  Pre- and post-selected (PPS) measurement, especially the weak PPS
measurement, is a useful protocol for amplifying small physical parameters.
However, it is difficult to retain both the attainable highest measurement
sensitivity and precision with the increase of the parameter to be measured.
Here, a modulated PPS measurement scheme based on coupling-strength-dependent
modulation is presented with the highest sensitivity and precision retained for
an arbitrary coupling strength. This idea is demonstrated by comparing the
modulated PPS measurement scheme with standard PPS measurementv scheme,
respectively, in the cases of balanced pointer and unbalanced pointer. By using
the Fisher information metric, we derive the optimal pre- and post-selected
states, as well as the optimal coupling-strength-dependent modulation without
any restriction on the coupling strength. We also give the specific strategy of
performing the modulated PPS measurement scheme, which may promote practical
application of this scheme in precision metrology.
