Deep phase modulation interferometry for test mass measurements on elisa

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Clementine Francis
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1 for test mass measurements on elisa Thomas Schwarze, Felipe Guzmán Cervantes, Oliver Gerberding, Gerhard Heinzel, Karsten Danzmann AEI Hannover

2 Table of content Introduction elisa Current status & outlook Conclusion 2

3 Introduction In his theory of general relativity, Albert Einstein predicted gravitational waves: tiny stretches and compressions of Space-Time due to heavy accelerated masses ( f.e. binary stars ) Detection requires highly sensitive methods for length measurements interferometry 3

4 Introduction General interferometry: - Using interference pattern of a single-source split beam - Constructive or destructive interference dependent on phase difference 4

5 Introduction Ground-based detectors: LIGO/VIRGO/GEO600 Seismic noise limits sensitivity in lower bandwidth ( mhz-hz ) space-based detector: elisa 5

6 elisa elisa = evolved Laser Interferometer Space Antenna Michelson-like interferometer through 3 satellites ( armlength 1 mio km ) Test masses ( TM ) on each spacecraft Aim: measurement of length-change between TMs due to GWs 6

7 elisa Length-changes (stretching and compressing) are oscillating: 7

8 Utilization of DPMI for LISA elisa interferometry will measure distance between TMs ( here: x ) Other degrees of freedom (DOF) also have to be measured Distance TM spacecraft TM-rotation ( can couple into main measurement ) To measure up to 6 DOF, a compact technique with a high dynamic range (mm) is needed DPMI 8

$interferometry low dynamic range: fraction$ of wavelength ( µm ) Heterodyne

9 Interferometer techniques Homodyne interferometry low dynamic range: fraction of wavelength ( µm ) Heterodyne interferometry Higher dynamic range Complex modulation part 9

10 Deep Phase Modulation Interferometry Phase modulated homodyne interferometry For m > π Deep phase modulation High dynamic range without complex modulation part ( functionality is put into phasemeter ) 10

11 Principle of DPMI Sinusoidal phase modulation leads to time-dependent pattern as interferogram 11

12 Principle of DPMI Modulation-pattern dependent on phase Extract phase from pattern 12

13 Phase extraction via FT Corresponding Fourier transform consists of the modulation frequency ( here: 1 Hz ) and higher harmonics ( here: up to 10 ) 13

14 Calculus Mathematical analysis leads to the following relation for the Fourier components (bins) : Over-dimensioned system of equations ( 10 bins ) can be solved to fit the phase (Levenberg-Marquardt algorithm) 14

15 Initial Experiment First design at the AEI ( Heinzel, Guzmán et al.) : - Modulation is performed by independent frequency generator - Fourier transform routine, solving and fitting is performed on PC 15

16 Former Design - Results Former design achieved 10 pm / Hz 16

17 Improvements New Design Simulations show: phase noise dependent on the modulation depth m Idea: stabilize system via feedback loop on certain m Problem: phase acquisition to slow for control loop: 10 Hz New, faster design 17

18 New design Former design New design Fourier transform: On PC Hardware (FPGA) Fit and phase calculation: On PC Microcontroller (softcore) Independent frequency generator Direct digital synthesis (DDS) on FPGA open closed Modulation generation: Control circuit for modulation depth: 18

19 New design FPGA New design includes a new hardware-phasemeter implemented on a Field Programmable Gate Array (FPGA) FPGA: Can implement (emulate) any synchronous sequential logic system Compromise between speed and flexibility 19

20 New design - FPGA Using Xilinx ML605 Board Virtex 6 FPGA ( includes dedicated DSP-Block and RAM ) several interfaces Preferred design-language: VHDL 20

21 New design - Setup Peforming multiple single bin Fourier transform (SBFT) ( only frequency bins of fmod and higher harmonics ) Calculated modulation depth is fed back into signal synthesis 21

22 FPGA architecture Modulation Photodetector 22

23 Current status & Outlook FPGA-Design: - SBFT-Pipelines and digital signal synthesis (NCO's) working - Custom Ethernet-interface connected - Softcore and ADC-Control-Unit have to be added Optical Design: Not yet implemented, planned to be fibre-based, using a RPZT or EOM for modulation Expected Phase acquisition rate with current parameters: khz ( 10 Hz for former design) 23

24 Conclusions DPMI is compact method for precise length measurement - usable for TM readout ( second DOF ) on elisa Former setup showed a noise level of 10 pm / Hz New setup with FPGA as hardware phasemeter - Multiple SBFT - Numerics in softcore High acquisition rate allows control circuit to stabilize on certain modulation depth - promises better performance 24

25 Thanks for your attention! 25

Ranging Implementation: Signal Processing Development

Ranging Implementation: Signal Processing Development Kendall Ackley University of Florida Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut) IREU August 11, 2009 Abstract The objective