Focal plane position detection with a diffractive optic for shack-hartmann wave-front sensor fabrication

During construction of a Shack-Hartmann wave-front sensor it is critical that the spacing between the lens array and the detector array be equal to the lens array focal length to obtain accurate and precise measurements of a wave front. This separation is often difficult to determine with large f/# lenses, because their focal spot diameter does not change substantially for small displacements on either side of the focal plane. We describe a method with an array of off-axis lens segments for determining the location of the focal plane. Because the lenses are off axis, changes in the distance from the optic to the detector array result in transverse focal spot position variations as a function of their separation from the lenses. By analyzing the focal spot pattern on a CCD, we achieved 12-mum rms error in the axial position measurement while moving a 4-mm-focal-length optic over 1 mm.     

Hierarchical wave-front sensing

We present a new wave-front sensing technique for adaptive optics based on use of several wave-front sensors dedicated to the sensing of a different range of spatial frequencies. We call it a hierarchical wave-front sensor. We present the concept of a hierarchical wave-front sensor and apply it to the Shack-Hartmann sensor. We show the gain that is expected with two Shack-Hartmann sensors. We obtain a gain that increases with the size of the largest sensor, and we detail the application of hierarchical wave-front sensing to extreme adaptive optics and extremely large telescopes.     

Transformer-type displacement sensors containing discretely profiled sensing elements

The paper considers the design and primary data processing for transformer-type coordinate sensors having discretely profiled magnetic circuits of plate and cylindrical types. The sensors provide protection of the working windings from contact with the moving elements.Translated from Izmeritel'naya Tekhnika, No. 4, pp. 25–27, April, 1995.     

Evaluating the effect of transmissive optic thermal lensing on laser beam quality with a shack-hartmann wave-front sensor

We examine wave-front distortion caused by high-power lasers on transmissive optics using a Shack-Hartmann wave-front sensor. The coupling coefficient for a thermally aberrated Gaussian beam to the TEM(00) mode of a cavity was determined as a function of magnitude of the thermally induced aberration. One wave of thermally induced phase aberration between the Gaussian intensity peak and the 1/e(2) radius of the intensity profile reduces the power-coupling coefficient to the TEM(00) mode of the cavity to 4.5% with no compensation. With optimal focus compensation the power coupling is increased to 79%. The theoretical shape of the thermally induced optical phase aberration is compared with measurements made in a neutral-density filter glass, Faraday glass, and lithium niobate. The agreement between the theoretical and the measured thermal aberration profiles is within the rms wave-front measurement sensitivity of the Shack-Hartmann wave-front sensor, which is a few nanometers.     

Noise propagation in wave-front sensing with phase diversity

The phase diversity technique is studied as a wave-front sensor to be implemented with widely extended sources. The wave-front phase expanded on the Zernike polynomials is estimated from a pair of images (in focus and out of focus) by use of a maximum-likelihood approach. The propagation of the photon noise in the images on the estimated phase is derived from a theoretical analysis. The covariance matrix of the phase estimator is calculated, and the optimal distance between the observation planes that minimizes the noise propagation is determined. The phase error is inversely proportional to the number of photons in the images. The noise variance on the Zernike polynomials increases with the order of the polynomial. These results are confirmed with both numerical and experimental validations. The influence of the spectral bandwidth on the phase estimator is also studied with simulations.     

Phase-diversity wave-front sensing with a distorted diffraction grating

We describe a novel wave-front sensor comprising a distorted diffraction grating, simple optics, and a single camera. A noniterative phase-diversity algorithm is used for wave-front reconstruction. The sensor concept and practical implementation are described in detail, and performance is validated against different Zernike modes and a representative atmospheric phase map.     

Analysis of stellar interferometers as wave-front sensors

The basic principle and theoretical relationships of an original method are presented that allow the wave-front errors of a ground or spaceborne telescope to be retrieved when its main pupil is combined with a second, decentered reference optical arm. The measurement accuracy of such a telescope-interferometer is then estimated by means of various numerical simulations, and good performance is demonstrated, except in limited areas near the telescope pupil's rim. In particular, it permits direct phase evaluation (thus avoiding the use of first- or second-order derivatives), which will be of special interest for the cophasing of segmented mirrors in future giant-telescope projects. Finally, the useful practical domain of the method is defined, which seems to be better suited for periodic diagnostics of space- or ground-based telescopes or to real-time scientific observations in some specific cases (e.g., the central star in instruments that search for extrasolar planets).     

