Design analysis of the astrometrical telescope facility

This paper presents a detailed analysis of a space-based telescope requiring an accuracy of 50 pico radians. A relationship between the geometric centroid of a diffraction image and wave aberrations is derived by a combination approach of diffraction optics and geometric optics. Based on sensitivity of the centroid, one-mirror and two-mirror aplanatic telescopes are investigated. The comparison among three telescopes, parabola, Schwartzschild and Ritchey-Chretien are quantitatively carried out in terms of their sensitivities to the systematic errors and random errors. The study shows that the Ritchey-Chretien design is the most preferable.