Divergence Characteristics of Outgoing Beam from a Collimating Illumination System with an Extended Source

The limiting distance for illumination from a collimating illumination system with an extended source is determined by the divergence of the outgoing beam. Herein, the analytical expression for the surface of the planoconvex collimating lens based on Fermat's principle was obtained. The formula for calculating the divergence angle of the outgoing beam in such a system was derived according to the theory of imaging optics. Simulations and experimental validation were also conducted. Results reveal that the divergence angle of the outgoing beam from the collimating illumination system with an extended source is proportional to the source size, inversely proportional to the focal length of the collimating lens, and independent of the lens aperture. This conclusion provides a theoretical basis for compressing the divergence angle of the outgoing beam and extending the limiting distance for illumination from a collimating illumination system with an extended source. It has guiding significance for the selection of the light source and the design of the collimating lens in the development of searchlights.