Harnessing caustics for wave-front sensing

Scintillation in measured wave fronts adds spurious dislocations and deformations to their reconstruction. The source of the problem is caustics formed by aberrations in intermediate planes. I propose to use intentional caustics to measure wave fronts under severe conditions such as low light level, fast scale variations, large aberrations, and discontinuities in the wave front. A simple realization is based on the Hartmann-Shack sensor, which samples the wave front with a lenslet array. Movement of the lenslets' foci is linear with slope changes. Here the lenslets are effectively formed in an acousto-optic device: Two standing waves are launched perpendicularly to the light beam and to each other. At some distance down the beam, each wave creates a comb of caustics, and the two orthogonal combs add up to an array of caustic spots. The spatial frequency of the array is linear with the temporal frequency of the standing sound waves. A simple Fourier demodulation scheme supplies the two wave-front gradients.     

Performance of a phase-conjugate engine implementing a finite-bit phase correction

The achievable Strehl ratio when a finite-bit correction to an aberrated wave front is implemented is examined. The phase-conjugate engine used to measure the aberrated wave front consists of a quadrature interferometric wave-front sensor, a liquid-crystal spatial light modulator, and computer hardware-software to calculate and apply the correction. A finite-bit approximation to the conjugate phase is calculated and applied to the spatial light modulator to remove the aberrations from the optical beam. The experimentally determined Strehl ratio of the corrected beam is compared with analytical expressions for the expected Strehl ratio and shown to be in good agreement with those predictions.     

Hybrid curvature and gradient wave-front sensor

A new wave-front sensor for adaptive optics that gives signals for the curvature and the two gradient components of the wave front simultaneously is proposed. The sensor uses quad cells placed at the foci of an array of astigmatic lenslets, giving three intensity-normalized differential signals. The parameters of a single subdetector are optimized to maximize the curvature signal. The performance of such a sensor designed for a membrane curvature mirror is analyzed. The good match between sensor and mirror is exhibited by an almost diagonal response matrix between the mirror actuator controls and the curvature signals.     

哈特曼波前传感器中采样点数的分析

随着哈特曼传感器测量口径的增大,采样点数对被测波前的空间分辨率、测量精度及动态范围的影响也随之增大,因此通过计算机仿真波前径向斜率拟合过程,分析出采样点数和斜率探测误差对测量精度和测量范围的影响。计算机仿真的波前斜率拟合所用泽尼克多项式达到121项,测量口径2m,测量精度要求λ/50,径向(半径)和切向最少采样点数分别为10点和21点。当径向和切向采样点数分别为40点和250点,斜率测量误差为0.045″时,所测波前的P-V值范围是0-4λ。     

Hartmann wave-front measurement at 13.4 nm with lambdaEUV/120 accuracy

We report, for the first time to our knowledge, experimental demonstration of wave-front analysis via the Hartmann technique in the extreme ultraviolet range. The reference wave front needed to calibrate the sensor was generated by spatially filtering a focused undulator beam with 1.7- and 0.6-microm-diameter pinholes. To fully characterize the sensor, accuracy and sensitivity measurements were performed. The incident beam's wavelength was varied from 7 to 25 nm. Measurements of accuracy better than lambdaEUV/120 (0.11 nm) were obtained at lambdaEUV = 13.4 nm. The aberrations introduced by an additional thin mirror, as well as wave front of the spatially unfiltered incident beam, were also measured.     

Generalized method for wave-front analysis

We suggest and demonstrate a new method for wave-front analysis based on common-path phase-shift interferometry. We introduce a formalism and an iterative mathematical algorithm in which the wave front is transformed, modified, and inversely transformed. The resulting intensity data are sufficient to reconstruct the entire wave front. In a more restricted case, in which the wave-front modifications are arbitrarily applied over arbitrary spatial regions of the wave front, the wave front is reconstructed semianalytically by use of a model that allows a local solution, followed by an iterative algorithm. Measurement results indicating that the suggested approach has an improved measurement accuracy with respect to existing quantitative phase measurement methods are presented.     

