3.1.

Aperture synthesis specificity

For a pupil diameter greater than 10 m, a diluted pupil is necessary to be compatible with the fairing volume. Only a few part of the pupil is used. This is the aperture synthesis principal. We then have to optimise pupil shape. When the pupil is diluted, the MTF may vary in the Fourier spectrum. We then have 2 kinds of pupil shape:

We then have 2 kinds of telescope:

Fig. 6:

Fizeau and Michelson telescope

3.2.

Imaging simulations

The major parameter for pupil sizing is the MTF. Imaging simulations where performed with complete and incomplete configurations and different MTF and SNR in order to determine the minimum acceptable MTF with the constraint that the MTF is greater to this minimum on all the Nyquist domain. For incomplete configurations, the Wiener method is used to combine the pictures. This method determines the optimal filter for the whole picture by minimising an error function. Before applying the Wiener filter, denoising is performed with wavelet.

Around 20 simulations for each configuration where performed. For incomplete configuration, we limited the number of requested elementary images to 20 to be compatible with the limited time duration of 15 mn in orbit. For simulation, the following methodology is applied:

Images where analysed and compared by one photo interpret to images with same quality criteria as Pleiades for reference. The comparison was performed on images after processing. It appears that incomplete configuration gives better final image since it is a combination of many images: the final MTF is higher for low spatial frequency.

Finally, a MTF of 2% and a SNR of 150 where selected. With those parameters, quality is comparable to this reference with incomplete configuration.

For incomplete configuration, we consider that at Nyquist, MTF is the root mean square of all pictures.

Fig. 7:

MTF criterion at Nyquist for incomplete configuration considering 20 pictures

Fig. 8:

Example of image from incomplete configuration before and after combining

3.3.

Pupil shape optimization

Then, we need to select between complete and incomplete configuration. For this we consider a pupil composed of circular elementary pupils with same diameter. With Golay or circular configuration and with previous hypothesis – MTF greater than 2% on all Nyquist domain – a minimum number of 12 elementary pupils with 2 m diameter is requested: Golay configuration has MTF hole inside Nyquist domain and circular configuration tends to an annular

Fig. 9:

MTF performances at Nyquist for Golay and circular configuration

This high number of pupils leads to a volume which is not compatible with Ariane 5 short fairing. Then, we consider in-line configuration. This configuration is optimised by considering square elementary pupils or segments.

3.4.

Telescope selection

We now have to select between Fizeau and Michelson. When considering Michelson telescope, one important impact is to have a constant optical patch length between all telescopes to the imaging telescope. This requests a high number of mirrors which needs to be deployed with the elementary pupils. Each pupil corresponds to one telescope. Then, we need to integrate 6 + 1 telescope leading to a more stringent WFE budget. Furthermore, this kind of telescope is more difficult to align in orbit – no compensation between axes - and request more mechanisms. Then, a Fizeau configuration is selected.

4.1.

Optical design

The pupil shape optimisation concluded to the use of 6 square pupils - or segments - of 1.1 m side. A Korsch optical combination is used to minimised stray light impact since it is not possible to have baffle for this size of instrument. The objective was to minimise primary mirror-secondary mirror distance which is still around 11 m.

The focal length of the telescope is 360 m. The most constraint mirror is the secondary mirror with a DY of 11 µm.

To take the requested 20 pictures, the satellite is in rotation. Then, we have to compensate the motion effect for each image. This is done by using 2 folding mirrors in the optical path. Another solution was to use an anti-rotating device but its size and the associated mechanism would have been too important. This also needs to have a telecentric optical combination. The final WFE of this optical combination in a field of view of 20000 x 20000 pixels is below 4 nm after motion effect compensation.

4.2.

WFE budget & Telescope alignment tolerances

The telescope must be aligned when in orbit: deployment mechanisms can not have a precision of a few nm or nrad, therefore alignment mechanisms are necessary. We will consider only rigid motions of primary and secondary mirrors; adding deformation mechanism on primary mirrors needs more mass and more sophisticated wavefront sensor. We then have 6 degrees of freedom for each segment + temperature and 6 degrees of freedom for secondary mirror + temperature. All folding mirrors, tertiary mirror and focal plane are located on a stable optical bench which also support all alignment sensors. This is the reference, and then no additional degree of freedom is to be considered. For fine tuning of the segments, only 3 axes out of 6 are necessary for each of them. By considering a WFE of 6 nm for each degree of freedom, we obtain the following allowable tolerances after correction by the 3 selected axes Translation z, Rotation x and Rotation y – see Fig. 9

In the WFE budget, we also need to consider the focal length variation between all segments. With a WFE budget of 6 nm, we obtain a tolerance on the focal length of ΔF/F = 2 E-6. By using interferometric measurement between all segments, we may obtain a precision of 2 E-5 after polishing. Then, a different temperature setting for each segment allows getting the final accuracy.

