The physical significance of the mixed dynamic form factor

Plasmon holographic experiments: theoretical framework

“…[6]) which describes the propagation of quasi monochromatic partially coherent waves through an optical system. The inelastic interaction with the object is taken into account using the mixed dynamic form factor [7] which received quite some attention recently [8][9][10][11][12].…”

“…Note that coherence can be measured with a 2 slit experiment but its value is dependent on the plane in which the experiment is performed. Coherence is not a physical quantity of a whole system [9] (e.g., coherence in the diffraction plane can be quite different from coherence in the image plane). A propagation formula exists relating the knowledge of the mutual intensity J 0 ðr 0 ; r 0 0 Þ in one plane with the mutual intensity J 1 ðr 1 ; r 0 1 Þ in another plane if the transmission coefficients between points in the two planes are known [6] …”

“…The MDOS describes the interaction with the sample by a transmission function between two incoming and two outgoing wavevectors k i ; This is similar to light of a star that can be partially coherent when seen through a telescope even when the light escaping from the star is definitely incoherent, the size of the star and the diameter of the telescope determine together whether the image of the star will be incoherent or partially coherent [6]. scattering amplitude only depends on the momentum transfer q ¼ k i À k o ; q 0 ¼ k 0 i À k 0 o and not on the orientation of the incoming wavevectors with respect to the sample (assume a symmetric sample) we have a simple relationship with the mixed dynamic form factor (MDFF) [5,7,9,10].…”

“…with K 0 the modified Bessel function of the second kind of zeroth order [13] (See also Appendix B of [9] which has a solution for the same integrals in a slightly different physical context). This result can be interpreted as follows: the chance for exciting a plasmon in the sample is independent on where you are in the sample (diagonal element is independent of r, plasmon is completely delocalised), and the coherence between two points only depends on the distance between these points (T is only dependent on jr À r 0 j).…”

Comment on “Experimental and theoretical evidence for the magic angle in transmission electron energy loss spectroscopy” by H. Daniels, A. Brown, A. Scott, T. Nichells, B. Rand and R. Brydson

“…What remains is the discrepancy to the experimental results which suggest a value close to 2y E : We envisage several possibilities in order to explain the disagreement: some hidden isotropic contribution to the spectra (such as superpositions of spectra from thermal diffuse or Bragg scattering), dynamical diffraction effects which can be important, close to a zone axis or a systematic row orientation [4]), or the breakdown of the atomic model for graphite (the p n peak has oscillator strength in the s n energy region). Finally, the possibility of non-dipole contributions should be considered.…”