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Akira Tonomura used electron holography to test the Aharonov-Bohm effect with magnetic flux confined away from the electron paths. A coated magnetic toroid let electron waves pass through its hole and outside it while a superconducting shield excluded the magnetic field from those paths. The measured relative phase still depended on the enclosed flux. The experiment isolates a quantum phase effect that cannot be inferred from the local classical magnetic force along either path.^[ref]

A physicist who developed electron holography and investigated the Aharonov-Bohm effect.^[ref]

An electron biprism uses the electric field around a biased fine wire to overlap coherent electron waves for interference. It provides object–reference overlap in electron holography.^[ref]

Electron holography uses electron object and reference waves to encode their relative wave phase in a hologram.^[ref]

Hiroji Yamada coauthored an Aharonov-Bohm effect experiment using electron holography. Electron paths passing through and outside a coated toroid acquired a relative phase shift even though superconductivity confined the magnetic flux away from the electron paths.^[ref]

Junji Endo coauthored an Aharonov-Bohm effect experiment using electron holography. Electron paths passing through and outside a coated toroid acquired a relative phase shift even though superconductivity confined the magnetic flux away from the electron paths.^[ref]

Nobuyuki Osakabe coauthored an Aharonov-Bohm effect experiment using electron holography. Electron paths passing through and outside a coated toroid acquired a relative phase shift even though superconductivity confined the magnetic flux away from the electron paths.^[ref]

In the magnetic Aharonov-Bohm effect, coherent electron paths enclose inaccessible magnetic flux even though the field vanishes along the paths. The magnetic vector potential contributes relative phaseRecombination turns this phase into a fringe displacement. For an electron $q=-e$, changing flux by $h/e$ gives one full fringe period. Reversing the loop orientation reverses the phase sign. A gauge change modifies each path's phase convention but leaves the closed-loop phase and observed interference unchanged. The accessible region surrounds excluded flux, so a globally trivial gauge cannot remove that phase.

A shielded toroidal magnet provides a concrete test: electron holography compared waves passing through its hole and outside it. Superconducting and copper coatings confined the field and excluded electrons from the magnet; the measured relative phase tested enclosed flux rather than a classical Lorentz deflection along the paths.^[ref]

In 1986, Akira Tonomura and collaborators coated a ferromagnet shaped as a torus with superconducting niobium and copper. A cooled stage held it in a 150 kV field-emission electron microscope. An electron biprism overlapped object and reference waves; film holograms were reconstructed optically. Room-temperature leakage screening selected samples; varying copper thickness tested electron penetration.^[ref]

Below the superconducting transition, through-hole and outside electron waves differed in wave phase by zero or $\pi$ modulo $2\pi$. Warming through it changed the interference reversibly. Leakage and coherent-penetration bounds do not prove zero magnetic field.^[ref]

Why these two phases? The shield's superconducting flux quantum is $h/(2e)$, whereas the probing electron has electric charge $-e$. Substituting $\Phi =Nh/(2e)$ givesAn odd $N$ therefore moves a carrier fringe by half its spacing; an even $N$ leaves it unchanged modulo a full spacing. The phase quantization provides an internal check on the superconducting enclosure. It does not mean that zero wave phase proves zero trapped magnetic flux.^[ref]

The readout is electron holography in the off-axis holography geometry: a known tilted reference converts an unknown relative wave phase into a spatial carrier displacement. Reconstructing a magnetic wave phase assumes stable reference phase, adequate coherence and a calibrated carrier; electrostatic charging and material traversal can also shift wave phase. Optical wave phase amplification rescales the displayed fringe displacement. The experiment's shielding and comparison tests support the magnetic inference; an interferogram by itself measures the total relative wave phase, rather than separately certifying every contribution. The ideal field-free model describes the limiting geometry, while finite leakage and penetration remain questions of experimental bounds.

Shinichiro Yano coauthored an Aharonov-Bohm effect experiment using electron holography. Electron paths passing through and outside a coated toroid acquired a relative phase shift even though superconductivity confined the magnetic flux away from the electron paths.^[ref]

Takeshi Kawasaki coauthored an Aharonov-Bohm effect experiment using electron holography. Electron paths passing through and outside a coated toroid acquired a relative phase shift even though superconductivity confined the magnetic flux away from the electron paths.^[ref]

Tsuyoshi Matsuda coauthored an Aharonov-Bohm effect experiment using electron holography. Electron paths passing through and outside a coated toroid acquired a relative phase shift even though superconductivity confined the magnetic flux away from the electron paths.^[ref]