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Aiming at improving the beam quality of thin-wall tube laser, a novel method based on the right-angle cone deformable mirror is proposed. In the method, a reflector with inner right-angle conical surface is used, and the annular laser beam successively passes through the opposite sides of the tube, compensating for the off-axis aberrations of the annular laser beam. Next, the residual aberrations are corrected by the deformation of the right-angle cone mirror to further improve the beam quality. The physical model of the right-angle cone deformable mirror is built up by using the finite element analysis method, followed by optimizing the structural parameters of the right-angle cone deformable mirror. The preliminarily optimized right-angle cone deformable mirror drived by 48 actuators with a radius of 1.5 mm for each actuator and an interval of 11 mm between actuators is then utilized to correct the beam quality of the thin-wall tube laser. Results indicate that the output beam quality of the thin-wall tube laser degrades rapidly with the increasing of the tube’s concentricity error, parallelism error, taper error and source’s parallelism error. Fortunately, the beam quality is significantly improved by using the right-angle cone deformable mirror and the β factor greatly decreases. In addition, the performance of the non-ideal right-angle cone deformable mirror with a 20-μrad taper error and a 10-mrad collimation error is compared with that of the ideal mirror, and the results show that the β factor is controlled within 1.14 after having been corrected by the non-ideal right-angle cone deformable mirror. Therefore, the simulation results theoretically prove that the novel method can effectively eliminate the typical aberrations caused by the errors from fabrication and alignment and correct the wavefront distortion of the large-aperture thin-wall tube laser, thus significantly improving the beam quality.
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Keywords:
- tube laser /
- right-angle cone deformable mirror /
- beam quality /
- adaptive optics
[1] 董俊, 王光宇, 任滢滢 2013 中国激光 40 27
Google Scholar
Dong J, Wang G Y, Ren Y Y 2013 Chin. J. Laser. 40 27
Google Scholar
[2] Wittrock U, Weber H, Eppich B 1991 Opt. Lett. 16 1092
Google Scholar
[3] Clarkson W A, Shori R K, Savich M 2015 Conference on Solid State Lasers San Francisco, USA, February 7, 2015 p934216
[4] 李宁, 张伟桥, 刘洋, 唐晓军 2018 中国激光 45 17
Google Scholar
Li N, Zhang W Q, Liu Y, Tang X J 2018 Chin. J. Las. 45 17
Google Scholar
[5] 李密, 周唐建, 徐浏, 高清松, 章健, 邬映臣, 汪丹, 胡浩, 唐淳, 于益, 吴振海, 李建民, 石勇, 赵娜 2018 光学学报 38 198
Google Scholar
Li M, Zhou T J, Xu L, Gao Q S, Zhang J, Wu Y C, Wang D, Hu H, Tang C, Yu Y, Wu Z H, Li J M, Shi Y, Zhao N 2018 Acta Opt. Sin. 38 198
Google Scholar
[6] Tian B Y, Zhong Z Q, Huang C 2019 IEEE Photonics J. 11 1
Google Scholar
[7] Burger L, Litvin I, Ngcobo S, Forbes A 2015 J. Opt. 17 015604
Google Scholar
[8] Cornelissen S A, Bierden P A, Bifano T G, Lam C V 2009 J. Micro-Nanolith. Mem. 8 767
Google Scholar
[9] Tokovinin A, Thomas S, Vdovin G 2004 SPIE Proceedings Advancements in Adaptive Optics Glasgow, USA, October 25, 2004 p580
