Optical systems—used for both ground- and space-based applications—such as interferometer setupsand telescope assemblies, require jointing technolo-gies with high dimensional stability. One exampleof the wide range of applications is represented bythe optical bench (OB) of the planned Laser Interfe-rometer Space Antenna (LISA, [1]) mission. Thestudy presented in this paper is strongly motivatedby the challenging requirements of the OB of theLISA mission, but also represents an integrationtechnology suitable to fulfill the requirements ofmany optical systems.
In the current baseline design of the joint ESA/NASA mission LISA, an interferometric system isused as a readout of the translation and tilt of a freeflying proof mass. The required accuracy for detec-tion of changes in the distance between the free float-ing proof mass and the OB is as low as a fewpm Hz−1=2 for frequencies between 10−4 Hz and 1 Hz.Beside this relative noise requirement, thermal cy-cling in the range of 253 K and 323 K, as well asmechanical loads occurring during launch and trans-portation of the spacecraft, should not lead to dero-gations of the absolute positional stability of theoptical components on the optical bench.
Materials of optical components constituting suchsystems have to feature specific optical properties.The choice of material is further driven by a low den-sity ρ, a low thermal distortion ratio α=κ, with the
coefficient of thermal expansion α and the thermalconduction κ, and a high specific stiffness E=ρ, whereE is the elastic modulus. Typical materials used inoptical applications are silicon carbide (SiC), carbonsilicon carbide (CSiC), fused silica, and glass cera-mics such as ULE and Zerodur.
The integration of optical systems requires joint-ing technologies, which permit an ultraprecise align-ment of the components, a high dimensional stability,and a highly stable bond. Jointing technologies beingamong the most widely used are mechanical clamp-ing, optical contacting, and hydroxide-catalysisbonding.
The jointing technology of hydroxide-catalysisbonding was invented and patented at Stanford Uni-versity [2,3] and used for jointing fused-quartzcomponents of the Gravity Probe-B star-trackingtelescope [4]. For the construction of the all fused si-lica suspension of the earth-based gravitational wavedetector GEO 600, hydroxide-catalysis bonding wassuccessfully applied [5].
In a detailed study [6], the applicability of hydro-xide-catalysis bonding for stable optical systems wasinvestigated. The settling time defines the timeavailable to align the components. It can be variedby using different molecular ratios (bonding solution:H2O) or by reducing the temperature below roomtemperature. However, the settling time remainsin the order of at most a few minutes.
For the fabrication of the LISA Technology Pack-age (LTP; aboard the LISA Pathfinder mission) inter-ferometer engineering model, fused silica opticalcomponents were mounted on a Zerodur baseplateusing the technology of hydroxide-catalysis bonding[7]. Several environmental and performance testswere successfully completed and demonstrate theapplicability of hydroxide-catalysis bonding as amature jointing technology for stable space-basedoptical systems.
In this study we investigate the jointing technol-ogy of adhesive bonding as a possible alternative in-tegration technology for ultrastable optical systems.Adhesive bonding provides an easy-to-handle inte-gration process, suitable to bond different or equalmaterials. The time available to align componentsin the integration process marks an important pro-cess parameter, as the efforts required to realize thealignment increase with a reduced time slot. Adhe-sive bonding provides a relatively long time slot,as the hardening of the adhesive takes up to severalhours, but can be brought down to several minutes, ifdesired. The curing time describes the time neededfor bonds to achieve full strength. Adhesive bondingtypically features a curing time of several daysor hours.
In this paper the applicability of adhesive bondingas a possible integration technology for optical sys-tems is investigated and compared with hydroxide-catalysis bonding as the proven state-of-the-arttechnology. A test setup is therefore designed andfabricated that utilizes both integration technolo-
gies. In Section 2 the design of this testboard is ex-plained and the procedure of fabrication is described.
To demonstrate the capability of adhesive bondedcomponents to withstand mechanical and thermalloads, vibration and shock tests, as well as thermalcycling, were carried out. Measurements of the tiltof the components before and after the tests are usedto verify the impact of the environmental tests on theadhesive bonded components. The optical setupsused for these tilt measurements are explained inSection 3; the procedure and results of the environ-mental tests in Section 4.
