Simulated Wavefront Research Articles

Simulation of a temporally dynamic atmospheric wavefront using the modified von-Kármán spectrum and Zernike-based method

In the simulation of the atmospheric wavefront, the Kolmogorov spectrum facilitates the mathematical treatments, but this model gives inaccurate predictions in cases where the effects of outer- and inner-scale can not be neglected. Therefore, we derive the covariance formula of Zernike coefficients based on the modified von-Kármán turbulence spectrum to improve the Zernike-based method. Further, using the frozen flow hypothesis, the temporal power spectra of Zernike coefficients are derived, and the effects of wind velocity and direction, as well as the outer and inner scales, are also taken into account. Then, we introduce a method for generating the temporally dynamic atmospheric wavefront using the inverse Fourier transform to draw random time-evolving coefficients from the temporal spectra. We evaluate the performance on simulated atmospheric wavefront, and the results confirm that accurate spatial and temporal statistics are obtained.

Off-axis point spread function reconstruction forsingle conjugate adaptive optics.

Modern giant segmented mirror telescopes (GSMTs) such as the Extremely Large Telescope, which is currently under construction, depend heavily on adaptive optics (AO) systems to correct for atmospheric distortions. However, a residual blur always remains in the astronomical images corrected by single conjugate AO (SCAO) systems due to fitting and bandwidth errors, which can mathematically be described by a convolution of the true image with a point spread function (PSF). Due to the nature of the turbulent atmosphere and its correction, the PSF is spatially varying, which is known as an anisoplanatic effect. The PSF serves, e.g.,as a quality measure for science images and therefore needs to be known as accurately as possible. In this paper, we present an algorithm for PSF reconstruction from pupil-plane data in directions apart from the guide star direction in an SCAO system. Our algorithm is adapted to the needs of GSMTs focused on estimating the contribution of the anisoplanatic and generalized fitting error to the PSF. Results obtained in an end-to-end simulation tool show a qualitatively good reconstruction of the PSF compared to the PSF calculated directly from the simulated incoming wavefront as well as stable performance with respect to imprecise knowledge of atmospheric parameters.

Inverse Hartmann test for radius of curvature measurement in a corneal topography calibration sphere

In this article, the use of a square Hartmann screen test to measure the radius of curvature of a corneal topography calibration test sphere is presented. The proposed technique is based on the image formation principle by specular reflection on convex reflective surfaces. Applying an inverse Hartmann test, a de-magnified virtual image (Hartmanngram) is obtained; considering their own scaled reference screen plate, a zonal wavefront retrieval approach is used and the radius of curvature obtained. Experimental setup along the obtained results is presented. A simulated spherical wavefront is used as a method to evaluate the error in the wavefront reconstruction. Since the measurements of radius of curvature fits in to ISO 10343, through suitable modifications the proposed method is potentially applicable in small F/# convex specular surfaces, as is the case in keratometry and corneal topography measurements.

X-ray grating interferometry design for the 4D GRAPH-X system

The 4D GRAPH-X (Dynamic GRAting-based PHase contrast x-ray imaging) project aims at developing a prototype of an x-ray grating-based phase-contrast imaging scanner in a laboratory setting, which is based on the Moirè single-shot acquisition method in order to be optimized for analysing moving objects (in the specific case, a dynamic thorax phantom), that could evolve into a suitable tool for biomedical applications although it can be extended to other application fields. When designing an x-ray Talbot-Lau interferometer, high visibility and sensitivity are two important figures of merit, strictly related to the performance of the system in obtaining high quality phase contrast and dark-field images. Wave field simulations are performed to optimize the setup specifications and construct a high-resolution and high-sensitivity imaging system. In this work, the design of a dynamic imaging setup using a conventional milli-focus x-ray source is presented. Optimization by wave front simulations leads to a symmetric configuration with 5.25 μm pitch at third Talbot order and 45 keV design energy. The simulated visibility is about 22%. Results from GATE based Monte Carlo simulations show a 19% transmission percentage of the incoming beam into the detector after passing through all the gratings and the sample. Such results are promising in view of building a system optimized for dynamic imaging.

Dynamic mode decomposition based predictive model performance on supersonic and transonic aero-optical wavefront measurements.

