(ed.). Gravitational waves (IOP, 2001)(422s).

Description of the LISA mission 123nearly free, except for small differential applied forces on the two test masses ina given spacecraft that are necessary to compensate for the difference in spuriousforces on them at dc and at frequencies below the useful measurement band.Because of the up to 1% difference in arm lengths expected, the phasenoise in the master laser has to be corrected for too high accuracy. The originalsuggestion that this was possible was made by Faller in the abstract for a 1981conference [3]. The basic idea is to use the apparent changes in the sum ofthe lengths of the two arms to estimate the laser phase noise, and then to applythe corresponding correction to the measured difference in the arm lengths.Approximate algorithms for doing this were published by Giampieri et al in1996 [12]. More recently, Armstrong, Tinto and Estabrook [13, 14] have givenwhat are believed to be rigorously correct algorithims, and it is planned to usethese during the LISA mission.So far, only the use of the signals from the two detectors on SC-1 has beendiscussed. In addition, the signal from one of the detectors on each of SC-2 andSC-3 is used to phase lock a laser to the received laser beam from SC-1. So thesignals measured on SC-2 and SC-3 from the beams sent between them can becombined to give the changes in length of the third arm. As discussed by Cutler[15], the length of the third arm minus the average of the lengths of the othertwo is an observable that gives the other polarization from the one determined bythe difference in lengths of the first two. Thus, having the measurements overthe third arm gives a valuable addition to the scientific information that can beobtained from a mission like LISA.In the recent papers of Armstrong, Tinto and Estabrook [13,14], the analysisis done in a way that assumes all the lasers are running independently, presumablystabilized by locking to their own stable reference cavities, but not locked toeach other. This appears to put some additional requirements on the missionmeasurement system, but they point out that there is additional information inthe resulting signals at the shorter gravitational wavelengths that is not availablewith the current baseline measurement system. It appears that this may beequivalent to the information that would be obtained from running LISA as aSagnac interferometer, but this possibility has not yet been considered in detail.In addition to providing the second polarization if all is going well, havingthe capability of making measurements over the third arm has another veryimportant benefit for the LISA mission. With two fully functional opticalassemblies on each of the three spacecraft, if something in one of the six were notoperating properly, the antenna would still provide two-arm gravitational-wavedata with the full planned sensitivity. Even if a second optical assembly were outof operation, provided the two were not on the same spacecraft, the two-arm datacould still be obtained. Thus, the third arm capability provides an essential levelof redundancy for the mission.In addition to the shot noise in the photocurrents from the received laserbeams, other noise sources in measuring changes in the arm length differencesalso have to be considered. One such source is fluctuations in the attitude of