Wavefront Estimation Research Articles

Validation of Intramural Wavefront Reconstruction and Estimation of 3D Conduction Velocity.

Changes in conduction velocity are indicative of a wide variety of cardiac abnormalities yet measuring conduction velocity is challenging, especially within the myocardial volume. In this study we investigated a novel technique to reconstruct activation fronts and estimate three-dimensional (3D) conduction velocity (CV) from experimental intramural recordings. From the intermittently sampled electrograms we both reconstruct the activation profile and compute the reciprocal of the gradient of activation times and a series of streamlines that allows for the CV estimation. The reconstructed activation times agreed closely with simulated values, with 50% to 70% of the nodes ≤ 1ms of absolute error. We found close agreement between the CVs calculated using reconstructed versus simulated activation times. Across the reconstructed stimulation sites we saw that the reconstructed CV was on average 3.8% different than the ground truth CV. This study used simulated datasets to validate our methods for reconstructing 3D activation fronts and estimating conduction velocities. Our results indicate that our method allows accurate reconstructions from sparse measurements, thus allowing us to examine changes in activation induced by experimental interventions such as acute ischemia, ectopic pacing, or drugs.

Influence of weighting function on accuracy of supersonic mixing layer wave-front variance estimation with linking equation

In aero optics, the linking equation proposed by Sutton is an important equation which can link the fluid-mechanic statistical parameters to the statistical optical degradation parameters. However, in the application of simplified linking equation (SLE) to subsonic flowfields, the weighting function is often ignored. The supersonic mixing layer flowfield is generated in the supersonic wind tunnel. The nanoparticle-based planar laser scattering technology is used to obtain the density field of flowfield. The optics errors between supersonic mixing layer wave-front variances calculated from the SLE and the generalized linking equation are analyzed. The results indicate the validity of using the SLE to estimate the wave-front variance of supersonic mixing layer flowfield. Moreover, the SLE with weighting function has better fitting accuracy than the SLE without weighting function. The weighting function for the application of SLE to the high correlated regions in the supersonic mixing layer is necessary.

Phase diversity technique with sparse regularization in liquid crystal adaptive optics system

Phase diversity (PD) technique is an effective method for wavefront sensing and image restoration in adaptive optics (AO). Classical PD with Tikhonov regularization can achieve proper wavefront estimation but constantly results in overly smooth images. Nonlocal centralized sparse representation (NCSR) based on nonlocal self-similarity and the sparsity model is combined with PD to obtain high-resolution images. The proposed method contains two steps: the first step is obtaining wavefront from ordinary PD with Tikhonov regularization, and the second step is deblurring the image with NCSR other than Tikhonov regularization. Numerical simulations show that the peak signal-to-noise ratios and structural similarity index metrics of deblurred images by the proposed method are higher than those by the traditional method. This work also studies the influence of weak noise. Initially, the proposed method is applied to a liquid crystal AO system, where the highest spatial resolutions that can be clearly distinguished are 1.59 × diffraction limitation with AO on, 1.41 × diffraction limitation with traditional PD, and 1.26 × diffraction limitation with the proposed method. The proposed approach can be widely used for AO postprocessing in ground-based telescopes, fluorescence microscopes, and other applications.

Nonlinear wavefront reconstruction methods for pyramid sensors using Landweber and Landweber-Kaczmarz iterations.

Accurate and robust wavefront reconstruction methods for pyramid wavefront sensors are in high demand, as these sensors are planned to be part of many instruments currently under development for ground-based telescopes. The pyramid sensor relates the incoming wavefront and its measurements in a nonlinear way. Nevertheless, almost all existing reconstruction algorithms are based on a linearization of the model. The assumption of a linear pyramid sensor response is justifiable in closed-loop adaptive optics (AO) when the measured phase information is small, but, depending on the system, may not be feasible due to unpreventable errors such as non-common path aberrations. In order to solve the nonlinear inverse problem of wavefront reconstruction from pyramid sensor data, we introduce two new methods based on the nonlinear Landweber and Landweber-Kaczmarz iterations. Using these algorithms, we experience high-quality wavefront estimation, especially for the non-modulated sensor, by still keeping the numerical effort feasible for large-scale AO systems.

Shape reconstruction of large optical surface with high-order terms in fringe reflection technique

A fast and effective shape reconstruction method of large aspheric specular surfaces with high order terms is proposed in fringe reflection technique, which combines modal estimation with high-order finitedifference algorithm. The iterative equation with highorder truncation errors is derived for calculating the specular surface with large aperture based on high-order finite-difference algorithm. To achieve the wavefront estimation and improve convergence speed, the numerical orthogonal transformation method based on Zernike polynomials is implemented to obtain the initial iteration value. The reconstruction results of simulated surface identified the advantages of the proposed method. Furthermore, a freeform in illuminating system has been used to demonstrate the validity of the improved method in practical measurement. The results show that the proposed method has the advantages of making the reconstruction of different shape apertures accurate and rapid. In general, this method performs well in measuring large complex objects with high frequency information in practical measurement.

