Fraunhofer pattern of a Josephson junction ($I_c(\Phi )=I_c(0)|\sin (\pi \Phi /{\Phi }_0)/(\pi \Phi /{\Phi }_0)|$)

A spatially uniform Josephson junction in a uniform transverse in-plane magnetic field has a linear gauge-invariant phase profile across its width. Integrating its sinusoidal local current-phase relation of a superconducting weak link gives a signed sinc coefficient multiplying the sine of the central phase. Maximizing over that phase gives the displayed nonnegative critical-current envelope. Zeros occur at nonzero integer multiples of the superconducting flux quantum. The relevant magnetic thickness includes electrode penetration when appreciable, and self-fields or nonuniform local critical current density alter the simple pattern.