1 Armstrong, J. W., “Low-Frequency Gravitational Wave Searches Using Spacecraft Doppler Tracking”, Living Rev. Relativity, 9, lrr-2006-1 (2006). [External LinkDOI], [External LinkADS]. URL (accessed 25 February 2014):
2 Armstrong, J. W., Estabrook, F. B. and Tinto, M., “Time-Delay Interferometry for Space-Based Gravitational Wave Searches”, Astrophys. J., 527, 814–826 (1999). [External LinkDOI], [External LinkADS].
3 Becker, T. and Weispfenning, V., Gröbner Bases: A Computational Approach to Commutative Algebra, Graduate Texts in Mathematics, 141, (Springer, Berlin; New York, 1993).
4 Bender, P. L. and Hils, D., “Confusion noise level due to galactic and extragalactic binaries”, Class. Quantum Grav., 14, 1439–1444 (1997). [External LinkDOI], [External LinkADS].
5 Bender, P. L. et al. (LISA Study Team), LISA. Laser Interferometer Space Antenna for the detection and observation of gravitational waves. An international project in the field of Fundamental Physics in Space. Pre-Phase A report, MPQ-233, (Max-Planck-Institut für Quantenoptik, Garching, 1998). Online version (accessed 6 July 2005):
External Link
6 Burnett, C. M., Development of an Ultra-precise Digital Phasemeter for the LISA Gravitational Wave Detector, Master’s thesis, (Lulea University of Technology, Kiruna, Sweden, 2010). Online version (accessed 25 February 2014):
External Link
7 Cornish, N. J. and Hellings, R. W., “The effects of orbital motion on LISA time delay interferometry”, Class. Quantum Grav., 20, 4851–4860 (2003). [External LinkDOI].
8 de Vine, G., Ware, B., McKenzie, K., Spero, R. E., Klipstein, W. M. and Shaddock, D. A., “Experimental Demonstration of Time-Delay Interferometry for the Laser Interferometer Space Antenna”, Phys. Rev. Lett., 104, 211103 (2010). [External LinkDOI], [External LinkADS], [External LinkarXiv:1005.2176 [astro-ph.IM]].
9 Dhurandhar, S. V., “Time-delay interferometry and the relativistic treatment of LISA optical links”, J. Phys.: Conf. Ser., 154, 012047 (2009). [External LinkDOI], [External LinkarXiv:0808.2696 [gr-qc]].
10 Dhurandhar, S. V., Rajesh Nayak, K. and Vinet, J.-Y., “Algebraic approach to time-delay data analysis for LISA”, Phys. Rev. D, 65, 102002 (2002). [External LinkDOI].
11 Dhurandhar, S. V., Rajesh Nayak, K. and Vinet, J.-Y., “Time Delay Interferometry for LISA with one arm dysfunctional”, Class. Quantum Grav., 27, 135013 (2010). [External LinkDOI], [External LinkarXiv:1001.4911 [gr-qc]].
12 Dhurandhar, S. V., Vinet, J.-Y. and Rajesh Nayak, K., “General relativistic treatment of LISA optical links”, Class. Quantum Grav., 25, 245002 (2008). [External LinkDOI].
13 “eLISA”, project homepage, Max Planck Institute for Gravitational Physics (Albert Einstein Institute). URL (accessed 26 February 2014):
External Link
14 Estabrook, F. and Wahlquist, H., “Response of Doppler spacecraft tracking to gravitational radiation”, Gen. Relativ. Gravit., 6, 439–447 (1975). [External LinkDOI], [External LinkADS].
15 Estabrook, F. B., Tinto, M. and Armstrong, J. W., “Time-delay analysis of LISA gravitational wave data: Elimination of spacecraft motion effects”, Phys. Rev. D, 62, 042002 (2000). [External LinkDOI], [External LinkADS].
16 Esteban, J. J., García, A. F., Barke, S., Peinado, A.M, Guzmán Cervantes, F., Bykov, I., Heinzel, G. and Danzmann, K., “Experimental demonstration of weak-light laser ranging and data communication for LISA”, Opt. Express, 19(17), 15937–15946 (2011). [External LinkDOI].
