Linear phase retrieval for wave-front sensing

Phase retrieval from one or more intensity measurements is a potentially powerful and appealing technique for real-time adaptive-optics wave-front sensors. Under the assumption of small wave-front phase excursions, one is able to derive an exact solution to the inverse problem given three or more intensity measurements with known phase offsets. Applications include a high-order wave-front sensor to correct for residual aberrations in an adaptive-optics system in tandem with a low-resolution Hartmann-Shack wave-front sensor. The formula can also furnish mathematical insights into the full nonlinear phase-retrieval task.     

Flow of optical patterns due to small lateral wave-front shifts in a nonlinear optical feedback system

Flow of a spontaneously formed optical pattern in a nonlinear optical feedback system consisting of a liquid crystal optically addressable spatial light modulator with feedback is induced by a lateral wave-front shift of the feedback light. We demonstrate the dependency of the flow speed on the wave-front shift by tilting an optical flat inserted in the feedback loop. We also demonstrate the application to real-time, high-sensitivity detection of small tilt angles of optical components.     

Investigation on high power phase compensation of strong aberrations via stimulated Brillouin scattering

The strong wave-front aberrations compensated by stimulated Brillouin scattering phase conjugate mirror (SBS-PCM) in a high power laser were investigated experimentally. The wave-front fluctuation of the 10 Hz 500 mJ Nd:YAG laser is 0.5λ. Transmitting through a random phase plate (RPP), it increases to 8.6λ. While using SBS-PCM in place of a high reflection mirror, the distortion induced by the RPP is compensated, and the wave-front fluctuation becomes 0.9λ. At the same time, obvious breakdown phenomena in the SBS cell were observed, and the reflectivity is unstable. A rotating wedge plate is introduced into the phase conjugating mirror to make the focus of the SBS cell rotate and optical breakdown is avoided effectively. The reflectivity becomes stable around about 70% and the instability is changed from ±4.1% to ±0.9%. Besides, the compensated wave-front fluctuation is only 0.6λ, which is near to the original wave-front distribution. The results show that the reflectivity of the SBS-PCM is very high and stable when there are no other nonlinear effects such as optical breakdown. Thus the compensating effects for strong wave-front errors are perfect.     

高斯光束通过非线性折射和吸收介质的光强分布

以衍射理论为基础,推导并模拟了高斯光束通过非线性折射和吸收效应介质后的远场光强分布。结果表明:入射高斯光束引起的介质折射率变化和光束波前曲率影响介质出射面光束的径向调制相位,安装在焦点前的有自聚焦效应的介质和安装在焦点后的有自散焦效应的介质具有闪耀光栅的能力,使远场出现中心为暗斑外侧为亮环的衍射图样。非线性折射效应为主的介质,其非线性吸收效应的变化同时改变远场衍射图样的数目和光强值,但对于非线性吸收效应为主的介质,衍射图样的数目随吸收效应的变化不明显,吸收效应只影响光强值。     

Direct measurement of wave-front distortion induced during second-harmonic generation: application to breakup-integral compensation

The wave-front distortion of femtosecond laser pulses recorded with a Shack-Hartmann analyzer makes it possible to retrieve the nonlinear index of refraction of different glasses and the nonlinear phase shift induced during second-harmonic generation in beta-barium borate (BBO) crystal versus the phase mismatch. It is shown that the nonlinear phase shift induced in a 2-mm-thick BBO crystal allows compensation for up to a 2pi breakup-integral induced in a 4-cm fused-silica glass. The stability of the compensation is reported to be from 10 to 100 GW cm(-2).     

Nonlinear three-wave interaction in photonic crystals

We present a multi-scale analysis of nonlinear three-wave-interaction processes in photonic crystals. Based on photonic Bloch functions as carrier waves, we derive the effective nonlinear coupled wave equations that govern pulse propagation in these systems and obtain the corresponding effective photonic crystal parameters directly from photonic band-structure computations. As an illustration, we show how hitherto inaccessible radiation-conversion processes such as wave-front reversal of optical pulses can be realized. Furthermore, we describe a novel regime of nonlinear three-wave interaction in photonic crystals associated with the nearly degenerate case and show how these results may be utilized to study experimentally certain problems from plasma physics and hydrodynamics in the context of nonlinear photonic crystals.     

Compensating laser wave-front aberration in atmosphere 1.27 km away with SBS

It is reported that the wave-front aberration produced by atmosphere disturbance can be compensated with nonlinear optics phase conjugate technology. The distance of laser propagating in atmosphere is up to 1.27 km away. The result shows that SBS phase conjugating beam energy can be focus in a little area on target. And the biggest energy of phase conjugating beam on target is up to 142 mJ.     

