A system to provide radiant energy of selectable spectral characteristic (e.g. a selectable color combination of light) uses an optical integrating cavity to combine energy of different wavelengths from different sources. Sources of radiant energy of different wavelengths, typically different-color LEDs, supply radiant energy into the interior of the cavity. The cavity has a diffusely reflective interior surface and an aperture for allowing emission of combined radiant energy. Control of the intensity of emission of the sources sets the amount of each wavelength of energy in the combined output and thus determines a spectral characteristic of the radiant energy output through the aperture. A variety of different elements may optically process the combined light output, such a deflector, a variable iris, a lens, a variable focusing lens system, a collimator, a holographic diffuser and combinations thereof. Such systems are useful in various luminous applications as well as various illumination applications.