Focal shifts of partially coherent light focused by an annular lens

The on-axis intensity distribution was investigated in the focal region of partially coherent light focused by an annular lens. The results show that, when the partially coherent light is focused by an annular lens, the best focusing point is not located at the geometrical focus. This means that the phenomenon of focal shifts occurs. Moreover, the amount of the focal shifts depends on the Fresnel number of the focusing lens, the spatial coherence of the partially coherent light and the central obstruction ratio of the annular lens etc. It is shown that the smaller the Fresnel number, the larger the focal shift; the lower the spatial coherence, the larger the focal shift;for a fixed Fresnel number, the larger the central obstruction ratio is, the larger the focal shift is. However, when the