[10] Li M, Hu H, Gao Q S, Wang J T, Zhang J, Wu Y C, Zhou T J, Xu L, Tang C, Zhao N, Liu P 2017 IEEE Photonics J. 9 1
Google Scholar
[11] 晏虎, 雷翔, 刘文劲, 王帅, 高源, 董理治, 杨平, 许冰 2012 强激光与粒子束 24 1663
Google Scholar
Yan H, Lei X, Liu W J, Wang S, Gao Y, Dong L Z, Yang P, Xu B 2012 High Pow. Las. Part. Beam. 24 1663
Google Scholar
[12] Yang P, Ning Y, Lei X 2010 Opt. Express 18 7121
Google Scholar
[13] Vdovin G, Loktev M, Simonov A, Gruneisen M T, Gonglewski J D, Giles M K 2005 SPIE Optics + Photonics San Diego, USA, August 18, 2005 p5894940 B
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Google Scholar
[15] Verpoort S, Rausch P, Wittrock U 2012 SPIE Proceedings Mems Adaptive Optics VI San Francisco, USA, January 21, 2012 p852909
[16] Bayanna A R, Louis R E, Chatterjee S, Mathew S K, Venkatakrishnan P 2015 Appl. Opt 54 1727
Google Scholar
[17] Lu J S, Su G 2012 SPIE Optical Engineering + Applications San Diego, USA, October 17, 2012 p84880D
[18] Bartsch D U, Freeman W R, Fainman Y, Zhu L, Sun P C 1999 Appl. Opt. 38 168
Google Scholar
[19] Wallace Ce B P, Hampton P J, Bradley C H, Conan R 2006 Opt. Express 14 10132
Google Scholar
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Google Scholar
[21] Mathur V, Vangala S R, Qian X, Goodhue W D, Khoury J 2009 IEEE/LEOS International Conference on Optical MEMS and Nanophotonics Tampa, USA, August 17, 2009 p156
[22] Hembrecht M A, He M, Kempf C J, Olivier S S, Bifano T G, Kubby J 2012 MEMS Adaptive Optics VI San Francisco, USA, February 6, 2012 p825307
[23] Sun C, Lei H, Wang D, Deng X, Zheng Y 2019 Opt. Express 27 9215
Google Scholar
[24] Wittrock U, Weber H, Eppich B 1989 Fourth International Meeting of the EUREKA HPSSL Project EU226 Berlin, Germany, October 12, 1989 p1175
[25] Loiko P A, Yumashev K V, Kuleshov N V, Savitski V G, Calvez S, Burns D 2009 Opt. Express 17 23536
Google Scholar
[26] Tashiro W H 2000 Opt. Commun. 175 189
Google Scholar
[27] Tian B Y, Yu J C, Zhang B 2020 Opt. Eng. 59 1
Google Scholar
[28] Harvey J E, Callahan G M 1978 Adaptive Optical Components I, Washington, D. C., USA, August 8, 1978 p50
[29] 李佳, 田博宇, 余江川, 张彬 2021 中国激光 48 67
Google Scholar
Li J, Tian B Y, Yu J C 2021 Chin. J. Las. 48 67
Google Scholar
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图 1 基于直角锥面变形镜的薄管激光畸变波前校正原理示意图
Figure 1. The principle schematic diagram of tube laser distortion wavefront correction based on the right-angle cone deformable mirror.
图 2 直角锥面变形镜驱动器分布示意图 (a) 变形镜后表面视图; (b) 变形镜侧视图
Figure 2. Schematic diagram of drive units arrangement of the right-angle cone deformable mirror: (a) Rear surface of deformable mirror; (b) side view of deformable mirror
图 3 等效变形镜示意图
Figure 3. The diagram of equivalent deformable mirror.
图 4 坐标变换示意图
Figure 4. The diagram of coordinate transformation.
图 5 薄管同心度误差为1 μm时的波像差分解及远场光强分布 (a) 薄管同心度误差1 μm时畸变波前波像差分解; (b) 远场光强分布
Figure 5. The wavefront aberration decomposition and far-filed intensity distributions with the concentricity error of 1 μm: (a) The wavefront aberration decomposition; (b) far-filed intensity distribution.
图 6 直角锥面变形镜的参数优化 (a) 环域离焦残余波前PV值随驱动器半径与主驱动器径向间距的变化; (b) 环域像散残余波前PV值随驱动器半径与主驱动器径向间距的变化
Figure 6. Parameters optimization: (a) The PV variation of annular defocusing residual wavefront; (b) the PV variation of annular astigmatism residual wavefront.
