A.

Single Channel Vs. Multichannel Architecture

The separation of the LI global FOV into multiple optical channel, taking into account the NBF positioned in the entrance pupil, allows mitigating the development risk of the critical items (NBF, detector and proximity electronics) and the optimization of the NBF performances.

Figure 4 shows the FOV layout for a single and double Optical Channel solutions fulfilling the coverage requirement.

Figure 4

LI coverage for Single and Double Optical Channels concept

The large FOV (8.7°) of the Single OC concept cannot be sustained by the NBF due to the blue spectral shift induced by the high angle of incidence which is not compatible with the bandwidth requirement. To limit such effect a Galileian telescope can be placed in front of the NBF (Figure 5) reducing the angle of incidence to 5.5°, but enlarging at the same time the filter diameter (~1.6X). This makes the achievement of the coating uniformity requirements more challenging. In addition this solution imposes the development of a very large detector array (about 5 Mpixels) and of a huge processing electronics (5 Gpixel per second to be processed in real-time) both considered unfeasible.

In case the global coverage is achieved by means of two or four Optical Channel, the detector size is reduced and the use of the Galileian telescope, requiring more mass ad envelope than available, is no more required.

The optical system parameters for single and multichannel configurations are reported in Table II.

The larger number of Optical Channels improves the NBF performance and the feasibility of detector and relevant processing electronics.

Figure 5

Single optical channel layout with Galileian telescope

TABLE II

– OPTICAL CHANNEL MAIN PARAMETERS VS. LI CONCEPT

B.

Definition of NBF Working Concept

The above mentioned NBF parallel beam concept has been compared with an alternative one, for which the filter is positioned close to focal plane (convergent beam optical configuration).

In this case to limit the spectral shift of the NBF bandwidth, the optical system must be telecentric and with an F# of 4.75, corresponding to a convergent beam of 6° maximum. The resulting pixel pitch of the detector is 65 μm producing a very large detector size and thus an increase of the effective focal length (~2.7X) compared with the NBF parallel beam concept.

However the trade-off between the NBF working concepts (parallel beam vs. convergent beam) is based on the Signal-to-Noise Ratio (SNR):

Where: SLP is the lightning pulse signal; SBKG is the background signal; nro is the read-out noise; NAVG is the background radiance averaging factor and corresponds to the number of background images averaged together.

Maximization of the SNR is achieved by proper specification of NBF bandwidth and in-band transmittance, taking into account, by means of a filter spectral response model (validated versus manufacturer test data), that minimizing the bandwidth leads to a decrease of the peak transmittance and vice versa.

Based on (1) and on the NBF spectral model, it can be demonstrated that SNR cannot be maximized for any illumination condition: in other words it is necessary to decide whether to increase SNR in night-time condition, maximizing the NBF transmittance, or in daylight condition, minimizing the filter bandwidth, the two solutions being in opposition.

The diurnal flash distribution provided by LIS data can be used to calculate a weighted SNR average, thus defining a Factor of Merit (FoM) that is not dependent on the illumination condition (see example in Figure 6), even if this statistics is not part of ESA/TAS requirement specification.

Figure 6

SNR weighted average

The FoM is calculated as a function of the NBF Full Width at Half Maximum (FWHM) for both the parallel and the convergent beam concepts. Results are reported in Figure 7 and Figure 8 respectively.

Figure 7

FoM in parallel beam concept

Figure 8

– FoM in convergent beam concept

The parallel beam concept provides a better average FoM for any value of the FWHM.

C.

Sizing of Main Optical System Parameters

The requirements for the Optical Channel design are defined on the basis of ADP estimated with the instrument performance model.

This section provides a justification for the definition of the entrance pupil and the GSD.

The ADP increases with the pupil size, as shown in Figure 9, thanks to a direct increase in signal collection. Nevertheless there is a set of constraints limiting the pupil diameter to 110 mm, in particular mass and envelope requirements, optical system complexity and NBF uniformity.

Figure 9

ADP vs. entrance pupil diameter

To evaluate the ADP sensitivity to GSD, the focal length is fixed to 190.8 mm (which corresponds to a GSD at SSP of 4.5 km with a 24 μm pixel size) and the pixel size is changed.