17 Faller, J. E. and Bender, P. L., “A possible laser gravitational wave experiment in space”, in Taylor, B. N. and Phillips, W. D., eds., Precision Measurement and Fundamental Constants II, Proceedings of the Second International Conference held at the National Bureau of Standards, Gaithersburg, MD, June 8 – 12, 1981, NBS Special Publication, 617, pp. 689–690, (U.S. Dept. of Commerce / National Bureau of Standards, Washington, DC, 1984).
18 Faller, J. E., Bender, P. L., Hall, J. L., Hils, D., Stebbins, R. T. and Vincent, M. A., “An antenna for laser gravitational-wave observations in space”, Adv. Space Res., 9, 107–111 (1989). [External LinkDOI], [External LinkADS]. COSPAR and IAU, 27th Plenary Meeting, 15th Symposium on Relativistic Gravitation, Espoo, Finland, July 18 – 29, 1988.
19 Faller, J. E., Bender, P. L., Hall, J. L., Hils, D. and Vincent, M. A., “Space antenna for gravitational wave astronomy”, in Longdon, N. and Melita, O., eds., Kilometric Optical Arrays in Space, Proceedings of the Colloquium held 23 – 25 October 1984, Cargèse, Corsica, France, ESA Conference Proceedings, SP-226, pp. 157–163, (ESA Publications Division, Noordwijk, 1985).
20 Finn, L. S., “Aperture synthesis for gravitational-wave data analysis: Deterministic sources”, Phys. Rev. D, 63, 102001 (2001). [External LinkDOI], [External Linkgr-qc/0010033].
21 Folkner, W. M., Hechler, F., Sweetser, T. H., Vincent, M. A. and Bender, P. L., “LISA orbit selection and stability”, Class. Quantum Grav., 14, 1405–1410 (1997). [External LinkDOI].
22 Gerberding, O., Sheard, B., Bykov, I., Kullmann, J., Esteban Delgado, J. J., Danzmann, K. and Heinzel, G., “Phasemeter core for intersatellite laser heterodyne interferometry: modelling, simulations and experiments”, Class. Quantum Grav., 30, 235029 (2013). [External LinkDOI].
23 Gerberding, O. et al., “Breadboard Model of the LISA Phasemeter”, in Auger, G., Binétruy, P. and Plagnol, E., eds., The 9th LISA Sympsium, Bibliothéque Nationale de France, Paris, 21 – 25 May 2012, ASP Conference Series, 467, pp. 271–275, (Astronomical Society of the Pacific, San Francisco, 2013).
24 Giampieri, G., Hellings, R. W., Tinto, M. and Faller, J. E., “Algorithms for unequal-arm Michelson interferometers”, Opt. Commun., 123, 669–678 (1996). [External LinkDOI].
25 Gruning, P., Halloin, H., Prat, P., Baron, S., Brossard, J., Buy, C. and Petiteau, A., “Progress towards an electro-optical simulator for space based, long arms interferometers”, arXiv, e-print, (2013). [External LinkADS], [External LinkarXiv:1309.1059 [gr-qc]].
26 Heinzel, G., Esteban, J. J., Barke, S., Otto, M., Wang, Y., Garcia, A. F. and Danzmann, K., “Auxiliary functions of the LISA laser link: ranging, clock noise transfer and data communication”, Class. Quantum Grav., 28, 094008 (2011). [External LinkDOI], [External LinkADS].
27 Hellings, R. W., “Elimination of clock jitter noise in spaceborne laser interferometers.”, Phys. Rev. D, 64, 022002 (2001). [External LinkDOI].
28 Jenkins, G. M. and Watts, D. G., Spectral Analysis and its applications, (Holden-Day, San Francisco, 1969).
29 Kreuzer, M. and Robbiano, L., Computational Commutative Algebra 1, (Springer, Berlin; New York, 2000). [External LinkGoogle Books].
