We develop a finite-distance framework for vacuum birefringence in static, spherically symmetric spacetimes threaded by strong magnetic fields. In the geometric optics limit of nonlinear electrodynamics, the two photon polarizations propagate along null geodesics of distinct effective (optical) metrics. Using a controlled weak-coupling expansion, we isolate the polarization dependent correction to the standard gravitational deflection and obtain a general expression for the differential bending angle Δα ≡ α + − α − . with the source and observer at arbitrary radii. The derivation is based on a finite-distance Gauss-Bonnet construction on the polarization dependent optical manifolds, thereby extending the usual scattering at infinity treatment. As an examples, we apply the formalism to Euler-Heisenberg QED and to Born-Infeld electrodynamics, the latter providing a non-birefringent consistency check with Δα BI = 0. We show that finite-distance truncation of the curvature flux generically suppresses the observable birefringence and provide explicit series corrections suitable for data analysis. For magnetar motivated field falloff and near surface emission, the suppression can reach the level of tens of percent and may approach ~ 1/2 for near-limb, outward only trajectories. These results supply an essential finite-distance calibration for interpreting X-ray polarimetry measurements and for placing unbiased constraints on strong-field QED and broader NLED parameters.
Ovgun et al. (2026) studied this question.