Optimization Of Molecular Imaging Method Based On Photoelectron Diffraction

Ultrafast and precise imaging of gas molecules is a desired and difficult task in the exploration of the structure of matter.It is also important for studying basic problems in physics,chemistry,biomedicine,and other fields.Due to the low molecular density of gas,in order to obtain sufficient signals,the laser must have a very high photon number density and a high signal yield of light and molecules.With the development of the new generation of X-ray free electron laser(XFEL)technology,one can make a beam of electrons moving near the speed of light passing through a row of magnets that periodically change direction,that is,an undulator,to produce a 10 fs pulse duration,including 1013 coherent photon ultra-strong and ultra-short laser.Using photoelectron diffraction,we can obtain diffraction signals that are 5-6 orders of magnitude higher than photon diffraction.Therefore,by studying the photoelectron diffraction signals excited by X-ray free electron lasers,we have the opportunity to do ultrafast imaging of gas molecules.Photoelectron diffraction is the process by which electrons first absorb photons to get excited,and then diffract.Depending on whether the electron wave packet is scattered by surrounding atoms during the propagation process,we divide the electron wave packet into unscattered direct waves and scattered waves.The final photoelectron diffraction spectrum is the result of the interference between direct waves and scattered waves.If the phase difference between the two waves can be analyzed from the photoelectron diffraction spectrum,the position of the atoms that scatter electrons can be deduced.We use a scattering factor to describe the effect on wave scattering.Unlike the scattering of photons,atomic scattering of electrons will cause the phase of the electron wave to change,that is,the atomic scattering factor of electrons has a significant phase.If we use the Helmholtz-Kirchhoff transform(HK transform)to analyze the phase in the photoelectron spectrum,the phase in the electron scattering factor becomes an additional position error.Therefore,our solution is to first use known information to simulate an electron scattering factor,and then remove the theoretically calculated scattering factor from the photoelectron diffraction spectrum to eliminate the error caused by the phase of the term.In the calculations,we first use a muffin-tin model to calculate the scattering factor of atoms,and then obtain the photoelectron diffraction spectrum of the molecules with fixed orientation.As for the photoelectron diffraction spectrum,the result of the general HK transformation will have a large position error.If the electron scattering factor is removed from the photoelectron diffraction spectrum and then HK transform is performed,the atomic position can be accurately inferred.For other algorithms,such as the photoelectron diffraction spectrum calculated by ePolyScat,our scheme will still have accurate results.Finally,we analyze the situation of different polarization directions,and consider the results of using circularly polarized light excitation,which fully demonstrates that after removing the scattering factor from the photoelectron diffraction spectrum,and then using the HK transform,the atom position information can be better obtained.Then we considered the effect of molecular alignment on our optimization scheme.First,we calculated the photoelectron diffraction spectra of iodine molecules under different alignment degrees,and then analyzed them by the optimized HK transform.The simulation results show that as the degree of alignment decreases,the atomic position error given by the optimized HK transform starts to become larger.Only in the case of extremely high degree of alignment can the atom position be better positioned.