压电变形镜控制方法及应用研究
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摘要
自适应光学技术是通过实时测量波前畸变,并利用相位共轭的原理实时补偿波前畸变,提高光学系统分辨率。自适应光学最初被提出并应用于天文望远镜,用于补偿诸如大气湍流等动态扰动的影响。自适应光学技术从提出至今经过数十年的发展,已经在天文望远镜、视网膜成像、激光核聚变系统、激光加工、生物显微、及激光通讯等很多领域得到了广泛的应用。压电变形镜作为一种常用波前校正器,具有大冲程、高带宽等优点,受到自适应光学研究者的青睐。本论文以压电变形镜控制方法及应用作为主要研究内容,主要进行了以下研究工作。
(1)研制了拟应用于天文领域的大口径214单元单压电片变形镜,该变形镜具有优异像差校正性能、轻量化、低驱动电压低功耗、高工艺稳定性等优点。建立了该变形镜的力学模型,并基于该力学模型确定了变形镜的结构参数,并通过数值仿真对变形镜变形量、波前像差校正性能等主要性能参数进行了仿真。研究了该变形镜制备流程及关键工艺、电气连接及封装技术。完成了该变形镜样机的研制,并对该变形镜初始面型、变形量、频率响应、初始像差校平及像差重构能力进行了测试表征。通过“地”电极偏置和双驱动模式变形镜两种方法实现了该变形镜正向电压驱动下的双向变形,从而实现了对自身像差的校平。通过以上理论分析、仿真与测试证明了该变形镜具有在天文应用中使用的潜力。
(2)对基于波前直接测量的自适应光学控制方法进行了研究。利用自研制单压电片变形镜构建了一套基于波前直接测量自适应光学实验系统,并使用最速下降方法、重复学习方法等控制方法控制单压电片变形镜,实现了对系统像差的校平及对特定Zernike像差的重构。同时,在该套自适应光学系统中测试了214单元单压电片变形镜的像差校正能力。
(3)针对无波前传感器控制方法中,爬山法校正效果受局部最优值问题制约,而遗传算法、模拟退火算法及随机梯度下降算法等几种全局优化算法校正效率低的问题,提出了模拟退火-爬山混合算法。该混合算法综合了两者的优势,降低了陷于局部最优值的可能性,保证了校正效果,同时提高了校正效率。为了更进一步提高校正效率,提出了基于Zernike正交基展开的模式爬山法。建立了该控制方法的数学模型,并从理论模型出发证明了该控制方法不受局部最优值问题影响。进行了数值仿真和远场光斑校正实验,仿真与实验结果说明该控制方法具有优异的校正效果,同时可以提高校正效率。另外还通过数值仿真和实验研究了基于Zernike模式爬山法对光斑校正中中心位置及口径不匹配因素的健壮性。
(4)针对飞秒激光加工中加工光斑一直受像差影响的问题,在飞秒激光加工系统中引入自适应光学系统对加工光斑进行校正。建立了飞秒激光加工中的折射率失配像差理论模型,并计算了加工深度、折射率失配情况、聚焦物镜数值孔径等因素对加工光斑能量的影响。完成了自适应飞秒激光光斑校正系统的搭建。进行了光斑校正实验,对系统像差及折射率失配像差分别进行了校正,实现了加工光斑光强及形状的提高。
基于以上研究,本论文在以下几个方面具有创新之处：1.提出了模拟退火-爬山混合算法和模式爬山法两种新的控制方法,保证校正效果的前提下大大提高了校正效率。2.针对天文应用研制了214单元单压电片变形镜,完成了该变形镜的设计、加工、封装及主要性能参数测试。3.在飞秒激光加工系统中引入自适应光学系统对加工光斑进行了校正,校正后加工光斑形状及峰值光强得到了提高。
Adaptive optics technology measures the wavefront distortion in real-time, and corrects the wavefront distortion based on the phase conjugate principle to improve the optical system resolution. Adaptive optics was first proposed and applied in astronomy telescopes to compensate the effect from some dynamic disturbances, such as the atmosphere turbulence. After several decades of development, adaptive optics technology has been widely used in many areas, such as astronomical telescopes, retinal imaging, laser fusion systems, laser fabrication, bio-microscopy and laser communications, and so on. As a frequently-used wavefront corrector, piezoelectric deformable mirror is attractive for its large stroke and high bandwidth. In this dissertation, the control method and application of the piezoelectric deformable mirror are selected as the main research content. The main research work are introduced as follows.
