An optical manifold for efficiently combining a plurality of LED outputs into a single, substantially homogeneous output, in a small, cost-effective package. The optical manifolds can be used to combine multiple LEDs of the same color and provide a high intensity output aperture with very high uniformity and sharp borders, or they can be used to generate a multiwavelength output, such as red, green, and blue LEDs that are combined to generate white light. Embodiments are also disclosed that use a single or multiple LEDs and a remote phosphor and an intermediate wavelength-selective filter arranged so that backscattered photoluminescence is recycled to boost the luminance and flux of the output aperture. The optical manifolds are designed to alleviate substantial luminance inhomogeneities inherent to LEDs. The optical manifold utilizes principles of non-imaging optics to transform light and provide directed, substantially uniform light sources.