Analysis of resolution criterion and aberrations for Fizeau interferometer

Abstract

The quest for higher angular resolution in astronomy will inevitably require the telescope with large aperture. However, the primary mirror diameter is limited by the fabrication problems, and the cost of monolithic optics increases faster than diameter squared. The Fizeau interferometer imaging system represents a promising new technology to overcome the above-mentioned problems. The sub-apertures of the system are phased together to synthesize an imaging system that has a large effective aperture than any of the independent sub-apertures. Due to discontinuation of pupil plane, the lost of circular symmetry and the increase of secondary peak indicate that the standard Rayleigh resolution criterion for the single-aperture system is not appropriate for the Fizeau interferometer imaging system. On the other hand, in order to obtain diffraction-limited performance, the sub-apertures of the system must be coherently phased together to much less than the wavelength of light, so the optical aberrations of sub-apertures can rapidly degrade system performance. The purpose of this paper is to analyze the resolution performance and the effect of aberrations for a Fizeau interferometer imaging system that consists of four identical sub-apertures. The resolution based on the threshold and contracted with directional property is deduced. The relationship between the system's Strehl ratio and the sub-apertures' aberrations is given with the exponential approximation, which implies that Strehl ratio contacts not only with each sub-aperture's aberrations, but also with the interference between sub-aperture's aberrations.