## Wittrock, Ulrich

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#### Keywords

- active optics, adaptive optics, sharpness metrics, aberration compensation, algorithm design (2) (remove)

With a view to future large space telescopes, we investigate image-based wavefront correction with active optics. We use an image-sharpness metric as merit function to evaluate the image quality, and the Zernike modes as control variables. In severely aberrated systems, the Zernike modes are not orthogonal to each other with respect to this merit function. Using wavefront maps, the PSF, and the MTF, we discuss the physical causes for the non-orthogonality of the Zernike modes with respect to the merit function. We show that for combinations of Zernike modes with the same azimuthal order, a flatter wavefront in the central region of the aperture is more important than the RMS wavefront error across the full aperture for achieving a better merit function. The non-orthogonality of the Zernike modes with respect to the merit function should be taken into account when designing the algorithm for image-based wavefront correction, because it may slow down the process or lead to premature convergence.

Active optics is an enabling technology for future large space telescopes. Image-based wavefront control uses an image-sharpness metric to evaluate the optical performance. A control algorithm iteratively adapts a corrective element to maximize this metric, without reconstructing the wavefront. We numerically study a sharpness metric in the space of Zernike modes, and reveal that for large aberrations the Zernike modes are not orthogonal with respect to this metric. The ﬁndings are experimentally veriﬁed by using a unimorph deformable mirror as
corrective element. We discuss the implications for the correction process and the design of control algorithms.