Shack-Hartmann sensor for fast infrared wave-front testing

Abstract

A Shack-Hartmann sensor has been designed for testing the wave front of CO₂ lasers. Fabrication of a lens array and a detector array with tight tolerances on position accuracy are essential steps. Parallel electronics allow for high-speed wave-front measurements with 1 kHz sampling frequency. The device has been used to investigate the behaviour of a high-power CO₂ laser. Besides the expected thermal drifts of beam direction at the beginning of laser action, periodic changes of beam direction, have been detected. The Shack-Hartmann sensor seems the appropriate device for controlling adaptive optics in high-power laser applications.     

Correcting ocular spherical aberration with soft contact lenses

Following aberroscopy, aspheric front surface soft contact lenses (SCLs) were custom-made to correct spherical refractive error and ocular spherical aberration (SA) of 18 myopic and five hypermetropic subjects (age, 20.5 +/- 5 yr). On-eye residual aberrations, logMAR visual acuity, and contrast sensitivity were compared with the best-correcting spectacle lens, an equally powered standard SCL, and an SCL designed to be aberration free in air. Custom-made and spherical SCLs reduced SA (p < 0.001; p < 0.05) but did not change total root-mean-square (rms) wave-front aberration (WFA). Aberration-free SCLs increased SA (p < 0.05), coma (p < 0.05), and total rms WFA. Visual acuity remained unchanged with any of the SCL types compared with the spectacle lens correction. Contrast sensitivity at 6 cycles/degree improved with the custom-made SCLs (p < 0.05). Increased coma with aspheric lens designs and uncorrected astigmatism limit the small possible visual benefit from correcting ocular SA with SCLs.     

Measuring seeing with a Shack-Hartmann wave-front sensor during an active-optics experiment

We describe the measurement of atmospheric enclosure seeing along a 120-m light path by use of a Shack-Hartmann wave-front sensor (S-H WFS) for the first time to our knowledge in the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) outdoor active-optics experiment system, based on the differential image motion method and a S-H WFS. Seeing estimates that were gained with the S-H WFS were analyzed and found to be in close agreement with the actual seeing conditions, the estimates of refractive-index structure constant, and the thin-mirror active optics results, which usually include the shape sensing precision and the active correction precision of the experimental system. Finally, some countermeasures against poor seeing conditions were considered and adopted.     

Sorting method to extend the dynamic range of the Shack-Hartmann wave-front sensor

We propose a simple and powerful algorithm to extend the dynamic range of a Shack-Hartmann wave-front sensor. In a conventional Shack-Hartmann wave-front sensor the dynamic range is limited by the f-number of a lenslet, because the focal spot is required to remain in the area confined by the single lenslet. The sorting method proposed here eliminates such a limitation and extends the dynamic range by tagging each spot in a special sequence. Since the sorting method is a simple algorithm that does not change the measurement configuration, there is no requirement for extra hardware, multiple measurements, or complicated algorithms. We not only present the theory and a calculation example of the sorting method but also actually implement measurement of a highly aberrated wave front from nonrotational symmetric optics.     

Generalized wave-front reconstruction algorithm applied in a Shack-Hartmann Test

A generalized numerical wave-front reconstruction method is proposed that is suitable for diversified irregular pupil shapes of optical systems to be measured. That is, to make a generalized and regular normal equation set, the test domain is extended to a regular square shape. The compatibility of this method is discussed in detail, and efficient algorithms (such as the Cholesky method) for solving this normal equation set are given. In addition, the authors give strict analyses of not only the error propagation in the wave-front estimate but also of the discretization errors of this domain extension algorithm. Finally, some application examples are given to demonstrate this algorithm.     

Method for measuring small optical absorption coefficients with use of a Shack-Hartmann wave-front detector

We present a method for measuring absorption at the 1 x 10(-5) cm(-1) level in high-quality optical materials. Using a Shack-Hartmann wave-front detector, thermal lensing in these materials may be measured. Then, the absorption coefficient may be estimated by fitting the observed deformation to a thermal lensing model based on the temperature dependences of the refractive index and the thermal expansion coefficient. For a particular sample of fused silica, the absorption coefficient was determined to be 1.8 +/- 0.4 x 10(-5) cm(-1). Obtaining this result requires a resolution in the optical path length better than +/- 0.1 nm.     