2. Testboard
For our study we used a Zerodur baseplate (70mm×70mm × 30mm) and six mirrors (7mm × 15mm×20mm) made of fused silica. The mirrors weremanufactured with a perpendicularity tolerancesmaller than 2 arc seconds between the reflectingand the bonding mirror surfaces. The six mirrorsare mounted on the baseplate in two parallel rows,whereas each row is made up of three mirrors.
The design of the testboard (see Fig. 1) enablesone to perform tests of the passive dimensional sta-bility, as well as environmental robustness tests. Toallow a direct comparison of adhesive bonding andhydroxide-catalysis bonding, both technologies areused to mount the mirrors on the same baseplate.The mirrors in the middle of each row are attachedby hydroxide-catalysis bonding. They serve as re-spective reference mirrors for the differentialmeasurements. In each row one mirror beside thereference mirror is affixed via hydroxide-catalysisbonding while the mirror on the opposite side ismounted by adhesive bonding.
A. Hydroxide-Catalysis Bonding Procedure
The quasi-monolithic structure of hydroxide-catalysis bonded components is obtained by siloxanechains, which can only be formed between two flatsurfaces. The polished bonding surface of the fusedsilica mirrors used for hydroxide-catalysis bonding,therefore, have an overall global flatness of λ=10
Fig. 1. (Color online) Testboard made up of two rows of fused si-lica mirrors mounted on a Zerodur baseplate. Mirrors 1 and 2 aremounted on the baseplate with the technology of adhesive bonding,while the other four mirrors are hydroxide-catalysis bonded.
(λ ¼ 632:8 nm). The bonding process was performedin a cleanroom environment to ensure the cleannessof the bonding surface, as particles or other impuri-ties in the bonding layer potentially lead to a failureof the jointing.
The solution used for hydroxide-catalysis bonding(sodium silicate solution: 10:6%Na2O2, 26:5%SiO2,Sigma Aldrich, Cat. No: 33,844—3) was diluted withDI-water (molar ratio sodium silicate solution: DI-water of 1∶4) and applied on the bonding surfacewith a pipette in two drops of 0:2 μl per mirror.
To remain within the tilt measuring range of thehigh precision interferometer, a parallel alignmentof the mirrors of 250 μrad is required. In order to rea-lize the required parallelism of the mirrors withinthe settling time of approximately 120 s, an align-ment jig has proven to be crucial. Therefore, an alu-minum jig was designed, which features a referencesurface with an overall global flatness of 10 μm (val-ley to peak). The mirrors were then aligned by apply-ing them to the reference surface of the jig.
The tilt between two adjacent mirror surfaces wasmonitored by an optical setup (Fig. 2) during thecomplete bonding process. In case of perfect paralle-lism of two mirror surfaces, the two laser spotssuperimpose on the CCD sensor. A parallel misalign-ment of the mirror leads to a deflection of the laserbeam and a displacement on the CCD sensor. The tiltis detected with an accuracy of about �250 μrad inthis case.
After the hydroxide-catalysis bonding, the test-board was left to cure for four weeks at ambient tem-perature to achieve full bonding strength.
B. Adhesive Bonding Procedure
For adhesive bonding of the mirrors on the testboard,the space qualified, two component adhesive HysolEA 9313 from Henkel was used. The uncured adhe-sive features a viscosity of 1.2 Pa s at 298 K. Asopposed to hydroxide-catalysis bonding, the bondingsurfaces of the mirrors used for adhesive bondingwere matte ground. The adhesive bonding was car-ried out in a laboratory environment at ambient tem-perature with bonding surfaces being free of particlesand other impurities. Two drops of the adhesive wereapplied on the bonding surface of each mirror, just
sufficient to moisten the entire surface when putin contact with the baseplate. The relative long cur-ing time of the adhesive (handling strength after 8 hat 298 K) enables one to align the mirror manually,without utilizing the aluminum jig. The alignment ofthe mirror was monitored with an optical setup simi-lar to the setup depicted in Fig. 2, but with an en-hanced resolution of �70 μrad. After alignment ofthe mirror, a fixture was used to apply a well-defined,punctiform pressure on the mirror top to localize themirror during hardening. By external heat supplythe handling strength of the adhesive was achievedafter 75 min. To obtain full adhesive strength, thebonded testboard was left to cure for five days at298 K. The curing time of adhesive bonded compo-nents with small masses might, however, be reducedto one hour by external heat supply [8].
