5.1

First order analysis

The first order paths are the ones by which straylight reaches the detector after only one scattering on telescope surfaces. In the case of the COROT telescope, such surfaces do not exist. Nevertheless, first order paths have been defined as being ones with two scattering: one on a baffle wall and one on the primary mirror. The roughness and particulate contamination of the primary mirror will scatter the straylight directly in the field of view and no more attenuation will occur (with the exception of the lens transmission).

Equivalent paths can also be defined with the secondary mirror but will not be taken into account here because they occur for field angles lower than 17°.

5.2

First order analysis of the vanes

The search for critical surfaces (implied in critical paths) consists in searching surfaces which are seen by external light (i.e. that see the aperture of the baffle) and which see the primary mirror. This search has been performed with Matlab.

In the Matlab procedure written to perform this analysis, a matrix of points is drawn on the primary mirror. Then, for any observation point inside the baffle, the number of point of the mirror matrix seen without obstruction is counted. The ratio of the number of visible points to the total number of points gives the portion of primary mirror seen.

This computation can be performed for any point in the baffle. Different procedures have been written to automatically perform these computations in the planes of the vanes. By comparing the surfaces that view the mirror with the vanes, critical surfaces can be verified. Figure 6 and Figure 7 are examples of the results obtained. The grey scale indicates the percentage of primary mirror seen from black (mirror not seen) to white (full mirror seen). The two circles indicate the tube diameter and the edge of the vane. These two pictures represent the situation in the plane of chicane 1 and chicane 4 (on the face oriented towards primary mirror). It clearly shows that the edge of chicane 1 is a critical element since it can be lightened by external light and directly see almost 80 % of the primary mirror. Chicane 4 is not a problem since positive margin exists. Rapid drawing analysis shows that the edge of chicane 1 is visible for luminous object up to 32.5 degrees from optical axis.

Figure 5:

Portion of the primary seen by a point in the baffle

Figure 6:

Chicane 1, the edge is a critical path because it sees about 80 % of primary mirror

Figure 7:

Chicane 4, the edge is not seen by primary mirror.

Table 1 summarises the results of the computations. In addition to some of the edges that can be considered as critical at first order, other surfaces (back of vanes S3bis, S3, S2 and 1) are second order critical surfaces. The light can go deeper in the baffle, be scattered back to the vane rear face and than scattered again towards primary mirror. These paths add one attenuation factor (due to scattering) and will be taken into account in the global straylight analysis.

Table 1:

First order analysis of vanes

5.3

First order analysis of the tubes

The previous analysis performed for all the vanes has shown that the tubes are never seen by the primary mirror, nevertheless, we decided to further analyze the second (smaller) tube which parts can be second order critical surfaces. If they are too small, it is possible that the ray-tracing computation will not be able to detect them. The considered paths are the one with one scattering on the small tube, one on the internal tube than one on the primary mirror. For that, the Matlab procedure is modified and instead of placing a matrix on the primary mirror, it is placed once on the entrance pupil and once on the baffle aperture. We assume that all light going through the pupil will be scattered on the telescope internal tube. Moving the observation point on the small tube surface for the two cases will determine which are the surfaces seen by the aperture and by the pupil.

Figure 8 shows the product of the surface viewed by the pupil by the surface viewed by the aperture of the baffle. This picture shows that the only non-null area is very close to the pupil and for very low field of view (< 20°). This is considered not critical (unknown about the real arrangement of the connection between baffle and telescope tube could invalidate any conclusion in this area).

Figure 8:

Detection of critical surfaces in the small tube (view from pupil times view from aperture). Only critical area is close to pupil (front of the picture)

As a conclusion, no critical surface exists in the second tube at first order. At the second order, the area is very marginal and for low field (< 20°).

5.4

ASAP modelling

Following first (and partial second) order analysis, a ray-tracing model was run for higher level analysis with the following observation: the only critical surfaces with small area are the edges. It means that they must be analyzed separately (see 5.6).

