A spatial integrator is an optical array characterized by a ray transfer matrix having a zero determinant. The design of a spatial integrator is explained using the relations among the geometric parameters of the array and the optical characteristics of its components. We focus our attention on spatial integrators constructed by using units composed of two thin lenses. The spatial integration does not depend on the focal length of the first lens. Although that focal length can be arbitrarily selected, we have found a range of its values that increases the amount of energy falling on the synthetic image and improves its uniformity. This analysis has been done for spatial integrator arrays having a spherical dome configuration and having a planar configuration. The study has been done both in the paraxial range and by using real ray-tracing tools. This optimization procedure is of interest in the design of spatial integrator arrays for illumination and natural lighting applications.
"Optimum focal length range for thin-lens optical arrays providing spatial integration," Optical Engineering 44(3), 033001 (1 March 2005). https://doi.org/10.1117/1.1869993