The alignment of the optically utilized surfacesorthogonal to the baseplate is mainly driven by theperpendicularity of the bonding surfaces. A non-uniform adhesive layer might also lead to orthogonalmisalignments of the bonded components. A uniformand thin adhesive layer is, thus, crucial.
By applying a perpendicularity tolerance smallerthan 2 arc seconds (≈10 μrad) on the bonding sur-face, tight alignment tolerances can be met usinghydroxide-catalysis bonding [6]. To obtain informa-tion on the forming of the adhesive layer, the thick-ness of the adhesive layer was measured. A polishedsilicon wafer was cut in chips of 8mm × 8 mm and16mm × 16mm size (thickness 512 μm) and gluedon a glass mask using Hysol EA 9313. Seven chipswere bonded to the glass mask with a surface pres-sure from 1:9 MPa to 30:7 MPa. No direct correlationbetween the applied surface pressure and the thick-ness of the adhesive layer was observed. A uniformthickness of ð1:4� 0:3Þ μmwasmeasured with a Car-ycompar profilometer, where �3:0μm is the error ofthe measurement system and there is no thicknessvariation. Although the thickness of adhesive layersexceeds the thickness of hydroxide-catalysis bondinglayers, the mirrors mounted on the baseplate withadhesive bonding were aligned with the same preci-sion as those integrated with hydroxide-catalysisbonding. The adhesive layer spreads uniformlyacross the bonding surfaces, and in conclusion doesnot lead to orthogonal misalignments.
3. Verification Approaches
The relative dimensional stability of optical compo-nents constituting an optical system is of paramountimportance. Performance tests, measuring the rela-tive alignment of the components, as well as theirlong-term positional stability, enable one to evaluatethe applicability of adhesive bonding. Environmentaltests, such as thermal cycling or shock and vibrationtests, may lead to changes in the alignment of theoptical components.
In the work presented in this paper we performedenvironmental tests and measured the alignment ofthe mirrors bonded to the testboard before and after
Fig. 2. A simple test setup was used for constantly controlling theparallelism of themirrors during the bonding procedure (BS, beamsplitter).
the tests were carried out. Possible changes in thealignment of the mirrors would thus enable conclu-sions on the mechanical and thermal stability ofadhesive bonding.
We use two optical setups to measure the positionand the alignment of themirrors: A heterodyne inter-ferometer suited for high precision translation andtilt measurements in the LISA frequency band anda second optical setup for absolute tilt measurementswith a lower resolution but a larger tilt measurementrange. Both setups will be described in the following.
A. Highly Sensitive Heterodyne Interferometer
A highly sensitive heterodyne interferometer de-signed in a cooperation of the Humboldt- UniversityBerlin, Astrium GmbH—Satellites, Germany, andthe University of Applied Sciences Konstanz permitstranslation and tilt measurements with noiselevels below 10 pm Hz−1=2 and 10 nrad Hz−1=2 for fre-quencies higher than 10 mHz. The systems allowmeasurement periods over several days [9]. A sche-matic of the interferometer setup including the test-board is shown in Fig. 3.
Two parallel laser beams are aimed on two adja-cent mirrors on the testboard. The two mirrors andassociated laser beams are denominated as follows:(i) reference mirror and reference beam, (ii) measure-ment mirror and measurement beam. The reflectedlaser beams at frequency f 1 are then superimposedwith a second set of parallel laser beams at frequencyf 2. The beat signals (reference and measurement sig-nals) are successively detected with the quadrantphotodiodes QPD1 and QPD2.
The translation between the reference and mea-surement mirrors is proportional to the phase dif-ference between the reference and measurementsignals.
To measure the tilt of the measurement mirror, themethod of differential wavefront sensing (DWS) [9] isapplied. The phase difference detected between op-posing quadrants is proportional to the wavefront tilt
between the measurement beam and the beam of sig-nal f 2. As the wavefront tilt of the measurementbeam is due to a tilt of the measurement mirror,the detected phase difference is proportional to thetilt of the measurement mirror.
The calibration of the experimental setup has beencarried out by a controlled tilt of the measurementmirror in previous experiments. During this calibra-tion tests it turned out that an approximately linearrelation between phase difference and tilt is onlygiven for angular below 250 μrad. It is possible tomeasure the changes in angle between two mirrorsurfaces as long as the setup is accordingly alignedbefore. A measurement of absolute angles largerthan 250 μrad is not possible. As no pair of the sixmirrors fulfills this requirement, an additional setupis needed to enable tilt measurements in a widerrange.