30 Królak, A., Tinto, M. and Vallisneri, M., “Optimal filtering of the LISA data”, Phys. Rev. D, 70, 022003 (2004). [External LinkDOI], [External LinkarXiv:gr-qc/0401108 [gr-qc]]. Erratum ibid. 76, 069901 (2007).
31 Laakso, T. I., Välimäki, V., Karjalainen, M. and Laine, U. K., “Splitting the Unit Delay”, IEEE Signal Proc. Mag., 1(30), 30–60 (1996). [External LinkDOI].
32 Miller, J., “Laboratory experiment shows that noise can be lessened for LISA”, Phys. Today, 63, 14–16 (2010). [External LinkDOI].
33 Mitryk, S. J., Mueller, G. and Sanjuan, J., “Hardware-based demonstration of time-delay interferometry and TDI-ranging with spacecraft motion effects”, Phys. Rev. D, 86, 122006 (2012). [External LinkDOI], [External LinkADS], [External Link1205.1934 [astro-ph.IM]].
34 Nelemans, G., Yungelson, L. R. and Portegies Zwart, S. F., “The gravitational wave signal from the Galactic disk population of binaries containing two compact objects”, Astron. Astrophys., 375, 890–898 (2001). [External LinkDOI], [External LinkADS], [External LinkarXiv:astro-ph/0105221].
35 “NGO: The New Gravitational Wave Observatory”, project homepage, European Space Agency. URL (accessed 26 February 2014):
External Link
36 Noble, B., Applied Linear Algebra, (Prentice-Hall, Englewood Cliffs, 1969).
37 Otto, M., Heinzel, G. and Danzmann, K., “TDI and clock noise removal for the split interferometry configuration of LISA”, Class. Quantum Grav., 29, 205003 (2012). [External LinkDOI], [External LinkADS].
38 Prince, T. A., Tinto, M., Larson, S. L. and Armstrong, J. W., “LISA optimal sensitivity”, Phys. Rev. D, 66, 122002 (2002). [External LinkDOI], [External LinkADS], [External LinkarXiv:gr-qc/0209039].
39 Rajesh Nayak, K., Dhurandhar, S. V., Pai, A. and Vinet, J.-Y., “Optimizing the directional sensitivity of LISA”, Phys. Rev. D, 68, 122001 (2003). [External LinkDOI].
40 Rajesh Nayak, K., Pai, A., Dhurandhar, S. V. and Vinet, J.-Y., “Improving the sensitivity of LISA”, Class. Quantum Grav., 20, 1217–1231 (2003).
41 Rajesh Nayak, K. and Vinet, J.-Y., “Algebraic Approach to Time-Delay Data Analysis: Orbiting case”, Class. Quantum Grav., 22, S437–S443 (2005). [External LinkDOI].
42 Selby, S. M., Standard of Mathematical Tables, (The Chemical Rubber Co., Cleveland, 1964).
43 Shaddock, D., Ware, B., Spero, R. E. and Klipstein, B., “Overview of the LISA Phasemeter”, in Merkowitz, S. M. and Livas, J. C., eds., Laser Interferometer Space Antenna: 6th International LISA Symposium, Greenbelt, MD, USA, 19 – 23 June 2006, AIP Conference Proceedings, 873, pp. 654–660, (American Institute of Physics, Melville, NY, 2006). [External LinkDOI], [External LinkADS].
44 Shaddock, D. A., “Operating LISA as a Sagnac interferometer”, Phys. Rev. D, 69, 022001 (2004). [External LinkDOI], [External LinkADS].
45 Shaddock, D. A., Tinto, M., Estabrook, F. B. and Armstrong, J. W., “Data combinations accounting for LISA spacecraft motion”, Phys. Rev. D, 68, 061303 (2003). [External LinkDOI].
46 Shaddock, D. A., Ware, B., Spero, R. E. and Vallisneri, M., “Postprocessed time-delay interferometry for LISA”, Phys. Rev. D, 70, 081101(R) (2004). [External LinkDOI].
