  It is not possible to make measurements of the phase of an optical mode using
linear optics without introducing an extra phase uncertainty. This extra phase
variance is quite large for heterodyne measurements, however it is possible to
reduce it to the theoretical limit of log(n)/(4n^2) using adaptive
measurements. These measurements are quite sensitive to experimental
inaccuracies, especially time delays and inefficient detectors. Here it is
shown that the minimum introduced phase variance when there is a time delay of
tau is tau/(8n). This result is verified numerically, showing that the phase
variance introduced approaches this limit for most of the adaptive schemes
using the best final phase estimate. The main exception is the adaptive mark II
scheme with simplified feedback, which is extremely sensitive to time delays.
The extra phase variance due to time delays is considered for the mark I case
with simplified feedback, verifying the tau/2 result obtained by Wiseman and
Killip both by a more rigorous analytic technique and numerically.
