Focal shift and focal switch of partially coherent annular beam focused by lens

Applying the Huygens-Fresnel diffractive integral,the on-axis intensity distribution and the phenomena of focal shift and focal switch are theoretical studied when a partially coherent annular light is focused by a lens.The results show that the amount of the focal shift depends on not only the Fresnel number of the annular beam,but also the spatial coherence and the central obstruction ratio of the incident partially coherent light.It is also shown that the greater the Fresnel number,the smaller the focal shift;the higher the spatial coherence,the smaller the focal shift.For a fixed Fresnel number,the larger the central obstruction ratio is,the larger the focal shift is.For a given spatial coherence,the phenomenon of focal switch will occur as the Fresnel number decreases.The results are helpful to the research of the focus of partially coherent annular beam.