A new partially coherent source which can generate a beam field with a ring-shaped twisted array profile is presented, and the distribution characteristics of spectral density and degree of coherence of the field are discussed. It is shown that both the spectral density and degree of coherence will rotate along the propagating direction, but in opposite rotating directions. Furthermore, we find that the distribution properties of the ring-shaped array of the spectral density, including the number of the rings, the number of the lobes of each ring, and the distance of all adjacent lobes, can be properly controlled by adjusting structural parameters of the source.

We introduced a new class of a partially coherent source that can generate a field with a hollow rectangular profile, named the hollow rectangular multi-Gaussian Schell-mode source. The dependence of distribution of far-zone spectral density on the properties of the proposed source was analyzed. The results show that one can control the distribution properties of the far-zone intensity profile, including the thickness of the hollow edge, the shape of the hollow, the size of the hollow, and the orientation of the hollow, by adjusting the corresponding structural parameters of the source.

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In order to control the distribution characteristics of the far-field ring-shaped array, we introduce a new light source to produce adjustable far-field distribution by the method of weight function superposition. It has been shown that, by changing the parameters of the light source, one can obtain far-field with various distribution, including distribution with decrease in spectral intensity of specified rings, distribution with disappearances of specified rings, distribution with different spectral intensity of part of lobes in the continuous rings, distribution with part of the lobes in specified rings disappearing and distribution with some lobes in specified rings being stronger. These results will produce some novel far-field distributions which may provide a new idea for further study concerning about the manipulations of far-field array distribution.

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