The Measurement of PSF Ellipticity of an Unobstructed Off-Axis Space Telescope: Error Analysis

It is an effective method to detect weak gravitational lensing (WL) in the universe by measuring ellipticities of galaxies via astronomical telescopes. Optical properties of telescopes are critical to WL detections. To ensure the used telescopes to be competent, it is necessary to measure point spread function (PSF) ellipticities of telescopes in labs. In this paper, a way based on simulated star target imaging is proposed to measure PSF ellipticity of an unobstructed off-axis space telescope. Related errors are identified and modeled carefully for the first time. Effects of detector noises, micro-vibration of optical platforms, defocusing of simulated star target, wavefront errors (WFEs) and central obstructions of collimators on PSF ellipticity measurements of the telescope are analyzed. Results show that the measurement error of PSF ellipticity decreases from 0.0105 to 0.0043 by adopting 10 iterations of the iterative weighted centroiding algorithm when SNRs are under 24 dB. To ensure PSF ellipticity measurement errors are not larger than 0.01, the micro-vibration angle of the optical platform should be less than
$0.05''$
. When focal length of the collimator is twice that of the telescope, the measurement errors of PSF ellipticity are under 0.01 if the defocusing of simulated star target is controlled to be not larger than 0.1 mm. In addition, WFEs and central obstructions of collimators change PSF ellipticity measurement errors to different degrees at different fields of view (FOVs). Due to 20 nm RMS WFE of the collimator, the maximum value of PSF ellipticity measurement errors over full FOVs is 0.1 and the average value is 0.0269. If the radius of central obscuration of the collimator is 150 mm, the maximum measurement error of PSF ellipticity over full FOVs is 0.0091. According to the results shown in this paper, significant references for high accuracy measurements of PSF ellipticity of telescopes can be provided.