Flat-topped beam theoretical model and unified theory of coherence and polarization of light are used as the bases in examining aberrated, partially coherent, electromagnetic, square, flat-topped pulsed beams focused by a thin lens. This study demonstrates that Astigmatism is not necessarily undesirable in certain circumstances, and a certain amount of astigmatism can be guaranteed a similar spatial envelope of the beams in the geometric focal plane as the source of aberrated, partially coherent, electromagnetic, square, flat-topped pulsed beams. This feature may be useful in determining the fidelity of high-power laser-beam transmission areas.