Abstract

Deformable mirror (DM) used for intracavity compensation in high-power lasers should be able to withstand very high laser intensity. This paper proposes a water-cooled unimorph DM which can withstand the laser power up to 10 kW in thermal simulation. The proposed DM consists of an annular PZT layer and a circular Si layer which are glued together with edge clamped. All the 32 piezoelectric actuators are distributed around the correction area and on the front side of the DM. The cooling water flows through the back side of the DM and cools the mirror directly. This design realizes the physical separation of the actuators and the coolant. The experimental results of a fabricated DM prototype show that the DM can reproduce typical low-order aberrations accurately with relatively large amplitude. The wavefront PV amplitudes of the reproduced tip/tilt, astigmatism, defocus, trefoil and coma shapes for 15 mm aperture are about 40 μm, 24 μm, 18.7 μm, 10 μm and 6 μm, respectively.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Thermally induced aberrations degrade the beam quality and output power, which is the main obstacle to be overcome in the power scaling of solid state lasers [1,2]. Most of the aberrations in this situation are low-order aberrations. However they change with the variation of the laser power [3]. Conventional approaches, such as cavity design, phase conjugating mirrors and diffractive optic elements, only compensate static and some specific aberrations [4,5]. A promising approach is to employ adaptive optics (AO) technology by using a deformable mirror (DM) as the intracavity mirror of the laser resonator to actively compensate the thermally induced aberrations in real time [6–10]. The beam quality and power have been proved to be enhanced efficiently.

Unimorph DMs are attractive for the laser applications due to their large stroke, low cost and high mirror quality [11–14]. Usually, laser energy absorption generates heat in the DM that might degrade the performance and even destroy the device [15], e.g., depolarization of the piezoelectric material, damage of the adhesive layer, and thermal deformation of the mirror surface. Therefore, the DM used for intracavity compensation, especially in case of long-term, high-power, continuous-wave operation, should be able to withstand very high laser intensity.

In order to improve the thermal tolerance of the unimorph DM, high reflectivity coating (up to 99.99%) can be used [16]. However, the absorption still cannot be ignored in high-power and extremely high-power lasers. Some researchers using wide-aperture DM to reduce the energy density on the mirror surface [17]. In such systems, an extra intracavity beam expender is needed to match the laser beam diameter (about 10 mm). It is not convenient in practical applications. A promising approach is to cool the DM actively. However, the actuators as well as the electric connection of the DM cannot be directly contacted with the coolant to avoid the device damage. The isolation of the cooling medium and the actuators makes the cooling of the DM very difficult. Samarkin et al. adopted a cooling unit on the periphery surface of the DM to actively reduce the thermal effect [18]. The cooling efficiency is limited since the heat transfer rate along the radial direction of the thin mirror is slow. The radial temperature gradient on mirror surface still causes an extra deformation. Furthermore, copper substrate with cooling channels inside was used to improve the cooling effect [19,20]. The fabrication of the DM is more complex and the cooling channels would reduce mirror quality.

In this paper, a new water-cooled unimorph DM is proposed for high-power laser applications. In Section 2, the new configuration and the features of the DM are described. A finite model of a 32-element DM is developed to predict the DM deformation. The actuator performance and correction performance are simulated. The thermal effects of the DM with and without cooling are also simulated. In Section 3, the fabrication process of DM is described briefly. In Section 4, the water-cooled unimorph DM is characterized in an AO system. The results will demonstrate the proposed DM can regenerate the first 9 Zernike mode aberrations accurately with very low residual errors.

2. Structure and simulation

2.1 DM structure

The schematic of the proposed water-cooled unimorph deformable mirror is illustrated in Fig. 1. It consists of an annular PZT layer and a circular Si layer which are glued together with edge clamped. The central area of the Si surface, which is coated with high reflectivity film, is used for correcting optical aberrations. The 32 sectorial electrodes are arranged in two rings on the outside surface of the annular PZT. The ground electrode with the same size of the PZT is on the inside surface. Unlike a conventional unimorph DM, this DM has no actuators within the effective aperture. The designed actuators on the periphery area can create a local curvature in the correction area. The reason is that the boundary restriction of the DM changes the stress distribution which causes an extra deformation in the center area. This means that the DM can reconstruct some complex deformations, such as coma and secondary astigmatism. This design is different with the conventional design theory of unimorph DM. For example, a unimorph DM with similar structure has no correction capability for coma and other complex aberrations [21]. It should be known that the correction capability of the DM for high-order aberrations is expected to be limited since all the actuators are arranged outside the correction area [22]. This DM is mainly designed to correct low-order aberrations, such as defocus, astigmatism and coma, which are dominant in laser beam correction.

 

Fig. 1 Cross-sectional view of the water-cooled unimorph DM.

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The DM has the advantages that it does not suffer from the print-through of the actuators because the mirror for correction is a homogeneous layer. Actuator print-through is sometimes encountered in unimorph DMs and leads to aberrations of high spatial frequencies [23]. Additionally, the thermal expansion of Si is similar to that of the PZT material, which reduces the temperature-induced deformation.

The cooling cavity is mounted on the back side of the DM. The mirror is directly contacted with the water coolant of which the temperature is always constant (e.g. 20°C). Thereby, the cooling performance can be improved greatly. Since the piezoelectric actuators are arranged on the front side of the DM, the actuators and coolant are physically separated by the mirror. The damage of electrical connection and actuators by the coolant is avoided. The designed DM could be satisfied for the application in high-power lasers.

2.2 Finite element model

A finite element model of the DM was built using a commercial FEM software ANSYS to aid the DM design. The PZT plate used in this study is from Suzhou Pant Piezoelectric Technology Co. Ltd. The silicon wafer is from Suzhou Crystal Silicon Electronic & Technology Co. Ltd. The material properties of Si and PZT used in the simulation are listed in Table 1, which are provided by the suppliers. The diameter and the thickness of the Si layer are 50 mm and 200 μm, respectively. The inner diameter and the outer diameter of the annular PZT layer are 20 mm and 50 mm, respectively. The thickness of PZT layer is 100 μm. The effective aperture for laser aberration correction is a little less than 20 mm in diameter to avoid the laser radiation on the PZT layer. The radial widths of the electrode in each ring, which are denoted by Act1 and Act2, are 6 mm and 4 mm, respectively. A three-dimensional (3-D) hexahedral structural element type (Solid-45) is chosen to model the Si layer, and a 3-D coupling-field solid element type (Solid-5) is chosen to model the PZT layer. The bonding layer and the electrode layer are neglected since the thickness is much smaller than PZT layer and Si layer. The edge area larger than 40 mm diameter is firmly fixed. The mesh of the model is shown in Fig. 2(a). Figure 2(b) shows the DM deformation when a voltage of 50 V is applied to Act1. The first order resonance frequency of the DM was further simulated, which is about 2.7 kHz.

