Abstract: A Lambertian light source assembly has high uniformity, large size, and high brightness, typically having a non-uniformity about 10% or less (e.g. about 5%), and a surface brightness of at least about 2000 footlamberts. The assembly includes a light emitting element (such as a single arc lamp, e.g. a metal halide lamp), a first reflector having an interior diffuse reflective surface comprising a portion of a surface of revolution and a center axis, a second reflector, and a diffuser. The diffuser is connected to the first reflector. The light emitting element is substantially centrally located on the center axis, and the second reflector is located between the diffuser and the light emitting element and reduces the apparent surface brightness at the center of the first reflector and blocks the majority (e.g. all, or almost all except adjacent the first reflector) of direct illumination of the diffuser by the light emitting element.