Fast iterative tomographic wavefront estimation with recursive Toeplitz reconstructor structure for large-scale systems.

Tomographic wavefront reconstruction is the main computational bottleneck to realize real-time correction for turbulence-induced wavefront aberrations in future laser-assisted tomographic adaptive-optics (AO) systems for ground-based giant segmented mirror telescopes because of its unprecedented number of degrees of freedom, N, i.e., the number of measurements from wavefront sensors. In this paper, we provide an efficient implementation of the minimum-mean-square error (MMSE) tomographic wavefront reconstruction, which is mainly useful for some classes of AO systems not requiring multi-conjugation, such as laser-tomographic AO, multi-object AO, and ground-layer AO systems, but is also applicable to multi-conjugate AO systems. This work expands that by Conan [Proc. SPIE9148, 91480R (2014)PSISDG0277-786X10.1117/12.2054472] to the multi-wavefront tomographic case using natural and laser guide stars. The new implementation exploits the Toeplitz structure of covariance matrices used in an MMSE reconstructor, which leads to an overall O(N log N) real-time complexity compared with O(N2) of the original implementation using straight vector-matrix multiplication. We show that the Toeplitz-based algorithm leads to 60nm rms wavefront error improvement for the European Extremely Large Telescope laser-tomography AO system over a well-known sparse-based tomographic reconstruction; however, the number of iterations required for suitable performance is still beyond what a real-time system can accommodate to keep up with the time-varying turbulence.

Predictive dynamic digital holography and image sharpening.

Digital holography is often combined with image sharpening for wavefront estimation and correction, and this combination has received recent attention for many imaging and sensing applications. A significant obstacle for digital holography and image sharpening in high-speed real-time applications is the fact that the process is computationally intensive, requiring iterative virtual wavefront propagation and hill-climbing algorithms to optimize sharpness criteria. This paper introduces a method for accelerating dynamic digital holography and image sharpening by wavefront prediction. The approach here integrates optimal state-space prediction filters with digital holography and image sharpening to short-circuit the computationally intensive process of virtual wavefront propagation and sharpness optimization.

GPU implementation for spline-based wavefront reconstruction.

This paper presents an adaptation of the distributed-spline-based aberration reconstruction method for Shack-Hartmann (SH) slope measurements to extremely large-scale adaptive optics systems and the execution on graphics processing units (GPUs). The introduction of a hierarchical multi-level scheme for the elimination of piston offsets between the locally computed wavefront (WF) estimates solves the piston error propagation observed for a large number of partitions with the original version. To obtain a fully distributed method for WF correction, the projection of the phase estimates is locally approximated and applied in a distributed fashion, providing stable results for low and medium actuator coupling. An implementation of the method with the parallel computing platform CUDA exploits the inherently distributed nature of the algorithm. With a standard off-the-shelf GPU, the computation of the adaptive optics correction updates is accomplished in under 1ms for the benchmark case of a 200×200 SH array.

Path integration guided with a quality map for shape reconstruction in the fringe reflection technique

A new local integration algorithm called quality map path integration (QMPI) is reported for shape reconstruction in the fringe reflection technique. A quality map is proposed to evaluate the quality of gradient data locally, and functions as a guideline for the integrated path. The presented method can be employed in wavefront estimation from its slopes over the general shaped surface with slope noise equivalent to that in practical measurements. Moreover, QMPI is much better at handling the slope data with local noise, which may be caused by the irregular shapes of the surface under test. The performance of QMPI is discussed by simulations and experiment. It is shown that QMPI not only improves the accuracy of local integration, but can also be easily implemented with no iteration compared to Southwell zonal reconstruction (SZR). From an engineering point-of-view, the proposed method may also provide an efficient and stable approach for different shapes with high-precise demand.

A zonal wavefront sensor with multiple detector planes

A conventional zonal wavefront sensor estimates the wavefront from the data captured in a single detector plane using a single camera. In this paper, we introduce a zonal wavefront sensor which comprises multiple detector planes instead of a single detector plane. The proposed sensor is based on an array of custom designed plane diffraction gratings followed by a single focusing lens. The laser beam whose wavefront is to be estimated is incident on the grating array and one of the diffracted orders from each grating is focused on the detector plane. The setup, by employing a beam splitter arrangement, facilitates focusing of the diffracted beams on multiple detector planes where multiple cameras can be placed. The use of multiple cameras in the sensor can offer several advantages in the wavefront estimation. For instance, the proposed sensor can provide superior inherent centroid detection accuracy that can not be achieved by the conventional system. It can also provide enhanced dynamic range and reduced crosstalk performance. We present here the results from a proof of principle experimental arrangement that demonstrate the advantages of the proposed wavefront sensing scheme.

