability of the instrument also needs to be addressed, by taking into account instrumental and platforminduced issues, as well as inorbit calibration capabilities. An experimental proof of concept is planned in the framework of the SCARBO project.
In conclusion, it is interesting to note that the NanoCarb concept is very flexible at the design level, allowing to target various spectral signatures and therefore several different species in the atmosphere. In each case, the instrument is spectrally and interferometrically optimized for the latter, assuming a good knowledge of what is to be measured. This feature is well suited for trace gasses in the Earth’s atmosphere. Thus, NanoCarb concept is more a CO_{2} and CH_{4}dedicated sensor than a classic spectrometer, which is unusual in earth observation, but a key feature of miniaturization.
Footnotes
Notes
Acknowledgements
This project has received funding from the European Union’s H2020 research and innovation program under grant agreement No 769032. The authors would like also to specially thank the FOCUS French label of excellence LabEx FOCUS (ANR11LABX0013) for their funding on parts of this work, as well as for their involvements in these challenging developments.
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