The interferometers with computer generated holograms (CGHs) have been used to measure off-axis aspherical mirrors. However, the conventional CGH interferometer could not produce a high lateral resolution because of the blur and the distortion of the interferogram of the test mirror caused by the non-zero order diffraction of the CGH. We further develop the application of CGHs concerning interferometers in order to improve the lateral resolution of the interferogram. In particular, we change the application of the CGH in such a way that the returned test beam passes through the CGH with zeroth order diffraction and demonstrates the performance of the CGH interferometer when used for the measurement of the primary mirror of the Okayama Astrophysical Observatory 3.8 m telescope project. As a result, our CGH interferometer produces a good interferogram with high resolution of 2.8 mm for the off-axis aspherical mirror with a size of 1.2 m. With improved usage of the CGH, we successfully demonstrated a high lateral resolution interferometer. (C) 2012 Optical Society of America