Tables Icon

Table 1. Material properties of the DM used in the simulation

 

Fig. 2 Finite element model of the unimorph DM: (a) mesh of the model and (b) mirror deformation under activation of Act1.

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2.3 Deformation of a single actuator

The deformation of the mirror surface driven by a single actuator was simulated. The simulated wavefront profiles of the DM under 50 V are shown in Fig. 3. The effective aperture of 15 mm was used. The figure shows that Act1 generates a local curvature in the effective aperture though the actuator locates the outside of the aperture. Act2 generates an edge warping in the effective aperture. The actuator performance is mainly affected by the radial location and size of the electrode. The aperture and electrode sizes used in this study were optimized.

 

Fig. 3 Simulated wavefront profiles of the DM driven by Act1 and Act2.

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2.4 Simulation reconstruction of typical aberrations

Zernike polynomials are commonly used to fit the wavefront aberrations in AO system. The correction capability of the DM can be evaluated by the reconstruction of Zernike mode shapes. The influence function of each actuator was obtained by FEM simulation. Then the driving voltages of the actuators were calculated using influence function control method [24]. Figure 4 shows that the DM reproduces astigmatism Z3 and coma Z7 aberrations accurately, with an extremely low residual error in theory. The applied voltage maps show that the actuators in the inner ring play a major role in reproduction of the coma aberration as expected.

 

Fig. 4 Simulated reconstruction of astigmatism Z3 and coma Z7.

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Furthermore, the first 14 Zernike aberrations were reproduced. The working voltage range is from −50 V to 50 V. The RMS values of the reproduced wavefront and normalized residual error are shown in Fig. 5. The normalized residual wavefront error is defined as the ratio of the residual wavefront error to the reconstructed Zernike mode. The proposed unimorph mirror with clamped edge and two rings of actuators outside the active aperture can generate only Zernike polynomials with indices [m, ± m] and [m, ± (m-2)] [25]. Figure 5 shows the DM has a good correction capability for these Zernike modes except spherical aberration Z12, with a normalized residual error less than 1%. The reconstructed RMS of astigmatism (Z3 and Z5) and the defocus (Z4) are about 3.4 μm and 2.3 μm, respectively. It is theoretically suitable for correcting thermal lensing effect that has the characteristic of low-order aberrations. The reconstructed amplitude decreases with the increase of the Zernike mode. Since there is no actuator in the center of the DM, the DM cannot correct spherical aberration (Z12), which is a defect of the DM.

 

Fig. 5 Simulation reproduction of the first 14 term Zernike modes: (a) RMS wavefront and (b) normalized residual wavefront error.

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2.5 Thermal effect of the DM

Since the water-cooled DM is designed for high power laser correction, the thermal effects of the DM with and without cooling were simulated. In the simulation, the heat transfer between the DM and air, the heat transfer through the water, and the heat conduction of the Si layer were included. A 15 mm-diameter Gauss laser beam was applied on the central area of mirror surface. The power of the laser was set to 10 kW and the lasting time was 20 seconds. The reflectivity of mirror surface is 99.9%. The thermal physical parameters of DM are shown in Table 1. The heat conductivities of Si and PZT are 173.6 W/(m·K) and 1.4 W/(m·K), respectively. The temperatures of water and surrounding environment were set to 20 °C. Heat transfer coefficient between the DM and surrounding environment is 8 W/(m2·K). The heat transfer coefficient along the water-cooled surface is 1000 W/(m2·K). The thermal simulation results are shown in Fig. 6. For no cooling case, the temperature of the mirror rises over time. For cooling case, the temperature achieves equilibrium state within 2 seconds. The temperature distribution on the mirror surface at 10 seconds is shown in Fig. 6(b). The maximum temperature of DM reaches to 145 °C which is harmful to the DM. With water cooling, the maximum temperature is reduced to 53 °C. The simulation result shows that the water coolant can reduce the heat of the mirror effectively. Figure 7 shows the Zernike coefficients of the thermal deformation caused by the laser energy absorption at 10 seconds. The thermal deformation is defocus. Other mode aberrations are very small and can be neglected. The wavefront RMS after cooling is only 0.256 μm which can be corrected by the DM itself easily.

 

Fig. 6 Thermal effect of the DM under laser radiation with and without cooling: (a) Thermal response curve and (b) temperature profiles of DM along the radial direction at 10 seconds.

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Fig. 7 Thermal wavefront deformation at 10 seconds.

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3. DM prototype

A prototype of the water-cooled DM was fabricated, as shown in Fig. 8. The fabrication process is similar to the previous method developed by our group [26]. First, an annular PZT plate was cut from a 50-mm-diameter and 100-μm-thick commercial PZT plate using a picosecond-laser system. The PZT plate is covered with silver layers on both surfaces. Then, the annular PZT plate and a 200-μm-thick super-polished Si wafer were glued together using epoxy adhesive. In order to reduce the curing stress, the adhesive was cured at room temperature. A wet etching method was used to pattern the electrodes of the DM. A flat quartz rim was used as the mounting structure which can reduce distortion of the mirror surface caused by the bonding stress. The unimorph DM was bonded to a cooling cavity which was fabricated by 3D printing method using PLA (trimethylene carbonate) material. The patterned electrodes were connected to a circuit board with enameled wires. Finally, the DM was packaged for testing. In this experiment, the mirror surface is not coated with any reflective coating which should be coated according to the laser wavelength in the practical applications. The reflective coating can be fabricated on the silicon substrate before it being adhesively bonded to the PZT plate, which has been adopted successfully in the fabrication of a 350-μm-thick unimorph DM [16]. The reflective coating may cause an extra mirror curvature. It can be reduced by subsequently bonding the DM to the flat mounting structure [26]. Additionally, the mirror in this design is possible to be coated on both sides of the mirror to balance the stress. The residual stress balance layer on the back side can be a metal film and an inorganic film, such as Au and SiO2, by controlling the stress strictly [27]. These films can work in the coolant.

