The LTP interferometer aboard SMART-2

Transcription

1 The LTP interferometer aboard SMART-2 Gerhard Heinzel Max-Planck-Institut für Gravitationsphysik, (Albert-Einstein-Institut), Hannover, presented at the LISA Symposium, PSU,

2 What is SMART-2? SMART stands for Small Missions for Advanced Research in Technology in ESA s scientific programme. SMART-2 is the second in this family of missions, to be launched in LISA relies on technologies that have never been tested and cannot be tested on Earth: Gravitational Sensors ( Disturbance Reduction System ). low-noise micronewton thrusters ultra-stable interferometry in space In LISA, interferometry is a separate, very difficult problem. In SMART-2, the interferometer is a diagnostic tool for the gravitational sensors. Nevertheless some key components of precision interferometry in space must be used and can be tested: lasers, fiber coupling, modulators, beamsplitters and other optical components, optical bench including mounting and alignment techniques, photodiodes,... These items will be included in the LISA technology package (LTP), one of the scientific payloads on SMART-2. 2

3 LISA and SMART-2 requirements force noise [N/ Hz] SMART2 LISA frequency [Hz] displacement noise [m/ Hz] LISA SMART frequency [Hz] The requirements of SMART-2 have been relaxed by a factor of ten both in frequency and sensitivity as compared to LISA. 3

4 SMART-2 requirements displacement noise [m/ Hz] SMART2 mission goal 10-4 interferometer budget 10-5 each interferometer contrib frequency [Hz] interferometer phase noise [rad/ Hz] The interferometer noise budget is a factor of 8.5 below the SMART-2 mission goal. Each individual noise contribution is another factor of 10 below that. This conservative requirement takes into account the possibility that some noise sources are correlated and might add linearly instead of quadratically. 4

5 The SMART-2 interferometer The interferometer on the LISA Technology Package on SMART-2 is needed to verify the performance of the gravitational sensors by monitoring the distance between two test masses. There are several possible modes of operation: the spacecraft follows one of the test masses and the other one is left freely floating; the second testmass may be controlled in only some of its degrees of freedom; the spacecraft follows a linear combination of both test mass positions with other linear combinations left freely floating... The interferometric sensing must be able to monitor the test mass position along the sensitive axis (called x-axis) with a noise level of 10 pm/ Hz between 3 mhz and 30 mhz, relaxing as 1/f 2 towards 1 mhz. The interferometer must do so without extering any influence on the test masses that might lead to a motion above that level. Furthermore, it must track the motion of the test mass distance while that distance changes by many µm with a speed of up to 20 µm/s, without losing track of the sign of the motion. 5

6 Physical constraints The area available for the interferometer is mm. Below is one possible mounting technique (under investigation by Astrium): 6

7 Inertial Sensor Optical bench 200x200x40mm ULE / Zerodur Test mass 40x40x40 mm Pt Au alloy 1 kg x required measurement: distance between test masses: x = x 1 x 2 x1 y optional measurements: x=x1 x2 distance between each test masses and optical bench: x 1, x 2. alignment of test masses distances in y-direction: y 1, y 2, y. x2 Note: No absolute length will be measured with high precision, but only fluctuations within the measurement frequency band. Inertial Sensor Test mass 40x40x40 mm Pt Au alloy 1 kg 7

8 Dynamic range Former ESA specification: 10 mm (presumably unnecessary). More realistic: 1 mm. In any case, many wavelengths of 1064 nm light. That makes it difficult to use traditional interferometers (Fabry-Perot cavities, Michelson on dark fringe) because these require an actuator to keep the interferometer at a specified operating point. No actuator with the required linearity and dynamic range is presently available. Large-scale mechanical motion is not allowed (effect on test mass). Hence we need an interferometer that yields a constant signal at any operating point. Furthermore, it must be able to track a motion with arbitrary changes of direction. If the dynamic range were only a few µm, other techniques (Fabry-Perot) could be used. 8

9 Interferometer comparison During the first months of 2002, Astrium Immenstaadt and AEI Hannover have conducted a detailed interferometer comparison study. It quickly became clear that the baseline will be a heterodyne Mach-Zehnder interferometer : Laser f0 AOM f1 AOM f2 f0+f1 f0+f2 φ PD1 PD2 f1 f2 = f het Photocurrent φ time 9

