We describe a phasemeter designed to autonomously acquire and track a heterodyne signal with low signal-to-noise ratio in a frequency band that spans from 1 MHz to 25 MHz. The background driving some of the design criterions of the phasemeter comes from studies on future space mission concepts such as orbiting gravitational wave observatories and next generation geodesy missions which all rely on tracking phasemeters in order to meet their mission goal. The phasemeter has been implemented within a field programmable gate array trying to minimize the requirement of computational resources and its performance has been tested using signal generators. Laboratory test has shown that the phasemeter is capable of locking to an input signal in less than half a millisecond, while its phase measurement accuracy is in the micro-radian range for measurement frequencies that span from mHz to Hz.

1.
S.
Kawamura
 et al, “
The Japanese space gravitational wave antenna - DECIGO
,”
Classical Quantum Gravity
23
,
125
(
2006
).
2.
T.
Appourchaux
 et al, “
Astrodynamical space test of relativity using optical devices I (ASTROD I) - A class M fundamental physics mission proposal for cosmic vision 2015-2025
,”
Exp. Astron.
23
,
491
(
2009
).
3.
P.
Aufmuth
, “
eLISA - Hunting waves in space
,” Vol. 4 (published online 2010), available at http://www.einstein-online.info/spotlights/eLISA.
4.
P.
Amaro-Seoane
 et al, “
Low-frequency gravitational-wave science with eLISA/NGO
,”
Classical Quantum Gravity
29
,
124016
(
2012
).
5.
N.
Wei-Tou
, “
ASTROD-GW: Overview and progress
,”
Int. J. Mod. Phys. D
22
,
1341004
(
2013
).
6.
P.
Silvestrin
,
M.
Aguirre
,
L.
Massotti
, and
S.
Cesare
, “
Next generation gravity mission: A step forward in the earth’s gravity field determination
,” in
EGU Gen. Assembly Conf. Abstracts
(
Vienna, Austria
,
2009
), Vol.
11
, additional information can be accessed at http://adsabs.harvard.edu/abs/2009EGUGA..11.2184S.
7.
W.
Folkner
 et al, “
Laser Frequency Stabilization for GRACE-II
,” in
Proc. 2010 Earth Science Technology Forum
(
Jet Propulsion Laboratory, National Aeronautics and Space Administration
,
Arlington, VA, USA
,
2010
), pp. 1–8, additional information can be accessed at http://trs-new.jpl.nasa.gov/dspace/handle/2014/41635.
8.
S.
Cesare
 et al, “
Satellite formation for a next generation gravity mission
,” in
Small Satellite Mission for Earth Observation
, edited by
R.
Sandau
,
H.
Roeser
, and
A.
Valenzuela
(
Springer
,
2010
), Chap. 3, pp.
125
133
.
9.
S.
Cesare
and
G.
Sechi
, “
Next generation gravity mission
,” in
Distribute Space Missions for Earth System Monitoring
, edited by
M.
D’Errico
(
Springer
,
2013
), pp.
575
598
.
10.
B.
Loomis
,
R.
Nerem
, and
S.
Luthcke
, “
Simulation study of a follow-on gravity mission to GRACE
,”
J. Geod.
86
,
319
335
(
2012
).
11.
A. M.
Cruise
,
D.
Hoyland
, and
S. M.
Aston
, “
Implementation of the Phasemeter for LISA LTP
,”
Classical Quantum Gravity
22
,
S165
(
2005
).
12.
H.
Audley
 et al, “
The LISA Pathfinder interferometry - hardware and system testing
,”
Classical Quantum Gravity
28
,
094003
(
2011
).
13.
O.
Jennrich
,
R. T.
Stebbinis
,
P.
Bender
, and
S.
Pollack
, “
Demonstration of the LISA phase measurement principle
,”
Classical Quantum Gravity
18
,
4159
4164
(
2001
).
14.
S.
Pollack
,
O.
Jennrich
,
R. T.
Stebbinis
, and
P.
Bender
, “
Status of LISA phase measurement work in US
,”
Classical Quantum Gravity
20
,
S193
S199
(
2003
).
15.
S.
Pollack
and
R. T.
Stebbinis
, “
Demonstration of the Zero-Crossing Phasemeter with a LISA test-bed interferometer
,”
Classical Quantum Gravity
23
,
4189
4200
(
2006
).
16.
B.
Ware
 et al, “
Phase measurement system for inter-spacecraft laser metrology
,” in
Earth Science Technology Conferences
(
NASA
,
2006
).
17.
D.
Shaddock
,
B.
Ware
,
P.
Halverson
,
R.
Spero
, and
B.
Klipstein
, “
Overview of the LISA phasemeter
,”
AIP Conf. Proc.
873
,
654
660
(
2006
).
18.
V.
Wand
,
F.
Guzman
,
G.
Heinzel
, and
K.
Danzmann
, “
LISA phasemeter development
,”
AIP Conf. Proc.
873
,
689
696
(
2006
).
19.
I.
Bykov
,
J. E.
Delgado
,
A. G.
Marin
,
G.
Heinzel
, and
K.
Danzmann
, “
LISA phasemeter development: Advanced prototyping
,”
J. Phys.: Conf. Ser.
154
,
012017
(
2008
).
20.
O.
Gerberding
 et al, “
Phasemeter core for intersatellite laser heterodyne interferomtry: Modelling, simulations and experiments
,”
Classical Quantum Gravity
30
,
235029
(
2013
).
21.
