Albert Einstein Institute (AEI) Hannover, Germany
Leibniz Universität Hannover Institute for Gravitational Physics
Ranging and phase measurement for LISA
Max Planck Institute for Gravitational Physics
J.J. Esteban Delgado, A.F García Marín, J. Eichholz, I. Bykov, J. Kullmann, G. Heinzel, K. Danzmann
Autocorrelation of 6 pseudo-random bit codes
Received beam
2GHz
Clock Power
2..20GHz Offset Clock Transfer sidebandsideband beat
2..20GHz Offset Beatnote carrier-carrier beam
Frequency
0
200
400
10
-80 0.4
Figure 3: Autocorrelation and cross-correlation between a possible set of pseudocodes
0.6
0.8
1
1.2 Frequency [Hz]
1.4
1.6
1.8
2 x 10
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Phase measurement system
FPGA ProAsic3E DAC_1 LPF I
Interferometer
Laser control
DLL DAC_2
LPF
LPF
ADC
sin
Downsampling
NCO
Remote Laser
Loop filter
cos
Q
Local Laser
DIOB
Floating-point processor (PC)
EPP
Phase reconstruction
ENCODER
Port I/O
Port I/O (Fs)
τ
delay unit
Pseudo - random noise Brcode ~ 1.5MHz
EOM1
[4-16] bits signed
Integrate and dump
Punctual
Channel 1
Channel 3
[4-16] bits signed
Early
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f=200
Late
Punctual
Lock
97KHz Integrate and dump
|abs|
97KHz Integrate and dump
|abs|
97KHz
|abs|
Integrate and dump
Pseudocode generator
mirror
Early
Photodiode
Fs Sampling frequency → 50MHz
x200
Lock correlation
early correlation Error delay
6KHz Gain Factor
Loop Filter late correlation
PRN1
fibre coupler beam dump PZT
Phase Readout (Phasemeter)
ROM memory
Index generator
Flag_mode
Late
PMS Breadboard
Phase Locking
TEMP
DLL (Demodulation) PRN1/2
Figure 2: Experiment setup to test the laser modulation scheme
Figure 6: General block diagram of the delay-lock loop implemented in the same board than the phasemeter and design parameters for DLL implemented in the simulation and FPGA prototype
Phase
The DLL presents two different modes of working:
Data Diagnostics Delay
10-2
0.1 Frequency (Hz)
t
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t
.PEVMBUJPOQBUUFSO13/TIJGUJOHCFUXFFOUXP voltage levels
t
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t
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t
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t
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t
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t
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Preliminary results
1
10
Lasers and optics
1
The functionality of our DLL has been verified in presence of 0.8
t
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t
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Acquisition mode (Figure 6): determines delay between the local and incoming PRN sequences with a coarse resolution of one code persiod (µs accuracy). Tracking mode Once the acquisition is finished, it determines the timing delay with higher resolution (ns accuracy). The performance of the current ranging implementation enables measurement rate at 6 KHz and meters distance determination precision.
0.6
~ 20 dB 0.4
0.2
t
13/DIJQQJOHSBUFPG_.)[BOEEBUBSBUFTPG_LCQT
0
-300
t %PQQMFSTIJGUDPVQMFEPOUPUIFQIBTFTJHOBM4JNVMBUFEBT TJOVTPJEBMWBSJBUJPOPGBOFRVJWBMFOUBNQMJUVEFPG_,NBOE FRVJWBMFOUGSFRVFODZPG_)[
-200
-100
0
Delay [µs]
100
200
300
Figure 9: Peak of correlation of the DLL 20
Ranging error
15
Performance of the current FPGA ranging implementation t
3BOHJOHSFTPMVUJPOPGOT
10
5
0
t t
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LISA Group Hannover (Germany) http://www.lisa.aei-hannover.de/
10-3
Step_ nseg
N length pseudo-random noise → 1024 bits
Modulator
-7
Control Logic
M integration factor→ 16
PRN2
Clock 2 50MHz
Mach-Zehnder interferometer
Delay-locked loop
Look-up table
Modulator
10
DATA
50MHz Integrate and dump
10-6
Channel 4
50MHz Integrate and dump
-5
EOM electro-optic modulator
Data decoder
DLL input
10
'JHVSF/PJTFQFSGPSNBODFPGUIFQIBTFNFUFSXJUI.)[JOQVUTJHOBM generated by an additional NCO implemented in FPGA.
FPGA ProAsic3E A3PE1500
signal output
10-4
LPF
The delay-locked loop technique correlates three different version of the local PRN code sequence the incoming PRN signal: an early, a punctual and a late one (Figure 6). The substracction between “early” and “late” correlators is used as error signal to update the time delay in the code generator. Punctual provides data acquisition and lock detection.
Random noise unit
isolator beam-splitting polarizer beamsplitter
The functionality of our PMS desined has been verified and Figure 8 shows its latest noise performance in the frequency window relevant for LISA. Input signal was internally generated in the FPGA.