Closed-loop aberration correction by use of a modal Zernike wave-front sensor

We describe the practical implementation of a closed-loop adaptive-optics system incorporating a novel modal wave-front sensor. The sensor consists of a static binary-phase computer-generated holographic element, which generates a pattern of spots in a detector plane. Intensity differences between symmetric pairs of these spots give a direct measure of the Zernike mode amplitudes that are present in the input wave front. We use a ferroelectric liquid-crystal spatial light modulator in conjunction with a 4-f system and a spatial filter as a wave-front correction element. We present results showing a rapid increase in Strehl ratio and focal spot quality as the system corrects for deliberately introduced aberrations.     

Dynamic range expansion of a Shack-Hartmann sensor by use of a modified unwrapping algorithm

An algorithm for expanding the dynamic range of Shack--Hartmann sensors is proposed. The distribution of the spot dislocations is treated with a modified unwrapping algorithm that is widely used in interferometry. The algorithm unwraps the spot dislocations and assigns the spots to their original subapertures, leading to a huge expansion of the dynamic range. For the proposed algorithm there remains a limitation on the maximum wave-front curvature instead of on the maximum wave-front slope. Examples are given that show spot fields that were wrapped four times; the measured wave front had a peak-to-valley value of 116 lambda .     

自适应光学曲率波前传感器的衍射理论及其方案分析

曲率波前传感器是自适应光学中的一种很有前途的新型波前传感器。在对衍射理论和几何光学进行近似的基础上,研究了曲率波前传感器的理论分析方法,分析了曲率波前传感器的光学方案和信号获取方法。结果表明,从曲率传感器输出的信号经放大后可直接作为力或弯曲力矩施加到反射镜上,而不需要任何复杂的计算。变形镜可自动地向满足泊松方程的表面形状会聚。利用曲率传感器与双压电晶片反射镜的结合,有望获得一种低价、快速闭环控制的系统。     

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。     

Adaptive-optics correction of a stellar interferometer with a single pyramid wave-front sensor

We investigate the pyramid wave-front sensor's capability to reconstruct in a closed loop, with only one sensor, the wave fronts on both apertures of a stellar interferometer, including the differential piston: The method consists of placing the principal element of this sensor, namely, a refractive-square-based pyramid, in a combined focal plane of the interferometer instead of using two sensors, one for each individual telescope. We show that the sensor signals allow one to measure the wave-front aberrations on both apertures and the differential piston at the same time. The performance of an adaptive-optics loop is computed numerically for the Large Binocular Telescope in terms of differential-piston rejection under several conditions. The results show that atmospheric correction including differential-piston compensation is possible as long as the corrected Strehl ratio at the wave-front sensing wavelength is greater than 20%.     

Dynamic axial-position control of a laser-trapped particle by wave-front modification

The axial position of a laser-trapped particle has been controlled by modification of the wave front by means of a membrane deformable mirror. The mirror gives wave-front modulation in terms of Zernike polynomials. By modulation of the Zernike defocus term we can modulate the particle position under conditions of laser trapping. A polystyrene particle of 1-microm diameter was moved along the optical axis direction for a distance of 2370 nm in minimum steps of 55.4 nm. We also demonstrated particle oscillation along the optical axis by changing the focal position in a sinusoidal manner. From the frequency dependency of the amplitude of particle oscillation we determined the spring constant as 91.7 nN/m.     

A braking drift current on the slopes of wind waves in an amplification zone

A drift current was experimentally studied on the slopes of wind waves in an amplification zone. It was found that the drift decreases proportionally to the wave steepness at the front wave slope. We tested a hypothesis that relates the decrease in the drift velocity at the front wave slope with the formation of vortices in a viscous air layer. A physical model of the event and a method for the calculation of the drift decrease at the front wave slope in an amplification zone are suggested. The model calculations agree well with experimental data within the measurement error, which is less than 10% of the measured value.     