B. Absolute Tilt Measurement
In order to overcome the limitations of the interfe-rometer described above, a complemental measure-ment setup was built. A sketch of the basic idea ofthe measurement setup is depicted in Fig. 4. It isa self-referencing design that minimizes positioningerrors of the testboard in the setup. Two parallel in-put beams pass through a 50∶50 beam splitter. Onebeam is reflected by the mirror in the middle of thetestboard, the other by the mirror at its left or rightside. On their way back both beams are reflected bythe beam splitter. Afterwards the distance Δ ¼ ym −
y0 between the spots can be measured. The absoluteangle between the two mirrors is given by
α ¼ 12· arctan
�ym − y0 − d
l
�; ð1Þ
where l is the distance from the mirror surfaces tothe point where y0 and ym are measured.
As a pretest at the beginning of each angle mea-surement, both beams are reflected by the mirrorin the middle, which ensures the parallelism ofthe incoming beams. In order to measure the spot
positions, we mounted a quadrant photodiode to alinear stage with 2 degrees of freedom (y and z).The distance between the spots—horizontal andvertical—can now be measured.
This setup has a measurement range of more than10 mrad and an uncertainty below 30 μrad. Afterdemounting and reinstallation of the testboard theresults are reproducible. Thus potential angular de-viations between all mirror pairs can be measuredwith this method.
4. Tests and Results
After the integration of all six mirrors to the base-plate we started a couple of performance tests, whichare described in the following. First we measure thepassive stability for frequencies between 1 mHz and1 Hz. Afterwards mechanical and thermal tests wereperformed to identify possible differences betweenadhesive bonding and hydroxide-catalysis bonding.
A. Noise Performance Tests
To gain information on the passive stability of adhe-sive bonding, measurements of the dimensionalstability over periods between 14 h and 60 h werecarried out. By the use of the high precision interfe-rometer, the differential translation between twoparallel mirrors was measured with a sub-nm reso-lution along the direction of the readout beams. Com-mon mode effects, such as dimensional motion of thetestboard due to temperature differences, are sup-pressed as they affect both signals of the inter-ferometer equally. The translation signal thus yieldsinformation on translations between the twomirrors,therefore representing their dimensional stabilitycharacteristics.
In addition to the translation, the tilts of each ofthe measured mirror pairs were determined by uti-lizing the method of DWS. Differential variations inthe tilts could be observed and conclusions on the di-mensional stability were possible. The differentialtilts were measured in two directions: (i) in-plane,with the tilt of a mirror causing a reflected laserbeam to remain in a plane parallel to the baseplatesurface, (ii) out-of-plane, with the tilt of a mirrorcausing a reflected laser beam to leave the plane par-allel to the baseplate surface.
In an earlier measurement, the noise performanceof the high precision interferometer was determinedby aiming the reference and the measurement beamon a single mirror surface [9]. Translations, as well astilts of the mirror, consequently, only lead to identicalchanges in the reference and measurement signals.The resulting noise performance levels of the inter-ferometer are depicted in Figs. 5 and 6.
After the mirrors were assembled on the Zerodurbaseplate as described in Section 2 and left to cure,the testboard was integrated in the interferometersetup (see Fig. 3). The interferometer breadboardwas embedded into a vacuum chamber mounted toan optical table.
The passive stability measurements were per-formed at ambient temperature with the mirrors un-derneath the baseplate, in order to apply a tensileload (caused by the weight of the mirrors) on thejointings.
Within this study several passive stability mea-surements of adjacent mirror pairs of the testboardwere carried out. In doing so, two configurations ofmirrors were measured: (i) two mirrors affixed withhydroxide-catalysis bonding and (ii) one mirror inte-grated with the technology of adhesive bonding andone with hydroxide-catalysis bonding.
In Figs. 5 and 6, the power spectral density (PSD)of a measurement with the reference beam aimed ona mirror affixed with hydroxide-catalysis bondingand the measurement beam aimed on a mirror af-fixed with adhesive bonding is shown. The measure-ment was done over ameasurement time of 14 h. ThePSD of the differential translation between the mir-rors, as depicted in Fig. 5, features a noise perfor-mance just above the noise performance level of
Fig. 5. (Color online) Root of the power spectral density (PSD1=2)of the differential translation signal between two mirrors. One isattached with adhesive bonding while the other is contacted viahydroxide-catalysis bonding.
