Short arc lamps are a key component for projection systems to achieve highest efficiency for small display sizes. Consequently UHP-lamps are now standard for high efficient projection systems. UHP lamps combine a very high luminance with a good spectrum and lifetime. The optical performance of UHP lamps can be further improved: A dichroic coating on one half of the UHP burner is applied to focus all light into one hemisphere. This allows for extremely compact reflector systems and an improvement by 20-30% in light collection. The design of projection optical systems requires reliable optical models of the light source. Two different approaches for the model description of lamps will be presented. 1) A physical model based on the geometrical description of all surfaces of the lamp. Volume emitters are used to describe the light generation. 2) A model based on high resolution goniophotometric measurements of the light source. Simulations using both types of models are verified by measurements and the benefits and shortcomings of both approaches are discussed. Special emphasis will be placed on the role of the light bulb as the first optical element in the system. The relatively thick quartz bulb of these high pressure lamps acts as a lens and shapes the beam of light.