Ranging and data communication
Data generator Brdata~97KHz
-2
front end
50MHz
waveplate λ/2
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The signal processing of the PMS develops two main architectures into the FPGA: t"%JHJUBMQIBTFMPDLFEMPPQUIBUJNQMFNFOUTUIFinterferometric readout of the main scientific measurement. The main carrier of the beatnote is fed into a in-phase/quadrature (I/Q) demodulator to acquire its phase. A control loop locks the phase of a Numerically Controlled Oscillator (NCO) to the incoming beatnote. The phase measurement is formed in a floating-point unit as the sum of a raw phase estimation from the NCO and the arctangent of I and Q component.
overall requirement phasemeter requirement 3600-7000 s, output PA 2000-14000 sec, output PIR
10-3
7
Phase noise (rad/Hz)
-200
Input signal to DLL
f=200
waveplate λ/4
3FBEPVUCBTFEPOB&11QPSUBOEGBTUEJHJUBM*0BDRVJTJUJPO systems phase-output PA/PIR, 08.01.2009, 12 MHz NCO input, no AAF, new LPF
97KHz
EOM2
x200
t
-60
t"%FMBZMPDLFEMPPQUSBDLTUIFSFDFJWFE13/DPEFBOEUIFSF fore the estimation of the time-delay between PRN sequences can be obtained as well as the data transmitted.
In order to achieve interspacecraft laser ranging and data communication, the carrier of the laser link is phase moduMBUFEXJUIBEJSFDUTFRVFODFTQSFBETQFDUSVN %444 TDIFNF'JHVSFTIPXTPVSFYQFSJNFOUBMTFUVQUPUFTUUIF NPEVMBUJPOTDIFNFUXPQIBTFMPDLFEMBTFSTXJMMCFNPEVMBUFEVTJOHBOFMFDUSPPQUJDNPEVMBUPS &0. BOEUSBOT mitted to the remote spacecraft after passing through a fiber amplifier. The LISA interferometry system will allow detection in conditions of weak-light optical power and in presence of additional sidebands modulations for local clock noise transmissions. The phase measurement system (PMS) performs the phase readout of the heterodyne signal and enables ranging measurement, data acquisition, clock synchronization and laser phase-locking as back end processing.
Clock 1 50MHz
'PVS"%$DIBOOFMTBOEUXP%"$DIBOOFM
-50
Channel 2
Figure 1: Proposed laser frequency scheme for LISA
lens
t
Normalized correlation
5M H z
Frequency
f=50
-40
Carrier BPSK + PRN code 1% Power
Laser 2 (Slave)
-20
-30
-400
Local beam
f=50
t5IFBVUPDPSSFMBUJPOBTJOHMFTIBSQQFBL[FSPTIJGU t5IFDSPTTDPSSFMBUJPOJTOFHMJHJCMFGPSBMMQPTTJCMFTIJGUT
-70
LISA is a huge Michelson-like interferometer in space with unequal armlength configuration. As consequence of the mismatch between LISA´s arms, a laser frequency noise in excess is coupled into the measured phase spoiling the scientific performance of the mission. Ranging measurements onboard combined with a post-processing onground known as time-delay interferometry (TDI) is able to reduce the influence of laser frequency noise contribution up to seven orders of magnitude.
Laser capabilities: Main scientific measurement Ranging Clock synchronization Data transfer
t'1("XIJDIFOBCMFTSBOHJOHBOEEBUBDPNNVOJDBUJPOBTCBDL end processing
-10
1 0.8 0.6 0.4 0.2 0 -0.2
Laser modulation scheme
Breadboard of the PMS (Figure 7) has been developed and manufactured.
A pseudo-random noise (PRN) sequence will be modulated onto the phase of each laser link and the travel time will be measured via the correlation of the local and incoming PRN code. The main correlation properties are shown in Figure 3 where:
Spectral density [dBm]
The LISA phase measurement system (PMS) will provide interferometric phase readout of the primary heterodyne signal at microcycle sensitivity, ranging measurements at meters accuracy and data communication at rates of several kilobits per seconds. Our investigations are focused on interspacecraft laser ranging and data communication for LISA VTJOH%JSFDU4FRVFODF4QSFBE4QFDUSVN %444 NPEVMBUJPOPOUPUIFMBTFSMJOLT8FQSFTFOUUIFPQUJDBMFYQFSJNFOUBM setup to test the levels of performance achievable with a single laser link as well as a new hardware prototype based on FPGA (Field Programmable Gate Array) processing to perform high-accuracy phase readout of the optical signal, ranging measurements, data communication, clock noise demodulation and laser-phase locking.
Laser 1 (Master)
Hardware
Phase readout processing for ranging
Distance[m]
Introduction
Acknowledgments: 8FHSBUFGVMMZBDLOPXMFEHFTVQQPSUCZ%FVUTDIFT;FOUSVNGVS-VGUVOE3BVNGBISU %-3 SFGFSFODF02
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−5
−10 0
0.05
0.1
0.15
0.2 0.25 Time [s]
0.3
0.35
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0.4
0.45