(1) An unimorph piezoelectric deformable mirror with214actuators was developed for telescope applications, and this deformable mirror has the following advantages, such as excellent aberration correction performance, lightweight, low driving voltage, low power consumption and high process stability. The mechanical model of this deformable mirror is built, and the structural parameters were determined based on the model. Then the key performance parameters, such as stroke, and aberration correction ability, were simulated through numerical simulation. In fabrication of this deformable mirror, fabrication flow and key technology, electrical connection and packaging technology were studied. After the prototype for this deformable mirror is developed, the key parameters, such as initial surface of the deformable mirror, actuator stroke, response frequency, and the ability for correction initial aberrations of the deformable mirror and reconstruction for Zernike aberrations were tested and characterized. Through "ground" electrode bias and double drive modes two kinds of methods, this deformable mirror achieved bi-directional deformation driven by only positive voltage. The results of these theoretical analysis, simulations and tests prove that this deformable mirror has the potential to be used in astronomical applications.
(2) The control methods for the adaptive optics system based on direct wavefront measurement were studied. An adaptive optics experimental system based on direct wavefront measurement was built using a home-made piezoelectric unimorph deformable mirror. The steepest descent method and iterative learning control method were used to control the piezoelectric unimorph deformable mirror in experiments of system aberration correction and specific Zernike aberration reconstruction. Besides, the aberration correction ability of the214-actuator unimorph piezoelectric deformable mirror was tested in the experimental system.
(3) In wavefront sensor-less adaptive system, there are several frequently-used control methods. While hill-climbing algorithm suffers from the local optimum problem, and the global optimum algorithms, such as genetic algorithm, simulated annealing algorithm, stochastic parallel gradient descent algorithm, have low correction efficiency. To solve this problem, hybrid simulated annealing-hill climbing algorithm is proposed, which can guarantee correction effect and improve correction efficiency. To improve correction efficiency furthermore, hill-climbing algorithm based on Zernike modes was proposed. The mathematical model for this algorithm was established, and this algorithm is proved to be not affected by the local optimum problem from the mathematical model. Numerical simulations and spot correction experiments were conducted, and the results indicated this algorithm can find the global optimal value with high efficiency. Besides, the robustness of this control algorithm for mismatched center position and aperture were studied by simulations and experiments.
(4) For femtosecond laser processing spot suffers from aberrations, an adaptive optics system is introduced into femtosecond laser processing system. The mathematical model for refractive index mismatch aberration is established, and the effect to processing spot intensity in different conditions of processing depth, refractive index mismatch degree, numerical aperture of the objective lens were calculated. A femtosecond laser processing system with an adaptive optics system was built. In experiments, system aberrations and refractive index mismatch aberrations are corrected separately. After correction, the peak intensity of focal spot is improved.
There are some creative points in this dissertation as follows:1. Two new algorithms, hybrid simulated annealing-hill climbing algorithm and hill-climbing algorithm based on Zernike modes are proposed to improve the correction effect and correction efficiency.2. For applications in telescopes, an unimorph piezoelectric deformable mirror with214actuators is proposed, and the design, fabrication, package and test of this deformable mirror are achieved.3. An adaptive optics system is introduce into femtosecond laser processing system to correct aberrations, and the peak intensity of focal spot is improved after correction.
(1)研制了拟应用于天文领域的大口径214单元单压电片变形镜,该变形镜具有优异像差校正性能、轻量化、低驱动电压低功耗、高工艺稳定性等优点。建立了该变形镜的力学模型,并基于该力学模型确定了变形镜的结构参数,并通过数值仿真对变形镜变形量、波前像差校正性能等主要性能参数进行了仿真。研究了该变形镜制备流程及关键工艺、电气连接及封装技术。完成了该变形镜样机的研制,并对该变形镜初始面型、变形量、频率响应、初始像差校平及像差重构能力进行了测试表征。通过“地”电极偏置和双驱动模式变形镜两种方法实现了该变形镜正向电压驱动下的双向变形,从而实现了对自身像差的校平。通过以上理论分析、仿真与测试证明了该变形镜具有在天文应用中使用的潜力。
(2)对基于波前直接测量的自适应光学控制方法进行了研究。利用自研制单压电片变形镜构建了一套基于波前直接测量自适应光学实验系统,并使用最速下降方法、重复学习方法等控制方法控制单压电片变形镜,实现了对系统像差的校平及对特定Zernike像差的重构。同时,在该套自适应光学系统中测试了214单元单压电片变形镜的像差校正能力。
(3)针对无波前传感器控制方法中,爬山法校正效果受局部最优值问题制约,而遗传算法、模拟退火算法及随机梯度下降算法等几种全局优化算法校正效率低的问题,提出了模拟退火-爬山混合算法。该混合算法综合了两者的优势,降低了陷于局部最优值的可能性,保证了校正效果,同时提高了校正效率。为了更进一步提高校正效率,提出了基于Zernike正交基展开的模式爬山法。建立了该控制方法的数学模型,并从理论模型出发证明了该控制方法不受局部最优值问题影响。进行了数值仿真和远场光斑校正实验,仿真与实验结果说明该控制方法具有优异的校正效果,同时可以提高校正效率。另外还通过数值仿真和实验研究了基于Zernike模式爬山法对光斑校正中中心位置及口径不匹配因素的健壮性。
(4)针对飞秒激光加工中加工光斑一直受像差影响的问题,在飞秒激光加工系统中引入自适应光学系统对加工光斑进行校正。建立了飞秒激光加工中的折射率失配像差理论模型,并计算了加工深度、折射率失配情况、聚焦物镜数值孔径等因素对加工光斑能量的影响。完成了自适应飞秒激光光斑校正系统的搭建。进行了光斑校正实验,对系统像差及折射率失配像差分别进行了校正,实现了加工光斑光强及形状的提高。
