3.1

Design Heritage Sentinel 2 MSI – SWIR and VNIR Filter Assemblies

In the frame of the Sentinel-2 – GMES-mission (in cooperation with instrument prime Airbus Defence and Space Toulouse), Fraunhofer IOF has been a supplier of Jena Optronik GmbH and was responsible for the manufacturing and the integration of the VNIR- and SWIR filter arrays. Optics Balzers Jena GmbH (OBJ) was responsible for spectral filter coatings. The manufacturing and the integration concept for SWIR- and VNIR filter assemblies, see figures 3 and 4, was developed during a Phase B Study [5] and was proven at the Phase C/D [6]. The Sentinel-2A satellite was launched in June 2015 and works successful. The Sentinel-2B satellite was launched in March 2017. Fraunhofer IOF has been working on the realization of the Sentinel-2C and -2D filter assemblies until 2018.

Figure 3:

VNIR (left) and SWIR (right) Filter Array for Sentinel 2 Multispectral Imager (MSI). [7]

Figure 4:

VNIR (left) and SWIR (right) filter assemblies – exploded assembly drawings

3.2

Mounting concept of filter arrays for Sentinel 2

The single filter elements are arranged into mechanical subassemblies made of titanium alloys and were aligned into the optical instrument in front of the detectors. During the integration of the single filter elements to filter arrays, the optical elements will be arranged into the mechanical holders with positioning accuracies of less than 10 μm. The optical apertures were realized by high precision manufacturing of the mechanical parts. Manufacturing accuracies of the functional opto-mechanical structures of less than ± 15 μm were achieved [7].

3.3

Design Baseline for LSTM DPF-SWIR Filter assemblies

The general design baseline for LSTM filter assemblies is to use as much as possible heritage in design, materials, and processes from Sentinel 2 MSI SWIR filter assemblies. The following design baseline was used during design development for LSTM DPF-SWIR filter assemblies:

5.1

Modal analysis

Modal parameters are the base for all the conducted dynamic analyses, as the random vibration and response spectrum analysis based on a superposition of modal separated oscillations with their specific sensitivity, i.e. their contribution to the total dynamic system. This contribution of each mode is typically expressed by the participation factors or equivalently by the modal mass of each eigenmode. Hence, a modal analysis with fixed interfaces was performed prior to the dynamic analyses to consider all modes up to 32kHz (70 modes). The results of this analysis are given in Table 4. Due to the design of the filter assembly, a significant part of the mass in the vicinity of the interfaces can be regarded as fixed “dead mass”, what means this mass is not dynamically active and do not contribute to modal masses in eigenmodes within the selected frequency range. This should be kept in mind when discussing the relatively low sum of the modal masses in the FEM model. However, the first 70 modes comprise all relevant mode shapes for the parts of interest.

Table 4:

Modal results. Listed are only eigenmodes with a modal mass contribution >3% to the total mass.

5.2

Random vibration Analysis

As mentioned above, the random acceleration load in x-, y-, z-direction on the filter assembly component is defined by a power spectrum density (PSD) diagram which is depicted in Figure 9. These random loads represent one of the load steps which yield relatively high stresses in some parts of the filter assembly, e.g., in x-direction in the spacers. However, no critical stresses have been reported for these load cases. The random vibration analysis was performed with 1% damping ratio (Q=50). One well-known main issue in all linear analyses are edge singularities which occur in nearly 90° concave edges (Figure 10). This numerical singularity cannot be solved by a finer spatial discretization. In a finer discretization the gradients of field variables which are based on a derivation of displacement solution results, would even be higher. One way to handle the problem is the approach to neglect stresses in the direct vicinity of such edges and evaluate solely stresses in a certain distance to the edge (not in the same element). The drawback is, that the real stress peaks at these edges stay unknown. However, a detailed modelling of existing radii between adhesive and housing or spacer cannot be implemented, nor can the physically existing nonlinearity of the adhesive be included due to lack of material data. Due to the large uncertainties regarding the material behavior of the adhesive and other parts, the filter assembly is additionally qualified in experimental environmental tests (Random, Shock and Thermal loads).

Figure 9:

Input PSD spectrum which was used for the random analyses and the acceleration response PSD spectrum of a corner point (located at a middle filter strip) and a corner point of a spacer (on the middle spacer). For the spacer point, significant acceleration excitations are visible (relevant spacer eigenmodes 625-730Hz) which are a result of the soft fixation by the adhesive.

