液晶波前校正器的过驱动研究
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摘要
液晶波前校正器是液晶自适应光学系统的核心器件，其响应速度慢是影响液晶系统工程化的关键问题。虽然通过设计合成高Δn低粘度的向列相液晶材料可以提高液晶波前校正器的响应速度，但是提升其响应速度的潜力越来越有限。本论文根据液晶动力学理论，研究了与驱动过程相关的液晶分子指向矢转动行为，看出驱动电压从高到低变换时，液晶分子指向矢的分布越接近平衡态转动速度越慢，严重的拖尾现象使响应速度大大降低，因此将过驱动方法应用于液晶波前校正器中。过驱动是指使用比正常驱动更大的电压差来驱动液晶分子使其快速到达目标位相。
本论文以液晶弹性体理论为基础，推导了无扭曲液晶指向矢的平衡态方程及响应过程所满足的动力学方程；通过对不同驱动电压下的液晶分子回落响应曲线的分析，看出液晶波前校正器的响应时间由撤除最高驱动电压后回落2π位相的响应时间所决定。提高器件最高驱动电压可以缩短液晶波前校正器的响应时间，同时必须在完成2π位相回落的时刻施加对应剩余位相值的稳定电压；液晶器件的最高驱动电压由集成电路所能承受的电压决定，无法大幅增加，而鉴于电场作用于液晶分子的扭矩由电场强度与液晶Δ的乘积决定，因此可通过提高材料的Δ进一步减少液晶的响应时间。
研究了成品液晶波前校正器过驱动的实现方法。本实验室所用液晶波前校正器，即使采用上述过驱动方法其响应时间也较长，为1.92ms，如果进一步缩短响应过程将导致部分像素的位相不到位，引起波前校正误差；但实际上大气湍流中的波前是在50Hz上下动态变化的，响应时间大于1ms的校正器都会由于时间延迟引起更大的误差，因此本研究尝试了过驱动条件下液晶波前校正器响应时间接近1ms的实验。由于所用液晶自适应光学系统中波前探测器数据读出时间为1.07ms，因此所设定的液晶波前校正器响应时间不能短于1.07ms，另外液晶波前校正器只能在驱动场交变帧周期(128.3us)整数倍时刻进行电压切换，因此液晶波前校正器的响应时间必须是128.3us的整数倍，因此选取1.155ms作为液晶波前校正器的响应时间。经仿真计算，液晶波前校正器的响应时间限定为1.155ms时液晶自适应光学系统的–3dB误差抑制带宽为35Hz，而当响应延迟时间增加至1.92ms时–3dB误差抑制带宽仅为26Hz，因此1.155ms是所用系统的液晶响应时间优化值。
计算了1.155ms响应时引入的不到位误差。利用湍流模拟器产生格林伍德频率为30和50Hz、大气相干长度为2.4cm、7.2cm和10cm、口径为1.2米的湍流波前，采用上述液晶自适应光学系统对湍流波前进行实时校正；得出位相响应不到位误差不超过1.5×10-2λ（λ=785nm）；1.2米望远镜的衍射极限分辨要求波前残差RMS值应小于0.07λ，看出由不到位引起的校正误差约为1/5衍射极限对应的误差，可认为对成像效果不产生影响。
过驱动成功应用于与1.2米口径望远镜对接的液晶自适应光学系统，获得清晰的环境卫星、 Com双星等图片。对北极星的校正成像实验显示，未校正时星像亮度的半高宽为2.02角秒，不使用过驱动时校正后半高宽为0.46角秒，采用1.155ms的单帧过驱动校正后半高宽减至0.31角秒。
在单帧过驱动的基础上进一步提出了单帧超调过驱动及多帧过驱动的方法。经分析，使用单帧超调过驱动及多帧过驱动可以进一步减少系统校正残差，提高系统的带宽。仿真结果表明多帧过驱动可将–3dB抑制带宽提高至37Hz。
通过数学推导及仿真分析，研究了时间起伏误差、过驱动矩阵测量误差、位相-灰度级关系标定误差对过驱动过程的影响。提出进一步提高位相-灰度级标定精度的方法及过驱动矩阵测量精度的方法。
Liquid crystal wavefront corrector is the core device of liquid crystal adaptiveoptical system. Slow response is the key problem which prevents the liquid crystaladaptive optical systems from engineering. The design and synthesis of high Δn andlow viscosity nematic liquid crystal materials can improve the response of liquidcrystal wavefront corrector. However, the potential of the improvement of theresponse become more and more limited. Therefore, based on the liquid crystaldynamics theory, this thesis researched the liquid crystal hydrodynamic process ofdirector rotation behavior. When the driving voltage changes from the higher voltageto the lower voltage, the distribution of the director of the liquid crystal is closer andcloser to the equilibrium state, and the rotational speed is slower and slower. Thisserious tailing phenomenon cause the average speed of response greatly reduced.Overdriving is applying a higher voltage difference than the normal driven to drivethe liquid crystal molecules to reach the target phase faster.
