Demonstration of an Ultraprecise Optical Bench for the Taiji Space Gravitational Wave Detection Pathﬁnder Mission

applied sciences

Article Demonstration of an Ultraprecise Optical Bench for the Taiji Space Gravitational Wave Detection Pathﬁnder Mission

Yupeng Li 1,2, Heshan Liu 3, Ya Zhao 1,2, Wei Sha 1, Zhi Wang 1,*, Ziren Luo 3,* and Gang Jin 3,4 1 Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China; [email protected] (Y.L.); [email protected] (Y.Z.); [email protected] (W.S.) 2 University of Chinese Academy of Sciences, Beijing 100049, China 3 Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China; [email protected] (H.L.); [email protected] (G.J.) 4 School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China * Correspondence: [email protected] (Z.W.); [email protected] (Z.L.)

Received: 19 April 2019; Accepted: 16 May 2019; Published: 21 May 2019

Abstract: For the Taiji space gravitational wave detection and its pathfinder mission, ultraprecise technology for optical assembly must be adopted to satisfy the high measurement sensitivities required. In this paper, we construct and evaluate an optical bench to assess its precision in optical assembly and bonding. We opted for hydroxide-catalysis bonding technology and designed a corresponding adjustment scheme to achieve an ultraprecise assembly for the optical bench. After alignment, the angular deviation between the interference beam and its ideal position in the global coordinate system is no more than 45 µrad, and positional deviation is less than 10 µm. The final experimental results indicate that the measurement precision of the evaluated board is 6 pm/√Hz, which meets the specifications required for the Taiji pathfinder.

Keywords: Taiji pathﬁnder; assembly; hydroxide-catalysis bonding; measurement precision

1. Introduction Following the detection of gravitational waves by the LIGO (Laser Interferometer Gravitational-wave Observatory) [1], detecting such waves at lower frequencies is the next exciting scientific challenge for the coming decade [2]. The LISA (Laser Interferometer Space Antenna) mission, proposed by ESA (European Space Agency) and with contributions by NASA (National Aeronautics and Space Administration), is the earliest and most mature plan to study gravitational waves in the frequency band between 0.1 mHz and 1 Hz [3,4]. The LISA mission with its three satellites will use heterodyne interferometry to convert the tiny displacements between test masses into a phase fluctuation in the interferometric signal. The length of the interferometer arms that are formed by LISA’s satellites is 2.5 million kilometers [5]. About two months before LIGO announced the first detection of gravitational waves, the LISA pathfinder was launched into space for technical validation [6,7]. After successful tests of the LISA pathfinder, the LISA mission is scheduled to be launched in the year 2034 [7,8]. Similar to LISA, the Taiji space gravitational wave detection, the length of the interferometer arm being 3 million kilometers, initiated by Chinese Academic of Sciences in 2008, plans to be launched in 2033 [9]. A pathfinder mission is planned to validate all key technologies prior to the Taiji mission [10–12]. In assembling the optical bench of Taiji and its pathfinder, an optical bonding technology is expected to be adopted in joining the optical components with their substrates [13–15]. The hydroxide-catalysis bonding [13], which has been successfully applied in the Gravity Probe B mission and the LISA

Appl. Sci. 2019, 9, 2087; doi:10.3390/app9102087 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, x 2 of 8

