A unified study of the effects of aberrations in focused laser beams

A theoretical and experimental investigation was conducted of the intensity distribution of radiation in the focal region for a laser beam focused by a lens. A Fourier optics approach was taken to derive the integral equations expressing the focused field resulting from a general amplitude and phase field distribution incident on a spherical surface lens. The effects of aberrations resulting from the lens as well as the propagation properties of the electromagnetic radiation were included, and these effects were expressed explicitly in terms of the optical system parameters. The lens effects were taken into account using a second-order series expansion derived from the thin lens approximation. Two approaches, one based upon the two-dimensional convolution integral and the other upon the two-dimensional Fourier transform integral, were derived to calculate the field as it propagates to focus. These equations were implemented on a digital computer to calculate transverse and meridional plane intensity distributions. Calculated data were displayed in image format for visual interpretation.

Experimental verification of the theory was performed for a plano-convex lens focusing a helium-neon laser beam. Data were acquired in image format with a digital image processor, and images were constructed of the meridional plane intensity distributions for several incident beam profiles. Strong agreement was found to exist both quantitatively and qualitatively between calculated and experimental results.