## Wittrock, Ulrich

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#### Publication Type

- Conference Proceeding (3)
- Article (2)

#### Keywords

- active optics, adaptive optics, sharpness metrics, aberration compensation, algorithm design (2)
- active optics, metrics, aberration compensation (1)
- adaptive optics; image-sharpness (1)
- laser crystal (1)
- praseodymium (1)
- refractive index change (1)
- thermal expansion coefficient (1)
- yttrium lithium fluoride (1)

Image-sharpness metrics can be used to optimize optical systems and to control wavefront sensorless adaptive
optics systems. We show that for an aberrated system, the numerical value of an image-sharpness metric can be
improved by adding specific aberrations. The optimum amplitudes of the additional aberrations depend on the
power spectral density of the spatial frequencies of the object.

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.

With a view to the next generation of large space telescopes, we investigate guide-star-free, image-based aberration correction using a unimorph deformable mirror in a plane conjugate to the primary mirror. We designed and built a high-resolution imaging testbed to evaluate control algorithms. In this paper we use an algorithm based on the heuristic hill climbing technique and compare the correction in three diﬀerent domains, namely the voltage domain, the domain of the Zernike modes, and the domain of the singular modes of the deformable mirror. Through our systematic experimental study, we found that successive control in two domains eﬀectively counteracts uncompensated hysteresis of the deformable mirror.

We report interferometric measurements of the temperature coefficient of the refractive index (dn=dT) and the coefficient of thermal expansion (a) of a praseodymium-doped yttrium lithium fluoride (Pr:YLF) crystal and of a fused silica reference sample. Our phase-resolved interferometric method yields a large number of data points and thus allows a precise measurement and a good error estimation. Furthermore, both dn=dT and a are obtained simultaneously from a single measurement which reduces errors that can occur in separate measurements. Over the temperature range from 20 °C to 80 °C, the value of dn=dT of Pr:YLF decreases from -5.2 x 10-6 /K to -6.2 x 10-6 /K for the ordinary refractive index and from -7.6 x 10-6 /K to -8.6 x 10-6 /K for the extraordinary refractive index. The coefficient of thermal expansion for the a-axis of Pr:YLF increases from 16.4 x 10-6 /K to 17.8 x 10-6 /K over the same temperature range.