Appl. Sci. 2019, 9, 2087 2 of 8 mission and the LISA pathfinder [16], was chosen for joins in the optical bench for the Taiji and its pathfinder mission. Different from the traditional epoxy glue, the hydroxide-catalysis bonding formspathfinder covalent [16], bonds was chosen between for materials joins in thethrough optical hy benchdration for and the hydrolysis. Taiji and itsThere pathfinder is no additional mission. materialDifferent layer from formed the traditional during the epoxy bonding glue, process, the hydroxide-catalysis and therefore satisfies bonding the special forms requirements covalent bonds of thebetween Taiji materialspathfinder, through such as hydration structural and strength, hydrolysis. reliability, There and is no extreme additional thinness material of layerthe adhesive formed layer.during the bonding process, and therefore satisfies the special requirements of the Taiji pathfinder, suchFor as structural principle strength,verification reliability, for the Taiji and extremepathfinder thinness mission, of thean optical adhesive bench layer. was built employing the hydroxide-catalysisFor principle verification bonding for and the tested Taiji pathfinder in our labo mission,ratory. In an this optical paper, bench the wasoptical built layout employing of the interferometerthe hydroxide-catalysis is given in bonding Section and 2. Next, tested the in ouradjustment laboratory. strategy In this of paper, the optical the optical bench layout assembly of the is presentedinterferometer in Section is given 3. Details in Section of the2. Next,hydroxide-catalysis the adjustment bonding strategy and of theassembly optical process bench assemblyare given isin Sectionspresented 4 and in Section 5. Finally,3. Details the noise of the performance hydroxide-catalysis of the optical bonding bench and is assemblygiven in Section process 6. are given in Sections4 and5. Finally, the noise performance of the optical bench is given in Section6. 2. Optical Layout 2. Optical Layout A prototype of the optical bench was built to help in the optimization of the hydroxide-catalysis bondingA prototype and in determining of the optical the bench precision was builtof the to optical help in assembly. the optimization As shown of thein Figure hydroxide-catalysis 1 (this figure wasbonding created and inusing determining the component the precision library of theby opticalAlexander assembly. Franzen, As shownAlbert in Einstein Figure1 (thisInstitution, figure Hannover,was created usingGermany, the component 2017), the library optical by Alexander layout Franzen,of the Albertinterferometer Einstein Institution,includes Hannover,a simple Mach–ZehnderGermany, 2017), interferometry the optical layout system. of the interferometerA laser beam from includes a frequency-stabilized a simple Mach–Zehnder laser interferometry (wavelength: 1064system. nm, A linear laser beampolarized, from and a frequency-stabilized single mode) is split laser by (wavelength:a 50/50 BS (Beam 1064 Splitter). nm, linear The polarized, transmitted and beamsingle directly mode) isaccesses split by an a 50AOM/50 BS (Acoustic-Optical (Beam Splitter). Modulator), The transmitted whereas beam the directly reflected accesses beam anaccesses AOM another(Acoustic-Optical AOM after Modulator), a reflector changes whereas its thedirection reflected of propagation. beam accesses Both another beams AOM are frequency after a reflector shifted bychanges the AOMs, its direction and the of propagation.difference between Both beams the modula are frequencyted values shifted is the by frequency the AOMs, of and the the heterodyne difference interferometricbetween the modulated signal. values Next, is the frequencythese two of thebeams heterodyne are interferometriccoupled into signal. a Next,single-mode these two polarization-maintainingbeams are coupled into a single-modefiber and sent polarization-maintaining into the interferometry fiber syst andem. sentThe intointerference the interferometry system is locatedsystem. in The the interference vacuum chamber system to is locatedreduce the in the influence vacuum of chamber air disturbance to reduce on the the influence measurement of air precision.disturbance The on theinterferometer measurement contains precision. two The FCPSs interferometer (Fiber Collimation contains twoPackage FCPSs Subassemblies) (Fiber Collimation for beamPackage collimating, Subassemblies) two BSs for and beam two collimating, BCs (Beam two Co BSsmbiners), and two which BCs (Beamperform Combiners), the interferometry. which perform Two PDsthe interferometry. (Photo-Detectors) Two convert PDs (Photo-Detectors) the optical signals convert into electric the optical signals. signals Finally, into electricthe phase signals. information Finally, ofthe the phase electric information signals from of the the electric PDs are signals obtained from using the PDs a phasemeter. are obtained using a phasemeter.

FigureFigure 1. SchematicSchematic representation representation of of the the layout layout of the interferometer used in demonstrations.

3. Adjustment Adjustment Strategy Strategy Ideally, in the global coordinate system of the assembly (Figure 22),), thethe incidentincident andand thethe reﬂectedreflected beams (red dashdash line)line) only only propagate propagate in in the the plane plane of of the the interferometer interferometer (the (the designated designated X-Y X-Y plane) plane) and andparallel parallel to the to bonding the bonding surface, surface, and establishes and establishe the “in-plane”s the "in-plane" [17]. Hence, [17]. if Hence, we adjust if we the adjust “in-plane” the "in-plane"angle of propagation, angle of propagation, we only need we toonly adjust need angle to adjustϕ. In angle accordance φ. In accordance with the principle with the of principle kinematic of kinematicconstraint, constraint, the adjustment the adjustment of the three of degrees the three of freedom degrees (x, of y, freedomϕ) in the (x, “in-plane” y, φ) in the can "in-plane" be accomplished can be accomplishedusing three points using (Figure three2 ).points For high (Figure adjustment 2). For high precision, adjustment a large-stroke precision, hexapod a large-stroke (Model P84, hexapod Core (ModelTomorrow, P84, Harbin, Core Tomorrow, China) is usedHarbin, to manipulateChina) is used the positionto manipulate of the the target. position The displacementof the target. The and displacementangular precision and of angular the piezoelectric precision actuators of the arepiezoelectric7 nm and actuators0.5 µrad, are respectively. ±7 nm and ±0.5 μrad, ± ± respectively. Appl. Sci. 2019, 9, 2087 3 of 8

Appl. Sci. 2019, 9, x 3 of 8

FigureFigure 2. 2.Diagram Diagramof of thethe globalglobal coordinate system system of of the the optical optical component. component.