 

Fig. 8 Photographs of the fabricated water-cooled DM: (a) unimorph DM and (b) packaged DM with cooling cavity.

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4. Experimental characterization

4.1 Actuator performance

The DM performance was characterized using an AO test system based on a Shack-Hartmann sensor [28], where a lenslet array of 21 × 21 was used for measurement and 65 Zernike polynomial modes were used for fitting the wavefronts. The wavefront deformation of the typical actuator was obtained by subtracting the initial mirror surface from the measured wavefront of the DM under a driving voltage of 50 V, as shown in Fig. 9. The measured wavefront profiles of Act1 and Act2 match with the simulation results quite well. The wavefront strokes of Act1 and Act2 at different aperture were also calculated and listed in Table 2. The stroke of the actuator increases with the aperture. The strokes of Act1 and Act2 at 15-mm aperture are 2.445 μm and 3.854 μm, respectively. The hysteresis of the actuators is about 10%.

 

Fig. 9 Comparison of simulated and measured wavefront deformation of actuator at the aperture of 20 mm.

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Tables Icon

Table 2. Wavefront strokes of Act1 and Act2 at different apertures

4.2 Mirror quality

The mirror wavefront surfaces of the DM before and after filling the cooling cavity with water were measured, as shown in Fig. 10. The fabricated DM was placed vertically. The wavefront PV value of the initial surface without cooling water is about 3 μm. The aberrations mainly consist of defocus and some other low-order aberrations which can be corrected by the DM itself easily. The wavefront PV value after correction using a closed-loop control method is reduced to 0.182 μm, corresponding to 0.026 μm RMS (~λ/40, λ = 1064 nm). The effect of the lateral pressure of the water on the mirror surface was evaluated by filling the cooling cavity with water without flowing. An additional deformation that is approximate to defocus is caused by the lateral pressure of the water under gravity effect. The total wavefront PV value of the mirror is increased to about 5 μm. The wavefront PV value after correction is reduced to 0.218 μm, corresponding to 0.042 μm RMS (~λ/25). This indicates that the deformation effect of the cooling water is acceptable. In order to reduce the deformation, the stiffness of the DM can be increased appropriately by increasing the thickness at the cost of reducing the stroke. Spherical aberration is predominant in the residual aberrations with and without cooling water, since the DM has no correction capability for the spherical aberration. The voltage map shows that about 20 V (20% of the working voltage) is used for flattening the mirror. This indicates that there will be enough voltage that can be used for correcting aberrations.

 

Fig. 10 Wavefront surface of the DM at 15 mm aperture before and after filling the cooling cavity with water.

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4.3 Reproduction of Zernike mode shapes

The first 14 Zernike mode shapes were reproduced experimentally using the fabricated DM without cooling water at 15 mm aperture, as shown in Fig. 11. The data were obtained by subtracting the flattened mirror surface from the reproduced wavefront. The corresponding wavefront PV and RMS values of each reproduced Zernike shape and the residual wavefront error were calculated to evaluate the performance of the DM. The DM has a good correction capability for these Zernike modes except the spherical aberration (Z12). The amplitude approximately decreases as the mode increases. The PV amplitude of tip/tilt is approximately 40 μm. The PV amplitudes of astigmatism aberrations (Z3 and Z5) are about 24 μm, with a normalized residual wavefront error of approximately 1%. The PV amplitude of the defocus aberration (Z4) is about 18.7 μm, with a normalized residual wavefront error of less than 1%. The PV amplitudes of the coma aberrations (Z7 and Z8) are about 6 μm, with a normalized residual wavefront error of approximately 3%. The normalized residual wavefront errors of the first 9 Zernike modes are less than 3.2% which is a little larger than the theoretical value due to the measurement error. The DM cannot correct the spherical aberration, which agrees with the simulation result.

 

Fig. 11 Experimental reproduction of the first 14 Zernike mode shapes using closed-loop control method. The wavefront PV value and RMS value are indicated for each mode.

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Furthermore, the correction capabilities of the fabricated DM at different apertures were characterized and compared, as shown in Fig. 12. The aperture affects the correction capability. The results show that the DM has a good correction capability for the aperture from 12.5 mm to 17.5 mm. The amplitude of the reproduced Zernike mode shape increases with the size of the aperture, since the stroke of the actuator increases with the aperture. The DM at 15 mm aperture has a less normalized residual error, since the electrodes were optimized for the 15 mm aperture. Most of the normalized residual errors are less than 0.1 for these three apertures. The DM with 12.5 mm aperture has a slightly poor correction capability for Z11 and Z13 modes. Overall, the proposed DM is very suitable for low-order aberrations correction.

 

Fig. 12 Experimental reproduction of the first 14 term Zernike mode shapes at different apertures: (a) wavefront RMS and (b) normalized residual wavefront error.

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5. Conclusion

In this paper, a new water-cooled unimorph DM is developed for high power laser applications. All the 32 piezoelectric actuators are distributed around the correction area on the front side of the DM. The cooling water flows through the back side of the DM. This design realizes the physical separation of the actuators and the coolant. A finite element model of the DM was established to predict the deformation behavior and the thermal effect of the DM. Thermal analysis result shows that the DM with water cooling can withstand 10 kW laser power. The experimental results in AO system show that the DM reproduces the typical low-order aberrations accurately with relatively large amplitude under the voltage range from −50 V to + 50 V. The wavefront PV amplitudes of the reproduced tip/tilt, astigmatism, defocus, trefoil and coma are about 40 μm, 24 μm, 18.7 μm, 10 μm and 6 μm, respectively. The normalized residual wavefront error of the first 9 Zernike modes are less than 3.2%. The simulation and experiment results demonstrate the proposed DM has potential applications in high-power lasers. In the future work, the DM with high reflectivity coating will be fabricated and the cooling test will be performed in a high-power laser system.

