Image quality evaluation for segmented mirror synthetic aperture optics

Exit pupil wavefront of the segmented mirror synthetic aperture optics (SAO) is discrete, which is much different from traditional systems. Two methods are used to evaluate SAO systems imaging. One is to get the exit pupil wavefront by interferometer and fit it into Zernike polynomial directly, then use the way of fast Fourier translation (FFT) to get system's modulation transfer function (MTF); the other is to integral the sub-exit-pupil's wavefront respectively, and calculate the complex amplitude distribution of each sub-mirror's, and overlap them in image plane, then get the MTF. As the fitted Zernike polynomial of exit pupil wavefront cannot express the discrete wavefront accurately, the former way is much different from the reality system. A segmented mirror system with three sub-mirrors primary is built, and the wavefront is obtained by ZYGO GPI interferometer, include overall exit pupil wavefront and each sub-exit-pupil wavefront. The two methods are compared, and the result shows the latter way is more precise but complex, and need much more computation; especially, the other more precise polynomial should be used to express the exit-pupil wavefront of abnormity figuration sub-mirror, can we get the more reasonable result.