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The effect of central obstruction on singularities and spectral anomalies of polychromatic, spatially coherent light diffracted by an annular aperture

The singularity changes and spectral behavior of polychromatic spatially fully coherent light diffracted by an annular aperture are studied. Detailed numerical calculation results are presented and illustrated. It is shown that the spectral anomalies take place in the vicinity of singularities in the diffraction field, namely the spectrum is red shifted at some points, blue shifted at others, and is split into two lines with equal height elsewhere, and this kind of spectral change depends on the central obstruction ratio ε and axial distance z. It is found that, with the increasing of the central obstruction ratio ε, axial singularities will shift to the aperture and at the off-axial positions new singularities will appear and split. With the further increasing of ε, the near field finally changes to the far field.