However,However, the the bottom bottom plane plane ofof thethe opticaloptical componentscomponents and and the the baseplate baseplate are are not not always always ideal ideal planes.planes. In In this this situation situation (Figure (Figure2), 2), “out-of-plane” “out-of-plane” refers refers to to the the beam beam position position evolutionevolution in the zz andand θ degrees𝜃 degrees of freedom, of freedom, which which is mainly is mainly caused caused by by the the following following three three parts: parts: (1)1) The The surface surface shape shape ofof thethe baseplatebaseplate exhibits a a shape shape of of an an approximate approximate sinusoidal sinusoidal curve curve [18] [18 ] with a flatness of λ/4 (peak-to-valley, ~160 nm, λ = 632.8 nm). For an optical element with 10 mm with a flatness of λ/4 (peak-to-valley, ~160 nm, λ = 632.8 nm). For an optical element with 10 mm thickness, the maximum value γ of the angular error introduced thereby is about ±5 μrad. thickness, the maximum value γ of the angular error introduced thereby is about 5 µrad. 2) The thickness of the glue layer introduced by the hydroxide-catalysis bonding± process is (2) The thickness of the glue layer introduced by the hydroxide-catalysis bonding process is about about a hundred nanometers order. The non-uniform distribution of the adhesive will cause the a hundred nanometers order. The non-uniform distribution of the adhesive will cause the unnecessary unnecessary surface tilt α. The value is about ±10 μrad. surface tilt α. The value is about 10 µrad. 3) For the limitation of the optical± lens processing, the parallelism between two optical surfaces is about(3) For 10 the μrad. limitation of the optical lens processing, the parallelism between two optical surfaces is about 10Therefore,µrad. the 𝜃 are obtained using the manufacturing tolerances (𝛽 and )𝛾 together with the uniformTherefore, bond thelayerθ thicknessare obtained (𝛼), and using this the degree manufacturing of freedom is tolerances uncontrolled (β andin theγ )assembly together process. with the uniformFor those bond values, layer an thickness additional (α ),“out-of-plane” and this degree error of is freedom actually is present uncontrolled of about in 5~30 the assemblyμrad. process. For those values, an additional “out-of-plane” error is actually present of about 5~30 µrad. 4. Hydroxide-Catalysis Bonding 4. Hydroxide-Catalysis Bonding Given the successful experience with the LISA pathfinder, the Taiji program adopted hydroxide-catalysisGiven the successful bonding experience technology with the for LISA the pathfinder, assembly theof Taijiits interferometer program adopted [13,19]. hydroxide-catalysis To improve bondingreliability, technology the bonding for the process assembly must ofbe itscompleted interferometer in a Class [13 ,10019]. clean To improve room, and reliability, the flatness the bondingof the processcomponent must bonding be completed surface in must a Class be within 100 clean a tolerance room, of and λ/10 the (~60 flatness nm, λ of= 632.8 the componentnm). The adhesive bonding surfacesolution must is prepared be within by a diluting tolerance 14% of λNaOH/10 (~60 and nm, 27%λ SiO= 632.82 silicate nm). solution The adhesive with deionized solution water is prepared in a byratio diluting of 1:6. 14% NaOH and 27% SiO2 silicate solution with deionized water in a ratio of 1:6. WithWith processing processing limitations, limitations, therethere isis aa certaincertain amount of of burring burring (~90 (~90 nm) nm) of ofthe the edge edge of ofthe the componentcomponent bonding bonding (bottom)(bottom) surface, which which influenc influenceses the the effectiveness effectiveness of bonding. of bonding. Therefore, Therefore, we weneed need to to re-polish re-polish the the component component with with cerium cerium oxide oxide before before bonding. bonding. A Alaser laser interferometer interferometer (ZYGO) (ZYGO) waswas used used to maketo make an imagean image comparison comparison of the of surface the surface of optical of optical components compon beforeents andbefore after and polishing. after polishing. Because the surface changes of optical elements before and after polishing are basically Because the surface changes of optical elements before and after polishing are basically the same, the same, we arbitrarily select a group of comparison results. As shown in Figure 3, the polishing has we arbitrarily select a group of comparison results. As shown in Figure3, the polishing has clearly clearly removed the peripheral burrs. removed the peripheral burrs. After ensuring the bonding environment and the flatness of the component surface, the bonding process can be divided into the following five steps: (1) Component Cleaning: every component was cleaned using an ultrasonic cleanser with a suitable cleaning solution to increase the hydrophilicity of the bonding surface after polishing. (2) Smear the transition solution and adjustment: when the optical element is adjusted on the baseplate, slow volatilization and low residual octane was used as a transitional solution between the two surfaces to avoid direct contact between the optical surfaces. (3) Smear Adhesives: when the component is adjusted to its ideal position, the transitional solution is replaced by the bonding solution, and then the optical component is returned. (4) Micro Adjustment:(a as) the adhesive takes about 100 s to cure, minute(b) adjustments of the optical element are still possible during this period. Appl. Sci. 2019, 9, x 3 of 8

Figure 2. Diagram of the global coordinate system of the optical component.

