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.     

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%。     

High-speed Shack-Hartmann wavefront sensor design with commercial off-the-shelf optics

Several trade-offs relevant to the design of a two-dimensional high-speed Shack-Hartmann wavefront sensor are presented. Also outlined are some simple preliminary experiments that can be used to establish critical design specifications not already known. These specifications include angular uncertainty, maximum measurable wavefront tilt, and spatial resolution. A generic design procedure is then introduced to enable the adaptation of a limited selection of CCD cameras and lenslet arrays to the desired design specifications by use of commercial off-the-shelf optics. Although initially developed to aid in the design of high-speed (i.e., megahertz-frame-rate) Shack-Hartmann wavefront sensors, our method also works when used for slower CCD cameras. A design example of our procedure is provided.     

Tomographic wavefront error using multi-LGS constellation sensed with Shack-Hartmann wavefront sensors

Noise effects induced by laser guide star (LGS) elongation have to be considered globally in a multi-LGS tomographic reconstruction analysis. This allows a fine estimation of performance and the comparison of different launching options. We present a modal analysis of the wavefront error with Shack-Hartmann wavefront sensors based on quasi-analytical matrix formalism. Including spot elongation and the Rayleigh fratricide effect, edge launching produces similar performance to central launching and avoids the risk of possible underestimation of fratricide scatter. Performance improves slightly with an optimized centroid estimator and is not affected by a slight field-of-view truncation of the subapertures. Finally we discuss detector characteristics for a LGS Shack-Hartmann wavefront sensor.     

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.     

Shack-Hartmann wavefront sensor measurement for dynamic temperature profiles in heat-capacity laser rods

A Shack-Hartmann sensor nonintrusive measurement for the temperature profile in a heat-capacity neodymium-doped glass rod is proposed. This technique is possible because the optical path length of the rod changes with temperature linearly over a wide range. The temperature change of the solid-state laser rod is often recorded by using a thermocouple, thermal camera, or phase-shifting interferometer. Based on an analysis of temperature-induced changes in length and index of refraction, we can get the temperature profiles from the wavefront reconstructions in real time. The results suggest the Shack-Hartmann sensors could replace microbolometer-based thermal cameras and phase-shifting interferometers for dynamic temperature profiles in heat-capacity laser rods with particular advantages. A strange temperature chaos of the Nd:glass rod just after the pump cycle is discovered.     

Study of a MEMS-based Shack-Hartmann wavefront sensor with adjustable pupil sampling for astronomical adaptive optics

We introduce a Shack-Hartmann wavefront sensor for adaptive optics that enables dynamic control of the spatial sampling of an incoming wavefront using a segmented mirror microelectrical mechanical systems (MEMS) device. Unlike a conventional lenslet array, subapertures are defined by either segments or groups of segments of a mirror array, with the ability to change spatial pupil sampling arbitrarily by redefining the segment grouping. Control over the spatial sampling of the wavefront allows for the minimization of wavefront reconstruction error for different intensities of guide source and different atmospheric conditions, which in turn maximizes an adaptive optics system's delivered Strehl ratio. Requirements for the MEMS devices needed in this Shack-Hartmann wavefront sensor are also presented.     

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.     

Efficient implementation of a spatial light modulator as a diffractive optical microlens array in a digital Shack-Hartmann wavefront sensor

A traditional Shack-Hartmann wavefront sensor (SHWS) uses a physical microlens array to sample the incoming wavefront into a number of segments and to measure the phase profile over the cross section of a given light beam. We customized a digital SHWS by encoding a spatial light modulator (SLM) with a diffractive optical lens (DOL) pattern to function as a diffractive optical microlens array. This SHWS can offer great flexibility for various applications. Through fast-Fourier-transform (FFT) analysis and experimental investigation, we studied three sampling methods to generate the digitized DOL pattern, and we compared the results. By analyzing the diffraction efficiency of the DOL and the microstructure of the SLM, we proposed three important strategies for the proper implementation of DOLs and DOL arrays with a SLM. Experiments demonstrated that these design rules were necessary and sufficient for generating an efficient DOL and DOL array with a SLM.     

Integration of a photodiode array and centroid processing on a single CMOS chip for a real-time shack-Hartmann wavefront sensor

A real-time VLSI optical centroid processor has been developed as part of a larger Shack-Hartmann wavefront sensor system for applications in adaptive optics. The implementation of the optical centroid detection system was demonstrated successfully using a hardware emulation system. Subsequently, the design has been implemented as a CMOS single-chip solution. This has advantages in terms of speed, power consumption, system size, and cost. The design of the different components of the system will be discussed along with test results of the fabricated device.     

Analysis of optimal centroid estimation applied to Shack-Hartmann sensing

The problem of estimating the centroid of an incoherently imaged point with a CCD array is analyzed. An exact analysis is presented that uses the actual short-exposure function at the CCD instead of the traditional Gaussian approximation. The analysis shows that, for Poisson noise, the centroid variance depends on the CCD size and that truncation effects play a significant part in determining the optimum CCD size. The effects of this on a wave-front reconstruction formed by a Shack-Hartmann sensor are described.     