47 Shannon, C. E., “Communication in the Presence of Noise”, Proc. IEEE, 86, 0018–9219-98 (1998). [External LinkDOI].
48 Spero, R. et al., “Progress in interferometry for LISA at JPL”, Class. Quantum Grav., 28, 094007 (2011). [External LinkDOI], [External LinkarXiv:1102.0799 [physics.ins-det]].
49 Summers, D., “Algorithm tradeoffs”, conference paper, (2003). Talk given at the 3rd progress meeting of the ESA funded LISA PMS Project. ESTEC, NL, February 2003.
50 Sutton, A., McKenzie, K., Ware, B. and Shaddock, D. A., “Laser ranging and communications for LISA”, Opt. Express, 18(20), 20759–20773 (2010). [External LinkDOI].
51 Tinto, M., “Spacecraft to spacecraft coherent laser tracking as a xylophone interferometer detector of gravitational radiation”, Phys. Rev. D, 58, 102001 (1998). [External LinkDOI], [External LinkADS].
52 Tinto, M., “The Cassini Ka-band gravitational wave experiments”, Class. Quantum Grav., 19, 1767–1773 (2002). [External LinkDOI].
53 Tinto, M. and Armstrong, J. W., “Cancellation of laser noise in an unequal-arm interferometer detector of gravitational radiation”, Phys. Rev. D, 59, 102003 (1999). [External LinkDOI].
54 Tinto, M., Armstrong, J. W. and Estabrook, F. B., “Discriminating a gravitational wave background from instrumental noise in the LISA detector”, Phys. Rev. D, 63, 021101(R) (2001). [External LinkDOI], [External LinkADS].
55 Tinto, M. and Estabrook, F. B., “Parallel beam interferometric detectors of gravitational waves”, Phys. Rev. D, 52, 1749–1754 (1995). [External LinkDOI].
56 Tinto, M., Estabrook, F. B. and Armstrong, J. W., Time-Delay Interferometry and LISA’s Sensitivity to Sinusoidal Gravitational Waves, (JPL / Caltech, Pasadena, CA, 2002). Online version (accessed 1 November 2013):
External Link
57 Tinto, M., Estabrook, F. B. and Armstrong, J. W., “Time-delay interferometry for LISA”, Phys. Rev. D, 65, 082003 (2002). [External LinkDOI], [External LinkADS].
58 Tinto, M., Estabrook, F. B. and Armstrong, J. W., “Time-delay interferometry with moving spacecraft arrays”, Phys. Rev. D, 69, 082001 (2004). [External LinkDOI].
59 Tinto, M., Shaddock, D. A., Sylvestre, J. and Armstrong, J. W., “Implementation of time-delay interferometry for LISA”, Phys. Rev. D, 67, 122003 (2003). [External LinkDOI].
60 Tinto, M., Vallisneri, M. and Armstrong, J. W., “Time-delay interferometric ranging for space-borne gravitational-wave detectors”, Phys. Rev. D, 71, 041101 (2005). [External LinkDOI].
61 Vallisneri, M., “Geometric time delay interferometry”, Phys. Rev. D, 72, 042003 (2005). [External LinkDOI], [External LinkADS], [External LinkarXiv:gr-qc/0504145 [gr-qc]].
62 Vallisneri, M., Crowder, J. and Tinto, M., “Sensitivity and parameter-estimation precision for alternate LISA configurations”, Class. Quantum Grav., 25, 065005 (2008). [External LinkDOI], [External LinkADS], [External LinkarXiv:0710.4369].
63 Wang, C., FPGA-based, 4-channel, High-speed Phasemeter for Heterodyne Interferometry, Master’s thesis, (University of Rochester, Rochester, NY, 2013). Online version (accessed 25 February 2014):
External Link
64 Wang, Y., Heinzel, G. and Danzmann, K., “The first stage of LISA data processing: clock synchronization and arm-length determination via a hybrid-extended Kalman filter”, arXiv, e-print, (2014). [External LinkADS], [External LinkarXiv:1402.6222 [gr-qc]].
65 Wolfram, S., “Wolfram Mathematica”, institutional homepage, Wolfram Research, Inc. URL (accessed 26 February 2014):
External Link