1 / 5

Inversion ?

multi-slice inversion (vanDyck,Griblyuk,Lentzen) Pade-inversion (Spence) local linearization. deviations from reference structures: displacement field (Head) algebraic discretization. parameter & potential. Inversion ?. atomic displacements. exit object wave.

arien
Download Presentation

Inversion ?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. multi-slice inversion (vanDyck,Griblyuk,Lentzen) Pade-inversion (Spence) local linearization deviations from reference structures: displacement field (Head) algebraic discretization parameter & potential Inversion ? atomic displacements exit object wave no iteration same ambiguities additional instabilities direct interpretation by data reduction: Fourier filtering QUANTITEM Fuzzy & Neuro-Net Srain analysis image reference beam (holography) defocus series Gerchberg-Saxton (Jansson)

  2. Data lost?Additional data? phases linearity reference beam defocus series Scattering process Imaging process lattices & bonds shape & orientation displacement field inelastic spectra 3d-2d projection atom positions

  3. regularization physically motivated Assumption: complex amplitudes are regular Cauchy relations: Ja/Jx = a.Jf/Jy Ja/Jy = -a.Jf/Jx Linear inversion: t(x+1,y)-2t(x,y)+t(x-1,y)=0 t(x,y+1)-2t(x,y)+t(x,y-1)=0

  4. Direct & Inverse: black box gedankenexperiment thickness local orientation structure & defects composition microscope g output f input operator A wave image theory, hypothesis, model of scattering and imaging if unique & stable inverse A-1 exists ill-posed & insufficient data => least square direct: g=A<f experiment, measurement invers 1.kind: f=A-1<g parameter determination invers 2.kind: A=g$f -1 identification, interpretation a priori knowledge intuition & induction additional data

  5. perfect crystal: f = e2piAt fo distorted object: Jf/Jz= pi(sA+Dxy+b) f f, Jf/Jz continuous at boundaries b = J(gu)/Jz displacement field J(ff*)/Jz = e-pmt energy conservation fo fo fg i,j-1 i,j i,j+1 i-1,j forward wave equation =>f(i+1,j) backward energy conservation =>b(i-1,j) i+1,j i,j-1 i,j i,j+1 solve equations of perfect crystal, discretize wave equations and boundary conditions =>algebraic equation system of f, b at all nodes (i,j,k) and SQge2pigu(i,j,k) = 0

More Related