We have investigated the optical design for the Japan astrometry satellite mission (JASMINE). In order to accomplish measurements of astrometric parameters with high accuracy, optics with a long focal length and a wide focal plane for astrometry are required. In 1977 Korsch proposed a three mirror system with a long focal length and a wide focal plane. The Korsch system is one of the convincing models. However, the center of the field is totally vignetted because of the fold mirror. Therefore we consider an improved Korsch system in which the center of the field is not vignetted. Finally, we obtain the diffraction limited optical design with small distortion. Our project needs a common astrometric technique to obtain precise positions of star images on solid state detectors to accomplish its objectives. In order to determine the centers of stars, an image of the point source must be focused onto the CCD array with a spread of a few pixels. The distribution of photons (photoelectrons) over a set of pixels enables us to estimate positions of stars with sub-pixel accuracy. We modify the algorithm to estimate the real positions of stars from the photon weighted mean, which was originally developed by the FAME (Full-Sky Astrometric Mapping Explorer) group. Finally, we obtain the results from the experiment that the accuracy of estimation of distance between two stars has a variance of about 1/300 pixel; that is, the error for one measurement is about 1/300 pixel, which is almost an ideal result given by Poisson photon noise. We also investigate the accuracy of estimation of positions with a different size of PSF. In this case also, we find that the accuracy of estimation has a variance of about 1/300 pixel.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html