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Elongated microvoids, internal fibrillar structure, and edge scattering from both surface refraction cause an equatorial streak in small angle X-ray scattering. A model for analyzing the edge scattering of fibers is proposed. Simulation results indicate that the intensity of edge scattering from surface refraction of a cylindrical fiber is strong and makes an important contribution to the equatorial streak. Two factors influence edge scattering intensity. One is the sample-to-detector distance (D); edge scattering intensity increases with increasing D. The equatorial streak becomes weak when D is shortened. The other factor is the refraction index. Edge scattering intensity increases as the real component of the refraction index decreases. In experiment, weak or even no equatorial streaks were found for samples measured in a roughly index-matching fluid. Edge scattering can be eliminated or weakened, and it can be calculated by comparing the intensities of a cylindrical fiber when it is measured in air and in index-matching fluid. The simulation data are basically in agreement with the experimental data. [ABSTRACT FROM AUTHOR]