Practical configuration for wave-front sensing with two-beam phase retrieval

A wave-front sensing approach based on two-beam phase retrieval is described. Light from an aberrated beam is split into two paths. A random phase and amplitude perturbation is applied to the beam in one path, and the interference patterns of the resultant two beams are measured in two planes along the axis of propagation. By modulation of one of the two beams, the intensity of each beam and the phase difference between the two beams are recovered in each plane. A rapidly convergent phase-retrieval algorithm is formulated by the method of sequential projections onto constraint sets. Examples are given illustrating the convergence properties of the approach.     

Scene-based Shack-Hartmann wave-front sensing: analysis and simulation

In many situations it is not possible for an adaptive optics system to use a point source to measure the phase derivative, such as imaging along slant paths through the atmosphere and observation of the earth from space with a lightweight optic. Instead, small subimages of the observed scene can be used in a scene-based wave-front sensing technique. This study presents three important advances in the understanding of this technique. Rigorous analysis shows how slope estimation performance depends precisely on scene content and illumination. Scaling laws for changes in illumination are derived. The technique, when applied to point sources, is more robust to detect size changes and background levels than current methods.     

Multiple-wave lateral shearing interferometry for wave-front sensing

Multiple-wave achromatic interferometric techniques are used to measure, with high accuracy and high transverse resolution, wave fronts of polychromatic light sources. The wave fronts to be measured are replicated by a diffraction grating into several copies interfering together, leading to an interference pattern. A CCD detector located in the vicinity of the grating records this interference pattern. Some of these wave-front sensors are able to resolve wave-front spatial frequencies 3 to 4 times higher than a conventional Shack-Hartmann technique using an equivalent CCD detector. Its dynamic is also much higher, 2 to 3 orders of magnitude.     

Redundant-channel fiber-optics displacement sensors

Translated from Izmeritel'naya Tekhnika, No. 10, pp. 4–5, October, 1990.     

Adaptive optics with advanced phase-contrast techniques. I. High-resolution wave-front sensing

High-resolution phase-contrast wave-front sensors based on phase spatial light modulators and micromirror/ liquid-crystal arrays are introduced. Wave-front sensor performance is analyzed for atmospheric-turbulence-induced phase distortions described by the Kolmogorov and the Andrews models. A high-resolution phase-contrast wave-front sensor (nonlinear Zernike filter) based on an optically controlled liquid-crystal phase spatial light modulator is experimentally demonstrated. The results demonstrate high-resolution visualization of dynamically changing phase distortions within the sensor time response of approximately 10 ms.     

Scanning displacement sensors with surface acoustic wave modulation

Translated from Izmeritel'naya Tekhnika, No. 10, pp. 3–4, October, 1990.     

Designing reflectometric fiber-optic displacement sensors

The general principles governing the operation of reflectometric fiber-optic sensors are considered. A classification is presented of all the known methods of controlling the characteristics of fiber-optic sensors. In addition, a new control method, involving the design of a specially designed optical inhomogeneity on the surface of the measurement object, is described. Translated from Izmeritel'naya Tekhnika, No. 1, pp. 28–30, January, 1997.     

Ensemble-averaged Shack-Hartmann wave-front sensing for imaging through turbid media

A technique is described for ensemble-averaging the light wave emerging from a turbid medium, enabling the recovery of optical information that is otherwise lost in a speckle pattern. The technique recovers both an amplitude and a phase function for a wave that has been corrupted by severe scattering, without the use of holography. With the phase estimated, an ensemble-averaged field is constructed that can be backprojected to form an image of the object obscured by the scattering medium. Experimental results suggest that the technique can resolve two object points whose signals are unresolved on the exit surface of a diffuser.     

