A waveguide version of a Kohler integrator is disclosed, utilizing geodesic lenses with a surface that can be mapped to a gradient-index Luneburg lens or to a nonfull-aperture Luneburg lens in such a way that the light paths in the gradient index lenses map into the geodesics of the surface, with the outer region of the gradient index lenses mapped into a flat surface. Arrays of these can be applied to lines of LEDs, as in CHMSLs, to mix light in intensity and in illumination as well as to avoid the deleterious effects of binning and burnout, or in multicolor arrays, to ensure complete chromatic mixing.