10 Interferometer comparison Test mass 1 40x40x40 mm test mass 1 40x40x40 mm diam. 138 mm Ref. mirror dummy window X2 PM2 Alternative design LTP Maurice te Plate esa/estec with hole QWP PBS1 QWP DM1 QWP HR1 HR2 Quarter wave plate Half wave plate PBS BS IF1 PBS4 PBS3 PBS5 PBS6 IF3 Fiber Output A PDR1 BS1 PD5 BS6 BS7 HWP2 BS11 PD1 BS12 PDA1 PD2 PBS2 BS10 QWP2 BS2 HR3 HR4 QWP1 PDF1 PBS1 BS3 PD4 PDA2 BS13 PD3 HWP1 CM2 BS9 PD6 BS8 CM3 CM1 PDF2 Fiber Output B 234 mm Ref. mirror Flange I/S diam. 186 mm 2 Quadrant photodiodes cylinder I/S diam. 138 mm X1+X2 dummy window dummy window Reference Ref. mirror freq 2 freq1 BS5 BS4 PDR2 PM1 incoming beams IF2 PBS2 QWP QWP Test mass 2 40x40x40 mm QWP DM2 y 200x200mm x IF4 test mass 2 40x40x40 mm diam. 138 mm Ref. mirror Opt. window IS dummy window X1 x 1 x 2, y 1, y 2 x 1 x 2, x 1, x 2 monolithic optical elements x 1 x 2, x 1, x 2 10

11 Interferometer comparison All the interferometers on the last page use polarizing components, which are known to have a number of problems, in particular when the temperature changes. It is very hard to find relevant data about polarizing components in the literature or from manufacturers. A quick experiment in our own lab mainly showed the difficulty in obtaining reproducible results and the necessity for fine-tuning all alignment degrees of freedom which will be impossible for SMART-2. Although we cannot prove that polarizing components will spoil the interferometer performance, we cannot guarantee to reach the performance, either. Hence we decided to use a non-polarizing interferometer. The price we have to pay is to give up the normal incidence on the testmasses. 11

12 Baseline interferometer Testmass dimension: 46 x 46 mm Testmass distance: 330 mm between surfaces 200 x 200 mm win1 win1r m11 m12 bs16 x1 bs11 bs6 bs9 bs4 bs5 bs8 Reference bs1 m4 win2r bs3 m5 bs2 m1 win2 m8 bs10 bs7 x1- x2 m10 m6 Frequency :36:21 GHH AEI Hannover extra blue length = mm pathlength difference x1- x2 = mm pathlength difference x1 = mm pathlength difference Reference = mm pathlength difference Frequency = mm m14 The optical bench contains 4 separate interferometers: x 1 x 2 This interferometer provides the main measurement: the distance between the two test masses and their differential alignment. x 1 This interferometer provides as auxiliary measurement the distance between one test mass and the optical bench and the alignment of that test mass. Reference This interferometer provides the reference phase for the above two measurements. Frequency This interferometer uses basically the same interference pattern as the Reference interferometer but with intentionally unequal pathlengths such as to measure laser frequency fluctuations. 12

13 Testmass 1 WIN1 PDA1 M12 PDFA M11 BS1 BS2 BS7 BS16 PDFB M8 BS11 BS4 BS9 M6 M10 PDA2 M4 BS6 BS8 BS3 PD1B M1 M14 PD1A BS5 PDRB M5 PD12B PDRA BS10 PD12A WIN2 Testmass with an extra pathlength of mm in the reference fiber, the pathlength difference is mm. 13

14 Testmass 1 WIN1 PDA1 M12 PDFA M11 BS1 BS2 BS7 BS16 PDFB M8 BS11 BS4 BS9 M6 M10 PDA2 M4 BS6 BS8 BS3 PD1B M1 M14 PD1A BS5 PDRB M5 PD12B PDRA BS10 PD12A WIN2 Testmass with an extra pathlength of mm in the reference fiber, the pathlength difference is mm. 14

15 Testmass 1 WIN1 PDA1 M12 PDFA M11 BS1 BS2 BS7 BS16 PDFB M8 BS11 BS4 BS9 M6 M10 PDA2 M4 BS6 BS8 BS3 PD1B M1 M14 PD1A BS5 PDRB M5 PD12B PDRA BS10 PD12A WIN2 Testmass with an extra pathlength of mm in the reference fiber, the pathlength difference is mm. 15

16 Testmass 1 WIN1 PDA1 M12 PDFA M11 BS1 BS2 BS7 BS16 PDFB M8 BS11 BS4 BS9 M6 M10 PDA2 M4 BS6 BS8 BS3 PD1B M1 M14 PD1A BS5 PDRB M5 PD12B PDRA BS10 PD12A WIN2 Testmass with an extra pathlength of mm in the reference fiber, the pathlength difference is mm. 16

17 System overview Frequency stabilization Laser head 1064 nm light Modulation bench 1064 nm light Optical Bench PD signals PD Front end A/D converter DPS phase meter pump light Pump module f het Master Oscillator Amp. Stab. Power Control Output sampling clock Output Spacecraft 17