Focal plane wave-front sensing algorithm for high-contrast imaging

High-contrast imaging provided by a coronagraph is critical for the direction imaging of the Earth-like planet orbiting its bright parent star. A major limitation for such direct imaging is the speckle noise that is induced from the wave-front error of an optical system. We derive an algorithm for the wave-front measurement directly from 3 focal plane images. The 3 images are achieved through a deformable mirror to provide specific phases for the optics system. We introduce an extra amplitude modulation on one deformable mirror configuration to create an uncorrelated wave-front, which is a critical procedure for wave-front sensing. The simulation shows that the reconstructed wave-front is consistent with the original wave-front theoretically, which indicates that such an algorithm is a promising technique for the wave-front measurement for the high-contrast imaging. Supported by the National Natural Science Foundation of China (Grant No. 10873024)     

Free-space laser communications with adaptive optics: Atmospheric compensation experiments

Refractive index inhomogeneities of the turbulent air cause wave-front distortions of optical waves propagating through the atmosphere, leading to such effects as beam spreading, beam wander, and intensity fluctuations (scintillations). These distortions are responsible for severe signal fading in free-space optical communications systems and therefore compromise link reliability. Wave-front distortions can be mitigated, in principle, with adaptive optics, i.e., real-time wave-front control, reducing the likeliness of signal fading. However, adaptive optics technology, currently primarily used in astronomical imaging, needs to be adapted to the requirements of free-space optical communication systems and their specific challenges.In this chapter we discuss a non-conventional adaptive optics approach that has certain advantages with respect to its incorporation into free-space optical communication terminals. The technique does not require wave-front measurements, which are difficult under the strong scintillation conditions typical for communication scenarios, but is based on the direct optimization of a performance quality metric, e.g., the communication signal strength, with a stochastic parallel gradient descent (SPGD) algorithm.We describe an experimental adaptive optics system that consists of a beam-steering and a higher-resolution wave-front correction unit with a 132-actuator MEMS piston-type deformable mirror controlled by a VLSI system implementing the SPGD algorithm. The system optimizes the optical signal that could be coupled into a single-mode fiber after propagating along a 2.3-km near-horizontal atmospheric path. We investigate characteristics of the performance metric under different atmospheric conditions and evaluate the effect of the adaptive system. Experiments performed under strong scintillation conditions with beam-steering only as well as with higher-resolution wave-front control demonstrate the mitigation of wave-front distortions and the reduction of signal fading.     

高斯光束通过非线性介质后的远场衍射图样的研究

 利用菲涅尔－基尔霍夫衍射积分公式，对发散和会聚高斯光束通过薄非线性介质时形成的远场衍射图样进行了研究。模拟计算结果表明：当发散高斯光束通过自散焦介质或会聚高斯光束通过自聚焦介质时，远场均会出现中央较暗、向外围逐渐增强、分布尺度较大的粗衍射环；当发散高斯光束通过自聚焦介质或会聚高斯光束通过自散焦介质时，远场均会出现中心强度最大、向外围逐渐减弱、分布尺度较小的细衍射环。不同远场衍射图样归根结底是入射高斯光束因介质折射率变化造成的空间自相位调制及其波前曲率共同作用的结果。     

LS解法和Fisher方程行波系统的定性分析

提出了求解非线性发展方程的新方法——LS解法.LS解法是基于(G’/G)展开法和扩展的双曲正切函数展开法.并引入了Poincar定性理论的思想,然后以Fisher方程为例进行了试验.通过定性分析首先获得了Fisher方程行波系统积分曲线的性质,然后解得了Fisher方程作为耗散系统时单调减少的波前解和作为扩张系统时单调递增的波前解.一些试验结果与Ablowitz所得结果一致.也得到了Fisher方程作为扩张系统时的新结果.LS解法是在定性理论指导下,在已获知解曲线性质的情况下进行精确求解的,求解目标明确.LS解法揭示了线性系统也可以用作辅助方程来求解非线性系统.     

Eye models for the prediction of contrast vision in patients with new intraocular lens designs

Theoretical calculations of the polychromatic modulation transfer function (MTF) and wave-front aberration were performed with physiological eye models. These eye models have an amount of spherical aberration that is representative of a normal population of pseudophakic eyes implanted with two different types of intraocular lens (IOL) made from high-refractive-index silicone. These theoretical calculations were compared with the measured contrast sensitivity function (CSF) under mesopic lighting conditions and with wave-front aberration (obtained with a Hartmann-Shack wave-front sensor) collected from 37 patients bilaterally implanted with the same types of lens. The relationships between the ocular wave-front aberration and the MTF predicted by the eye models and the CSF and the ocular wave-front aberration measured in eyes implanted with IOLs were investigated. The predicted improvements in MTF and wave-front aberration correlated well with the improvements measured in practice. Physiological eye models are therefore useful tools for IOL design.     