Funding

National Natural Science Foundation of China (51675288, 51505238); Technological Research for Public Welfare Projects of Zhejiang Province (LGF18E050001); Natural Science Foundation of Ningbo (2017A610078); K.C. Wong Magna Fund in Ningbo University.

References and links

1. W. Koechner, Solid-state Laser Engineering (Springer, 2013).

2. T. Y. Cherezova, S. S. Chesnokov, L. N. Kaptsov, V. V. Samarkin, and A. V. Kudryashov, “Active laser resonator performance: formation of a specified intensity output,” Appl. Opt. 40(33), 6026–6033 (2001). [PubMed]  

3. W. Clarkson, “Thermal effects and their mitigation in end-pumped solid-state lasers,” J. Phys. D Appl. Phys. 34(16), 2381–2395 (2001).

4. E. Wyss, M. Roth, T. Graf, and H. P. Weber, “Thermooptical compensation methods for high-power lasers,” IEEE J. Quantum Electron. 38(12), 1620–1628 (2002).

5. S. Makki and J. Leger, “Solid-state laser resonators with diffractive optic thermal aberration correction,” IEEE J. Quantum Electron. 35(7), 1075–1085 (1999).

6. R. R. Stephens and R. C. Lind, “Experimental study of an adaptive-laser resonator,” Opt. Lett. 3(3), 79–81 (1978). [PubMed]  

7. J. M. Spinhirne, D. Anafi, R. H. Freeman, and H. R. Garcia, “Intracavity adaptive optics. 1: Astigmatism correction performance,” Appl. Opt. 20(6), 976–984 (1981). [PubMed]  

8. W. Lubeigt, G. Valentine, and D. Burns, “Enhancement of laser performance using an intracavity deformable membrane mirror,” Opt. Express 16(15), 10943–10955 (2008). [PubMed]  

9. S. Piehler, T. Dietrich, P. Wittmüss, O. Sawodny, M. A. Ahmed, and T. Graf, “Deformable mirrors for intra-cavity use in high-power thin-disk lasers,” Opt. Express 25(4), 4254–4267 (2017). [PubMed]  

10. P. Yang, Y. Ning, X. Lei, B. Xu, X. Li, L. Dong, H. Yan, W. Liu, W. Jiang, L. Liu, C. Wang, X. Liang, and X. Tang, “Enhancement of the beam quality of non-uniform output slab laser amplifier with a 39-actuator rectangular piezoelectric deformable mirror,” Opt. Express 18(7), 7121–7130 (2010). [PubMed]  

11. S. Kokorowski, “Analysis of adaptive optical elements made from piezolectric bimorphs,” J. Opt. Soc. Am. 69(1), 181–187 (1979).

12. E. Steinhaus and S. Lipson, “Bimorph piezoelectric flexible mirror,” J. Opt. Soc. Am. 69(3), 478–481 (1979).

13. P. Hyunkyu and D. A. Horsley, “Single-crystal PMN-PT MEMS Deformable Mirrors,” J. Microelectromech. 20(6), 1473–1482 (2011).

14. P. Rausch, S. Verpoort, and U. Wittrock, “Unimorph deformable mirror for space telescopes: environmental testing,” Opt. Express 24(2), 1528–1542 (2016). [PubMed]  

15. C. Reinlein, M. Appelfelder, S. Gebhardt, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermomechanical design, hybrid fabrication, and testing of a MOEMS deformable mirror,” J. Micro/Nanolith. MEMS MOEMS 12(1), 013016 (2013).

16. S. Verpoort, P. Rausch, and U. Wittrock, “Characterization of a miniaturized unimorph deformable mirror for high power cw-solid state lasers,” Proc. SPIE 8253, 825309 (2012).

17. M. Gerber, T. Graf, and A. Kudryashov, “Generation of custom modes in a Nd: YAG laser with a semipassive bimorph adaptive mirror,” Appl. Phys. B 83, 43–50 (2006).

18. V. Samarkin, A. Aleksandrov, V. Dubikovsky, and A. Kudryashov, “Water-cooled bimorph correctors,” Proc. SPIE 6018, 60180Z (2005).

19. J.-H. Lee, Y.-C. Lee, and E.-C. Kang, “A cooled deformable bimorph mirror for a high power laser,” J. Opt. Soc. Korea 10(2), 57–62 (2006).

20. A. V. Kudryashov and V. V. Samarkin, “Control of high power CO2 laser beam by adaptive optical elements,” Opt. Commun. 118, 317–322 (1995).

21. L. N. Kaptsov, A. V. Kudryashov, V. V. Samarkin, and A. Seliverstov, “Control of parameters of solid-state industrial YAG: Nd3+ laser radiation using methods of adaptive optics. II. Spherical adaptive mirror,” Sov. J. Quantum Electron. 22(6), 533–534 (1992).

22. C. Zhou, Y. Li, A. Wang, and T. Xing, “Concept and Modeling Analysis of a High Fidelity Multimode Deformable Mirror,” Appl. Opt. 54(17), 5436–5443 (2015). [PubMed]  

23. R. Bastaits, D. Alaluf, M. Horodinca, I. Romanescu, I. Burda, G. Martic, G. Rodrigues, and A. Preumont, “Segmented bimorph mirrors for adaptive optics: segment design and experiment,” Appl. Opt. 53(29), 6635–6642 (2014). [PubMed]  

24. G. T. Kennedy and C. Paterson, “Correcting the ocular aberrations of a healthy adult population using microelectromechanical (MEMS) deformable mirrors,” Opt. Commun. 271, 278–284 (2007).

25. G. Vdovin, O. Soloviev, A. Samokhin, and M. Loktev, “Correction of low order aberrations using continuous deformable mirrors,” Opt. Express 16(5), 2859–2866 (2008). [PubMed]  

26. J. Ma, Y. Liu, T. He, B. Li, and J. Chu, “Double Drive Modes Unimorph Deformable Mirror for Low-Cost Adaptive Optics,” Appl. Opt. 50(29), 5647–5654 (2011). [PubMed]  

27. L. B. Freund and S. Suresh, Thin film materials: stress, defect formation and surface evolution (Cambridge University, 2004).