Fig. 6. (Color online) PSD1=2 of the two differential tilt signals,horizontal and vertical.
the interferometer for frequencies >10mHz . Thedifferential translation between the mirrors, if at alloccurring, is thus in the magnitude of the measure-ment capability of the interferometer. Over a timescale of about 7 h, the differential translation issmaller than 350 pm (see Fig. 5).
Also the noise level of the differential tilts, in-planeand out-of-plane, of the two mirrors almost coincideswith the interferometer noise performance levelfor frequencies >10mHz (see Fig. 6). In the subplotof Fig. 6, the measured differential tilts in-plane andout-of-plane between an adhesive bonded andhydroxide-catalysis bonded mirror over a time ofabout 7 h is depicted. The differential tilt betweenthe mirrors is smaller than 250 nrad.
The small difference between the measured trans-lation and tilt noise in this work and the earlierestablished noise floor of the interferometer is inter-preted to be due to a difference in the contrast of theheterodyne signals achieved here. In previous inves-tigations, a similar sensitivity of the measurementnoise floor to contrast has been observed and con-firmed. We therefore conclude it to be limited indeedby measurement noise and not by actual relativemotion of the mirrors.
The noise performance of the tilt of the hydroxide-catalysis bonded mirror (not shown in this paper),shows a similar behavior as the noise performanceof the adhesive bonded mirror. The integrationtechnologies of adhesive bonding and hydroxide-catalysis bonding do, both, obtain a substantial pas-sive stability.
B. Mechanical Tests
Crucial in the context of space projects is, in particu-lar, the capability of the selected integration technol-ogy to withstand environmental loads. Mechanicalrequirements mainly result from the loads ex-perienced during launch, transfer, and potentiallyseparation shocks. The capability of adhesive bondingto withstand those loads was tested. According to theEuropean Cooperation for Space Standardizationstandards, equipment, which is part of space vehicles,has to resist sinusoidal and random tests, as well asshock tests. Qualification testing requires a sinusoi-dal test with a maximum acceleration of 20 g at60 Hz, a random test load of 0:8 g2 Hz−1 in a fre-quency range from 100 Hz to 300 Hz and a shock re-sponse spectrum equivalent to a half sinusoidal pulseof 0:5 msduration and 200 g (0 peak). The levels shallbe increased by a qualification margin, specific to theexpected mission level.
The testboard was subjected to several vibrationand shock tests in the Vibration Test Facilities(VTF) of the Astrium GmbH site in Friedrichshafen.The vibration tests were carried out with the shakerElin VIB 7500. The shock tests were done with theshock table of the VTF. An overview of all vibrationtest levels and shock response spectrums (SRSs) ap-plied on the testboard is given in Tables 1 and 2.
To mount the testboard to the shaker and theshock table, a specific mounting bracket was de-signed. The testboard was clamped to the mountingbracket and secured with an additional closure head.In order not to damage the testboard, Teflon bufferswere used on all contact surfaces. By using an addi-tional 90° bracket, fixed on the shaker head andshock table, respectively, the mounting bracket al-lowed loads to be applied in all directions of the test-board. To record the actual acceleration occurringduring the tests, several accelerometers were gluedon the baseplate nearby the bonds and the mountingbracket. Figure 7 shows the testboard in the mount-ing bracket attached to the shaker.
Prior to the first vibration test, a resonance searchrun was done with a sinusoidal excitation for fre-quencies from 5 Hz to 2000 Hz at a constant accel-eration level of 0:5 g. Within this frequency range,no resonance mode of the testboard or mountingbracket was detected.
Between all vibration tests, resonance search runswere carried out to determine possible changes in theresonance mode characteristics of the mountingbracket. Thus, possible deviations would have been ahint to changes in the mounting bracket (forexample, a loosening of a screw). However, no devia-tions were detected throughout the complete testprocedure.
The required parameters for a sinusoidal vibrationtest were met on the Zerodur baseplate, and a max-imum acceleration of 75 g was measured at 61 Hz.The measured root mean square (RMS) acceleration
Table 1. Test Levels of Vibration Tests
Sinusodial texta
Frequency Load Sweep rate5–61 Hz ð0:5–75Þg 0:5 oct=minRandom testb
(on the baseplate) of the vibration test with randomexcitation was 23:5 g (max: 0:98 g2 Hz−1 at 276 Hz).