Figure 10 shows that the optimal GSD_SSP size is 4.5 Km, about half of the lightning reference diameter used for the evaluation.

Figure 10

ADP vs. GSD

A.

Optical Configuration Trade-Off

A single primary optics with four relay and four detectors (in field splitting) has been evaluated.

With this configuration some Earth areas are not covered due to detectors borders. Therefore to get proper sampling of the image on the focal plane special arrangement is needed. For example in the following Figure 11 the image in the intermediate focal plane is split in four parts using a fore-optics, wedges, to avoid un-covered Earth areas, mirrors and relay optics.

Figure 11

single primary with four relay approach

The above first order concept might be realized by using a Schmidt-Cassegrain telescope as fore optics. Such an approach has the following advantages and drawbacks:

Advantages :

Drawback:

Although the present solution might appears attractive, due to its weight and volume this concept presents no advantages respect to a multi-channels approach that is described in the following.

The catadioptric approach consisting of a Schmidt telescope with relay optics is shown in Figure 12.

Figure 12:

Catadioptric approach: Schmidt with relay

A field stop of suitable shape to image the required Earth portion, is placed in the intermediate focal plane.

Advantages :

Drawbacks :

Figure 13:

Schmidt telescope vignetting

The blue rays correspond to the axial FOV, the green rays are the ones of the maximum FOV. The yellow area, coming from the maximum FOV, is blocked from internal baffling. This loss of radiation increases with FOV and can be compensated by means of an extra pupil diameter to guarantee the required aperture at the maximum FOV. Nevertheless the lens equivalent aperture changes with respect to the FOV and it is maximum on axis and decreases with the FOV.

Some of the above drawbacks can be solved using a more complex telescope (three mirrors) increasing however weight, volume and complexity.

Considering the narrow spectral bandwidth, a dioptric design allows compact configurations with reduced complexity when compared to mirrors based solutions.

In Figure 14 a primary objective is coupled with a relay to realize an intermediate focal plane. In the intermediate focal plane a suitable shaped stop is placed while the interference filter is positioned in front of the fore optics.

Figure 14:

Dioptric with relay optical layout

Advantages :

Drawback :

B.

Selected Configuration

The selected optical layout is composed by four optical channels, each one with an independent single stage lens, detector and baffle.

Figure 15 shows the optical layout of the baseline solution, whose main optical characteristics are reported in Table III.

Figure 15

– Selected optical layout

TABLE III

– OPTICAL SYSTEM MAIN CHARACTERISTICS

The first two parallel plates are the Solar Rejection Filter and the Narrow Band Filter (both in green). The imager is composed of 6 lenses, all made of radiation resistant glass. All the lenses have spherical profile except one.

The lenses diameter are larger sized to insert some “light traps” and to limit the straylight caused from the lenses border and internal objective walls.

The Solar Rejection Filter, the first from left, is placed tilted to mitigate the ghosts images due to multiple reflections between filters.

Using a pixel projection model, the GSD corresponding to the above mentioned optical system parameters is represented in Figure 16 at SSP and at 45°N latitude and SSP longitude.

Figure 16:

GSD model for reference LP event longitude and latitude

The dimension of the GSD, considering the rotated FOV are:

GSD at 45° Lat= 6.42 x 6.37 [km]

GSD at SSP = 4.50 x 4.50 [km]

The nominal optical system performances at 20°C are shown from Figure 17 to Figure 21.

Figure 17:

MTF

The RMS wavefront error, on axis (Figure 18), is 0.029 waves, corresponding to 22 nm.

Figure 18:

On axis RMS wavefront error function

The RMS wavefront error, at maximum FOV (Figure 19), is 0.072 waves, corresponding to 56 nm.

Figure 19:

maximum FOV RMS wavefront error function

The instrument performance model indicates that the energy fraction in one pixel should be larger than 0.9 to ensure a proper ADP. Figure 20 shows that there is a margin with respect to the nominal design to account for image quality degradation due to manufacturing, alignment, thermal effects and other perturbations.