Based on the elastic theory of liquid crystal, this thesis derived the equilibriumequation and the hydrodynamic equation of the liquid crystal devices under theelectric field without distortion. The effect of the cell gap and voltage on the phaseresponse process is researched. Through the optimization of cell gap, the responsedelay of liquid crystal wavefront corrector can be reduced. By increasing Δ, theresponse delay can be shortened under the overdriving condition.
This thesis studied the driving scheme of the commercial liquid crystalwavefront corrector and the optimization of various parameters systematically. Bythe analysis of the time domain error and simulation, according to the relevantparameters of the system,1.155ms was choosed as the optimal response delay. Thefast overdriving matrix data processing and transition are realized using GPU. Thetime needed is about30us which makes this method can be directly applied tocommercial liquid crystal wavefront corrector. The single frame overdriving isapplied to the open-loop Liquid crystal adaptive optics system. The bandwidth testand the outfield experiment showed that the system performance is significantlyimproved. The–3dB bandwidth is improved from27Hz to35Hz. on the basis of thesingle frame overdriving, the single frame overshoot overdriving and multi-frameoverdriving is proposed, which can further reduce the residual wavefront correctionerror.
Through mathematical derivation, the mathematical relationship between theinput and the output of the residual error was obtained. The precised calibrationscheme was proposed to improve the phase level to gray level map precision further.The improved method of overdriving matrix measurement is put forward. The effectof temperature on the overdriving was studied.
本论文以液晶弹性体理论为基础，推导了无扭曲液晶指向矢的平衡态方程及响应过程所满足的动力学方程；通过对不同驱动电压下的液晶分子回落响应曲线的分析，看出液晶波前校正器的响应时间由撤除最高驱动电压后回落2π位相的响应时间所决定。提高器件最高驱动电压可以缩短液晶波前校正器的响应时间，同时必须在完成2π位相回落的时刻施加对应剩余位相值的稳定电压；液晶器件的最高驱动电压由集成电路所能承受的电压决定，无法大幅增加，而鉴于电场作用于液晶分子的扭矩由电场强度与液晶Δ的乘积决定，因此可通过提高材料的Δ进一步减少液晶的响应时间。
研究了成品液晶波前校正器过驱动的实现方法。本实验室所用液晶波前校正器，即使采用上述过驱动方法其响应时间也较长，为1.92ms，如果进一步缩短响应过程将导致部分像素的位相不到位，引起波前校正误差；但实际上大气湍流中的波前是在50Hz上下动态变化的，响应时间大于1ms的校正器都会由于时间延迟引起更大的误差，因此本研究尝试了过驱动条件下液晶波前校正器响应时间接近1ms的实验。由于所用液晶自适应光学系统中波前探测器数据读出时间为1.07ms，因此所设定的液晶波前校正器响应时间不能短于1.07ms，另外液晶波前校正器只能在驱动场交变帧周期(128.3us)整数倍时刻进行电压切换，因此液晶波前校正器的响应时间必须是128.3us的整数倍，因此选取1.155ms作为液晶波前校正器的响应时间。经仿真计算，液晶波前校正器的响应时间限定为1.155ms时液晶自适应光学系统的–3dB误差抑制带宽为35Hz，而当响应延迟时间增加至1.92ms时–3dB误差抑制带宽仅为26Hz，因此1.155ms是所用系统的液晶响应时间优化值。
计算了1.155ms响应时引入的不到位误差。利用湍流模拟器产生格林伍德频率为30和50Hz、大气相干长度为2.4cm、7.2cm和10cm、口径为1.2米的湍流波前，采用上述液晶自适应光学系统对湍流波前进行实时校正；得出位相响应不到位误差不超过1.5×10-2λ（λ=785nm）；1.2米望远镜的衍射极限分辨要求波前残差RMS值应小于0.07λ，看出由不到位引起的校正误差约为1/5衍射极限对应的误差，可认为对成像效果不产生影响。
过驱动成功应用于与1.2米口径望远镜对接的液晶自适应光学系统，获得清晰的环境卫星、 Com双星等图片。对北极星的校正成像实验显示，未校正时星像亮度的半高宽为2.02角秒，不使用过驱动时校正后半高宽为0.46角秒，采用1.155ms的单帧过驱动校正后半高宽减至0.31角秒。
在单帧过驱动的基础上进一步提出了单帧超调过驱动及多帧过驱动的方法。经分析，使用单帧超调过驱动及多帧过驱动可以进一步减少系统校正残差，提高系统的带宽。仿真结果表明多帧过驱动可将–3dB抑制带宽提高至37Hz。
