Focal shift of flat-topped beams passing through a lens system with or without aperture

We theoretically investigated on the focal shift of flat-topped beams (FTBs) passing through a lens system with or without aperture. We find that the position of on-axis peak intensity of focused FTBs strongly depends on the Fresnel number, the flatness order of FTBs, the truncation of the aperture, as well as the relative incident distance. The results indicate that the focal shift away from the geometrical focus of the focused FTBs appears when the relative incident distance does not equal to 1 and increases with the decreasing of the Fresnel number or the beam flatness order for both the apertured and unapertured lens systems. In the lens system with aperture, the focal shift effect decreases with the increase of the truncation parameter.