Shock wave experiments contemplated on powerful CO2 lasers require uniform planar illuminations over spot sizes much larger than the diffraction limit focal spot size of the focusing optics. Cost as well as space considerations limit one's choice of optics to parabolic mirrors with focal lengths between 78 and 150 cm, and apertures to 35 cm. Within these constraints one either modifies the incident laser energy distribution to modify the focal spot shape, or works out of the focal plane. I analyze the latter option using a fast Fourier method to calculate the intensity distributions for two focal lengths (78 and 132 cm) and various measured optical distortions (Phase only) for the focusing optics. I found that a 78 cm element produced more uniform spots of diameter 500 pm. The 132 cm element was less sensitive to focusing/positioning error than the 78 cm element.
George A. Kyrala,
"Out-Of-Focus Intensity Distribution: Effects Of Focal Number And Aberration", Proc. SPIE 0288, Los Alamos Conf on Optics '81, (30 December 1981); doi: 10.1117/12.932024; https://doi.org/10.1117/12.932024