Improvement in error propagation in the Shack-Hartmann-type zonal wavefront sensors.

Estimation of the wavefront from measured slope values is an essential step in a Shack-Hartmann-type wavefront sensor. Using an appropriate estimation algorithm, these measured slopes are converted into wavefront phase values. Hence, accuracy in wavefront estimation lies in proper interpretation of these measured slope values using the chosen estimation algorithm. There are two important sources of errors associated with the wavefront estimation process, namely, the slope measurement error and the algorithm discretization error. The former type is due to the noise in the slope measurements or to the detector centroiding error, and the latter is a consequence of solving equations of a basic estimation algorithm adopted onto a discrete geometry. These errors deserve particular attention, because they decide the preference of a specific estimation algorithm for wavefront estimation. In this paper, we investigate these two important sources of errors associated with the wavefront estimation algorithms of Shack-Hartmann-type wavefront sensors. We consider the widely used Southwell algorithm and the recently proposed Pathak-Boruah algorithm [J. Opt.16, 055403 (2014)JOOPDB0150-536X10.1088/2040-8978/16/5/055403] and perform a comparative study between the two. We find that the latter algorithm is inherently superior to the Southwell algorithm in terms of the error propagation performance. We also conduct experiments that further establish the correctness of the comparative study between the said two estimation algorithms.

Nonlinear spline wavefront reconstruction through moment-based Shack-Hartmann sensor measurements.

We propose a spline-based aberration reconstruction method through moment measurements (SABRE-M). The method uses first and second moment information from the focal spots of the SH sensor to reconstruct the wavefront with bivariate simplex B-spline basis functions. The proposed method, since it provides higher order local wavefront estimates with quadratic and cubic basis functions can provide the same accuracy for SH arrays with a reduced number of subapertures and, correspondingly, larger lenses which can be beneficial for application in low light conditions. In numerical experiments the performance of SABRE-M is compared to that of the first moment method SABRE for aberrations of different spatial orders and for different sizes of the SH array. The results show that SABRE-M is superior to SABRE, in particular for the higher order aberrations and that SABRE-M can give equal performance as SABRE on a SH grid of halved sampling.

Enhancing wavefront estimation accuracy by using higher-order iterative compensations in the Southwell configuration.

Accurate wavefront integration based on gradient fields is crucial for various indirect measurement techniques, such as Shack-Hartmann sensing, shearography, and the fringe reflection technique. In this paper, a higher-order iterative compensation algorithm is proposed to enhance the reconstruction accuracy for the finite-difference-based least-squares integration (FLI) method. In this method, higher-order gradient fields are reconstructed and the calculated residual gradient fields compensate the truncation error with the traditional FLI by iterations. A comparison of different FLI methods, including traditional FLI, iterative FLI, higher-order FLI, and the proposed FLI method, is conducted. The result shows that the reconstructed wavefront with the proposed method is more accurate than those with other FLI methods. In addition, the impact of the gradient measurement noise is also discussed.

Zonal wavefront sensing with enhanced spatial resolution.

In this Letter, we introduce a scheme to enhance the spatial resolution of a zonal wavefront sensor. The zonal wavefront sensor comprises an array of binary gratings implemented by a ferroelectric spatial light modulator (FLCSLM) followed by a lens, in lieu of the array of lenses in the Shack-Hartmann wavefront sensor. We show that the fast response of the FLCSLM device facilitates quick display of several laterally shifted binary grating patterns, and the programmability of the device enables simultaneous capturing of each focal spot array. This eventually leads to a wavefront estimation with an enhanced spatial resolution without much sacrifice on the sensor frame rate, thus making the scheme suitable for high spatial resolution measurement of transient wavefronts. We present experimental and numerical simulation results to demonstrate the importance of the proposed wavefront sensing scheme.

Framework to trade optimality for local processing in large-scale wavefront reconstruction problems.

We show that the minimum variance wavefront estimation problems permit localized approximate solutions, in the sense that the wavefront value at a point (excluding unobservable modes, such as the piston mode) can be approximated by a linear combination of the wavefront slope measurements in the point's neighborhood. This enables us to efficiently compute a wavefront estimate by performing a single sparse matrix-vector multiplication. Moreover, our results open the possibility for the development of wavefront estimators that can be easily implemented in a decentralized/distributed manner, and in which the estimate optimality can be easily traded for computational efficiency. We numerically validate our approach on Hudgin wavefront sensor geometries, and the results can be easily generalized to Fried geometries.