The final WFE budget including polishing, mechanism tolerances, 0 gravity … is of 50 nm including some margin for thermal control tolerances.

Fig. 10:

Tolerance after fine tuning

4.3.

Mechanism definition

The 6 segments are deployed 3 by 3 using deployment mechanisms as used for telecom antennas. This mechanism has also 2 rotation axes for in orbit alignment. To determine the necessary mechanisms with associated performances – precision and range – we consider a maximum range for each mechanism of +/- 5000 steps.

We finally need 47 mechanisms: some are “low” accuracy - µm or µrad- the ones used for fine tuning are in the range of nm or nrad.

Fig. 11:

synthesis of needed mechanisms

4.4.

Alignment strategy

To be able to perform in-orbit alignment, we need wavefront sensors. By using external source – star of ground beacon– we need to modify the orientation of the satellite for each alignment and then to assess that this alignment will not be modified. This will require many analyses with the risk that alignment is needed before each picture and this will add delay on the time to get the picture. Then, we designed a completely internal wavefront sensor which is able to keep the alignment even during pictures. This sensor measures the alignment of each segment and of the secondary mirror. After deployment, a reference alignment needs to be performed with beacon on ground. Then this alignment is kept as a reference using only the internal wavefront sensor. The following sequence is proposed for this first alignment:

4.5.

Thermal control

We need to be able to take picture during whole day. Due to the big size of this instrument, we will not consider baffle. We have analysed that it is possible to have a thermal control of the primary mirror - which is the most critical part - without baffle at ~ 25°C with an average thermal power of only 520 W during day and night.

For the secondary mirror, specific baffling is needed to avoid illumination while taking picture.

The thermal flux variation due to a modification of the orientation of the telescope is completely negligible compared to the solar flux variation. Since the thermal control is able to compensate the solar flux variation, any orientation is allowed to take picture.

With this thermal control, it would be even possible to consider an infrared mission during night. We just need to avoid pictures too close to the sun mainly for straylight impact.

4.6.

Mechanical architecture

For the mechanical architecture, segments are deployed 3 by 3 using 2 arms which are folded on the sides of the spacecraft during launch. An optical bench is located at the top of the spacecraft. It supports the tertiary and folding mirrors, the filter wheel for color pictures, the detector and the wavefront sensor. This is a stable support that is used as the reference for the alignment.

For all structure and mirrors, we will consider Silicon Carbide. This material has a high specific stiffness E/ρ and a high conductivity. This helps to minimise mass and to improve thermal control.

For deployment of the secondary mirror, we consider the use of Collapsible Tube Mast. This is a bi-convex tube that is rolled after being flat. This mechanism was developed for a solar sail.

Fig. 12:

Deployed configuration of the telescope

Fig. 13:

Satellite in launch configuration

The final mass budget for the whole telescope including wavefront sensors, thermal control, mechanisms and associated electronic is ~ 1600 kg including margin. This mass is well in the capacity of the E3000 spacecraft.

4.7.

Operations

For the operation of such telescope, we have to keep in mind that the whole 20 pictures must be taken in less than 15 mn.

Then, the spacecraft is put in rotation around the optical axe at 1 turn in 10 mn: we then have the requested 20 picture in 5 mn. We then have 5 mn to start the rotation of the satellite – only 2 s are required using bipropellant. Once the satellite is in rotation, it is possible the change its orientation to take more pictures around the same area.

We now consider having one picture in panchromatic and 4 colors. We then need to take 80 pictures in 5 mn. We have 15 s between each set of picture for one given position. We use a filter wheel with a constant speed of 20 turns in 5 mn to avoid any disturbances.

We then have the following time-line for the pictures:

Fig. 14:

Time-line for elementary picture

4.8.

System impact

In the MTF budget, we have considered that the stability of the spacecraft must be below 0.05 µrad/s in order to get a MTF degradation of 0.8. This stability is accessible only with a specific AOCS using star trackers, gyro, µ thrusters … Momentum wheels are then not allowed.

For rotation of the satellite, we have 2 options: we may consider reaction wheels but it leads to ~ 5 mn to get the speed rotation or using bi-propellant it will last only few seconds. But this will impact the propellant mass budget which is critical for geostationary orbit.

To limit this propellant consumption, it is possible to consider the satellite to be in rotation during the whole daylight period. This will then impact the power budget since solar arrays will not be perpendicular to the sun. Hopefully, an estimation of the telescope power budget is ~ 2.5 kW, well within the maximum 8.5 kW allowed for a telecom payload on E3000

For data telemetry, we consider that we could obtain a compression ratio of 2 bit/pixel for the whole images: effectively, in the final image we have the same information as in the 20 elementary pictures. Then a horn antenna with a RF power of 100 W could deliver one picture in ~ 1 mn using a dish antenna of 4.5 m in X band.

Then, we are well within the 15 mn to get an image on ground.