通过数学推导及仿真分析，研究了时间起伏误差、过驱动矩阵测量误差、位相-灰度级关系标定误差对过驱动过程的影响。提出进一步提高位相-灰度级标定精度的方法及过驱动矩阵测量精度的方法。
Liquid crystal wavefront corrector is the core device of liquid crystal adaptiveoptical system. Slow response is the key problem which prevents the liquid crystaladaptive optical systems from engineering. The design and synthesis of high Δn andlow viscosity nematic liquid crystal materials can improve the response of liquidcrystal wavefront corrector. However, the potential of the improvement of theresponse become more and more limited. Therefore, based on the liquid crystaldynamics theory, this thesis researched the liquid crystal hydrodynamic process ofdirector rotation behavior. When the driving voltage changes from the higher voltageto the lower voltage, the distribution of the director of the liquid crystal is closer andcloser to the equilibrium state, and the rotational speed is slower and slower. Thisserious tailing phenomenon cause the average speed of response greatly reduced.Overdriving is applying a higher voltage difference than the normal driven to drivethe liquid crystal molecules to reach the target phase faster.
Based on the elastic theory of liquid crystal, this thesis derived the equilibriumequation and the hydrodynamic equation of the liquid crystal devices under theelectric field without distortion. The effect of the cell gap and voltage on the phaseresponse process is researched. Through the optimization of cell gap, the responsedelay of liquid crystal wavefront corrector can be reduced. By increasing Δ, theresponse delay can be shortened under the overdriving condition.
This thesis studied the driving scheme of the commercial liquid crystalwavefront corrector and the optimization of various parameters systematically. Bythe analysis of the time domain error and simulation, according to the relevantparameters of the system,1.155ms was choosed as the optimal response delay. Thefast overdriving matrix data processing and transition are realized using GPU. Thetime needed is about30us which makes this method can be directly applied tocommercial liquid crystal wavefront corrector. The single frame overdriving isapplied to the open-loop Liquid crystal adaptive optics system. The bandwidth testand the outfield experiment showed that the system performance is significantlyimproved. The–3dB bandwidth is improved from27Hz to35Hz. on the basis of thesingle frame overdriving, the single frame overshoot overdriving and multi-frameoverdriving is proposed, which can further reduce the residual wavefront correctionerror.
Through mathematical derivation, the mathematical relationship between theinput and the output of the residual error was obtained. The precised calibrationscheme was proposed to improve the phase level to gray level map precision further.The improved method of overdriving matrix measurement is put forward. The effectof temperature on the overdriving was studied.
引文
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