Figure 20:

Ensquared energy function

The maximum distortion is less than 0.2% at maximum FOV as shown in Figure 21

Figure 21:

distortion and field curvature

To fulfill the performance requirements in the whole temperature range the optical system has to be athermalized. For that purpose the lens mounting is made of titanium to better fit the optical system expansion coefficient and limit the thermal defocus.

The optical performance computed at the temperature extremes are shown from Figure 22 to Figure 25.

Figure 22:

MTF at the operative temperature limits

Figure 23:

Ensquared energy function at the operative temperature limits.

The worst RMS wavefront error within the operative temperature range, on axis (Figure 24), is 0.039 waves, corresponding to 30 nm.

Figure 24:

Wavefront function on axis at the operative temperature limits

The worst RMS wavefront error within the operative temperature range, for all the FOV positions (Figure 25), is 0.079 waves, corresponding to 61 nm at maximum FOV.

Figure 25:

Wavefront function at maximum FOV at the operative temperature limits

The optical system performances at the limit of the operative temperature are almost unchanged with respect the 20°C ones.

The transmittance of the optical system at 777.4 nm has been maximized selecting an anti-reflective coating providing a transmittance of 99.78% for each of the 12 optical surfaces. Taking into account the transparency of the radiation resistant glass (99.7% at 700nm for 10mm thickness) and the overall lenses thickness (65mm), the overall transmittance of the 6 lenses is estimated as:

C.

Baffle Design

The preliminary straylight analysis demonstrates that when the Sun directly illuminates the optical system components (i.e. when the Sun is within the baffle cut-off angle) the straylight becomes a critical issue for achieving the required absolute radiometric accuracy.

In order to limit to 2.5% the mission time when this criticality is present, a cut off of 16°, compatible with mass and envelope requirement, has been defined.

The other baffle geometrical parameters are:

Figure 26:

Baffle layout

D.

LI Spectral Filters

The Solar rejection Filter (SRF) is devoted to reflect the solar radiation. It also works in synergy with the Narrow Band Filter (NBF) to obtain the required spectral filtering. It is directly exposed to the external space environment. Its mechanical mounting is thermally decoupled with respect the NBF and the optical system; its temperature range is much larger than optical system. The useful diameter is 118 mm.

In Table IV the performance requirements for SRF are provided in terms of transmittance at the scientific band and transmitted, reflected and absorbed energy in the 200 ÷ 2000 nm spectral range that includes almost the whole Sun radiance energy. The latter are estimated according the following formulas, where S(λ) is the Planck distribution for an equivalent black body at 5780K.

The calculation of SRF Total Energy Transmitted, Reflected and Absorbed are reported respectively in (1), (2) and (3).

TABLE IV

– SRF PERFORMANCE REQUIREMENTS

The performances have to be satisfied for the following temperature ranges:

The NBF, placed between the SRF and the first lens, performs the spectral discrimination of the lightning pulse from the Earth background radiance. It is supported by the lenses mounting so its operative thermal range is the same of the optical system. The useful diameter is 112 mm.

In Table V the performance requirements for NBF are provided in terms of:

The integral has been defined on a spectral range sufficiently wide to allow the manufacturer to optimize the coating design regardless of the proposed pass band shape.

Table V:

NBF PERFORMANCE REQUIREMENTS

The ideal NBF bandwidth would be the scientific bandwidth (0.34 nm). Nevertheless, the actual bandwidth is specified in a figure of 1.9 nm to guarantee the required transmittance in the scientific bandwidth for all the working conditions and considering also the coating manufacturing errors.

These effects/errors are:

The NBF performances have to be satisfied for the following temperature ranges:

The out of band rejection requirements for the combined operations of the fully coated SRF and NBF (including substrate contributions) is specified in Table VI.

Requirements are given in the spectral range of the detector sensitivity (assumed from 200nm to 1100nm), with the exception of the 10 nm not covered by (5)

Requirements are provided in terms of:

The Combined Out of Band Mean Transmittance calculation is reported in (6).

Table VI:

SRF AND NBF COMBINED OUT OF BAND TRANSMITTANCE REQUIREMENTS