It has been in great use for the integrated rod illumination system in integrated rod projection display field because of its simple structure

low cost

high efficiency and uniformity.The principle is that with the application of the ray reflected several times in integrated rod the ray can form well-proportioned rectangular illumination in the end of the rod.With the reduction of the light modulator dimension

the advance system is required to analyze and design with the concept of Etendue value. It is complicated to analyze data of the light source.In this paper the solid source model is induced and with the space distribution and angular distribution of the intensity

the model method is given.It is helpful to estimate and simulate the uniformity

optical efficiency and optimum Etendue value by exactly analyzing.Expanding the reflection ray in integrated rod by law

the merge and the center of the rod can be found because different ray has different location.These rays have different reflection times before they reach the end surface of the rod also.The formulation and the function of rod uniformity are given. The Etendue value is reduced with the reduction of modulator dimension.So how to reduce Etendue value but keep the efficiency is a big problem for the illumination and light source design.An improved light source reflector

which can reduce Etendue value effectively

is introduced.It is fit for 1.3～1.8 cm light modulator judged by computer simulation.