  A weak value is an effective description of the influence of a pre and
post-selected 'principal' system on another 'meter' system to which it is
weakly coupled. Weak values can describe anomalously large deflections of the
meter, and deflections in otherwise unperturbed variables: this motivates
investigation of the potential benefits of the protocol in precision metrology.
We present a visual interpretation of weak value experiments in phase space,
enabling an evaluation of the effects of three types of detector noise as
'Fisher information efficiency' functions. These functions depend on the
marginal distribution of the Wigner function of the meter, and give a unified
view of the weak value protocol as a way of protecting Fisher information from
detector imperfections. This approach explains why weak value techniques are
more effective for avoiding detector saturation than for mitigating detector
jitter or pixelation.
