Wave aberration corrections in PSF ellipticity measurements of astronomical telescopes using a multi-objective optimization.

The weak gravitational lensing (WGL) produces a shear effect on the observed galactic ellipticity that is much smaller than the endogenous ellipticity of the galaxy itself. Achieving such a high-level astronomical observation requires the superior performance of telescopes. To ensure the optical properties of telescopes to be competent in WGL detections, it is very necessary to measure point spread function (PSF) ellipticity of telescopes in labs. In this paper, a 2 m off-axis telescope that would be used to detect WGL in space is analyzed and studied. A collimator whose aperture is 2 m has been built to measure PSF ellipticity of the telescope. The wave aberrations of the collimator are roughly equal to those of the telescope, so they are important systematical errors and must be removed. However, it is difficult to precisely measure the wave aberrations of optical systems that have large apertures and long focal lengths. In addition, a 2 m flat mirror, which is indispensable to measure wave aberrations of optical systems, has significant surface errors. In this paper, a multi-objective optimization method is proposed to eliminate the effects of wave aberrations on PSF ellipticity measurements of the telescope. By constructing an equivalent model, the wave aberrations from collimators and flat mirrors can be corrected so that PSF ellipticity measurement error is reduced to within 0.01. Measurement accuracy of PSF ellipticity of the telescopes can be improved significantly.