Abstract: The speckle fields and their phase singularities produced respectively by the square loop aperture and circular ring aperture are studied. It is found that the zero-contour of the real and imaginary parts occurs in the complicated tangential and intersectional situations. The tangential and intersectional points can also form phase singularities, around which the phase distribution shows the characteristics of symmetry and discontinuity，which differs from the spiral distribution around the traditional singular points formed by the zero crossings of the real and imaginary parts. The speckle particle distributions in the speckle fields produced by the square loop aperture and circular ring aperture is different from those by the traditional square aperture, and the speckle particle distributions are modulated by the scattering aperture, in stripes of horizontal or vertical outlines and circular outlines respectively. In addition, an interesting phenomenon occurs that a lot of disc-like dark regions appear in the intensity pattern of the speckle fields. We call it “light intensity dark nucleus”, whose center corresponds to a vortex with homogeneous phase distribution.

Keywords: 
• speckle fields /
• phase singularity /
• interference field