However, the bottom plane of the optical components and the baseplate are not always ideal planes. In this situation (Figure 2), “out-of-plane” refers to the beam position evolution in the z and 𝜃 degrees of freedom, which is mainly caused by the following three parts: 1) The surface shape of the baseplate exhibits a shape of an approximate sinusoidal curve [18] with a flatness of λ/4 (peak-to-valley, ~160 nm, λ = 632.8 nm). For an optical element with 10 mm thickness, the maximum value γ of the angular error introduced thereby is about ±5 μrad. 2) The thickness of the glue layer introduced by the hydroxide-catalysis bonding process is about a hundred nanometers order. The non-uniform distribution of the adhesive will cause the unnecessary surface tilt α. The value is about ±10 μrad. 3) For the limitation of the optical lens processing, the parallelism between two optical surfaces is about 10 μrad. Therefore, the 𝜃 are obtained using the manufacturing tolerances (𝛽 and )𝛾 together with the uniform bond layer thickness (𝛼), and this degree of freedom is uncontrolled in the assembly process. For those values, an additional “out-of-plane” error is actually present of about 5~30 μrad.

4. Hydroxide-Catalysis Bonding Given the successful experience with the LISA pathfinder, the Taiji program adopted hydroxide-catalysis bonding technology for the assembly of its interferometer [13,19]. To improve reliability, the bonding process must be completed in a Class 100 clean room, and the flatness of the component bonding surface must be within a tolerance of λ/10 (~60 nm, λ = 632.8 nm). The adhesive Appl. Sci. 2019, 9, x 4 of 8 solution is prepared by diluting 14% NaOH and 27% SiO2 silicate solution with deionized water in a ratio of 1:6. FigureWith 3. processingComparison limitations, of surface thereof optical is a certain componen amountts between of burring (left) (~90 before nm) and of the(right) edge after of the Appl. Sci. 2019, 9, 2087 λ 4 of 8 componentpolishing. Thebonding unit of (bottom) pix is 0.2 surface,mm, and which wave denotesinfluenc wavelengthes the effectiveness ( = 632.8 ofnm). bonding. Although Therefore, the edge we needcollapse to re-polish causes an the increase component in the withPV (Peak cerium to valley) oxide value,before the bonding. bonding A effectlaser isinterferometer not affected in (ZYGO) this wascase.(5) Curingused (a) Theto after makesurface alignment: an of image optical comparison Thecomponent beam alignment beforeof the polishing;surface needs of ( tob optical) beThe completed surface compon of ents asoptical quickly before component asand possible after withinpolishing.after 100s, polishing. otherwise Because the we needsurface to repeatchanges the of above optical process elements for re-bonding.before and after After polishing bonding, are it needsbasically to be curedtheat same, room we temperature arbitrarily select for one a group week of to comparison have sufficient results. bonding As shown strength in Figure between 3, the the polishing components has After ensuring the bonding environment and the flatness of the component surface, the andclearly the baseplate removed [19 the]. peripheral burrs. bonding process can be divided into the following five steps: 1) Component Cleaning: every component was cleaned using an ultrasonic cleanser with a suitable cleaning solution to increase the hydrophilicity of the bonding surface after polishing. 2) Smear the transition solution and adjustment: when the optical element is adjusted on the baseplate, slow volatilization and low residual octane was used as a transitional solution between the two surfaces to avoid direct contact between the optical surfaces. 3) Smear Adhesives: when the component is adjusted to its ideal position, the transitional solution is replaced by the bonding solution, and then the optical component is returned. 4) Micro Adjustment: as the adhesive takes about 100 s to cure, minute adjustments of the optical element are still possible during this period. 5) Curing after alignment:(a) The beam alignment needs to be completed(b) as quickly as possible withinFigure 100s, 3. otherwiseComparison we of need surface to of repeat optical the components above process between for (left) re-bonding. before and (right)After afterbonding, polishing. it needs to beThe cured unit at of pixroom is 0.2 temperature mm, and wave for denotes one week wavelength to have (λ sufficient= 632.8 nm). bonding Although strength the edge between collapse the componentscauses an and increase the baseplate in the PV (Peak [19]. to valley) value, the bonding effect is not affected in this case. (a) The surface of optical component before polishing; (b) The surface of optical component after polishing. 5. Assembly 5. Assembly The nominal optical layout has perfectly matched paths, but constructing an interferometer The nominal optical layout has perfectly matched paths, but constructing an interferometer without path mis-match is difficult. In the process of assembly, the precise position of the beam is without path mis-match is difficult. In the process of assembly, the precise position of the beam is first measured, so that the position of the optical element can be adjusted by the beam position. The first measured, so that the position of the optical element can be adjusted by the beam position. The measurement of the beam requires a CQP (Calibrated Quadrant-photodiode Pair) device (Figure 4) measurement of the beam requires a CQP (Calibrated Quadrant-photodiode Pair) device (Figure4)[ 20]. [20]. The CQP is an auxiliary measuring equipment, which consists of a BS, two reflectors, and two The CQP is an auxiliary measuring equipment, which consists of a BS, two reflectors, and two quadrant quadrant photodiodes (QPDs). The measurement principle of the CQP is to determine the unique photodiodes (QPDs). The measurement principle of the CQP is to determine the unique straight line straight line through two QPDs. If a beam passes through the centers of the two QPDs, a particular through two QPDs. If a beam passes through the centers of the two QPDs, a particular set of position set of position parameters exists with the CQP, i.e. the incident point and the directional vector of the parameters exists with the CQP, i.e. the incident point and the directional vector of the beam are beam are constant in value in the CQP reference coordinate system. After calibrated[20], the position constant in value in the CQP reference coordinate system. After calibrated [20], the position parameters parameters under the reference coordinate system is known and can be converted to the global under the reference coordinate system is known and can be converted to the global coordinate system coordinate system by means of Coordinate Measuring Machine (CMM). Because of the by means of Coordinate Measuring Machine (CMM). Because of the measurement precision of CMM measurement precision of CMM (1.5 μm + 1 μm/m) and the fitting error of parameters, the (1.5 µm + 1 µm/m) and the fitting error of parameters, the measurement precision of the position measurement precision of the position parameters under the global coordinate system is ±5 μm, ±30 parameters under the global coordinate system is 5 µm, 30 µrad. μrad. ± ±

