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01:01:34 Linear Imaging Theory Linear Imaging Theory	Linear Imaging Theory 2017 PARADIM Linear Imaging Theory Robert Hovden d.n.a. dark field aperture size object function total intensity collaboration increases concepts in physics convergence angle area spherical aberration wide range covering today geometric shapes d.n.a. structure central minimum electron microscopy focal point intensity increases linear imaging model wave vectors control theory optical devices collection angle larger aperture electron microscope high angle architectural elements signal processing photography high pass filter transfer function uncorrected system phase shift darkfield regime functional form scattered electrons higher frequency bright field stem egyptian artefact types diffraction pattern science of photography point spread function high intensity probe elementary geometry integrals spatial frequency optics objective lens bright field regime bright spots real space low frequency reciprocal space blurring contribution sphere collaboration uncorrected instrument characteristic dimension incoherent imaging condition surfaces aperture function wave front atomic physics imaging mode contract transfer function white noise scanning transmission electron cohere imaging previous lecture distant plane elementary shapes stem higher angles high resolution incoherent linear image mil rating detector geometries field cone geometry types of functions aberration corrected constant phase length lower frequencies chromatic aberration conic sections amplitude squared aberration free scientific techniques microscopes measuring instruments intensity squared optic axis intensity decreases contrast transfer diffraction limit stem image individual atom radio spectrum incoherent imaging quantum mechanics aberration free probe multivariable calculus people meters focal plane bright field low angle amateur radio systems theory image plane coherent imaging condition collecting electrons blurring function transmission electron microscopy physical quantities digital photography angular spread double integral coherent imaging largest range face shift higher order aberrations raleigh criterion pio fairly interpretable transmission electron microscope square pulse geometrical optics digital signal processing 1st order caption complete probe tails nyquist limit blue curve subroutines broadcasting filter frequency response maximum frequency high frequency caustic curve hand side low pass filter spatial coordinates atoms closer coherent image sparrow criterion structural system pico meter dark background frequency space optimal aperture t.m. complex conjugate contrast transfer function wave function measure ultimately imaging condition annular darkfield incoherent imaging mode atomic number field stem atomic column inelastic interactions nobel prize angle medium chemistry focal imaging probe size From James Overhiser on February 15th, 2019 36 plays