28. J. Ma, K. Chen, J. Chen, B. Li, and J. Chu, “Closed-loop correction and ocular wavefronts compensation of a 62-element silicon unimorph deformable mirror,” Chin. Opt. Lett. 13(4), 042201 (2015).

References

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  1. W. Koechner, Solid-state Laser Engineering (Springer, 2013).
  2. T. Y. Cherezova, S. S. Chesnokov, L. N. Kaptsov, V. V. Samarkin, and A. V. Kudryashov, “Active laser resonator performance: formation of a specified intensity output,” Appl. Opt. 40(33), 6026–6033 (2001).
    [PubMed]
  3. W. Clarkson, “Thermal effects and their mitigation in end-pumped solid-state lasers,” J. Phys. D Appl. Phys. 34(16), 2381–2395 (2001).
  4. E. Wyss, M. Roth, T. Graf, and H. P. Weber, “Thermooptical compensation methods for high-power lasers,” IEEE J. Quantum Electron. 38(12), 1620–1628 (2002).
  5. S. Makki and J. Leger, “Solid-state laser resonators with diffractive optic thermal aberration correction,” IEEE J. Quantum Electron. 35(7), 1075–1085 (1999).
  6. R. R. Stephens and R. C. Lind, “Experimental study of an adaptive-laser resonator,” Opt. Lett. 3(3), 79–81 (1978).
    [PubMed]
  7. J. M. Spinhirne, D. Anafi, R. H. Freeman, and H. R. Garcia, “Intracavity adaptive optics. 1: Astigmatism correction performance,” Appl. Opt. 20(6), 976–984 (1981).
    [PubMed]
  8. W. Lubeigt, G. Valentine, and D. Burns, “Enhancement of laser performance using an intracavity deformable membrane mirror,” Opt. Express 16(15), 10943–10955 (2008).
    [PubMed]
  9. S. Piehler, T. Dietrich, P. Wittmüss, O. Sawodny, M. A. Ahmed, and T. Graf, “Deformable mirrors for intra-cavity use in high-power thin-disk lasers,” Opt. Express 25(4), 4254–4267 (2017).
    [PubMed]
  10. P. Yang, Y. Ning, X. Lei, B. Xu, X. Li, L. Dong, H. Yan, W. Liu, W. Jiang, L. Liu, C. Wang, X. Liang, and X. Tang, “Enhancement of the beam quality of non-uniform output slab laser amplifier with a 39-actuator rectangular piezoelectric deformable mirror,” Opt. Express 18(7), 7121–7130 (2010).
    [PubMed]
  11. S. Kokorowski, “Analysis of adaptive optical elements made from piezolectric bimorphs,” J. Opt. Soc. Am. 69(1), 181–187 (1979).
  12. E. Steinhaus and S. Lipson, “Bimorph piezoelectric flexible mirror,” J. Opt. Soc. Am. 69(3), 478–481 (1979).
  13. P. Hyunkyu and D. A. Horsley, “Single-crystal PMN-PT MEMS Deformable Mirrors,” J. Microelectromech. 20(6), 1473–1482 (2011).
  14. P. Rausch, S. Verpoort, and U. Wittrock, “Unimorph deformable mirror for space telescopes: environmental testing,” Opt. Express 24(2), 1528–1542 (2016).
    [PubMed]
  15. C. Reinlein, M. Appelfelder, S. Gebhardt, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermomechanical design, hybrid fabrication, and testing of a MOEMS deformable mirror,” J. Micro/Nanolith. MEMS MOEMS 12(1), 013016 (2013).
  16. S. Verpoort, P. Rausch, and U. Wittrock, “Characterization of a miniaturized unimorph deformable mirror for high power cw-solid state lasers,” Proc. SPIE 8253, 825309 (2012).
  17. M. Gerber, T. Graf, and A. Kudryashov, “Generation of custom modes in a Nd: YAG laser with a semipassive bimorph adaptive mirror,” Appl. Phys. B 83, 43–50 (2006).
  18. V. Samarkin, A. Aleksandrov, V. Dubikovsky, and A. Kudryashov, “Water-cooled bimorph correctors,” Proc. SPIE 6018, 60180Z (2005).
  19. J.-H. Lee, Y.-C. Lee, and E.-C. Kang, “A cooled deformable bimorph mirror for a high power laser,” J. Opt. Soc. Korea 10(2), 57–62 (2006).
  20. A. V. Kudryashov and V. V. Samarkin, “Control of high power CO2 laser beam by adaptive optical elements,” Opt. Commun. 118, 317–322 (1995).
  21. L. N. Kaptsov, A. V. Kudryashov, V. V. Samarkin, and A. Seliverstov, “Control of parameters of solid-state industrial YAG: Nd3+ laser radiation using methods of adaptive optics. II. Spherical adaptive mirror,” Sov. J. Quantum Electron. 22(6), 533–534 (1992).
  22. C. Zhou, Y. Li, A. Wang, and T. Xing, “Concept and Modeling Analysis of a High Fidelity Multimode Deformable Mirror,” Appl. Opt. 54(17), 5436–5443 (2015).
    [PubMed]
  23. R. Bastaits, D. Alaluf, M. Horodinca, I. Romanescu, I. Burda, G. Martic, G. Rodrigues, and A. Preumont, “Segmented bimorph mirrors for adaptive optics: segment design and experiment,” Appl. Opt. 53(29), 6635–6642 (2014).
    [PubMed]
  24. G. T. Kennedy and C. Paterson, “Correcting the ocular aberrations of a healthy adult population using microelectromechanical (MEMS) deformable mirrors,” Opt. Commun. 271, 278–284 (2007).
  25. G. Vdovin, O. Soloviev, A. Samokhin, and M. Loktev, “Correction of low order aberrations using continuous deformable mirrors,” Opt. Express 16(5), 2859–2866 (2008).
    [PubMed]
  26. J. Ma, Y. Liu, T. He, B. Li, and J. Chu, “Double Drive Modes Unimorph Deformable Mirror for Low-Cost Adaptive Optics,” Appl. Opt. 50(29), 5647–5654 (2011).
    [PubMed]
  27. L. B. Freund and S. Suresh, Thin film materials: stress, defect formation and surface evolution (Cambridge University, 2004).
  28. J. Ma, K. Chen, J. Chen, B. Li, and J. Chu, “Closed-loop correction and ocular wavefronts compensation of a 62-element silicon unimorph deformable mirror,” Chin. Opt. Lett. 13(4), 042201 (2015).

