  Programmable linear optical interferometers are important for classical and
quantum information technologies, as well as for building hardware-accelerated
artificial neural networks. Recent results showed the possibility of
constructing optical interferometers that could implement arbitrary
transformations of input fields even in the case of high manufacturing errors.
The building of detailed models of such devices drastically increases the
efficiency of their practical use. The integral design of interferometers
complicates its reconstruction since the internal elements are hard to address.
This problem can be approached by using optimization algorithms [Opt. Express
29, 38429 (2021)]. In this paper, we present a novel efficient algorithm based
on linear algebra only, which does not use computationally expensive
optimization procedures. We show that this approach makes it possible to
perform fast and accurate characterization of high-dimensional programmable
integrated interferometers. Moreover, the method provides access to the
physical characteristics of individual interferometer layers.

Optics;Quantum Physics