LISA will not only be the worlds largest interferometer, it will be the laser interferometer with the world's largest arm length difference. This arm length difference presents one of the most challenging problems of LISA. Fluctuations in the laser frequency in a standard Michelson interferometer scale with the arm length difference and produce a noise background, which could limit the sensitivity of the interferometer. A direct Michelson interferometer type measurement would require a frequency stability proportional to the frequency of the used laser field and the ratio between required displacement sensitivity and arm length difference.

The arm length of the equivalent LISA interferometer will have a length difference of up to 50.000 km, the laser frequency is about 300 THz, and the required sensitivity is 10pm. This would call for a frequency stability of the order of a few uHz.

Ultra-stable frequency stabilization systems use the length of an ultra-low expansion (ULE) glass rod as their frequency reference. The material has a thermal expansion coefficient of ~ 1E-8/K. Laboratories like the LISA lab at Goddard Space Flight Center or at the Joint Institute for Laboratory Astrophysics have succeeded in generating environments with sub micro Kelvin temperature fluctuations (see Material Studies). This has reduced the laser frequency noise into the Hz range. It is expected that the temperature fluctuations on the LISA spacecraft will be in the same range and that the laser frequency noise in LISA will also reach the Hz range. The remaining noise would be about 6 orders of magnitude above the required noise level for a direct Michelson interferometer type measurement.

Several solutions to this apparent discrepancy were proposed. The most favored solution uses a technique called time delay interferometry (TDI) to create an artifical equal arm length Michelson interferometer. It detects fluctuations in the two arms of the interferometer independently from each other and then forms linear combinations between the instantaneous signals and earlier measured (time delayed) signals. This linear combination will be insensitive to laser frequency noise just like the interferometer signal of an equal arm length Michelson interferometer.

Arm locking is another discussed solution. The idea is to use the arms of the LISA interferometer as the reference for the laser frequency and stabilize or lock the laser frequency to this reference. This elegant solution has the disadvantage that the long light travel time between the spacecraft put severe constrains on the feedback loop and it is unlikely that the loop will have enough gain to suppress the entire laser frequency noise. However, a partial suppression of the laser frequency noise could significantly reduce the very tight requirements on TDI.

A full test of TDI or arm locking depends on our ability to simulate the long light travel time between the LISA spacecraft. Until recently, it was assumed that this was impossible and that experimental tests could only be performed on the subsystem level and that only simulations can bridge the gap to the final instrument. However, our group succeeded to develop a light travel time simulator: the Electronic Phase Delay technique. We are now on our way to test all TDI and arm locking in a realistic LISA like interferometer configuration.