  Diverse applications in photonics and microwave engineering require a means
of measurement of the instantaneous frequency of a signal. A photonic
implementation typically applies an interferometer equipped with three or more
output ports to measure the frequency dependent phase shift provided by an
optical delay line. The components constituting the interferometer are prone to
impairments which results in erroneous measurements. It is shown that the
information to be retrieved is encoded by a three-component vector that lies on
a circular cone within a three-dimensional Cartesian object space. The measured
data belongs to the image of the object space under a linear map that describes
the action of the interferometer. Assisted by a learning algorithm, an inverse
map from the image space into the object space is constructed. The inverse map
compensates for a variety of impairments while being robust to noise.
Simulation results demonstrate that, to the extent the interferometer model
captures all significant impairments, a precision limited only by the level of
random noise is attainable. A wavelength meter architecture is fabricated on
Si3N4 photonic integration platform to prove the method experimentally. Applied
to the measured data, greater than an order of magnitude improvement in
precision is achieved by the proposed method compared to the conventional
method.