Figure 4. 4. CQP(CalibratedCQP (Calibrated Quadrant-photodiode Quadrant-photodiode Pair) Pair) prototype prototype and andassembly assembly process process diagram. diagram. The useThe process use process of CQP of CQP is: first, is: ﬁrst, the theglobal global and and referenc referencee coordinate coordinate system system of of th thee system system are are established established using the CMMCMM (Coordinate（Coordinate Measuring Measuring Machine); Machine Next,）; Next, the CQP the isCQP aligned is aligned with the with beam the (the beam number (the numbershown onshown the two on quadrantthe two quadrant photodiodes photodiodes is 0), and is the 0), positionand the ofposition the beam of the within beam the within reference the coordinate system is determined according to the known positional parameters; Finally, the position parameters of beam is converted to the global coordinate system by a coordinate transformation. Appl. Sci. 2019, 9, x 5 of 8

reference coordinate system is determined according to the known positional parameters; Finally, the position parameters of beam is converted to the global coordinate system by a coordinate Appl. Sci.transformation.2019, 9, 2087 5 of 8

In the alignment process (Figure 5), the FCPS of the interference system acts as a light source to In the alignment process (Figure5), the FCPS of the interference system acts as a light source provide a stable and collimated Gaussian beam, which is directed into the starting position of the to provide a stable and collimated Gaussian beam, which is directed into the starting position of the interferometer. Because of influences from pre-assembly and measurement errors, the beams may interferometer. Because of inﬂuences from pre-assembly and measurement errors, the beams may show large deviations once the components are directly positioned in their geometric model show large deviations once the components are directly positioned in their geometric model positions. positions. The specific operation procedure for the FCPS assembly is the following: a) First, the CQP The speciﬁc operation procedure for the FCPS assembly is the following: (a) First, the CQP pose is pose is adjusted using the hexapod platform to ensure the beam passes through the center of the two adjusted using the hexapod platform to ensure the beam passes through the center of the two QPDs. QPDs. b) Second, with the aid of the CQP, the absolute position of the beam in the global coordinate (b) Second, with the aid of the CQP, the absolute position of the beam in the global coordinate system system is read by the CMM. c) Finally, the position of the FCPS is adjusted iteratively until the is read by the CMM. (c) Finally, the position of the FCPS is adjusted iteratively until the exiting light exiting light reaches the desired position. Then, the location of the BS and BC are determined in the reaches the desired position. Then, the location of the BS and BC are determined in the same way. same way.

Figure 5.5. Photograph Photograph of of the the setup setup of of the the optical optical platform platform assembly. assembly. The The actuator actuator is used is used to adjust to adjust the degreesthe degrees of freedom of freedom of the of components; the components; the role the of role the CMMof the isCMM to assist is to the assist CQP the to measureCQP to measure the absolute the positionabsolute ofposition the beam; of the the beam; hexapod the is hexapod used to adjustis used the to CQPadjust posture the CQP and posture align it withand align the beam; it with FCPS: the Fiberbeam; Collimation FCPS: Fiber Package Collimation Subassemblies. Package Subassemblies.