2017 (1)

2016 (1)

2015 (2)

2014 (1)

2013 (1)

C. Reinlein, M. Appelfelder, S. Gebhardt, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermomechanical design, hybrid fabrication, and testing of a MOEMS deformable mirror,” J. Micro/Nanolith. MEMS MOEMS 12(1), 013016 (2013).

2012 (1)

S. Verpoort, P. Rausch, and U. Wittrock, “Characterization of a miniaturized unimorph deformable mirror for high power cw-solid state lasers,” Proc. SPIE 8253, 825309 (2012).

2011 (2)

P. Hyunkyu and D. A. Horsley, “Single-crystal PMN-PT MEMS Deformable Mirrors,” J. Microelectromech. 20(6), 1473–1482 (2011).

J. Ma, Y. Liu, T. He, B. Li, and J. Chu, “Double Drive Modes Unimorph Deformable Mirror for Low-Cost Adaptive Optics,” Appl. Opt. 50(29), 5647–5654 (2011).
[PubMed]

2010 (1)

2008 (2)

2007 (1)

G. T. Kennedy and C. Paterson, “Correcting the ocular aberrations of a healthy adult population using microelectromechanical (MEMS) deformable mirrors,” Opt. Commun. 271, 278–284 (2007).

2006 (2)

J.-H. Lee, Y.-C. Lee, and E.-C. Kang, “A cooled deformable bimorph mirror for a high power laser,” J. Opt. Soc. Korea 10(2), 57–62 (2006).

M. Gerber, T. Graf, and A. Kudryashov, “Generation of custom modes in a Nd: YAG laser with a semipassive bimorph adaptive mirror,” Appl. Phys. B 83, 43–50 (2006).

2005 (1)

V. Samarkin, A. Aleksandrov, V. Dubikovsky, and A. Kudryashov, “Water-cooled bimorph correctors,” Proc. SPIE 6018, 60180Z (2005).

2002 (1)

E. Wyss, M. Roth, T. Graf, and H. P. Weber, “Thermooptical compensation methods for high-power lasers,” IEEE J. Quantum Electron. 38(12), 1620–1628 (2002).

2001 (2)

1999 (1)

S. Makki and J. Leger, “Solid-state laser resonators with diffractive optic thermal aberration correction,” IEEE J. Quantum Electron. 35(7), 1075–1085 (1999).

1995 (1)

A. V. Kudryashov and V. V. Samarkin, “Control of high power CO2 laser beam by adaptive optical elements,” Opt. Commun. 118, 317–322 (1995).

1992 (1)

L. N. Kaptsov, A. V. Kudryashov, V. V. Samarkin, and A. Seliverstov, “Control of parameters of solid-state industrial YAG: Nd3+ laser radiation using methods of adaptive optics. II. Spherical adaptive mirror,” Sov. J. Quantum Electron. 22(6), 533–534 (1992).

1981 (1)

1979 (2)

1978 (1)

Ahmed, M. A.

Alaluf, D.

Aleksandrov, A.

V. Samarkin, A. Aleksandrov, V. Dubikovsky, and A. Kudryashov, “Water-cooled bimorph correctors,” Proc. SPIE 6018, 60180Z (2005).

Anafi, D.

Appelfelder, M.

C. Reinlein, M. Appelfelder, S. Gebhardt, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermomechanical design, hybrid fabrication, and testing of a MOEMS deformable mirror,” J. Micro/Nanolith. MEMS MOEMS 12(1), 013016 (2013).

Bastaits, R.

Beckert, E.

C. Reinlein, M. Appelfelder, S. Gebhardt, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermomechanical design, hybrid fabrication, and testing of a MOEMS deformable mirror,” J. Micro/Nanolith. MEMS MOEMS 12(1), 013016 (2013).

Burda, I.

Burns, D.

Chen, J.

Chen, K.

Cherezova, T. Y.

Chesnokov, S. S.

Chu, J.

Clarkson, W.

W. Clarkson, “Thermal effects and their mitigation in end-pumped solid-state lasers,” J. Phys. D Appl. Phys. 34(16), 2381–2395 (2001).

Dietrich, T.

Dong, L.

Dubikovsky, V.

V. Samarkin, A. Aleksandrov, V. Dubikovsky, and A. Kudryashov, “Water-cooled bimorph correctors,” Proc. SPIE 6018, 60180Z (2005).

Eberhardt, R.

C. Reinlein, M. Appelfelder, S. Gebhardt, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermomechanical design, hybrid fabrication, and testing of a MOEMS deformable mirror,” J. Micro/Nanolith. MEMS MOEMS 12(1), 013016 (2013).

Freeman, R. H.

Garcia, H. R.

Gebhardt, S.

C. Reinlein, M. Appelfelder, S. Gebhardt, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermomechanical design, hybrid fabrication, and testing of a MOEMS deformable mirror,” J. Micro/Nanolith. MEMS MOEMS 12(1), 013016 (2013).

Gerber, M.

M. Gerber, T. Graf, and A. Kudryashov, “Generation of custom modes in a Nd: YAG laser with a semipassive bimorph adaptive mirror,” Appl. Phys. B 83, 43–50 (2006).

Graf, T.

S. Piehler, T. Dietrich, P. Wittmüss, O. Sawodny, M. A. Ahmed, and T. Graf, “Deformable mirrors for intra-cavity use in high-power thin-disk lasers,” Opt. Express 25(4), 4254–4267 (2017).
[PubMed]

M. Gerber, T. Graf, and A. Kudryashov, “Generation of custom modes in a Nd: YAG laser with a semipassive bimorph adaptive mirror,” Appl. Phys. B 83, 43–50 (2006).

E. Wyss, M. Roth, T. Graf, and H. P. Weber, “Thermooptical compensation methods for high-power lasers,” IEEE J. Quantum Electron. 38(12), 1620–1628 (2002).

He, T.

Horodinca, M.

Horsley, D. A.

