3.1

Spatial sizing and scanning principle

Table 1 presents the key spatial and temporal requirements. The SSD is achieved by choosing the right detector pitch / focal length combination for the FTS along both spatial dimensions and along the field direction for the DS, and the right scan speed / TSI combination for the DS along the scan direction.

Table 1 –

Specified SSD, spatial coverage and repeat cycle for MTG-IRS (see table 2 for the definition of the spectral bands, IRS-1 to IRS-7)

While Fig. 1 implicitly assumed that the full image can be covered with a single scan (of the x axis or of the OPD), this would require array sizes of up to 3700x3700 detectors (FTS concept, IRS-5 to IRS-7). In reality, a high number of square sub-images for the FTS and strips along the scan direction for the DS are acquired successively to cover the Earth by sequentially moving the LOS, as shown on Fig. 2. The number of required steps or scans is driven by the instrument field of view, which is limited by a theoretical limit (described for instance by Beer [2]) on the array dimension in detectors due to self-apodization (FTS only), the limits of optical design with regard to aberrations and vignetting, and the limits of IR FPA technology in terms of number of detectors and array physical size.

Figure 2 –

Scanning principle for the FTS concept (left) and for the DS concept (right). The square with thick edges represents the restricted spatial domain for simplification of the study.

Yet it is clear from Fig. 2 that, neglecting the time lost for stepping from one LOS position to the other, the spatial extent of this analysis can be restricted to a spatial domain equal to one subimage of the FTS, by rewriting the requirements in the following way:

where M is the size in detectors of the FTS array (assumed square). The number of frames that are necessary for the DS to acquire this subimage is:

where r is the ratio between the array size of the FTS and the array size of the DS along the cross-scan direction:

with the DS array size in detectors along the field direction. As for the number of frames for the FTS, N^FTS, and the size of the array along the spectral direction for the DS, , they are linked to the spectral requirements which are discussed in next paragraph.

3.2

Spectral sizing

As already stated in part 2, a DS provides an approximately constant Instrument Spectral Response Function (ISRF) and uniform spectral sampling on the wavelength scale while a FTS provides a constant ISRF and a uniform spectral sampling on the wavenumber scale. In order to have a unique specification applicable for both concepts, the spectral resolution is specified in [1] in terms of the required resolving power 𝕽 at the central wavelength (DS) or wavenumber (FTS) of the band; these specifications are recalled in table 2.

Table 2 –

MTG-IRS spectral requirements

It can be shown that this is equivalent to specifying an equal number of spectral resolution elements for both concepts; in addition for the DS, a requirement in [1] explicitly specifies a spectral oversampling factor of 2. The resulting number of spectral samples for the DS, which is also the required array size in detectors along the spectral direction , is shown in table 3.

Table 3 –

Required array size along the spectral direction for the DS and number of frames for the FTS

For the FTS, the spectral oversampling requirement is implicit: the spectral resolution δσ₀ is defined as the FWHM of the unapodized spectral response function, and it is a well known result (cf Beer [2], for instance) that the ratio between this quantity and the spectral sampling for an ideal FTS is 1.207. This required spectral sampling gives access to the maximum OPD of the interferometer; by considering the minimum sampling wavenumber, which is imposed by the Shannon sampling theorem (twice the maximum frequency of the measured spectrum, σ_max), the minimum number of interferogram samples which is also the number of frames for the FTS can be calculated. The results are also shown in table 3.

Two study cases are distinguished in table 3: in the first case (“SC7”, for “Study Case 7 FPAs”), each IRS band enjoys a dedicated FPA, in the second case (“SC2”, for “Study Case 2 FPAs”) the bands are grouped according to their spatial resolution and thus covered by only two distinct FPAs.

On one hand, with SC7, the detector characteristics (material, cutoff wavelength) can be fine-tuned independently for each band, which is highly desirable from a performance point of view.

On the other hand, SC2 is by far preferable from a cost point of view, because each additional FPA and its associated optical train, coolers and electronics lead to a significant increase of volume and mass. But for the FTS, inherently to the instrument principle, it is detrimental to the performance since each detector records the signals corresponding to all wavenumbers covered by the FPA simultaneously and cannot be optimized for all the bands covered; while, for the DS the “stichting” technique makes it possible to implement several distinct detector modules along the spectral direction with different characteristics on the same monolithic ROIC, at the price of the presence of dead zones of a few spectral channels between detector modules.