After curingcuring the the optical optical element, element, the deviationthe deviation of the positionof the position parameters parameters between thebetween theoretical the beamtheoretical and thebeam measured and the beammeasured (the absolutebeam (the deviation absolute of deviation the beam of itself) the beam of the itself) twointerference of the two positionsinterference under positions the global under coordinate the global system coordinate is re-measured system is re-measured using the CMM using with the CMM CQP.The with results CQP. showThe results that comparedshow that tocompared theoretical to theoretical position at position the PD ata, the PD positiona, the position and angle and (directional angle (directional vector sumvector of sum “in-plane” of "in-plane" and “out-of-plane”) and "out-of-plane") of deviation of deviation of the of two the beamstwo beams are 3areµm, 3 μ 18m,µ rad18 μ andrad and 9 µm, 9 42μm,µ rad,42 μ respectively;rad, respectively; the corresponding the corresponding result result for the for deviation the deviation at the PDat theb is PD 5 µbm, is 305 μµm,rad 30 and μrad 10 andµm, 4510 µμrad,m,45 respectively. μrad, respectively. Finally, Finally, PDa and PD PDa bandare PD fixedb are in fixed suitable in suitable positions positions so that theso that energy the ofenergy the two of interferencethe two interference beams on beams the PD on is the not PD clipped. is not clipped. Based on the above data, the relative positional deviation at PD a andand PD PDbb areare 6 6 μµmm and and 5 5 μµm, and the angular deviationdeviation are 2424 µμradrad andand 1515 µμrad,rad, respectively.respectively. Unlike the relative deviationdeviation between the beams, the absolute deviation will result in a relative path length difference difference between the interferometer PDPDaa andand the the interferometer interferometer PD PDb,b which, which will will aff ectaffect the the final final interferometric interferometric precision precision [20]. The[20]. relative The relative position position deviation deviation between between beams mainlybeams amainlyffects the affects interference the interference contrast, i.e.,contrast, the di ffii.e.culty the ofdifficulty signal extraction.of signal extraction.

6. Results and Discussions Discussion

After assembly, thethe demonstrationdemonstration interferometer interferometer was was tested tested in in a a vacuum vacuum chamber chamber at at 22 22 ±0.10.1 ◦℃C ± temperature. The noise performance is shown in Figure6 6.. The sensitivity of the interferometer reaches 6 pm/√Hz in the frequency band from 0.03 Hz to 1 Hz. Compared with our previous result [12], the noise has largely decreased because the diﬀerence in relative path length between the PDa and PDb interferometers has decreased with the equipment being precisely positioned. In the case of frequency noise, it is the relative path length diﬀerence between the PDa and PDb interferometers which is important, i.e. that the frequency noise signal at Appl. Sci. 2019, 9, 2087 6 of 8

the PDa interferometer is the same as that of a PDb interferometer such that it can be subtracted out as a common mode signal [22]. Among them, unequal arm lengths ∆x of the interferometer due to assembly errors will couple frequency noise δv as noise in the displacement measured, which can be expressed as [23]: δv δx = ∆x v where v is the frequency of the laser; the laser wavelength is 1064 nm, and the frequency noise of the laser used is about 1 MHz/√Hz in this experiment. In our previous research, the interferometer system was based on individual opto-mechanical components with a clamping structure. The positioning precision was about 0.5~1 cm, the difference in the arm lengths also being about 1 cm. Therefore, the theoretical value of the noise from frequency jitter is about 35 pm/√Hz. Considering the estimated error of ∆x, it is reasonable that the final tested result is 15 pm/√Hz, where the dominant noise is from frequency jitter. From the optical bonding and precision positioning technology, the relative path length difference between the two interferometers is mainly affected by the manufacturing error of the optical components, which was reduced to less than 0.5 mm in the demonstration optical bench. Therefore, the frequency jitter noise, which in our previous result was the dominant noise from the Appl. Sci. 2019, 9, x 6 of 8 frequency source, is theoretically less than 2 pm/√Hz in this current setup.