P. Hyunkyu and D. A. Horsley, “Single-crystal PMN-PT MEMS Deformable Mirrors,” J. Microelectromech. 20(6), 1473–1482 (2011).

Hyunkyu, P.

P. Hyunkyu and D. A. Horsley, “Single-crystal PMN-PT MEMS Deformable Mirrors,” J. Microelectromech. 20(6), 1473–1482 (2011).

Jiang, W.

Kang, E.-C.

Kaptsov, L. N.

T. Y. Cherezova, S. S. Chesnokov, L. N. Kaptsov, V. V. Samarkin, and A. V. Kudryashov, “Active laser resonator performance: formation of a specified intensity output,” Appl. Opt. 40(33), 6026–6033 (2001).
[PubMed]

L. N. Kaptsov, A. V. Kudryashov, V. V. Samarkin, and A. Seliverstov, “Control of parameters of solid-state industrial YAG: Nd3+ laser radiation using methods of adaptive optics. II. Spherical adaptive mirror,” Sov. J. Quantum Electron. 22(6), 533–534 (1992).

Kennedy, G. T.

G. T. Kennedy and C. Paterson, “Correcting the ocular aberrations of a healthy adult population using microelectromechanical (MEMS) deformable mirrors,” Opt. Commun. 271, 278–284 (2007).

Kokorowski, S.

Kudryashov, A.

M. Gerber, T. Graf, and A. Kudryashov, “Generation of custom modes in a Nd: YAG laser with a semipassive bimorph adaptive mirror,” Appl. Phys. B 83, 43–50 (2006).

V. Samarkin, A. Aleksandrov, V. Dubikovsky, and A. Kudryashov, “Water-cooled bimorph correctors,” Proc. SPIE 6018, 60180Z (2005).

Kudryashov, A. V.

T. Y. Cherezova, S. S. Chesnokov, L. N. Kaptsov, V. V. Samarkin, and A. V. Kudryashov, “Active laser resonator performance: formation of a specified intensity output,” Appl. Opt. 40(33), 6026–6033 (2001).
[PubMed]

A. V. Kudryashov and V. V. Samarkin, “Control of high power CO2 laser beam by adaptive optical elements,” Opt. Commun. 118, 317–322 (1995).

L. N. Kaptsov, A. V. Kudryashov, V. V. Samarkin, and A. Seliverstov, “Control of parameters of solid-state industrial YAG: Nd3+ laser radiation using methods of adaptive optics. II. Spherical adaptive mirror,” Sov. J. Quantum Electron. 22(6), 533–534 (1992).

Lee, J.-H.

Lee, Y.-C.

Leger, J.

S. Makki and J. Leger, “Solid-state laser resonators with diffractive optic thermal aberration correction,” IEEE J. Quantum Electron. 35(7), 1075–1085 (1999).

Lei, X.

Li, B.

Li, X.

Li, Y.

Liang, X.

Lind, R. C.

Lipson, S.

Liu, L.

Liu, W.

Liu, Y.

Loktev, M.

Lubeigt, W.

Ma, J.

Makki, S.

S. Makki and J. Leger, “Solid-state laser resonators with diffractive optic thermal aberration correction,” IEEE J. Quantum Electron. 35(7), 1075–1085 (1999).

Martic, G.

Ning, Y.

Paterson, C.

G. T. Kennedy and C. Paterson, “Correcting the ocular aberrations of a healthy adult population using microelectromechanical (MEMS) deformable mirrors,” Opt. Commun. 271, 278–284 (2007).

Piehler, S.

Preumont, A.

Rausch, P.

P. Rausch, S. Verpoort, and U. Wittrock, “Unimorph deformable mirror for space telescopes: environmental testing,” Opt. Express 24(2), 1528–1542 (2016).
[PubMed]

S. Verpoort, P. Rausch, and U. Wittrock, “Characterization of a miniaturized unimorph deformable mirror for high power cw-solid state lasers,” Proc. SPIE 8253, 825309 (2012).

Reinlein, C.

C. Reinlein, M. Appelfelder, S. Gebhardt, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermomechanical design, hybrid fabrication, and testing of a MOEMS deformable mirror,” J. Micro/Nanolith. MEMS MOEMS 12(1), 013016 (2013).

Rodrigues, G.

Romanescu, I.

Roth, M.

E. Wyss, M. Roth, T. Graf, and H. P. Weber, “Thermooptical compensation methods for high-power lasers,” IEEE J. Quantum Electron. 38(12), 1620–1628 (2002).

Samarkin, V.

V. Samarkin, A. Aleksandrov, V. Dubikovsky, and A. Kudryashov, “Water-cooled bimorph correctors,” Proc. SPIE 6018, 60180Z (2005).

Samarkin, V. V.

T. Y. Cherezova, S. S. Chesnokov, L. N. Kaptsov, V. V. Samarkin, and A. V. Kudryashov, “Active laser resonator performance: formation of a specified intensity output,” Appl. Opt. 40(33), 6026–6033 (2001).
[PubMed]

A. V. Kudryashov and V. V. Samarkin, “Control of high power CO2 laser beam by adaptive optical elements,” Opt. Commun. 118, 317–322 (1995).

L. N. Kaptsov, A. V. Kudryashov, V. V. Samarkin, and A. Seliverstov, “Control of parameters of solid-state industrial YAG: Nd3+ laser radiation using methods of adaptive optics. II. Spherical adaptive mirror,” Sov. J. Quantum Electron. 22(6), 533–534 (1992).

Samokhin, A.

Sawodny, O.

Seliverstov, A.

L. N. Kaptsov, A. V. Kudryashov, V. V. Samarkin, and A. Seliverstov, “Control of parameters of solid-state industrial YAG: Nd3+ laser radiation using methods of adaptive optics. II. Spherical adaptive mirror,” Sov. J. Quantum Electron. 22(6), 533–534 (1992).

Soloviev, O.

Spinhirne, J. M.

Steinhaus, E.

Stephens, R. R.

Tang, X.

Tünnermann, A.

C. Reinlein, M. Appelfelder, S. Gebhardt, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermomechanical design, hybrid fabrication, and testing of a MOEMS deformable mirror,” J. Micro/Nanolith. MEMS MOEMS 12(1), 013016 (2013).

Valentine, G.

Vdovin, G.