高分辨力哈特曼传感器的快速波面重构和拼接

建立哈特曼传感器的模型,证明在高空间分辨力下,可以采用Hudgin模型进行波面重构,避免了采用Fried模型带来的复杂性。对哈特曼子孔径缺失破坏连续性的问题进行了分析,介绍了相应的边缘处理算法。完成了基于离散傅里叶变换的波面重构算法数值模拟,实现了波面的无损重构。针对实际应用中输入波面在被遮挡处不连续的问题,提出了基于最小二乘解的拼接方案,实现了非连续波面拼接。分析了影响波面重构速度的主要因素,提出了提高波面重构性能的方法。     

基于分区域耦合的随机并行梯度下降自适应光学

基于随机并行梯度下降(SPGD)方法的自适应光学(AO)系统通过直接优化系统的性能评价函数来控制波前校正器以补偿光束中存在的波前畸变。为了提高这种无模型优化自适应光学系统的收敛速度, 提出了基于分区域耦合的新方法以改进传统随机并行梯度下降自适应光学系统的工作方式。将波前校正器光学孔径分成多块子区域, 每块子区域对应着的所有驱动器作为一个整体控制单元, 从形式上可以得到一个空间分辨率较低的分区域波前校正器。该校正器与原校正器同步工作, 并采用随机并行梯度下降算法对同一个性能评价函数进行优化, 从而构成了双校正器的耦合工作结构。对256单元分立活塞式波前校正器建立了自适应成像系统的数值模型, 结果表明这种分区域耦合的随机并行梯度下降自适应光学系统比传统随机并行梯度下降自适应光学系统具有更快的收敛速度和更好的渐近态。     

测量噪声对波前重构精度的影响

 Hartmann-Shack波前传感器斜率测量误差是自适应光学系统中影响波前重构精度的一个主要误差来源。针对模式法波前重构算法,推导出了普遍适用的模式法波前重构误差传递系数计算公式;利用61单元自适应光学系统中的Hartmann-Shack波前传感器测量的斜率数据,验证了模式法波前重构误差传递系数计算公式的正确性。     

平行光管气流扰动的液晶自适应光学校正

利用液晶自适应光学技术,建立了一套验证系统.使用哈特曼传感器为波前探测器件,反射式的LCOS液晶器件为波前校正器件,以闭环控制校正方式工作.初步实现了波前PV值从1.02λ下降到0.37λ（λ＝633 nm）的校正准确度,成像质量明显提高.系统的调制传递函数由校正前的不到10 lp/mm提高到了校正后的超过50 lp/mm.     

一种大型望远系统波前检测的方法

 对传统S-H波前检测方法进行了改进的基础上,设计了一套适应于大型望远系统的波前检测方案。利用五角棱镜光束转向系统形成大型望远系统各子孔径准参考光束,实现依次扫描各子孔径;并用改进的S-H波前传感器实现依次探测各子孔径的波前。理论分析证明了由五角棱镜的制造误差和运动误差引起的波前倾斜误差在微变情况下,可通过波前修正方法予以修正,可有效地再现出望远系统自身波前误差。该方案可适用于大口径望远系统的波前检测。     

由焦面附近光强分布实现波前重构

介绍了一种由光束在焦面附近几个面上的强度分布重构出光束近场波前的方法。把波前重构问题作为一个非线性优化问题,利用光束口径区域内的正交多项式模拟光束波前相位分布,通过优化多项式各项的系数,使对应的波前分布在焦面附近相应的几个面上的强度分布与已知强度分布的偏差最小,即认为由此时的多项式系数决定的近场波前代表了真实的光束波前。针对方光束口径,利用Legendre多项式模拟光束波前分布,利用共轭梯度算法对多项式系数进行了优化计算;优化过程分为几步进行以减少计算时间。重构得到的波前分布与参考波前分布符合得很好。     

高功率激光装置中局部波前畸变的非线性传输

 根据高功率激光装置中强激光束传输的特点,建立了描述光束通过光学元件时引入的局部波前畸变模型,并利用纹波传输的线性化处理方法,研究了带有局部波前畸变的高强度光束的传输规律。以一个连续的非增益激光介质为例,用该模型进行数值模拟,给出了不同空间尺度的局部波前畸变的频谱分布、不同空间频率的纹波引起的振幅非线性增长曲线、不同B积分的非线性增益随光束传输距离的变化曲线,光束振幅非线性增益达到最大时光束的传输距离和标准传输距离不同时由局部波前畸变引入的振幅分布。研究表明为了防止光学元件损坏,应避免光学元件表面出现半径为0.5~2.0 mm的局部瑕疵。     

Wave-front spacing in the focal region of high-numerical-aperture systems

The wave-front spacing in the focal region of an aplanatic focusing system is investigated by use of the vector theory of electromagnetic diffraction for monochromatic, linearly polarized incident light. It is shown that, in systems of high numerical aperture, the wave-front spacing near the focus is significantly larger than the wavelength of the incident light and that the wave-front spacing changes significantly within a few wavelengths of the focus and can be less than a wavelength.