基于以上研究,本论文在以下几个方面具有创新之处：1.提出了模拟退火-爬山混合算法和模式爬山法两种新的控制方法,保证校正效果的前提下大大提高了校正效率。2.针对天文应用研制了214单元单压电片变形镜,完成了该变形镜的设计、加工、封装及主要性能参数测试。3.在飞秒激光加工系统中引入自适应光学系统对加工光斑进行了校正,校正后加工光斑形状及峰值光强得到了提高。
Adaptive optics technology measures the wavefront distortion in real-time, and corrects the wavefront distortion based on the phase conjugate principle to improve the optical system resolution. Adaptive optics was first proposed and applied in astronomy telescopes to compensate the effect from some dynamic disturbances, such as the atmosphere turbulence. After several decades of development, adaptive optics technology has been widely used in many areas, such as astronomical telescopes, retinal imaging, laser fusion systems, laser fabrication, bio-microscopy and laser communications, and so on. As a frequently-used wavefront corrector, piezoelectric deformable mirror is attractive for its large stroke and high bandwidth. In this dissertation, the control method and application of the piezoelectric deformable mirror are selected as the main research content. The main research work are introduced as follows.
(1) An unimorph piezoelectric deformable mirror with214actuators was developed for telescope applications, and this deformable mirror has the following advantages, such as excellent aberration correction performance, lightweight, low driving voltage, low power consumption and high process stability. The mechanical model of this deformable mirror is built, and the structural parameters were determined based on the model. Then the key performance parameters, such as stroke, and aberration correction ability, were simulated through numerical simulation. In fabrication of this deformable mirror, fabrication flow and key technology, electrical connection and packaging technology were studied. After the prototype for this deformable mirror is developed, the key parameters, such as initial surface of the deformable mirror, actuator stroke, response frequency, and the ability for correction initial aberrations of the deformable mirror and reconstruction for Zernike aberrations were tested and characterized. Through "ground" electrode bias and double drive modes two kinds of methods, this deformable mirror achieved bi-directional deformation driven by only positive voltage. The results of these theoretical analysis, simulations and tests prove that this deformable mirror has the potential to be used in astronomical applications.
(2) The control methods for the adaptive optics system based on direct wavefront measurement were studied. An adaptive optics experimental system based on direct wavefront measurement was built using a home-made piezoelectric unimorph deformable mirror. The steepest descent method and iterative learning control method were used to control the piezoelectric unimorph deformable mirror in experiments of system aberration correction and specific Zernike aberration reconstruction. Besides, the aberration correction ability of the214-actuator unimorph piezoelectric deformable mirror was tested in the experimental system.
(3) In wavefront sensor-less adaptive system, there are several frequently-used control methods. While hill-climbing algorithm suffers from the local optimum problem, and the global optimum algorithms, such as genetic algorithm, simulated annealing algorithm, stochastic parallel gradient descent algorithm, have low correction efficiency. To solve this problem, hybrid simulated annealing-hill climbing algorithm is proposed, which can guarantee correction effect and improve correction efficiency. To improve correction efficiency furthermore, hill-climbing algorithm based on Zernike modes was proposed. The mathematical model for this algorithm was established, and this algorithm is proved to be not affected by the local optimum problem from the mathematical model. Numerical simulations and spot correction experiments were conducted, and the results indicated this algorithm can find the global optimal value with high efficiency. Besides, the robustness of this control algorithm for mismatched center position and aperture were studied by simulations and experiments.
(4) For femtosecond laser processing spot suffers from aberrations, an adaptive optics system is introduced into femtosecond laser processing system. The mathematical model for refractive index mismatch aberration is established, and the effect to processing spot intensity in different conditions of processing depth, refractive index mismatch degree, numerical aperture of the objective lens were calculated. A femtosecond laser processing system with an adaptive optics system was built. In experiments, system aberrations and refractive index mismatch aberrations are corrected separately. After correction, the peak intensity of focal spot is improved.
There are some creative points in this dissertation as follows:1. Two new algorithms, hybrid simulated annealing-hill climbing algorithm and hill-climbing algorithm based on Zernike modes are proposed to improve the correction effect and correction efficiency.2. For applications in telescopes, an unimorph piezoelectric deformable mirror with214actuators is proposed, and the design, fabrication, package and test of this deformable mirror are achieved.3. An adaptive optics system is introduce into femtosecond laser processing system to correct aberrations, and the peak intensity of focal spot is improved after correction.
引文
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