图 7 校正前后β因子变化 (a) β因子随薄管同心度误差变化; (b) β因子随薄管平行度误差变化; (c) β因子随薄管锥度误差变化; (d) β因子随光源平行度误差变化
Figure 7. The curves of β factor: (a) Tube’s concentricity error; (b) tube’s parallelism error; (c) tube’s taper error; (d) source’s parallelism error.
图 8 多误差耦合作用下校正前后远场光强分布及β因子 (a) Δx = 1 μm, Δθ = 5 μrad, Δθa = 100 μrad, Δθs = 100 μrad; (b) Δx = 0.5 μm, Δθ = 15 μrad, Δθa = 150 μrad, Δθs = 200 μrad; (c) Δx = 1 μm, Δθ = 10 μrad, Δθa = 200 μrad, Δθs = 150 μrad
Figure 8. Far-filed intensity distributions and β factor before and after correction under multi-error coupling: (a) Δx = 1 μm, Δθ = 5 μrad, Δθa = 100 μrad, Δθs = 100 μrad; (b) Δx = 0.5 μm; Δθ = 15 μrad; Δθa = 150 μrad; Δθs = 200 μrad; (c) Δx = 1 μm, Δθ = 10 μrad, Δθa = 200 μrad; Δθs = 150 μrad.
图 9 非理想直角锥面变形镜校正后远场光强分布及β因子 (a) Δx = 1 μm, Δθ = 5 μrad, Δθa = 100 μrad, Δθs = 100 μrad; (b) Δx = 0.5 μm, Δθ = 15 μrad, Δθa = 150 μrad, Δθs = 200 μrad; (c) Δx = 1 μm, Δθ = 10 μrad, Δθa = 200 μrad, Δθs = 150 μrad
Figure 9. Comparisons of far-filed intensity distribution and β factor under nonideal circumstances: (a) Δx = 1 μm, Δθ = 5 μrad, Δθa = 100 μrad, Δθs = 100 μrad; (b) Δx = 0.5 μm, Δθ = 15 μrad, Δθa = 150 μrad, Δθs = 200 μrad; (c) Δx = 1 μm, Δθ = 10 μrad, Δθa = 200 μrad, Δθs = 150 μrad.
表 1 材料力学参数
Table 1. Material parameters.
Parameters BK7 PZT Young’s mudulus/Gpa 81 70 Poisson’s ratio 0.17 0.33 Density/(kg·m–3) 2400 7700 
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表 2 直角锥面变形镜变形镜结构参数
Table 2. The parameters of the right-angle cone deformable mirror.
Parameters Value Parameters Value ri 26 mm H 30.7 mm ro 31 mm ΔHsub 25 mm α 45° ΔHmain 11 mm γ 30° ΔCsub_o 19.5 mm rDi 11.2 mm ΔCsub_i 10.3 mm rDo 41.8 mm ΔCmain_o 16.9 mm RDi 13.2 mm ΔCmain_i 12.9 mm RDo 43.8 mm
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[1] 董俊, 王光宇, 任滢滢 2013 中国激光 40 27
Google Scholar
Dong J, Wang G Y, Ren Y Y 2013 Chin. J. Laser. 40 27
Google Scholar
[2] Wittrock U, Weber H, Eppich B 1991 Opt. Lett. 16 1092
Google Scholar
[3] Clarkson W A, Shori R K, Savich M 2015 Conference on Solid State Lasers San Francisco, USA, February 7, 2015 p934216
[4] 李宁, 张伟桥, 刘洋, 唐晓军 2018 中国激光 45 17
Google Scholar
Li N, Zhang W Q, Liu Y, Tang X J 2018 Chin. J. Las. 45 17
Google Scholar
[5] 李密, 周唐建, 徐浏, 高清松, 章健, 邬映臣, 汪丹, 胡浩, 唐淳, 于益, 吴振海, 李建民, 石勇, 赵娜 2018 光学学报 38 198
Google Scholar
Li M, Zhou T J, Xu L, Gao Q S, Zhang J, Wu Y C, Wang D, Hu H, Tang C, Yu Y, Wu Z H, Li J M, Shi Y, Zhao N 2018 Acta Opt. Sin. 38 198
Google Scholar
[6] Tian B Y, Zhong Z Q, Huang C 2019 IEEE Photonics J. 11 1
Google Scholar