R. E.
Best
,
Phase-Locked Loops: Design, Simulation, & Applications
, 6th ed. (
Mc-Graw-Hill Professional
,
2007
).
22.
D.
Abramovitch
, “
Phase-locked loops: a control centric tutorial
,”
Proc. 2002 Am. Control Conf.
1
,
1
15
(
2002
).
23.
F.
Ales
,
P.
Gath
,
U.
Johann
, and
C.
Braxmaier
, “
Modeling and simulation of a laser ranging interferometer acquisition and guidance algorithm
,”
J. Spacecr. Rockets
51
,
226
238
(
2014
).
24.
C.
Mahrdt
, “
Laser link acquisition for the GRACE follow-on laser ranging interferometer
,” Ph.D. thesis,
Gottfried Wilhelm Leibniz University Hannover
, Hannover, Germany,
2014
.
25.
D.
Wuchenich
 et al, “
Laser link acquisition demonstration for the GRACE Follow-On mission
,”
Opt. Express
22
,
11351
(
2014
).
26.
T.
Schwarze
 et al, “
Advanced phasemeter for deep phase modulation interferometry
,”
Opt. Express
22
,
18214
(
2014
).
27.
D. F.
Walnut
,
An Introduction to Wavelet Analysis
(
Birkhäuser
,
2001
).
28.
P.
Lian
, “
Improving tracking performance of PLL in high dinamic applications
,” Diploma thesis,
University of Calgary, Department of Geomatics Engineering
, Calgary, Alberta, Canada,
2004
.
29.
Y.
Li
,
X.
Xu
, and
T.
Zhang
, “
Improving tracking performance of PLL based on wavelet packet de-noising technology
,” in
Advances in Computer Science, Environment, Ecoinformatics, and Education
,
Communications in Computer and Information Science
Vol.
214
, edited by
S.
Lin
and
X.
Huang
(
Springer Berlin Heidelberg
,
2011
), pp.
449
456
.
30.
M.
Mosavi
and
I.
EmamGholipour
, “
De-noising of GPS receivers positioning data using wavelet transform and bilateral filtering
,”
Wireless Pers. Commun.
71
,
2295
2312
(
2013
).
31.
S. V.
Dhurandhar
,
K. R.
Nayak
,
S.
Koshti
, and
J.-Y.
Vinet
, “
Fundamentals of the LISA stable flight formation
,”
Classical Quantum Gravity
22
,
481
(
2005
).
32.
C.
Diekmann
,
F.
Steier
,
B.
Sheard
,
G.
Heinzel
, and
K.
Danzmann
, “
Analog phase lock between two lasers at LISA power levels
,”
J. Phys.: Conf. Ser.
154
,
12020
(
2009
).
33.
F. G.
Cervantes
,
J.
Livas
,
R.
Silverberg
,
E.
Buchanan
, and
R.
Stebbins
, “
Characterization of photoreceivers for LISA
,”
Classical Quantum Gravity
28
,
094010
(
2011
).
34.
B.
Sheard
 et al, “
Intersatellite laser ranging instrument for the GRACE follow-on mission
,”
J. Geod.
86
,
1083
1095
(
2012
).
35.
G.
Heinzel
 et al, “
Laser ranging interferometer for grace follow-on
,” in
Proceeding of International Conference on Space Optics (ICSO)
(
Ajaccio, Corsica, France
,
2012
).
36.
D.
Schütze
 et al, “
LISA-like laser ranging for grace follow-on
,”
9th LISA Symposium, ASP Conference Series
(
Astronomical Society of the Pacific Conference Series
,
Paris, France
,
2012
), Vol.
46
, pp.
285
289
.
37.
O.
Mandel
,
F.
Ales
, and
P.
Gath
, “
A digital phase measurement unit that integrates an automated signal acquisition stage for signals buried into noise
,” patent pending (17 November 2014).
38.
F.
Langford-Smith
,
Radiotron Designer’s Handbook
(
RCA
,
1953
), Vol.
4
.
39.
E.
Hogenauer
, “
An economical class of digital filters for decimation and interpolation
,”
IEEE Trans. Acoust., Speech, Signal Process.
29
,
155
162
(
1981
).
40.
D.
Schlichthärle
,
Digital Filters, Basics and Design
, 2nd ed. (
Springer
,
2011
).
41.
Alter®
, FFT MegaCore Function - User Guide 9.1, 2009.
42.
R.
Walden
, “
Analog-to-digital converter survey and analysis
,”
IEEE J. Sel. Areas Commun.
17
,
539
550
(
1999
).
43.
H.
Kobayashi
,
M.
Morimura
,
K.
Kobayashi
, and
Y.
Onaya
, “
Aperture jitter effects in wideband ADC systems
,” in
Proceedings 6th IEEE International Conference Electronics, Circuits and Systems (ICECS)
(
IEEE
,
Pafos, Cyprus
,
1999
), pp.
1705
1708
.
44.
C.
Burnett
, “
Development of an Ultra-precise digital phasemeter for the LISA gravitational wave detector
,” M. Eng. thesis,
Lulea University of Technology
, Kiruna, Sweden,
2010
.
45.
P.
Welch
, “
The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms
,”
IEEE Trans. Audio Electroacoust.
15
,
70
73
(
1967
).
46.
F.
Harris
, “
On the use of windows for harmonic analysis with the discrete Fourier transform
,”
Proc. IEEE
66
,
51
83
(
1978
).
You do not currently have access to this content.