ASAP model is geometric description, it means that no thickness has been given for the walls except for the vanes (40 μm). The junctions between all elements are supposed perfect. The modeling made by CSL should have been only done on the baffle itself but in this case, the results would have been hardly understandable in terms of performances for scientific observations. It has been decided to include in the model the afocal telescope (including entrance and exit pupil and intermediate focus) and the optical cavities of these two mirrors (they are strongly involved in the global straylight baffling performance of the payload).

The output of the computation is thus the straylight coming out of the afocal telescope and entering the dioptric objective. This can be also split in straylight in the field of view that will go directly on the detector and straylight outside the field of view that will be further scattered by the objective housing.

Different coatings have been modeled by their correspondent BRDF i.e. Aeroglaze Z306 for the baffle and for the mirror cavities. The definition of the curves used is in a first approximation using data found in literature. The mirror roughness and contamination (baseline 2000 ppm) has also been modeled by their respective BRDF. Roughness modeling is based on previous measurements on representative samples and the BRDF caused by contamination has been theoretically computed using Mie scattering theory.

5.5

ASAP analysis

The main drawback of ASAP is the very high number of rays that have to be created to reach a good accuracy on the result after several scattering. CSL has made a specific effort in order to reduce the number of rays. This has been achieved by using new possibilities in ASAP and developing specific routines working with the sequential aspect of the system. The baffle has been divided in 8 sections. At the end of a section, a virtual detector has been placed to catch the rays going to the next section. Once the computation is complete in a section, the next one starts with a source being the rays caught at previous detector. This allows a high number of scatterings for the useful rays while reducing the useless rays.

Figure 13 presents the level of straylight in the field of view of the dioptric objective. The embedded drawing representing the aperture of the baffle defines the FOV and the azimuth.

Figure 9:

ASAP model for the straylight analysis.

Figure 10:

step-by-step analysis principle

Figure 11:

Model profile and separation in sections

Figure 12:

Results of the analysis for the different steps

Figure 13:

Results of the straylight analysis for different azimuths.

These curves indicate a good symmetry of the baffle above 20 degrees. They also reflect the geometry of the baffle: below 20°, external light directly enters into the mirror tube (FOV of the transition depends on the azimuth due to asymmetry of the pupil). Up to 27°, the light enters the smaller baffle tube, up to 32°, the light goes through the vane 1 (first stage). Above this value, the rejection is higher than 10¹².

These results have been used by the COROT scientific community to determine the level of straylight reaching the detector. According to these results, the selection of targets has been initiated.

5.6

Edges

As mentioned earlier, the edges can be considered as critical surfaces as it will never be possible to avoid that some part of it will see primary mirror and be lightened by external light. In a first step, the diffraction of the light by the edges has been analyzed and we rapidly concluded that diffraction was negligible in this case.

For scattering, early studies have defined the edges as flat surfaces (parallel to optical axis) with a thickness of 40 μm. These surfaces are too small to be touched statistically by rays of the global ray-tracing analysis. It was then necessary to perform a dedicated study with ASAP.

A source has been created specifically to lighten one of the edges with a sufficient number of rays and the scattered rays have been oriented preferably towards the primary mirror. Figure 14 represents resulting straylight at the level of the output pupil (FOV of dioptric objective) for all edges except vane 3 and 4. It confirms the first order analysis (Table 1), vanes 1, s2, s2bis and s3bis are the most critical ones (highest level). Nevertheless, most of that straylight will be negligible compared with the higher levels in the global scattering analysis (Figure 13). Vane 1 is the only one generating a level of straylight comparable to the global one.

Figure 14:

Level of straylight in the FOV of the dioptric objective due to edges scattering

Figure 15 shows a comparison of both effect (edges straylight has been summed).

Figure 15:

Comparison of levels due to global scattering and due to edges

6.1

Introduction

Before concluding, some analyses have been performed to evaluate the sensitivity to the hypotheses and the statistical accuracy of the ray-tracing studies.