In fact, as far as the DS concept is concerned, for array sizes so large as the ones predicted in table 3 for SC2, stitching is bound to be necessary anyway due to the technological limits with regard to the maximum size of a single detector module. Even for SC7, the DS array size along the spectral direction reaches values over 1000 detectors in the MWIR range, and this is imposed by the requirements, while the FTS array size M can be chosen as small as possible by the designer.

The pixel readout frequencies per array can be calculated for each concept thanks to:

which leads, by injecting Eqs. (4) and (5) for the DS, to

The ratio between the pixel readout frequencies per arrray for the FTS concept and for the DS concept appears to be independent from r : it is simply . It is indicated in table 3 for each study case: the FTS is disadvantaged, by factors up to 7 (IRS-3, SC7). However this corresponds to the readout frequency at the output of each array, thus at the level of the raw interferogram; what can be concluded from these numbers is that the internal readout rates are higher for the FTS and that more on-board processing is needed than for the DS in order to bring the downlink data rate at the same levels.

3.3

Radiometric sizing

The primary purpose of the radiometric sizing of the detection chain is to size the integration capacitance of individual readout cells so that it matches the maximum expected signal. Assuming that only the surface underneath the detector is available for implementation of the capacitance, there is a technological limit to its value. With p_det the detector pitch, c₀ the feasible surface capacitance density and V_max the ROIC output voltage swing, the maximum input-referred full well capacity per detector in electrons is:

where q is the charge on the electron. If the maximum signal exceeds this value, temporal oversampling is necessary to avoid saturation, with the temporal oversampling factor given by

where S_max is the maximum signal, which can be computed thanks to Eq. (1) and (2) using the specified maximum target spectral radiance for L̅.

Another technological limitation not yet taken into account is the maximum pixel readout frequency per video output, f_max. This limitation is overcome by increasing the number of video outputs N_out of the ROIC:

where f_ro can be calculated from Eq. (7).

Using (8), (9) and (10), a numerical example for the required temporal oversampling and number of video outputs is presented in table 4 for both the DS and the FTS, and for the two afore-mentioned study cases, with realistic values for c₀, V_max, τ^DS, τ^FTS and for an entrance aperture of 0.3 m (value currently considered in the baseline concepts), a detector pitch of 50 microns (IRS-5 to IRS-7) / 100 microns (IRS-1 to IRS- 4), and for M = 256 (IRS-5 to -7) / 128 (IRS-1 to -4).

Table 4 –

Temporal oversampling factor and number of video outputs for a particular set of parameters

Because the level of the signals recorded by the FTS are orders of magnitude higher than the signals recorded by the DS, temporal oversampling is needed for the FTS in the LWIR range while it is not for the DS. This further increases the readout rate at the output of each array, already found to be higher than for the DS in paragraph 3.2. These high pixel readout frequencies impose a great number of video outputs. This number increases and becomes even unrealistic when considering SC2, because a broader spectral range is then incident on the detectors (the results for the DS are unchanged with respect to SC7 and not shown in table 4, because the incident signal is the same).

4.1

Considered noise sources

Three additional noise sources have been considered: the photonic noise due to the photosignal generated by the thermal emission from the instrument, the shot noise due to the dark current signal, and the readout noise due to the ROIC. Similarly to the photonic noises, the variance of the dark current shot noise is equal to the dark signal itself:

where I_d is the dark current in e-/s.

The variance of the readout noise must account for temporal oversampling, i.e. the noise of each readout adds quadratically to the total noise for a cell of the raw data cube:

where ν_ro is the total RMS noise voltage generated at each readout by all contributors in the readout electronics up to the input of the A/D converter (which is supposed not to add any further noise thanks to a sufficient number of bits) and CF is the conversion factor, which is by definition equal to the output voltage swing divided by the integration capacitance:

4.2

Dark current and FPA cooling

Equations (1) or (2) (away from ZPD for the FTS) and (11) yield the maximum tolerable dark current for each concept:

which shows that, for the same detector size, the FTS concept is inhenrently much more immune to dark current, by a factor

Thanks to recent dark current models, Eq. (1) and (2) have been translated into requirements on the maximum FPA temperature; the details are not presented here but the results are shown in table 5 for SC7.

Table 5 –

Maximum FPA temperature for each concept with SC7 and realistic dark current models

The DS concept is clearly more demanding in terms of FPA cooling temperature, because of the weaker photosignal from the target scene; this disadvantage has already been noted in literature [4].

