Although much efforts have been made to develop higher performance excimer lasers mainly in Europe and Japan supported by the community and the government, an interdisciplinary subject in the paper title has not ever been investigated in detail. To take care of this un- attacked research region lying between various research groups, we tried to measure the beam quality of a discharge-pumped KrF laser under a rather high repetition rate operation. As we are interested in the diagnostics of various high speed phenomena, we measured the beam quality with advanced high speed photography. The spatial and temporal beam patterns were observed under various experimental conditions, and they were analyzed to start our high repetition-rate experiments. The results showed that an unstable resonator could produce high quality laser beams with the lower beam divergence angle.