6.2

Number of rays

The first point was to determine the number of rays in the first source grid located at the entrance of the baffle. The number of rays will directly determine the duration of calculation but also the pitch of the grid and thus the size of the smallest object seen. The baseline selected size was 171 x 171 (one ray per 20 mm²). Several runs were performed for one azimuth and one field of view with different grid size. From 101 x 101 to 311 x 311 no important variation is observed.

6.3

Edges thickness

The thickness of the edges is another important point of the model. Computations have been performed with 100 μm, 40 μm and 10 μm edges.

Results clearly indicate that the straylight due to the edges is directly proportional to the thickness.

6.4

Cleanliness

Sensitivity to contamination of the mirrors will also define the margins we have on the contamination budget for the telescope and the baffle. The 2000-ppm is the value after launch as estimated by a contamination budget. Calculation with other contamination on the mirrors has been performed. Once again, a proportional behavior is observed (see Figure 16, note that the following computations are taken from a previous review of the analysis and thus the global result can differ from previous figures).

Figure 16:

Variation with mirror contamination

6.5

Ray-tracing statistics

Finally, several computations were performed at the same azimuth and field of view but changing each time the statistical parameters in ASAP. The variation of the final result stays within 15 % of the average result. This variation can be considered small with respect to the factor 2 generally considered for the accuracy of the result of such analysis.

8.1

Painting

The internal geometry of the baffle after mechanical design is in most areas in line with the optical design. Some screws and brackets are added for fixation of the vanes. The most important change is the internal stiffening structure. This structure has been correctly hidden in the cavity and is not a critical element but it will be included in an updated straylight analysis.

The important factor for the straylight analysis is also the choice of coating. The use of aluminum suggests black anodization. Some measurements indicate that the absorption of coated samples is not as good as the assumption used in ASAP. Improvement could have been reached by sandblasting the aluminum sheet. This solution has been considered too risky due to the very low thickness of the shell plate for the baffle cylinder. The choice has thus been made to use Aeroglaze Z306 which is a well known paint for space applications. Measurements made on samples indicate that BRDF was close to the modeled one.

8.2

Edges design

Second critical point of the mechanical design is the manufacturing of the edges. Specification required a flat edge of 40 μm. Different solutions have been analyzed:

stainless steel foil cut by laser or by waterjet, milled aluminum with or without paint.

The stainless steel sheet was one of the solutions, the problem was to cut the circular aperture. Both laser and waterjet techniques were tested. Laser cutting was rapidly rejected because the process creates at the edge a large local increase of thickness. The waterjet cutting resulted in a very rough edge, inducing non uniformity of the edge behavior depending on the measured location (see Figure 18). The main drawback of the stainless steel foil was also the impossibility to blacken the foil because of its very low thickness. The second solution envisaged is a milled aluminum sheet: starting from a 0.4-mm sheet, the aperture was milled using a cutting angle of 15°. The resulting edge was of very good quality. Starting from a painted edge, this process results in a large shinny surface (2 mm in the case of 0.4-sheet), moreover, the cutting of the paint could have caused adhesion problems (see Figure 20).

Figure 17:

Internal stiffening structure between vane S1 and 1.

Figure 18:

Waterjet cut stainless steel foil

Figure 19:

Milled then painted aluminium sheet

Figure 20:

Painted then milled aluminium sheet

Another test has been performed with a sample first milled then painted (see Figure 19). The resulting thickness was higher (radius of 70 μm) and it was necessary to compare the obtained results with the original modelling of the edges. A small ASAP model has been built representing the test set-up. The 40 μm flat edge and a 100 μm rounded edges were modelled. Figure 21 shows the comparison between the different results. 40 μm flat and 100 μm rounded give similar results and the measured edge is of the same order of magnitude. This last solution has been chosen as baseline.

Figure 21:

Comparison of measurements with computation