On-axis Relative Density for Fresnel Number Related to Aberrant Laser Beam

The diffraction integral of small Fresnel number focusing laser system is obtained in the presence of aberration.The general approximate formula for the on-axis relative density distribution is also derived,as well as the on-axis relative density distribution formula for a spherical aberration laser system.In the conditions of aberration-free and non-truncation,the formulae can be simplified which fit well with the results obtained by former researchers.