用于大孔径凸非球面检测的部分补偿透镜的优化设计

针对部分补偿法和子孔径拼接技术对大孔径凸非球面进行测量时,部分补偿透镜的优化设计是关键技术之一,基于ZEMAX软件对用于大孔径凸非球面的部分补偿透镜进行了优化设计,以波前斜率作为优化目标,通过直接观察弥散圆半径对全口径的光线进行优化。设计结果表明,用结构简单的单片部分补偿透镜即可实现对大孔径凸非球面的面形测量,在不同的子孔径区域,部分补偿系统在理想焦面处的弥散圆最大半径均小于165 μm,满足设计要求,验证了结合部分补偿法和子孔径拼接技术测量大孔径凸非球面的可行性。     

Generalized phase diversity for wave-front sensing

Phase diversity is a phase-retrieval algorithm that uses a pair of intensity images taken symmetrically about the wave front to be determined. If these images are taken about the system input pupil this is equivalent to a curvature-sensing algorithm. Traditionally a defocus aberration kernel is used to produce the phase-diverse data. We present a generalization of this method to allow the use of other functions as the diversity kernel. We discuss the necessary and sufficient conditions that such a function must satisfy for use in a null wave-front sensor. Computer simulations were used to validate these results.     

用数字干涉仪测量变形镜影响函数的实验研究

分析了变形反射镜面形影响函数的意义，鉴于自适应光学系统中波前探测大都以测量波前斜率为基础的特点，提出应研究斜率影响函数，并在此基础上构成波前复原矩阵。还介绍了用数字干涉仪测量变形镜影响函数的方法和结果，并对测量结果进行了分析，得到了影响函数的各种参数，例如：交连值，高斯指数，特征宽度等。并将干涉法测量斜率影响函数的结果与实际的哈特探测器的测试结果进行了比较。     

Intensity profile of chirped polychromatic laser in an apertured system

Propagation expression of chirped polychromatic laser in an aperture system is deduced in our investigation. Influences of the chirp parameter and the aperture width on the intensity profile of the chirped polychromatic laser are studied and illustrated by numerical calculation. The results showed that intensity of the wave rear presents spreading effect but that of the wave front presents narrowing effect. Namely, the intensity distribution spreads with decreasing the aperture width and increasing the chirp parameter in the wave rear whereas it tends to concentrate with increasing the chirp parameter in the wave front. A physical explanation based on a simplified representation indicated that the influence of the chirp parameter on the intensity was determined not only by its quantity but also by the sign of the local time.     

Adaptive wave-front correction by means of all-optical feedback interferometry

A novel adaptive wave-front correction system based on an all-optical feedback interferometer is described. In this system the two-dimensional output fringe intensity from a Mach-Zehnder interferometer with large radial shear is optically fed back to an optically addressed phase-only liquid-crystal spatial light modulator. Consequently, without a separate aberration-free reference wave, the modulator phase approximates the conjugate of the interferometer phase that is directly related to the phase of the input aberrated wave front, so this system is applicable in adaptive optics. We successfully achieved real-time correction of aberrated wave fronts: A diffraction pattern that was seriously distorted because of aberrations was transformed into a diffraction-limited spot immediately after the feedback loop was closed.     

Programmable focal spot shaping of amplified femtosecond laser pulses

We describe the programmable spatial beam shaping of 100-kHz, 4-microJ amplified femtosecond pulses in a focal plane by wave-front modulation. Phase distributions are determined by a numerical iterative procedure. A nonpixelated optically addressed liquid-crystal light valve is used as a programmable wave-front tailoring device. Top-hat, doughnut, square, and triangle shapes of 20-microm size are obtained in a focal plane. Their suitability for femtosecond laser machining is demonstrated.     

热环境中的光传输与光学校正仿真

对折射率不均匀分布的窗口中的光线传输进行了分析,利用光线追迹得到的光程差再现了光波通过窗口后的波前图。通过研究图像获取和处理方法,提出了用相位互异散斑(PDS)技术进行图像补偿和校正由大气扰动造成的波前变形。结果表明,图像的清晰度和对比度得到了提高。