Improving the accuracy of a Shack-Hartmann wavefront sensor on extended scenes

In order to achieve higher resolutions, current earth-observation satellites use larger lightweight main mirrors which are usually deformed over time, impacting on image quality. In the context of active optics, we studied the problem of correcting this main mirror by performing wavefront estimation in a closed loop environment. To this end, a Shack-Hartman wavefront sensor (SHWFS) used on extended scenes could measure the incoming wavefront. The performance of the SHWFS on extended scenes depends entirely on the accuracy of the shift estimation algorithm employed, which should be fast enough to be executed on-board. In this paper we specifically deal with the problem of fast accurate shift estimation in this context. We propose a new algorithm, based on the global optical flow method, that estimates the shifts in linear time. In our experiments, our method proved to be more accurate and stable, as well as less sensitive to noise than all current state-of-the-art methods.

Improving wavefront sensing with a Shack-Hartmann device.

To achieve higher resolutions, current earth observation satellites use larger, lightweight primary mirrors that can deform over time, affecting the image quality. To overcome this problem, we evaluated the possibility of combining a deformable mirror with a Shack-Hartman wavefront sensor (SHWFS) directly in the satellite. The SHWFS's performance depends entirely on the accuracy of the shift estimation algorithm employed, which should be computationally cheap to execute onboard. We analyzed the problem of fast, accurate shift estimation in this context and have proposed a new algorithm, based on a global optical flow method that estimates the shifts in linear time. Based on our experiments, we believe our method has proven to be more accurate and stable, as well as less sensitive to noise, than all current state-of-the-art methods, permitting a more precise onboard wavefront estimation.

Expected gain in the pyramid wavefront sensor with limited Strehl ratio

Context. One of the main properties of the pyramid wavefront sensor is that, once the loop is closed, and as the reference star image shrinks on the pyramid pin, the wavefront estimation signal-to-noise ratio can considerably improve. This has been shown to translate into a gain in limiting magnitude when compared with the Shack-Hartmann wavefront sensor, in which the sampling on the wavefront is performed before the light is split into four quadrants, which does not allow the quality of the focused spot to increase. Since this property is strictly related to the size of the re-imaged spot on the pyramid pin, the better the wavefront correction, the higher the gain.Aims. The goal of this paper is to extend the descriptive and analytical computation of this gain that was given in a previous paper, to partial wavefront correction conditions, which are representative for most of the wide field correction adaptive optics systems.Methods. After focusing on the low Strehl ratio regime, we analyze the minimum spatial sampling required for the wavefront sensor correction to still experience a considerable gain in sensitivity between the pyramid and the Shack-Hartmann wavefront sensors.Results. We find that the gain can be described as a function of the sampling in terms of the Fried parameter.

Improved quantitative visualization of hypervelocity flow through wavefront estimation based on shadow casting of sinusoidal gratings.

A simple noninterferometric optical probe is developed to estimate wavefront distortion suffered by a plane wave in its passage through density variations in a hypersonic flow obstructed by a test model in a typical shock tunnel. The probe has a plane light wave trans-illuminating the flow and casting a shadow of a continuous-tone sinusoidal grating. Through a geometrical optics, eikonal approximation to the distorted wavefront, a bilinear approximation to it is related to the location-dependent shift (distortion) suffered by the grating, which can be read out space-continuously from the projected grating image. The processing of the grating shadow is done through an efficient Fourier fringe analysis scheme, either with a windowed or global Fourier transform (WFT and FT). For comparison, wavefront slopes are also estimated from shadows of random-dot patterns, processed through cross correlation. The measured slopes are suitably unwrapped by using a discrete cosine transform (DCT)-based phase unwrapping procedure, and also through iterative procedures. The unwrapped phase information is used in an iterative scheme, for a full quantitative recovery of density distribution in the shock around the model, through refraction tomographic inversion. Hypersonic flow field parameters around a missile-shaped body at a free-stream Mach number of ∼8 measured using this technique are compared with the numerically estimated values. It is shown that, while processing a wavefront with small space-bandwidth product (SBP) the FT inversion gave accurate results with computational efficiency; computation-intensive WFT was needed for similar results when dealing with larger SBP wavefronts.

In-focus wavefront sensing using non-redundant mask-induced pupil diversity.

Wavefront estimation using in-focus image data is critical to many applications. This data is invariant to a sign flip with complex conjugation of the complex amplitude in the pupil, making for a non-unique solution. Information from an in-focus image taken through a non-redundant pupil mask (NRM) can break this ambiguity, enabling the true aberration to be determined. We demonstrate this by priming a full pupil Gerchberg-Saxton phase retrieval with NRM fringe phase information. We apply our method to measure simulated aberrations on the segmented James Webb space telescope (JWST) mirror using full pupil and NRM data from its near infrared imager and slitless spectrograph (NIRISS).