  For a HOM interferometer with two independent incident pulses, the
interference pattern can be affected by adding a dispersion medium on one of
the incident directions, but there hasn't been a method to reconstruct the
phase constant of the medium from the interference pattern. To solve it, we
adapted two phase retrieval algorithms and used them to recover the phase
difference function between the two incident fields, from which the phase
constant can be derived. Through simulations, we verified the convergence,
accuracy, and robustness of the algorithms, indicating that this phase recovery
process can be completed well with negligible error. Our research finds a new
application direction for the phase recovery algorithm, provides an algorithmic
tool for high-order dispersion measurement using two-photon interference, and
paves the way for a higher resolution and phase-sensitive quantum tomography.