18 Beam preparation AOM Fiber Laser BS AS f2 AOM AS f1 from fiber end Fiber from fiber end On the laser bench, the beam is split into two parts. Each of them is frequency-shifted by an acousto-optical modulator (AOM). The driving frequencies of the two AOMs differ by a few khz, such that the two resulting beams differ in frequency by that amount (f het ). 18

19 Amplitude stabilization The laser power P reflected from the gravitational sensors produces a force on the masses. Fluctuations in the laser power will produce fluctuating forces on the gravitational sensors which could limit the sensitivity of the measurement. The displacement fluctuation δy caused by the power fluctuation δp is given by δy = 2 δp m c ω 2, where m is the test mass (assumed to be 1 kg) and ω the Fourier frequency of the fluctuation. Accordingly, the required relative power stability for 1 mw of light in the measurement arm is found (assuming a δy of 1 pm/ Hz and f = 3 mhz) by 1 mission goal δp P = m c ω2 2P δy / Hz between 1 mhz and 3 mhz, relaxing as f 2 for frequencies up to 30 mhz. relative power fluctuations [1/ Hz] ifo. budget AM noise frequency [Hz] 19

20 Amplitude stabilization 2 Note that there is a very conservative total safety factor of 85 (between this noise contribution and the mission goal sensitivity) included in this requirement. At the heterodyne frequency f het, of some khz, the (more stringent) requirement is δp /P 10 7 / Hz due to direct coupling to the phase measurement. Depending on the details of the phase measurement algorithm, a considerable common mode rejection factor is expected and the actual requirements may be more relaxed. This is still more than an order of magnitude above the shot noise in 1 mw of light. In any case, stabilization of the laser power will be necessary. In order to compensate fluctuations of the fiber coupling efficiency and fiber transmission, it will be done by measuring the power at the end of each fiber and feeding a correction signal back to the respective AOM driver. 20

21 AOM driver A laboratory prototype of the AOM driver was built and characterized. It consists of two independent TCVCXO s, which are frequency-locked by a PLL to give a constant difference frequency (e.g. 1 khz). LF 10 MHz Input 10 MHz Output φ f Σ 1 TCVCXO 80 MHz Hz DBM TCVCXO 80 MHz 250 Hz ΑΟΜ1 ΑΟΜ2 500 Hz LP 500 Hz Input φ f LF Comp Sign Comp φ f Div /16 Div /16 5 MHz ε 5 MHz +ε 5 MHz +ε BP DBM 5 MHz ε BP 10 MHz BP Comp rad rms / Hz TCVCXO = temperature compensated voltage controlled crystal oscillator LP = lowpass filter BP = bandpass filter LF = loop filter Comp = comparator to generate logic level signals Div = digital frequency divider DBM = double balanced mixer φ f = digital phase/frequency detector Both the difference frequency ( 500 Hz) and the average frequency (80 MHz) are controlled by phase-locked loops (PLL) k 10k 100k Fourier frequency [Hz] The phase noise of each oscillator is < 10 6 rad/ Hz at 1 khz. 21

22 TCVCXO 80 MHz DBM 2 W PA 20 db DC 2 W out BP Det LP LF 10VRef AM input TCVCXO = Temp. compens. VCXO DBM = double balanced mixer (used as attenuator) PA = Power Amplifier DC = Directional Coupler BP = 80 MHz Bandpass Det = Schottky Detector LP = 10 MHz Lowpass LF = Loop Filter 1/sqrt(Hz) 1e-05 free 1e-06 outloop 1e-07 1e-08 inloop 1e-09 preamp 1e Hz The RF amplitude of each oscillator is stabilized to 10 8 / Hz at 1 khz and has a fast input (BW > 100 khz) to compensate light power fluctuations that are measured at the fiber end. 22

23 Voltage Reference For the amplitude stabilization, a low-noise reference is necessary. We have tested a standard 10 V Reference (AD587) with low-pass filter in unstabilized laboratory conditions: filtered voltage reference noise in thermally unstable environment [1/ Hz] Frequency [Hz] It is expected that in thermally very stable conditions the noise will be sufficiently low. 23

24 bs3 m1 Testmass dimension: 46 x 46 mm Testmass distance: 330 mm between surfaces The paths travelled by the reference and measurement beams are as similar as possible to reduce the effects of laser frequency noise. The pathlengths are equal to within 4 µm, with an extra delay of 39 cm in all reference paths. 200 x 200 mm win1 win1r m11 m12 bs16 bs11 bs6 bs4 bs9 bs1 bs2 m8 bs7 m10 m6 Frequency The conversion factor of frequency fluctuations δω [rad/s] to phase fluctuations δϕ [rad] is given by the differential time delay l/c. m4 bs8 x1 Reference bs5 win2r m5 win2 bs10 x1- x :36:21 GHH AEI Hannover extra blue length = mm pathlength difference x1- x2 = mm pathlength difference x1 = mm pathlength difference Reference = mm pathlength difference Frequency = mm m14 The frequency fluctuations are measured with the extra interferometer called Frequency. This signal can be used to correct the other output signals or as error signal for a frequency stabilization. 24

