Wittrock, Ulrich
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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.
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.
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.
We present, to the best of our knowledge, the first intracavity pumped Yb:YAG thin-disk laser. It operates at 1050.7 nm with a quantum defect of just 1.74% due to pumping at 1032.4 nm. Low absorption of the pump light at the pump wavelength of 1032.4 nm is compensated for by placing the disk inside the resonator of another Yb:YAG thin-disk laser which is diode-pumped at 940 nm. The intra-cavity pumped laser has an output power of 10.3 W and a slope efficiency of 8.3%
Cross-saturation of the gain media in intra-cavity pumped lasers leads to complex dynamics of the laser power. We present experimental results and a detailed theoretical analysis of this nonlinear dynamics for an intra-cavity pumped Yb:YAG thin-disk laser in the framework of a rate-equation model. The gain medium of this laser is residing in the resonator of a conventional, diode-pumped Yb:YAG thin-disk laser. Continuous-wave operation, periodic pulse trains, and chaotic fluctuations of the optical power of both lasers were observed. The dynamics is not driven by external perturbations but arises naturally in this laser system. Further examination revealed that these modes of operation can be controlled by the resonator length of the diode-pumped laser but that the system can also show hysteresis and multi-stability.
We have developed a new type of unimorph deformable mirror for the correction of low-order Zernike modes. The mirror features a clear aperture of 50 mm combined with large peak-to-valley amplitudes of up to 35 μm. Newly developed fabrication processes allow the use of prefabricated, coated, super-polished glass substrates. The mirror's unique features suggest the use in several astronomical applications like the compensation of atmospheric aberrations seen by laser beacons, low light astronomy, and the use in woofer-tweeter systems. Additionally, the design enables an efficient correction of the inevitable wave-front error imposed by the floppy structure of primary mirrors in future large space telescopes. We have modeled the mirror by using analytical as well as finite element models. We will present design, key features and manufacturing steps of the deformable mirror.
We present a novel unimorph deformable mirror with a diameter of only 10 mm that will be used in adaptive resonators of high power solid state lasers. The relationship between applied voltage and deformation of a unimorph mirror depends on the piezoelectric material properties, layer thicknesses, boundary conditions, and the electrode pattern. An analytical equation for the deflection of the piezoelectric unimorph structure is derived, based on the electro-elastic and thin plate theory. The validity of the proposed analytical model has been proven by numerical finite-element modelling and experimental results. Our mirror design has been optimized to obtain the highest possible stroke and a high resonance frequency.
We have developed a new type of unimorph deformable mirror, designed to correct for low-order Zernike modes. The mirror has a clear optical aperture of 50 mm combined with large peak-to-valley Zernike amplitudes of up to 35 μm. Newly developed fabrication processes allow the use of prefabricated super-polished and coated glass substrates. The mirror's unique features suggest the use in several stronomical applications like the precompensation of atmospheric aberrations seen by laser beacons and the use in woofer-tweeter systems. Additionally, the design enables an efficient correction of the inevitable wavefront error imposed by the floppy structure of primary mirrors in future large space-based telescopes. We have modeled the mirror by using analytical as well as finite element models. We will present design, key features and manufacturing steps of the deformable mirror.
Novel unimorph deformable mirror with monolithic tip-tilt functionality for solid state lasers
(2011)
We present a new type of unimorph deformable mirror with monolithic tip-tilt functionality. The tip-tilt actuation is based on a spiral arm design. The mirror will be used in high-power laser resonators for real-time intracavity phase control. The additional tip-tilt correction with a stroke up to 6 μm simplifies the resonator alignment significantly. The mirror is optimized for a laser beam footprint of about 10 mm. We have modeled and optimized this mirror by finite element calculations and we will present design criteria and tradeoffs for this mirrors. The mirror is manufactured from a super-polished glass substrate with very low surface scattering and excellent dielectric coating.
Efficient quasi-three-level laser operation requires the generation of the highest possible pump rate from a given pump source. We derive the fundamental scaling laws for the pump rate and we extract optimization criteria for pump concepts from these laws. The analysis is then applied to the thin-disk laser. Based on the results, a novel pump concept for thin-disk lasers is proposed, which allows for several tens of pump beam passes and reduces the optical complexity of conventional pump concepts. Furthermore, the beam quality of the pump source is preserved almost completely, facilitating the highest possible pump rate.