Research And Application On The Propagation Of Partially Coherent Light In Synchrotron Beamlines

Coherence optics become more and more important since the third-generation synchrotron radiation facilities and the x-ray free-electron lasers have been developed rapidly around the world.The x-ray with good coherence expands new insights in many fields including biology,particle physics and condensed matter physics.Coherent light is important in many x-ray technologies,such as x-ray photon correlation spectroscopy,x-ray interference lithography,x-ray holography and coherent x-ray diffraction imaging,etc.It is necessary to analyze the coherence property propagation through beamlines since high coherence beamlines has been designed and constructed.Based on statistical optics,Mutual Optical Intensity(MOI),is applied to describe the wavefront of the partially coherent light,a new model is established to analyze the partial coherence in synchrotron beamlines.The wavefront is separated into many elements.It is assumed that in every element the beam has full coherence and constant complex amplitude,which is reasonable as long as the dimension of element is much smaller than the coherent length and beam spot size.Second,the propagation of MOI for every element can be calculated with Fraunhofer or Fresnel approximations.Finally,the total MOI after propagation can be obtained from sum of the contribution of all elements.The propagation of the MOI from the incident to the exit plane of the mirror is realized by local ray tracing.The effects of figure errors can be expressed as phase shifts obtained by either the phase projection approach or the direct path length method.The MOI model is extended to include the propagation of partially coherent radiation through non-ideal mirrors.By consideration of the phase shift and the amplitude attenuation induced by the diffraction grating,the MOI model is developed to analyse EUV-IL with partially coherent lightWe analyzed the MOI propagation through the STXM beamline and got the MOI of the beam at the endstation with the established model.An experiment of single window diffraction was performed to measure the beam size and coherence length at the endstation for comparison with the theoretical results.The experimental results have a good agreement with the theoretical ones.It indicates that the model is applicable in the analysis of partial coherence propagation in soft x-ray beamlines.We analyzed MOI propagation through non-ideal mirrors.The MOI model is benchmarked against SRW and HYBRID.The MOI model is extended to the simulation of the interference pattern produced by extreme ultraviolet lithography with partially coherent light.The fringe intensity profiles at the exposure area are calculated using the MOI model at different coherence conditions,including the coherence length,the photonstop size and the propagation distance.The profiles show that the fringe intensities are not uniform but have envelope lines much like Fresnel diffraction within the exposure area,which is explained by diffraction from the finite grating modelled as a single aperture.Despite the intensity oscillations,the pattern period and fringe visibility remain constant within the whole exposure area.The MOI model is benchmarked against the RCWA algorithm and used to determine the diffraction efficiency of phase gratings composed of various materials and thicknesses.The MOI model was used to analyze partially coherent light propagation through synchrotron beamlines,including STXM beamline,XIL beamline,MX beamline and FEL-SASE beamline at SSRF,and In-Situ Nanoprobe at APS,etc.The MOI model can provide accurate results in different coherence conditions.Since the full MOI is stored at any calculation plane,sequential simulation of beamline optics can be realised.Furthermore,the accuracy and efficiency of the MOI model can be balanced by simply changing the number of elements within the wavefront.These merits make the MOI model an ideal tool for advanced beamline simulation,especially for beamlines that rely on the coherence properties of the beam.