Figure 10:

3-sigma (99.73%) equivalent stresses (Segalman approach) of the random vibration analysis in x-direction. Left: High, but admissible stresses occur in x-direction in the softly suspended spacers (fixed solely by the adhesive). In reality, the spacers will contact the side of the filter stripes which would restrict the maximum deformation and thus the maximum stresses. However, this effect cannot be considered in a linear analysis. Right: Stresses mapping in the adhesive. The stress is heavily influenced by edge singularities. Visibility of some parts is suppressed in both figures.

5.3

Shock Analysis

Similar to the Random vibration analysis, the Shock load analysis – which is performed as a response spectrum analysis – based on a modal analysis of the assembly, too. Modes are excited by the input response spectrum according to their frequencies and participation factors and the modal results are combined using the mode combination method. The Complete Quadratic Combination (CQC) method is an improvement of the square root of Summation of Squares (SRSS) method for the case of closely spaced modes as present in the model (see Table 4). The SRSS method is usually an approach which is too conservative and overestimates the results in models featuring closely spaced modes. As for the Random analysis, a damping of Q=50 (1%) is used for the Shock analysis which is necessary for the CQC mode combination method. The given input shock response spectrum (SRS) is shown in Figure 11.

Figure 11:

Used input response spectrum with +6dB and -3dB testing limits (dashed curves).

As a result, a mapping of maximum occurring stresses in the component can be plotted, which is exemplarily shown for z-direction shock loading in Figure 12. Similar to random vibration, an SRS analysis does not provide information about when these maximum stresses occur, because the phase information of the superimposed modes is lost.

Figure 12:

Maximum occurring stress in the SRS analysis from shock loading in z-direction (cross section of filter assembly). Critical points are bending stresses located in an edge to the interfaces (influenced by edge singularities).

However, it should be mentioned that results of response spectrum analyses should generally be regarded with caution as this kind of analysis solely provides an estimation of maximal occurring quantities. To verify the response spectrum analysis of this model, a transient analysis which is based on modal superposition with a synthetically derived transient half sine pulse [4] from the input response spectrum was used. Table 5 gives a comparison of maximum stress results between the random vibration and transient analysis. The deviation between the values is a result of the inadequate approximation of the original SRS by the half sine SRS (Figure 13) and a result of the mode combination method in the response spectrum method. However, despite these deviations it can be stated that the SRS approximation is within an acceptable limit and can be used for a conservative estimation of maximum stresses.

Figure 13:

Left: Synthetic transient half sine pulse from the given SRS (black curve in right diagram). Right: Comparison of the SRS between the half sine pulse and the original one.

Table 5:

Deviation of maximum stress values from random vibration and transient analysis.

5.4

Thermal analysis

The minimum non-operational temperature, 190K, was also analyzed in a load step. As mentioned above, the thermal model considers geometrical nonlinearity because of the contact of filter stripes and spacer parts to the housing (upper and lower frames) of the assembly. Furthermore, a molybdenum alloy base plate (CTE = 4.77 μm/m/K) was considered for this analysis and the fixation/origin is set symmetric to the fixation of the assembly as visible in Figure 8 right.

Figure 14:

Deformation (scale factor: 150) in the 190K load step. The displacement of the base plate is fixed in three planes which are located as described in Figure 8 right.

As a result from the thermal analyses, the RMS and peak-to-valley deformations of the optical clear apertures of filter stripes have been evaluated for the operational temperature and the maximum occurring forces and moments at the interfaces. There occur significant shear forces and in-plane moments due to the shrinkage of the titanium frames and the CTE mismatch to the base plate. This shrinkage is also visible in the deformation shape in Figure 14.

5.5

Interface imperfections

To analyze the impact of interface (IF) imperfections on the maximum stress values and interface forces, possible deflections on all interfaces have been investigated. As the model is symmetric to the xz-plane (middle plane between interface #1 and #3), interface deformations must only be applied to one of these interfaces and considered twice in the RMS sum of the interface deformations. Hence, 6 load cases are to be considered: 4 rotations (Rx, Ry at IF #1 and IF#2) and 2 displacements (Uz at IF #1 and IF#2). Figure 15 depicts exemplarily the deformation field and shape for a rotation imperfection at interface #2. All imperfection contributions have been totalized by the square root sum of squares (SRSS) and added to the maximum stresses or forces from the dynamic or thermal load steps.

Figure 15:

Deformation (scale factor: 1000) due to a rotation of 0.84mrad around x-axis at interface #2.