A photonic implementation of a wavelength meter typically applies an interferometer to measure the frequency-dependent phase shift provided by an optical delay line. This work shows that the information to be retrieved is encoded by a vector restricted to a circular cone within a 3D Cartesian object space. The measured data belong to the image of the object space under a linear orthogonal map. Component impairments result in broken orthogonal symmetry, but the mapping remains linear. The circular cone is retained as the object space, which suggests that the conventional conic section fitting for the wavelength meter application is a premature reduction of the object space from R3 to R2. The inverse map, constructed by a learning algorithm, compensates impairments such as source intensity fluctuation and errors in delay time, coupler transmission, and photoreceiver sensitivity while being robust to noise. The simple algorithm does not require initial estimates for all parameters except for a broad bracket of the delay; further, weak nonlinearity introduced by uncertain delay can be corrected by a robust golden search algorithm. The phase-retrieval process is invariant to source power and its fluctuation. Simulations demonstrate that, to the extent that the ten parameters of the interferometer model capture all significant impairments, a precision limited only by the level of random noise is attainable. Applied to measured data collected from a fabricated Si3N4 wavelength meter, greater than an order of magnitude improvement in precision compared with the conventional method is achieved.