4.3

Instrument background and cooling of the optics

Without a detailed optical design, it is difficult to assess the background flux incident on the FPA. However, a significant difference exists between the FTS and the DS: while the radiation from all the optical elements are spectrally filtered in the same way as the radiation from the scene for the FTS (by the bandpass filter associated with the considered FPA), two types of contributions must be distinguished for the DS concept:

The contribution from these elements to the background signal can be roughly modelled by a gray body with effective emittance ε, seen with the same geometrical throughput as the scene. Using Eqs. (1) and (2), the temperature T_max for which the contribution of the instrument background to the photosignal is equal to the contribution of the target scene verifies:

for the DS and

for the FTS, which shows that the DS is more sensitive to the instrument background, by the same factor as for the dark current, in paragraph 4.2. Using Eqs. (16) and (17), the maximum temperature of the optics has been computed for a realistic value ofε. The numerical results are shown in table 6 for SC7.

Table 6 –

Maximum tolerable temperature of the optics for each concept and for a realistic emittance

Just as for the FPA cooling, the DS is more demanding for the cooling of the optics than the FTS. A technological solution to this, which has already been used successfully with dispersive spectrometers in the thermal infrared [5], is the use of a Linear Variable Filter (LVF) for suppression of the radiation from the proximity optics. The trade-off for the DS is then between an added development effort (LVF) or more cooling needs.

While the temporal oversampling factor and conversion factor involved in Eq. (12) are imposed by the sizing of the detection chain, ν_ro is a technological parameter and the requirement on the maximum tolerable value of readout noise can be considered as a requirement on the minimum value of the ROIC dynamic range DR_min, classically defined as the ratio between V_max and ν_ro. Combining Eqs. (12), (13) and (9), DR_min verifies:

where S_typ is the typical signal due to the target scene and computed from Eq. (1) and (2).

Two distinct behaviours of Eq. (18) can be distinguished: if S_max < S₀ (no temporal oversampling) then DR_min is proportional to the square root of the maximum signal:

If S_max >> S₀ (high temporal oversampling) then DR_min converges towards a constant value:

In Eqs. (19) and (20), β is defined by:

β is a concept-independent measure of the specified “dynamic range” in terms of target spectral radiances; its numerical values are indicated in table 7.

Table 7 –

Ratio between the specified maximum and typical target radiances per IRS band

With the same parameters as for the numerical example of paragraph 3.3, DR_min has been quantified for SC7 and the results are shown in table 8.

Table 8 –

Minimum ROIC dynamic range for each concept and for SC7

The FTS is strikingly more demanding in terms of FPA dynamic range, with values up to 90 dB which is considered as very challenging with the current technologies and may call for the use of advanced on-chip techniques such as skimming or non-linear conversion.

6.1

AOCS

Fourier transform spectrometers are known to be very susceptible to temporal fluctuations of the target spectrum. In the case of an imaging spectrometer, these fluctuations can be produced by the combination of a heterogeneity in the pixel (presence of a cloud) and any LOS instability or “jitter”. Bennett has shown that even low jitter amplitudes can cause a rather high level of noise in the measured spectrum [6].

This is particularly critical in the configuration of MTG-IRS combining GEO orbit and relatively high spatial resolutions (6 km / 3 km), because the same angular LOS instability will lead to much higher fluctuations of the signal than in LEO orbit (by a factor around 40). This requirement on LOS stability applies over the full dwell time Δt of the FTS concept, i.e. 8 s for the numerical example used throughout this document.

For the DS concept, not only are the requirements on LOS stability much less stringent in terms of amplitude (they are in this case linked to spatial requirements), but they apply only over the integration time per spatial sample, i.e. a few milliseconds. This is quantified in table 9 for the numerical example used throughout this document; the dwell time is presented for each concept, along with the corresponding maximum admissible angular drift, based on the relevant requirement [1] for a maximum LOS instability of 11 μrad.

Table 9 –

Dwell time and associated maximum drift for each concept

As a consequence, it is foreseen that the requirements on AOCS at spacecraft level will be much more severe for the FTS concept than for the DS concept. Given the sensitivity of the FTS concept not only to the amplitude but also to the frequency spectrum of jitter, greater care will have to be put in the mechanical design of the optical bench and spacecraft (micro-vibrations) and/or the interferogram processing.

6.2

Spectral calibration

While the radiometric calibration process is likely to be similar, the spectral calibration process will be different for each concept. Regardless of the estimated performance of the spectral calibration algorithm in terms of radiometric accuracy, it can be anticipated that: