The resolving power of an electron microscope is determined by the optics and the stability of the instrument. Recently, progress has been obtained towards subångström resolution at beam energies of 80 kV and below but a discrepancy between the expected and achieved instrumental information limit has been observed. Here we show that magnetic field noise from thermally driven currents in the conductive parts of the instrument is the root cause for this hitherto unexplained decoherence phenomenon. We demonstrate that the deleterious effect depends on temperature and at least weakly on the type of material. DOI: 10.1103/PhysRevLett.111.046101 PACS numbers: 68.37.Og, 05.40.Ca, 41.85.Gy During the last 15 years after the introduction of aberration-corrected transmission electron microscopy (TEM) [1,2] the resolving power of the electron microscope could be improved from the Scherzer resolution [3] $100 set by the previously unavoidable spherical aberration of the objective lens C s and the wave length of the electron down to about 25 for beam energies of 60-300 kV [2,[4][5][6][7]. Recently, with the simultaneous correction of the spherical and the chromatic aberration C c , linear contrast transfer for spacings of 80 pm at a beam energy of 80 kV ( ¼ 4:2 pm) could be achieved [8]. The further improvement of the information limit of the TEM has exceptional importance as a driver for atomic-resolution imaging in materials science [9,10] and at even lower energies for light-atom materials sensitive to knock-on damage [11][12][13].The results obtained for the latest C c -and C s -corrected instruments are very convincing. Beyond that it could be demonstrated that the lateral incoherence and focus spread due to residual aberrations and instabilities are so small that a significant better instrumental information limit should be achievable than the one actually observed [8]. Therefore, during the development of new instrumentation we thoroughly analyzed this discrepancy and excluded possible parasitic effects like electronics noise, ac stray fields, higher-order aberrations, Coulomb interaction in the beam, and nonperfect vacuum conditions. However, the observed mismatch did not disappear. Also for the information limit achieved in aberration-corrected Lorentz microscopy [14] with the specimen in the field-free region, we discovered an unexplained discrepancy. By careful measurements of the contrast transfer as a function of the spatial frequency g we found that the mismatch can be described very well by an isotropic contrast envelope function of the form exp½À2ð jgjÞ 2 where is a characteristic image spread [8]. The resulting information limit g il % 1=ð Þ does not depend on the numerical aperture and scales proportional to the electron wavelength (i.e., like a magnetic force) for different beam energies. Hence, we were faced with a coherence loss of unknown reason in the process of image formation.There is a long record of detailed experimental and theoretical investigations of decoherence phenomena in transmission el...