Figure 6. Figure 6.Experimental Experimental results results from from the the interferometer interferometer tests. tests. The The pathlength pathlength noise noise budget budget of of the the Taiji Taiji pathfinder optical bench (20 pm/√Hz) is similar to that of Lisa pathfinder [21] (18 pm/√Hz) in the pathfinder optical bench (20 pm/√Hz) is similar to that of Lisa pathfinder [21] (18 pm/√Hz) in the frequency band from 0.03 Hz to 1 Hz. frequency band from 0.03 Hz to 1 Hz. Because of thermal drift, the sensitivity curve is slightly higher for frequencies below 0.03 Hz, The sensitivity of the interferometer reaches 6 pm/√Hz in the frequency band from 0.03 Hz to 1 but its value is still lower than the specifications for the Taiji pathfinder. In addition, compared to the Hz. Compared with our previous result [12], the noise has largely decreased because the difference previous experiment, the noise of this experiment decreased more seriously in the frequency band from in relative path length between the PDa and PDb interferometers has decreased with the equipment 0.003 Hz to 0.03 Hz. That is, the hydroxide-catalysis bonding is an effective way to reduce the adhesive being precisely positioned. In the case of frequency noise, it is the relative path length difference stress and internal stress of the optical components. Therefore, under our laboratory conditions, between the PDa and PDb interferometers which is important, i.e. that the frequency noise signal at the related thermal deformation of the optical components and baseplate has also decreased. the PDa interferometer is the same as that of a PDb interferometer such that it can be subtracted out Δ 7.as Conclusions a common mode and Outlook signal [22]. Among them, unequal arm lengths x of the interferometer due to assembly errors will couple frequency noiseδ v as noise in the displacement measured, which can be expressedAn ultraprecise as [23]: demonstration optical bench was constructed and tested for the Taiji pathfinder mission. With the precise positioning of the equipment,δ thev angular deviation from the theoretical beam in the two end PDs of the interferometerδ xx were=Δ found to be less than 42 µrad and 45 µrad, and their deviation in position were 9 µm and 10 µm, respectively.v Compared with our previous v results,Where the sensitivity is the frequency of this optical of the bench laser; reached the laser 6 pm wavelength/√Hz in the is frequency1064 nm, and band the from frequency 0.03 Hz noise to 1 Hz,of the thus laser representing used is about a significant 1 MHz/√Hz improvement. in this experiment. This was In our because previous the noiseresearch, from the frequency interferometer jitter system was based on individual opto-mechanical components with a clamping structure. The positioning precision was about 0.5~1 cm, the difference in the arm lengths also being about 1 cm. Therefore, the theoretical value of the noise from frequency jitter is about 35 pm/√Hz. Considering the estimated error of Δx , it is reasonable that the final tested result is 15 pm/√Hz, where the dominant noise is from frequency jitter. From the optical bonding and precision positioning technology, the relative path length difference between the two interferometers is mainly affected by the manufacturing error of the optical components, which was reduced to less than 0.5 mm in the demonstration optical bench. Therefore, the frequency jitter noise, which in our previous result was the dominant noise from the frequency source, is theoretically less than 2 pm/√Hz in this current setup. Because of thermal drift, the sensitivity curve is slightly higher for frequencies below 0.03 Hz, but its value is still lower than the specifications for the Taiji pathfinder. In addition, compared to the previous experiment, the noise of this experiment decreased more seriously in the frequency band from 0.003 Hz to 0.03 Hz. That is, the hydroxide-catalysis bonding is an effective way to reduce the adhesive stress and internal stress of the optical components. Therefore, under our laboratory conditions, the related thermal deformation of the optical components and baseplate has also decreased.

7. Conclusions and Outlook Appl. Sci. 2019, 9, 2087 7 of 8 decreased considerably as a result of the precision positioning technology and the use of better optical bonding. The frequency jitter in the laser beam has therefore been largely suppressed in this optical bench. Although the demonstration system has been constructed and tested, the optical bench of the Taiji pathfinder is much more complex. Moreover, its mechanical and thermal reliability, which must satisfy environmental simulation tests of the Taiji pathfinder space flight, remains to be verified.

