  In this work, we discuss two phase-measurement methods for the Mach-Zehnder
interferometer (MZI) in the presence of internal losses and give the
corresponding optimum conditions. We find theoretically that when the core
parameters (reflectivities, phase difference) are optimized, the phase
sensitivity of the two methods can reach a generalized bound on precision:
standard interferometric limit (SIL). In the experiment, we design an MZI with
adjustable beam splitting ratios and losses to verify phase sensitivity
optimization. The sensitivity improvements at loss rates from 0.4 to 0.998 are
demonstrated based on difference-intensity detection, matching the theoretical
results well. With a loss up to 0.998 in one arm, we achieve a sensitivity
improvement of 2.5 dB by optimizing reflectivity, which equates to a 5.5 dB
sensitivity improvement in single-intensity detection. Such optimal phase
measurement methods provide practical solutions for the correct use of
resources in lossy interferometry.