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。     

Signal-to-noise comparison of deconvolution from wave-front sensing with traditional linear and speckle image reconstruction

It is well known that atmospheric turbulence severely degrades the performance of ground-based imaging systems. Techniques to overcome the effects of the atmosphere have been developing at a rapid pace over the past 10 years. These techniques can be grouped into two broad categories: predetection and postdetection techniques. A recent newcomer to the postdetection scene is deconvolution from wave-front sensing (DWFS). DWFS is a postdetection image-reconstruction technique that makes use of one feature of predetection techniques. A wave-front sensor (WFS) is used to record the wave-front phase distortion in the pupil of the telescope for each short-exposure image. The additional information provided by the WFS is used to estimate the system's point-spread function (PSF). The PSF is then used in conjunction with the ensemble of short-exposure images to obtain an estimate of the object intensity distribution through deconvolution. With the addition of DWFS to the suite of possible postdetection image-reconstruction techniques, it is natural to ask "How does DWFS compare with both traditional linear and speckle image-reconstruction techniques?" In the results we make a direct comparison based on a frequency-domain signal-to-noise-ratio performance metric. This metric is applied to each technique's image-reconstruction estimator. We find that DWFS nearly always results in improved performance over the estimators of traditional linear image reconstruction such as Wiener filtering. On the other hand, DWFS does not always outperform speckle-imaging techniques, and in cases that it does the improvement is small.     

Target-in-the-loop beam control: basic considerations for analysis and wave-front sensing

Target-in-the-loop (TIL) wave propagation geometry represents perhaps the most challenging case for adaptive optics applications that are related to maximization of irradiance power density on extended remotely located surfaces in the presence of dynamically changing refractive-index inhomogeneities in the propagation medium. We introduce a TIL propagation model that uses a combination of the parabolic equation describing coherent outgoing-wave propagation, and the equation describing evolution of the mutual correlation function (MCF) for the backscattered wave (return wave). The resulting evolution equation for the MCF is further simplified by use of the smooth-refractive-index approximation. This approximation permits derivation of the transport equation for the return-wave brightness function, analyzed here by the method of characteristics (brightness function trajectories). The equations for the brightness function trajectories (ray equations) can be efficiently integrated numerically. We also consider wave-front sensors that perform sensing of speckle-averaged characteristics of the wave-front phase (TIL sensors). Analysis of the wave-front phase reconstructed from Shack-Hartmann TIL sensor measurements shows that an extended target introduces a phase modulation (target-induced phase) that cannot be easily separated from the atmospheric-turbulence-related phase aberrations. We also show that wave-front sensing results depend on the extended target shape, surface roughness, and outgoing-beam intensity distribution on the target surface. For targets with smooth surfaces and nonflat shapes, the target-induced phase can contain aberrations. The presence of target-induced aberrations in the conjugated phase may result in a deterioration of adaptive system performance.     

Evaluation of least-squares phase-diversity technique for space telescope wave-front sensing

Because of mechanical aspects of fabrication, launch, and operational environment, space telescope optics can suffer from unforeseen aberrations, detracting from their intended diffraction-limited performance goals. We give the results of simulation studies designed to explore how wave-front aberration information for such near-diffraction-limited telescopes can be estimated through a regularized, low-pass filtered version of the Gonsalves (least-squares) phase-diversity technique. We numerically simulate models of both monolithic and segmented space telescope mirrors; the segmented case is a simplified model of the proposed next generation space telescope. The simulation results quantify the accuracy of phase diversity as a wave-front sensing (WFS) technique in estimating the pupil phase map. The pupil phase is estimated from pairs of conventional and out-of-focus photon-limited point-source images. Image photon statistics are simulated for three different average light levels. Simulation results give an indication of the minimum light level required for reliable estimation of a large number of aberration parameters under the least-squares paradigm. For weak aberrations that average a 0.10lambda pupil rms, the average WFS estimation errors obtained here range from a worst case of 0.057lambda pupil rms to a best case of only 0.002lambda pupil rms, depending on the light level as well as on the types and degrees of freedom of the aberrations present.     

Practical issues in wave-front sensing by use of phase diversity

We present the results of the phase-diversity algorithm applied to simulated and laboratory data. We show that the exact amount of defocus distance does not need to be known exactly for the phase-diversity algorithm on extended scene imaging. We determine, through computer simulation, the optimum diversity distance for various scene types. Using laboratory data, we compare the aberrations recovered with the phase-diversity algorithm and those measured with a Fizeau interferometer that uses a He-Ne laser. The two aberration sets agree with a Strehl ratio of over 0.9. The contrast of the recovered object is found to be ten times that of the raw image.