Author Contributions: Conceptualization, Z.L. and H.L.; methodology, Y.Z.; writing—original draft preparation, Y.L.; writing—review and editing, H.L. and, G.J.; funding acquisition, Z.W. and, W.S. Funding: This research was funded by the Strategic Priority Research Program of the Chinese Academy of Science (XDB23030000). Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Abbott, B.P.; Abbott, R.; Abbott, T.D.; Abernathy, M.R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R.X.; et al. Observation of Gravitational Waves from a Binary Black Hole Merger. Phys. Rev. Lett. 2016, 116, 061102. [CrossRef] 2. Vitale, S. Space-borne gravitational wave observatories. Gen. Relativ. Gravit. 2014, 46, 1730. [CrossRef] 3. Danzmann, K.; LISA Study Team. LISA: Laser interferometer space antenna for gravitational wave measurements. Class. Quantum Gravity 1996, 13, 247–250. [CrossRef] 4. Danzmann, K.; Rüdiger, A. LISA technology-concept, status, prospects. Class. Quantum Gravity 2003, 20, S1–S9. [CrossRef] 5. Amaro-Seoane, P.; Audley, H.; Babak, S.; Baker, J.; Barausse, E.; Bender, P.; Berti, E.; Binetruy, P.; Born, M.; Bortoluzzi, D.; et al. Laser interferometer space antenna. arXiv 2017, arXiv:1702.00786. 6. Antonucci, F.; Armano, M.; Audley, H.; Auger, G.; Benedetti, M.; Binetruy, P.; Bogenstahl, J.; Bortoluzzi, D.; Bosetti, P.; Brandt, N.; et al. The LISA Pathfinder Mission. JPC 2015, 610, 012005. [CrossRef] 7. Armano, M.; Audley, H.; Auger, G.; Baird, J.T.; Bassan, M.; Binetruy, P.; Born, M.; Bortoluzzi, D.; Brandt, N.; Caleno, M.; et al. Sub-Femto-gFree Fall for Space-Based Gravitational Wave Observatories: LISA Pathfinder Results. Phys. Rev. Lett. 2016, 116, 231101. [CrossRef] 8. Armano, M.; Audley, H.; Baird, J.; Binetruy, P.; Born, M.; Bortoluzzi, D.; Castelli, E.; Cavalleri, A.; Cesarini, A.; Cruise, A.M.; et al. Beyond the Required LISA Free-Fall Performance: New LISA Pathfinder Results down to 20 muHz. Phys. Rev. Lett. 2018, 120, 061101. [CrossRef] 9. Hu, W.R.; Wu, Y.L. The Taiji Program in Space for gravitational wave physics and the nature of gravity. Natl. Sci. Rev. 2017, 4, 685–686. [CrossRef] 10. Liu, H.-S.; Dong, Y.-H.; Gao, R.-H.; Luo, Z.-R.; Jin, G. Principle demonstration of the phase locking based on the electro-optic modulator for Taiji space gravitational wave detection pathfinder mission. Opt. Eng. 2018, 57, 054113. [CrossRef] 11. Liu, H.-S.; Luo, Z.-R.; Jin, G. The Development of Phasemeter for Taiji Space Gravitational Wave Detection. Microgravity Sci. Technol. 2018, 30, 775–781. [CrossRef] 12. Luo, Z.-R.; Liu, H.-S.; Jin, G. The recent development of interferometer prototype for Chinese gravitational wave detection pathfinder mission. Opt. Laser Technol. 2018, 105, 146–151. [CrossRef] 13. Elliffe, E.J.; Bogenstahl, J.; Deshpande, A.; Hough, J.; Killow, C.; Reid, S.; Robertson, D.; Rowan, S.; Ward, H.; Cagnoli, G. Hydroxide-catalysis bonding for stable optical systems for space. Class. Quantum Gravity 2005, 22, S257–S267. [CrossRef] 14. Dehne, M.; Tröbs, M.; Heinzel, G.; Danzmann, K. Verification of polarising optics for the LISA optical bench. Opt. Express 2012, 20, 27273–27287. [CrossRef][PubMed] 15. Ressel, S.; Kronast, W.; Gohlke, M.; Weise, D.; Mescheder, U.; Rauen, D.; Braxmaier, C.; Schuldt, T.; Johann, U. Ultrastable assembly and integration technology for ground- and space-based optical systems. Appl. Opt. 2010, 49, 4296–4303. [CrossRef][PubMed] 16. Robertson, D.I.; Fitzsimons, E.D.; Killow, C.J.; Perreur-Lloyd, M.; Ward, H.; Bryant, J.; Cruise, A.M.; Dixon, G.; Hoyland, D.; Smith, D.; et al. Construction and testing of the optical bench for LISA Pathfinder. Class. Quantum Gravity 2013, 30, 085006. [CrossRef] Appl. Sci. 2019, 9, 2087 8 of 8

17. Killow, C.J.; Fitzsimons, E.D.; Hough, J.; Perreur-Lloyd, M.; Robertson, D.I.; Rowan, S.; Ward, H. Construction of rugged, ultrastable optical assemblies with optical component alignment at the few microradian level. Appl. Opt. 2013, 52, 177–181. [CrossRef] 18. Shen, J.; Liu, S.; Yi, K.; He, H.; Shao, J.; Fan, Z. Subsurface damage in optical substrates. Opt. Int. J. Light Electron Opt. 2005, 116, 288–294. [CrossRef] 19. Van Veggel, A.M.A.; Killow, C.J. Hydroxide catalysis bonding for astronomical instruments. Adv. Opt. Technol. 2014, 3, 293–307. [CrossRef] 20. Fitzsimons, E.D.; Bogenstahl, J.; Hough, J.; Killow, C.J.; Perreur-Lloyd, M.; Robertson, D.I.; Ward, H. Precision absolute positional measurement of laser beams. Appl. Opt. 2013, 52, 2527–2530. [CrossRef] 21. Racca, G.D.; McNamara, P.W. The LISA Pathﬁnder Mission. Space Sci. Rev. 2010, 151, 159–181. [CrossRef] 22. Hechenblaikner, G. Common mode noise rejection properties of amplitude and phase noise in a heterodyne interferometer. J. Opt. Soc. Am. Opt. Image Sci. 2013, 30, 941–947. [CrossRef] 23. Gerberding, O.; Isleif, K.-S.; Mehmet, M.; Danzmann, K.; Heinzel, G. Laser-Frequency Stabilization via a Quasimonolithic Mach-Zehnder Interferometer with Arms of Unequal Length and Balanced dc Readout. Phys. Rev. Appl. 2017, 7, 024027. [CrossRef]

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