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.     

Optimization of scanning strategy of digital Shack-Hartmann wavefront sensing

In the traditional Shack-Hartmann wavefront sensing (SHWS) system, a lenslet array with a bigger configuration is desired to achieve a higher lateral resolution. However, practical implementation limits the configuration and this parameter is contradicted with the measurement range. We have proposed a digital scanning technique by making use of the high flexibility of a spatial light modulator to sample the reflected wavefront [X. Li, L. P. Zhao, Z. P. Fang, and C. S. Tan, "Improve lateral resolution in wavefront sensing with digital scanning technique," in Asia-Pacific Conference of Transducers and Micro-Nano Technology (2006)]. The lenslet array pattern is programmed to laterally scan the whole aperture. In this paper, the methodology to optimize the scanning step for the purpose of form measurement is proposed. The correctness and effectiveness are demonstrated in numerical simulation and experimental investigation.     

Three-dimensional surface profiling and optical characterization of liquid microlens using a Shack-Hartmann wave front sensor

We demonstrate three-dimensional (3D) surface profiling of the water-oil interface in a tunable liquid microlens using a Shack-Hartmann wave front sensor. The principles and the optical setup for achieving 3D surface measurements are presented and a hydrogel-actuated liquid lens was measured at different focal lengths. The 3D surface profiles are then used to study the optical properties of the liquid lens. Our method of 3D surface profiling could foster the improvement of liquid lens design and fabrication, including surface treatment and aberration reduction.     

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.     

Hybrid wavefront sensor for the fast detection of wavefront disturbances

Strongly aberrated wavefronts lead to inaccuracies and nonlinearities in holography-based modal wavefront sensing (HMWS). In this contribution, a low-resolution Shack-Hartmann sensor (LRSHS) is incorporated into HMWS via a compact holographic design to extend the dynamic range of HMWS. A static binary-phase computer-generated hologram is employed to generate the desired patterns for Shack-Hartmann sensing and HMWS. The low-order aberration modes dominating the wavefront error are first sensed with the LRSHS and corrected by the wavefront modulator. The system then switches to HMWS to obtain better sensor sensitivity and accuracy. Simulated as well as experimental results are shown for validating the proposed method.     

Intrinsic limitations of Shack-Hartmann wavefront sensing on an extended laser guide source

In this paper we investigate the behavior of various centroiding methods (weighted center of gravity, matched filtering, and correlation) classically used in Shack-Hartmann wavefront sensing when dealing with an elongated asymmetric spot. We study the impact of model errors on these centroiding methods at high signal-to-noise ratios, and, using a one-dimensional formalism, we show that the associated estimates all suffer from a bias uncorrelated with the actual spot displacement if its shape is not known precisely. Additionally, we show that the correlation method provides an estimate with a unitary gain whatever the parameters used, while the other two methods introduce a non-unitary gain in the estimation process. Finally, we show that the sampling of the spot structures after filtering by some convolution kernels is crucial to get an unbiased estimate of the spot displacement.     

Measurement of wave-front aberration in soft contact lenses by use of a Shack-Hartmann wave-front sensor

Lower- and higher-order wave-front aberrations of soft contact lenses were accurately measured with a Shack-Hartmann wave-front sensor. The soft contact lenses were placed in a wet cell filled with lens solution to prevent surface deformation and desiccation during measurements. Aberration measurements of conventional toric and multifocal soft contact lenses and a customized soft contact lens have proved that this method is reliable. A Shack-Hartmann wave-front sensor can be used to assess optical quality of both conventional and customized soft contact lenses and to assist in enhancing lens quality control.     

Calibration and performance of a pyramid wavefront sensor for the eye

We describe the calibration and performance of a pyramid wavefront sensor designed for use in a retinal imaging camera. The effect of the image modulation and the sensor binning on the measurements are explained in detail and various tests to validate the performance are described. The wavefront sensor was incorporated into an adaptive optics system that used a magnetically actuated deformable mirror, and results on static test optics are shown.     

Experimental comparison of a Shack-Hartmann sensor and a phase-shifting interferometer for large-optics metrology applications

We performed a direct side-by-side comparison of a Shack-Hartmann wave-front sensor and a phase-shifting interferometer for the purpose of characterizing large optics. An expansion telescope of our own design allowed us to measure the surface figure of a 400-mm-square mirror with both instruments simultaneously. The Shack-Hartmann sensor produced data that closely matched the interferometer data over spatial scales appropriate for the lenslet spacing, and much of the <20-nm rms systematic difference between the two measurements was due to diffraction artifacts that were present in the interferometer data but not in the Shack-Hartmann sensor data. The results suggest that Shack-Hartmann sensors could replace phase-shifting interferometers for many applications, with particular advantages for large-optic metrology.