Fundamental Limitations of Absolute Ranging via Deep Frequency Modulation Interferometry

Deep frequency modulation interferometry (DFMI) resolves phase ambiguity in absolute distance measurements by jointly estimating two length-encoding parameters: the coarse and unambiguous effective modulation depth ($m$), and the fine but ambiguous interferometric phase ($\phi$). We establish a comprehensive framework quantifying the fundamental precision limits and practical accuracy constraints of this technique. A Fisher-information analysis defines the intrinsic estimator precision for $m$ and $\phi$, while the contribution of carrier frequency drift introduces an additional, time-dependent source of random error. Numerical simulations reveal a structured error landscape with previously unrecognized ``valleys of robustness,'' where systematic biases from common hardware imperfections are suppressed by orders of magnitude. An analytical model based on signal orthogonality explains their origin and predicts their locations. The results yield a consolidated error budget accounting for both random and systematic errors, providing a quantitative design paradigm for absolute length metrology via DFMI.