Modeling soft contact lenses in raytrace code

The surface interferogram feature of raytrace codes is used to model the optical performance of soft contact lenses, especially in situations where the lens is decentered. The contact lens is totally defined by a thickness data file, which can easily be shifted relative to the corneal vertex of a schematic eye model.     

基于哈特曼波前探测的流场层析重建系统仿真

基于哈特曼波前探测的流场层析重建技术结合了光学波前探测技术和计算机层析技术。重建系统由哈特曼传感器探测平行光束穿过流场后的投影波前,采用计算机层析技术重建流场物理量的空间分布。在介绍哈特曼流场层析重建原理的基础上,对流场重建的整个过程进行了计算机仿真,重建的RMS误差为0.0726。结果表明,该技术可以很好地实现流场的层析重建,在材料、流场研究等工程实际测量中具有良好的应用前景。     

Binocular open-view Shack-Hartmann wavefront sensor with consecutive measurements of near triad and spherical aberration

We have developed a binocular open-view Shack-Hartmann wavefront sensor for measuring time variation of binocular accommodation, vergence, pupil sizes (i.e., the binocular near triad), and monochromatic aberrations. The device measures these values16 times per second for up to 1 min. Our purpose is to introduce the new instrument. We have confirmed the accuracy of the device. Refractions for a 4 mm pupil were accurate across the range of measurements of model eyes and normal human eyes. We measured binocular dynamics of accommodation, vergence, and spherical aberrations.     

热风式大气湍流模拟装置的哈特曼测量

大气湍流是由于大气温度、压强的随机变化引起大气折射率随机改变而产生的。遵循这一原理,热风式湍流模拟装置对传输光束周围的空气加热,用风扇抽吸热空气产生湍流,通过改变加热温度和风扇的转速,模拟不同强弱的湍流。用哈特曼传感器对该装置进行测量并采集数据,通过波前斜率处理复原波前,在此基础上从时间域和空间域等方面分析所产生湍流的特点,并与理论进行比较。结果表明,该装置能产生基本符合大气湍流统计理论的湍流。     

Validation of a combined corneal topographer and aberrometer based on Shack-Hartmann wave-front sensing

A corneal aberrometer based on Shack-Hartmann wave-front sensing was developed and validated by using calibrated aspheric surfaces. The aberrometer was found to accurately measure corneal reflective aberrations, from which corneal topography and corneal refractive aberrations were derived. Measurements of reflective aberrations correlated well with theory (R2 = 0.964 to 0.994). The sag error root mean square (RMS) was small, ranging from 0.1 to 0.17 microm for four of the five calibrated surfaces with the fifth at 0.36 microm as a result of residual defocus. Measured refractive aberrations matched with theory and whole-eye aberrometry to within a small fraction of a wavelength. Measurements on three human corneas revealed very large refractive astigmatism (0.65-1.2 microm) and appreciable levels of trefoil (0.08-0.47 microm), coma (0.14-0.19 microm), and spherical aberration (0.18-0.25 microm). The mean values of these aberrations were significantly larger than the RMS in repeated measurements.     

Misalignment effects of the Shack-Hartmann sensor

The Shack-Hartmann sensor uses a microlens array and a CCD camera for wave-front measurements. To obtain wave-front measurements with high accuracy, an accurate relative alignment of both is essential. The different states of misalignment of the Shack-Hartmann sensor are divided into groups and are treated theoretically and experimentally. Their effect on the accuracy of wave-front measurements is evaluated. In addition, a practical method for proper alignment of the Shack-Hartmann sensor is proposed.     

Detection of phase singularities with a Shack-Hartmann wavefront sensor

While adaptive optical systems are able to remove moderate wavefront distortions in scintillated optical beams, phase singularities that appear in strongly scintillated beams can severely degrade the performance of such an adaptive optical system. Therefore the detection of these phase singularities is an important aspect of strong-scintillation adaptive optics. We investigate the detection of phase singularities with the aid of a Shack-Hartmann wavefront sensor and show that, in spite of some systematic deficiencies inherent to the Shack-Hartmann wavefront sensor, it can be used for the reliable detection of phase singularities, irrespective of their morphologies. We provide full analytical results, together with numerical simulations of the detection process.     