25 Alignment measurement with quadrant photodiodes With each photodiode being a single-element photodiode, the longitudinal information (motion along x-axis) can be determined. More information can be obtained by replacing each photodiode with a quadrant diode and forming three signals from each diode: Σ = A + B + C + D; y = A + B C D; x = A + C B D; Reference A C B D QPD Phase meter avg pathlength change testmass longitudinal Phase meter diff wavefront angle testmass tilt 25

26 Alignment measurement with quadrant photodiodes The first signal, Σ, is used as before for the longitudinal readout. The latter two signals, y and x, are used to determine alignment drifts of the interferometer and in particular of the test masses by applying the same phase measurement as is done for the longitudinal signal ( differential wavefront sensing ). The expected sensitivity is α x d 10 nrad/ Hz, ( x = longitudinal sensitivity, d = beam diameter). This is expected to be better than the angular readout capability of the capacitive sensors. Indeed this optical alignment readout may be used to stabilize the alignment of the test masses. 26

27 Optocad model Testmass WIN PDA1 M12 M11 PDFA BS1 BS2 BS BS11 BS16 BS4 BS9 M8 PDFB M PDA2 BS6 BS8 M4 BS3 M10 PD1B M PD1A BS5 PDRB M5 PD12A M14 PDRA BS PD12B WIN Testmass The Mathematica program exports the relevant coordinates into an Optocad file. Optocad computes all beams, including stray beams. It is clear that at least some stray beams must be suppressed, e.g. by selective coating or blackening of beamsplitters. 27

28 Computing rotational sensitivity with Mathematica: Create a model of the well-aligned ifo (mirrors, beamsplitters) by tracing the beam center. Trace important beam through ifo, using reflection and refraction, remembering the path as list of points. Choose a center of rotation (Random within 200 mm < {x, y, z} < +200 mm. Rotate both test masses by a small angle ε around chosen center. 28

29 Computing rotational sensitivity 2: Trace again beam through misaligned ifo until it hits the photodiode. Compare in the plane of the photodiode: parallel beam shift. change in pathlength. change in beam angle. Repeat for several centers of rotation (Monte-Carlo) 29

30 Interpretation of results A pure parallel shift ideally will not affect the length measurement, Beam 1 Beam 2 Photodiode if the photodiode is large enough to detect the whole beam and is homogeneous. Depending on the wavefront curvature, the beam shift will, however, be detected by the quadrant diode. 30

31 Interpretation of results 2 An change in beam angle does not appear in the direct measurement. Beam 1 Beam 2 Photodiode In the indirect measurements, however, it will appear and will induce an error (depending on the wavefront curvature). 31

32 Present work Phase measurement: A stopwatch technique with a 100 MHz clock or 10 khz sampling with 16 bit and FFT processing are both expected to have low enough quantization noise. The influence of amplitude noise must be studied. Prediction of output signals: Numerical computation of the modified beams with Optocad and numerical integration of the intensity on the photodiode yields contrast and phase for each quadrant. Windows: Astonishingly, the vacuum in orbit is not good enough for the gravitational sensors (outgassing of the spacecraft). They will be enclosed in separate vacuum tanks. The interferometer optical path includes windows. Their thermal expansion and dn/dt may spoil the measurement. 32

33 Preparations in Hannover We have set up an interferometry laboratory in Hannover in order to test the heterodyne Mach- Zehnder interferometry. The following items are ready: laboratory with infrastructure (optical tables, power supplies, computer etc.) laser with Pound-Drever system and ultra-stable reference cavity optical components low-noise AOM drivers with PLL to lock the heterodyne frequency quadrant diodes with front-end electronics data acquisiton system with anti-aliasing filters etc. first version of phase measurement software (FFT based) The first experiment will be verification of differential wavefront sensing. First results are expected very soon. 33

34 Numerical integration I(x, y, ϕ) = A 1 (x, y) + A 2 (x, y) exp(iϕ) mm mm The numerical integration is performed using an adaptive two-dimensional algorithm with automatic error control. 34

35 Signal prediction P (ϕ) = dx dy I(x, y, ϕ) power on photodiode [max=2] phase [rad] A discrete Fourier transform (i.e. fit to a sine wave) yields as main results: - the phase shift between the wavefronts - the average power and contrast This computation can now be repeated with different beam parameters as e.g. OPTOCAD predicts them for tilted test masses etc. 35