Coherence properties of the radiation from X-ray free electron laser

We present a comprehensive analysis of coherence properties of the radiation from X-ray free electron laser (XFEL). We consider practically important case when XFEL is optimized for maximum gain. Such an optimization allows to reduce significantly parameter space. Application of similarity techniques to the results of numerical simulations allows to present all output characteristics of the optimized XFEL as functions of the only parameter, ratio of the emittance to the radiation wavelength, . Our studies show that optimum performance of the XFEL in terms of transverse coherence is achieved at the value of the parameter of about unity. At smaller values of the degree of transverse coherence is reduced due to strong influence of poor longitudinal coherence on a transverse one. At large values of the emittance the degree of transverse coherence degrades due to poor mode selection. Comparative analysis of existing XFEL projects, European XFEL, LCLS, and SCSS is presented as well.     

Height distribution on a rough plane and specularly diffracted light amplitude are Fourier transform pair

In this report we show that the amplitude of specularly diffracted light from a plane rough surface as a function of incident angle cosine is Fourier transform of the height distribution on the surface. Therefore, an even height distribution function, which is the case for many rough surfaces, can be obtained by measuring the specularly diffracted light intensities. Also, it is observed that for polychromatic illumination the spectrum of the specularly diffracted light is modified and the modification depends on roughness, incident angle, and wavelength. It is also shown that, for a fixed incident angle, the height distribution on the rough plane is Fourier transform of the spectral modifying function. Experimental studies on some surfaces of different roughnesses, prepared by grinding sheet-glasses by powders of different grain sizes, show that the corresponding height distributions are Gaussian and the rms heights obtained by the two approaches are quite consistent.