[7] Burger L, Litvin I, Ngcobo S, Forbes A 2015 J. Opt. 17 015604
Google Scholar
[8] Cornelissen S A, Bierden P A, Bifano T G, Lam C V 2009 J. Micro-Nanolith. Mem. 8 767
Google Scholar
[9] Tokovinin A, Thomas S, Vdovin G 2004 SPIE Proceedings Advancements in Adaptive Optics Glasgow, USA, October 25, 2004 p580
[10] Li M, Hu H, Gao Q S, Wang J T, Zhang J, Wu Y C, Zhou T J, Xu L, Tang C, Zhao N, Liu P 2017 IEEE Photonics J. 9 1
Google Scholar
[11] 晏虎, 雷翔, 刘文劲, 王帅, 高源, 董理治, 杨平, 许冰 2012 强激光与粒子束 24 1663
Google Scholar
Yan H, Lei X, Liu W J, Wang S, Gao Y, Dong L Z, Yang P, Xu B 2012 High Pow. Las. Part. Beam. 24 1663
Google Scholar
[12] Yang P, Ning Y, Lei X 2010 Opt. Express 18 7121
Google Scholar
[13] Vdovin G, Loktev M, Simonov A, Gruneisen M T, Gonglewski J D, Giles M K 2005 SPIE Optics + Photonics San Diego, USA, August 18, 2005 p5894940 B
[14] Wittrock U, Verpoort S 2010 Appl. Opt. 49 G37
Google Scholar
[15] Verpoort S, Rausch P, Wittrock U 2012 SPIE Proceedings Mems Adaptive Optics VI San Francisco, USA, January 21, 2012 p852909
[16] Bayanna A R, Louis R E, Chatterjee S, Mathew S K, Venkatakrishnan P 2015 Appl. Opt 54 1727
Google Scholar
[17] Lu J S, Su G 2012 SPIE Optical Engineering + Applications San Diego, USA, October 17, 2012 p84880D
[18] Bartsch D U, Freeman W R, Fainman Y, Zhu L, Sun P C 1999 Appl. Opt. 38 168
Google Scholar
[19] Wallace Ce B P, Hampton P J, Bradley C H, Conan R 2006 Opt. Express 14 10132
Google Scholar
[20] Guzmán D, Juez F, Myers R, Guesalaga A, Lasheras F S 2010 Opt. Express 18 21356
Google Scholar
[21] Mathur V, Vangala S R, Qian X, Goodhue W D, Khoury J 2009 IEEE/LEOS International Conference on Optical MEMS and Nanophotonics Tampa, USA, August 17, 2009 p156
[22] Hembrecht M A, He M, Kempf C J, Olivier S S, Bifano T G, Kubby J 2012 MEMS Adaptive Optics VI San Francisco, USA, February 6, 2012 p825307
[23] Sun C, Lei H, Wang D, Deng X, Zheng Y 2019 Opt. Express 27 9215
Google Scholar
[24] Wittrock U, Weber H, Eppich B 1989 Fourth International Meeting of the EUREKA HPSSL Project EU226 Berlin, Germany, October 12, 1989 p1175
[25] Loiko P A, Yumashev K V, Kuleshov N V, Savitski V G, Calvez S, Burns D 2009 Opt. Express 17 23536
Google Scholar
[26] Tashiro W H 2000 Opt. Commun. 175 189
Google Scholar
[27] Tian B Y, Yu J C, Zhang B 2020 Opt. Eng. 59 1
Google Scholar
[28] Harvey J E, Callahan G M 1978 Adaptive Optical Components I, Washington, D. C., USA, August 8, 1978 p50
[29] 李佳, 田博宇, 余江川, 张彬 2021 中国激光 48 67
Google Scholar
Li J, Tian B Y, Yu J C 2021 Chin. J. Las. 48 67
Google Scholar
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