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The transverse focusing properties at the ‘pseudo-focal’ plane of coherent Bessel beams with angular momentum are analyzed in detail. The transverse magnification of the central dark region of Bessel beams at this pseudo-focal plane is derived for the first time by calculating the ratio of the magnitude of the transverse components of the corresponding wave vectors before and after the focusing lens. We test our results experimentally with coherent laser Bessel beams and excellent agreement is observed. Then, an LED light source is used to generate Bessel beams. By modifying the coherence of the LED light source, we observe that by reducing coherence a smaller and shallower central dark region of Bessel beams with angular momentum is produced at the pseudo-focal plane. This technique can be used as a method to characterize the degree of coherence of vortex beams. [ABSTRACT FROM AUTHOR]

The Fresnel diffraction of an aperture with a rough edge is studied in this paper. Circular and elliptical apertures with sinusoidal and random edges are chosen as examples to investigate the influence of the aperture edge on the diffraction. The numerical calculation results indicate intuitively the variations of the transverse and longitude diffraction intensity distributions with the edge parameters of the aperture. The data files of aperture models are obtained through the numerical calculations, and the aperture samples are obtained with the help of a liquid crystal light modulator (LCLM). Thus, the practical experiments of the diffractions of apertures with rough edges are carried out. The measured results are consistent with the calculated ones. The approximate analytic expressions of the diffraction by the modified aperture are deduced on the basis of the Fresnel diffraction theory and the statistic optics, and the reasonable explanations for the influence of edge parameters on the diffraction are given through the theoretical analysis. [ABSTRACT FROM AUTHOR]