Verpoort, S.

P. Rausch, S. Verpoort, and U. Wittrock, “Unimorph deformable mirror for space telescopes: environmental testing,” Opt. Express 24(2), 1528–1542 (2016).
[PubMed]

S. Verpoort, P. Rausch, and U. Wittrock, “Characterization of a miniaturized unimorph deformable mirror for high power cw-solid state lasers,” Proc. SPIE 8253, 825309 (2012).

Wang, A.

Wang, C.

Weber, H. P.

E. Wyss, M. Roth, T. Graf, and H. P. Weber, “Thermooptical compensation methods for high-power lasers,” IEEE J. Quantum Electron. 38(12), 1620–1628 (2002).

Wittmüss, P.

Wittrock, U.

P. Rausch, S. Verpoort, and U. Wittrock, “Unimorph deformable mirror for space telescopes: environmental testing,” Opt. Express 24(2), 1528–1542 (2016).
[PubMed]

S. Verpoort, P. Rausch, and U. Wittrock, “Characterization of a miniaturized unimorph deformable mirror for high power cw-solid state lasers,” Proc. SPIE 8253, 825309 (2012).

Wyss, E.

E. Wyss, M. Roth, T. Graf, and H. P. Weber, “Thermooptical compensation methods for high-power lasers,” IEEE J. Quantum Electron. 38(12), 1620–1628 (2002).

Xing, T.

Xu, B.

Yan, H.

Yang, P.

Zhou, C.

Appl. Opt. (5)

Appl. Phys. B (1)

M. Gerber, T. Graf, and A. Kudryashov, “Generation of custom modes in a Nd: YAG laser with a semipassive bimorph adaptive mirror,” Appl. Phys. B 83, 43–50 (2006).

Chin. Opt. Lett. (1)

IEEE J. Quantum Electron. (2)

E. Wyss, M. Roth, T. Graf, and H. P. Weber, “Thermooptical compensation methods for high-power lasers,” IEEE J. Quantum Electron. 38(12), 1620–1628 (2002).

S. Makki and J. Leger, “Solid-state laser resonators with diffractive optic thermal aberration correction,” IEEE J. Quantum Electron. 35(7), 1075–1085 (1999).

J. Micro/Nanolith. MEMS MOEMS (1)

C. Reinlein, M. Appelfelder, S. Gebhardt, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermomechanical design, hybrid fabrication, and testing of a MOEMS deformable mirror,” J. Micro/Nanolith. MEMS MOEMS 12(1), 013016 (2013).

J. Microelectromech. (1)

P. Hyunkyu and D. A. Horsley, “Single-crystal PMN-PT MEMS Deformable Mirrors,” J. Microelectromech. 20(6), 1473–1482 (2011).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Korea (1)

J. Phys. D Appl. Phys. (1)

W. Clarkson, “Thermal effects and their mitigation in end-pumped solid-state lasers,” J. Phys. D Appl. Phys. 34(16), 2381–2395 (2001).

Opt. Commun. (2)

A. V. Kudryashov and V. V. Samarkin, “Control of high power CO2 laser beam by adaptive optical elements,” Opt. Commun. 118, 317–322 (1995).

G. T. Kennedy and C. Paterson, “Correcting the ocular aberrations of a healthy adult population using microelectromechanical (MEMS) deformable mirrors,” Opt. Commun. 271, 278–284 (2007).

Opt. Express (5)

Opt. Lett. (1)

Proc. SPIE (2)

S. Verpoort, P. Rausch, and U. Wittrock, “Characterization of a miniaturized unimorph deformable mirror for high power cw-solid state lasers,” Proc. SPIE 8253, 825309 (2012).

V. Samarkin, A. Aleksandrov, V. Dubikovsky, and A. Kudryashov, “Water-cooled bimorph correctors,” Proc. SPIE 6018, 60180Z (2005).

Sov. J. Quantum Electron. (1)

L. N. Kaptsov, A. V. Kudryashov, V. V. Samarkin, and A. Seliverstov, “Control of parameters of solid-state industrial YAG: Nd3+ laser radiation using methods of adaptive optics. II. Spherical adaptive mirror,” Sov. J. Quantum Electron. 22(6), 533–534 (1992).

Other (2)

L. B. Freund and S. Suresh, Thin film materials: stress, defect formation and surface evolution (Cambridge University, 2004).

W. Koechner, Solid-state Laser Engineering (Springer, 2013).

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Figures (12)

Fig. 1
Fig. 1 Cross-sectional view of the water-cooled unimorph DM.
Fig. 2
Fig. 2 Finite element model of the unimorph DM: (a) mesh of the model and (b) mirror deformation under activation of Act1.
Fig. 3
Fig. 3 Simulated wavefront profiles of the DM driven by Act1 and Act2.
Fig. 4
Fig. 4 Simulated reconstruction of astigmatism Z3 and coma Z7.
Fig. 5
Fig. 5 Simulation reproduction of the first 14 term Zernike modes: (a) RMS wavefront and (b) normalized residual wavefront error.
Fig. 6
Fig. 6 Thermal effect of the DM under laser radiation with and without cooling: (a) Thermal response curve and (b) temperature profiles of DM along the radial direction at 10 seconds.
Fig. 7
Fig. 7 Thermal wavefront deformation at 10 seconds.
Fig. 8
Fig. 8 Photographs of the fabricated water-cooled DM: (a) unimorph DM and (b) packaged DM with cooling cavity.
Fig. 9
Fig. 9 Comparison of simulated and measured wavefront deformation of actuator at the aperture of 20 mm.
Fig. 10
Fig. 10 Wavefront surface of the DM at 15 mm aperture before and after filling the cooling cavity with water.
Fig. 11
Fig. 11 Experimental reproduction of the first 14 Zernike mode shapes using closed-loop control method. The wavefront PV value and RMS value are indicated for each mode.
Fig. 12
Fig. 12 Experimental reproduction of the first 14 term Zernike mode shapes at different apertures: (a) wavefront RMS and (b) normalized residual wavefront error.

Tables (2)

Tables Icon

Table 1 Material properties of the DM used in the simulation

Tables Icon

Table 2 Wavefront strokes of Act1 and Act2 at different apertures

Metrics