New modal wave-front sensor: a theoretical analysis

We present a new design of a modal wave-front sensor capable of measuring directly the Zernike components of an aberrated wave front. The sensor shows good linearity for small aberration amplitudes and is particularly suitable for integration in a closed-loop adaptive system. We introduce a sensitivity matrix and show that it is sparse, and we derive conditions specifying which elements are necessarily zero. The sensor may be temporally or spatially multiplexed, the former using a reconfigurable optical element, the latter using a numerically optimized binary optical element. Different optimization schemes are discussed, and their performance is compared.     

Modulation effect of the atmosphere in a pyramid wave-front sensor

The pyramid wave-front sensor in its original form works with a mechanical modulation that adapts the linear range of the sensor to seeing and sensing conditions. For adaptive optics systems working in an astronomical context, the way in which the aberrations produced by the atmospheric turbulence, which are not seen by the sensor owing to its limited temporal bandwidth, act as modulators is shown. These aberrations have the same effect of increasing the linear range and localizing the measurement as does mechanical modulation. The effect of residual wave-front aberrations is estimated for some example conditions of telescope diameter, system bandwidth, wind velocity, and Fried parameter.     

Analytical expressions for the wave-front aberration coefficients of a tilted plane-parallel plate

An expression is given for the aberration imparted by a tilted plane-parallel plate to a converging or diverging pencil of rays. Analytical expressions for the wave-front aberration coefficients up to the sixth order are derived. These expressions, among others, are of importance when reading an optical disk through its substrate or when using a plane-parallel plate as a beam splitter. Differences with previous expressions from the literature are noted.     

Calibration of a Shack-Hartmann sensor for absolute measurements of wavefronts

We demonstrate a method with which to calibrate a Shack-Hartmann sensor for absolute wavefront measurement of collimated laser beams. Nearly perfect spherical wavefronts originating from a single-mode fiber were used as references. After the calibration, the uncertainty of the wavefront was less than lambda/100 peak to valley across a diameter of 6 mm. For example, this method allowed us to balance aberrations and prepare collimated beams with wavefronts that are plane to lambda/500 across 1 mm.     

小波滤波在Shack-Hartmann传感器上的应用

在使用Shack-Hartmann传感器进行大口径非球面镜面检测中,外部环境的各种振动影响以及气流、温差的干扰都会使检测精度下降。针对这个问题,提出了一种新的时域小波滤波技术。这项技术可以对传感器的信号干扰在时间域上进行不同层次的小波分析,提取干扰信号的先验特征,对测量数据进行有效的滤波,减小波前的扰动起伏,以更准确地探测质心。实验结果表明,采用这种技术后,Shack-Hartmann波前传感器对光学镜面检测的静态测量精度提高了50%以上,离散性减少到原来的20%-30%。     

Highly sensitive wave-front sensor with a non-zero-order phase plate

We propose a novel highly sensitive wave front detection method for a quick check of a flat wave front by taking advantage of a non-zero-order pi phase plate that yields a non-zero-order diffraction pattern. When a light beam with a flat wave front illuminates a phase plate, the zero-order intensity is zero. When there is a slight distortion of the wave front, the zero-order intensity increases. The ratio of first-order intensity to that of zero-order intensity is used as the criterion with which to judge whether the wave front under test is flat, eliminating the influence of background light. Experimental results demonstrate that this method is efficient, robust, and cost-effective and should be highly interesting for a quick check of a flat wave front of a large-aperture laser beam and adaptive optical systems.     

Measuring the centroid gain of a Shack-Hartmann quad-cell wavefront sensor by using slope discrepancy

Shack-Hartmann wavefront sensors (SH WFS) are used by many adaptive optics (AO) systems to measure the wavefront. In this WFS, the centroid of the spots is proportional to the wavefront slope. If the detectors consist of 2 x 2 quad cells, as is the case in most astronomical AO systems, then the centroid measurement is proportional to the centroid gain. This quantity varies with the strength of the atmospheric turbulence and the angular extent of the beacon. The benefits of knowing the centroid gain and current techniques to measure it are discussed. A new method is presented, which takes advantage of the fact that, in a SH-WFS-based AO system, there are usually more measurements than actuators. Centroids in the null space of the wavefront reconstructor, called slope discrepancy measurements, contain information about the centroid gain. Tests using the W. M. Keck Observatory AO system demonstrate the accuracy of the algorithm.