Definitions and statistical characterization of core position errors in multicore fibers

Cross-sectional images of multicore fibers include an arbitrary rotational offset, making core-position errors dependent on the reference-angle definition. This dependence is practically important when specifications or standards impose upper limits, because heavy-tailed definitions can reduce apparent inspection yield through conservative pass/fail decisions. We formulate reference-angle determination as norm minimization after translation to the cladding-center origin, and compare four criteria: L₁, L₂, L₄, and L_∞, which respectively minimize the sum, sum of squares, sum of fourth powers, and maximum of the per-core deviations. Monte Carlo simulations with Gaussian fabrication perturbations and center-localization noise show that L₁ gives the smallest mean but the heaviest upper tail, while L_∞ suppresses extremes but is noise-sensitive. Among the examined criteria, L₄ provides the best balance, combining L_∞-like tail suppression with L₂-like robustness.