  We propose a numerical interferometry method for identification of optical
multiply-scattering systems when only intensity can be measured. Our method
simplifies the calibration of optical transmission matrices from a quadratic to
a linear inverse problem by first recovering the phase of the measurements. We
show that by carefully designing the probing signals, measurement phase
retrieval amounts to a distance geometry problem---a multilateration---in the
complex plane. Since multilateration can be formulated as a small linear system
which is the same for entire rows of the transmission matrix, the phases can be
retrieved very efficiently. To speed up the subsequent estimation of
transmission matrices, we design calibration signals so as to take advantage of
the fast Fourier transform, achieving a numerical complexity almost linear in
the number of transmission matrix entries. We run experiments on real optical
hardware and use the numerically computed transmission matrix to recover an
unseen image behind a scattering medium. Where the previous state-of-the-art
method reports hours to compute the transmission matrix on a GPU, our method
takes only a few minutes on a CPU.
