In a projector, for example a digital projector, there are two main optical paths—illumination and projection paths.  The illumination path generally comprises a light source such as an elliptical lamp (e.g. an elliptical Hg lamp), an integrator for generating a more uniform beam of light from the light source (i.e. an integrator rod), and illumination relay optics for conveying light from the integrator to the projection path (including the image generation light modulators, such as a digital multi-mirror device (DMD)).  The elliptical lamp generally consists of a light source, such as a burner arc, and an elliptical reflector. 
However, there is a general problem of mismatch in F-number between the elliptical lamp, the illumination relay optics and the light modulator apparatus.  For example, the F-number of commercially available elliptical lamps is generally 0.8 to 1.0, and the F-number of commercially available light modulators is generally about 2.5 (e.g. in a 3-chip projectors Regardless of the F-number chosen for the illumination relay optics, then, light will be lost as it travels from the elliptical lamp to the integrator, and through the illumination relay optics to the light modulator due to the loss in high cone angle light from the low F-number elliptical lamp as it tries to enter the high F-number light modulator. 
One approach to this problem has been to match the input F-number of the illumination relay optics to the elliptical lamp, and provide the illumination relay optics with a magnification factor of 2.5/0.8=3.125, such that the output F-number matches the F-number of the light modulator.  However, such a large magnification factor requires that the cross section of the integrator be very small, and hence lowers the light collection efficiency of the system due to the overfilling of the large focal spot from the elliptical lamp on the integrator.  A partial solution to the problem may be to increase the input F-number of the illumination relay optics such that a larger illumination rod can be used.  For example, if the input F-number is 1.3 and the output F-number is 2.5, the magnification factor of the illumination relay optics will be only 1.923 instead of 3.125, as above.  However, the F-number of the elliptical lamp remains small, light with high incident angle will be lost due to the F-number mismatch at the input face of the integrator, again reducing the overall light collection efficiency of the system. 
Furthermore, optical integrators are well known components used in illumination systems for electronic projectors.  An optical integrator is a hollow or solid internally reflective “light pipe” that uses multiple reflections of a focused light source to obtain homogenization of round or irregular patterns of illumination and converts them into a uniform rectangular pattern.  This pattern can be imaged onto a panel such as an LCD (Liquid Crystal Display) or DMD (Digital Micromirror Device) by a relay lens system, and then projected to a screen.  Thus, the optical integrator rod is used to improve uniformity and efficiently match the aspect ratio of the illumination source to the panel. 
There are two basic types of reflective integrators: a hollow pipe which is made of four mirrors, and a solid glass integrator or “solid rod integrator”.  The latter type is more efficient than the former since it works on lossless multiple reflections using total internal reflection (TIR) of the glass rod.  On the other hand, hollow pipe can provide a clean exit surface with manageable suffering from light loss due to the non-perfect reflectivity of the mirrors.  Applicant has previously combined both features in U.S. Pat.  No.  6,205,271. 
It is generally advantageous to provide a two or more lamps in a projector, both to increase brightness and add redundancy in the event one lamp burns out.  However, each lamp must be independently coupled to the reflector.  This is a particularly difficult problem as while each lamp can be focussed onto the entrance of the integrator, they must then be locally positioned and heat management becomes an issue.  This further necessitates an awkward physical arrangement between the lamps making access to them difficult, for example when they burn out.  While this problem has been previously addressed in US Patent Application 2007/0058372, to Sacre et al.,  the integrator disclosed therein is extremely inflexible in design.  Furthermore, prior art dual lamp integrators, transmitted 1.40 times single lamp integrators, meaning 0.6 of the light from both of the lamps were lost.