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Based on the requirements from a conceptual design of a polarized positron beam for future linear colliders, we constructed a special collision system with a short focal length of 150 mm of the laser beams so as to produce γ rays through inverse Compton scattering. In order to achieve efficient laser-electron collisions, we created a special optics to produce very small e^{-}-beam sizes of σ_{e_{x0}}=7.6   μm and σ_{e_{y0}}=5.4   μm in the horizontal and vertical directions at the collision point. Using laser light with a wavelength of 532 nm and an e^{-} beam of 1.28 GeV, provided from the ATF-damping ring at KEK, we generated 2×10^{5} γ rays with a time duration of 26 ps in rms, leading to a peak brightness of 1.7×10^{18}/(mrad^{2} mm^{2} 0.1%bandwidth s) near to the maximum energy of 56 MeV.