The shock tests according to the LISA Pathfinderrequirements and ECSS standards were done withthe shock response spectrums (Q ¼ 10) applied onall directions. Because of excitations with frequen-cies being closer to the eigenfrequency of the test-board, the shock tests were more critical to thebonds. However, all shock tests were passed withoutany damages of the testboard. The measured accel-erations were according to the SRS parameters with-in a tolerance of �2 dB.
In order to detect changes in the alignment of themirrors on the testboard, tilt measurements as de-scribed above were carried out before and after themechanical tests. No changes in the alignment ofthe mirrors were observed within the measurementaccuracy.
Visual inspection of the bonding layers before andafter the mechanical tests did not show any changesas well.
C. Thermal Test
To determine the thermal stability of adhesive bond-ing, the testboard was subjected to thermal cyclingaccording to the expected LISA requirements.
Prior to the test, mirror tilts were measured as de-scribed above. One pair of mirrors (one adhesivebonded, one hydroxide-catalysis bonded) was testeddifferentially (but with higher accuracy) via DWS.The testboard was integrated into the interferom-eter, as shown in Fig. 3. To calibrate the setup, the
mirrors of the interferometer as well as the externalmirrors were tilted, so that the quadrant signals ofboth photodiodes were in phase.
This approach does not provide absolute angles;only changes in tilt can be detected. It features repro-ducibility before and after comparison with an uncer-tainty below 5 μrad in a range of 100 μrad.
The testboard was cycled eight times in a tempera-ture range between 253 and 323 K. Minimum andmaximum temperatures were held for two hours, andthe rate of change was 2 K=min. As depicted in Fig. 8the testboard was positioned upright, so that gravi-tation acts maximally on the glue joint during thetest. Temperatures were recorded on the testboardto ensure that the testboard reaches the requiredtemperatures.
Visual inspection after the test verifies that thetestboard has not been mechanically damaged bythe thermal test. Shortly after the test, the testboardwas checked with the interferometer setup. To rein-stall the testboard into the setup, the testboard wasaligned with two screws, adjusting the quadrant sig-nals of the reference photodiode in phase again. Thequadrant signals of the measurement photodiodenow contains information about changes in tilt.
The measurements before and after the thermaltests show no change of the tilt of the mirrors with-in the given uncertainties of the setup. Both verifica-tion approaches did not detect an effect of thermalstress in the range of ð253–323Þ K on the integrationtechnologies.
Fig. 7. (Color online) Picture of the testboard in the mountingbracket attached to the shaker. Accelerometers were glued tothe baseplate (1, 2) and the mounting bracket (3).
Fig. 8. (Color online) Testboard in thermal chamber. The thermalcycling range is −20 °C to 50 °C.
A novel adhesive bonding technology for ultrastableoptomechanical systems has been developed thatfeatures convenient time scales for integration andalignment (~hours), as well as comparatively shortcuring times (~hours). Mechanical and thermal testshave proven its principal suitability for applicationin tough environments, and thus make it an attrac-tive option in particular for space-based metrologysystems. Examples like LISA, DARWIN, or missionsaiming at precision geodesy demonstrate the increas-ing importance of such applications. In comparison tothe established technology of hydroxide-catalysisbonding, a similar passive stability of the bonded set-ups was demonstrated within the given uncertain-ties of our test facility. A translational stability ofbetter than 5pm=
ffiffiffiffiffiffiffiHz
pand a tilt stability of better
than 4nrad=ffiffiffiffiffiffiffiHz
phave been verified for frequencies
>0.1 Hz, both increasing with about 1=ffiffiffif
ptowards
lower frequencies.Canonical future investigations would include the
study of long-term alignment stability of the bondedsetups over time scales of months or years, as well asa systematic check of achievable absolute alignmenttolerances. A potentially interesting feature of adhe-sive bonding may further be the principal possibilityto remove bonded components again by appropriatechemical treatment of the bonding areas.
This work is financially supported by theEuropean Union under European Funds for RegionalDevelopment (EFRE) and the State Baden Württem-berg within the program ZAFH “Photonn
” and theGerman Aerospace Center (Deutsches Zentrum fürLuft- und Raumfahrt, DLR) within the program“LISA Performance Engineering” (DLR contractnumber 50OQ0701). The authors thank AchimPeters and Evgeny Kovalchuk from the Humboldt-
University Berlin for support and fruitfuldiscussions.
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