Air density variations around an airborne directed energy system distort a beam's wavefront, resulting in degraded performance after propagation into the far field. Adaptive optics (AO) can be used to correct for these rapidly evolving aero-optical aberrations; however, in some conditions, the inherent latency between measurement and correction in state-of-the-art AO systems results in significantly reduced performance. Predictive AO control methods utilize future state predictions to compensate for rapidly evolving distortions and are promising techniques for mitigating this limitation. This paper demonstrates an application of the dynamic mode decomposition (DMD) method on turbulent boundary layer wavefront data from supersonic and transonic wind tunnel flow from the Air Force Research Laboratory's Aero-Effects Laboratory. DMD is a lightweight algorithm used to isolate spatiotemporal patterns in a dataset into physically meaningful modes with associated dynamics, which were used to predict future states from a given wavefront. This method showed notable improvements in simulated wavefront correction, providing a reduction of residual wavefront distortion, measured as root mean square over the aperture, by up to 25.4% over a simulated latency model, which could accordingly result in higher laser system performance.

Iterative wavefront reconstruction for strong turbulence using Shack-Hartmann wavefront sensor measurements.

An iterative wavefront reconstruction method using Shack-Hartmann wavefront sensor (SHWFS) measurements is presented in this paper. A new cost function for the wavefront reconstruction problem is derived and the solution is obtained iteratively using the gradient descent method. The proposed method aims to effectively handle the scintillated SHWFS measurements and to provide simpler and accurate ways to achieve branch-point-tolerant wavefront reconstruction suitable for adaptive optics compensation of strong turbulence. Simulated iterative wavefront reconstruction results show the effectiveness of the proposed method. A laboratory optical testbed is also presented to show the experimental implementation of the proposed method.

The Measurement of PSF Ellipticity of an Unobstructed Off-Axis Space Telescope: Error Analysis

It is an effective method to detect weak gravitational lensing (WL) in the universe by measuring ellipticities of galaxies via astronomical telescopes. Optical properties of telescopes are critical to WL detections. To ensure the used telescopes to be competent, it is necessary to measure point spread function (PSF) ellipticities of telescopes in labs. In this paper, a way based on simulated star target imaging is proposed to measure PSF ellipticity of an unobstructed off-axis space telescope. Related errors are identified and modeled carefully for the first time. Effects of detector noises, micro-vibration of optical platforms, defocusing of simulated star target, wavefront errors (WFEs) and central obstructions of collimators on PSF ellipticity measurements of the telescope are analyzed. Results show that the measurement error of PSF ellipticity decreases from 0.0105 to 0.0043 by adopting 10 iterations of the iterative weighted centroiding algorithm when SNRs are under 24 dB. To ensure PSF ellipticity measurement errors are not larger than 0.01, the micro-vibration angle of the optical platform should be less than $0.05''$ . When focal length of the collimator is twice that of the telescope, the measurement errors of PSF ellipticity are under 0.01 if the defocusing of simulated star target is controlled to be not larger than 0.1 mm. In addition, WFEs and central obstructions of collimators change PSF ellipticity measurement errors to different degrees at different fields of view (FOVs). Due to 20 nm RMS WFE of the collimator, the maximum value of PSF ellipticity measurement errors over full FOVs is 0.1 and the average value is 0.0269. If the radius of central obscuration of the collimator is 150 mm, the maximum measurement error of PSF ellipticity over full FOVs is 0.0091. According to the results shown in this paper, significant references for high accuracy measurements of PSF ellipticity of telescopes can be provided.

Plane wave transmitted wavefront simulation and measurement of filter with multi-spectrum

Plane wave transmitted wavefront simulation and measurement of filter with multi-spectrum

Analyzing the propagation of EUV waves and their connection with type II radio bursts by combining numerical simulations and multi-instrument observations

Context. EUV (EIT) waves are wavelike disturbances of enhanced extreme ultraviolet (EUV) emission that propagate away from an eruptive active region across the solar disk. Recent years have seen much debate over their nature, with three main interpretations: the fast-mode magneto-hydrodynamic (MHD) wave, the apparent wave (reconfiguration of the magnetic field), and the hybrid wave (combination of the previous two). Aims. By studying the kinematics of EUV waves and their connection with type II radio bursts, we aim to examine the capability of the fast-mode interpretation to explain the observations, and to constrain the source locations of the type II radio burst emission. Methods. We propagate a fast-mode MHD wave numerically using a ray-tracing method and the WKB (Wentzel-Kramers-Brillouin) approximation. The wave is propagated in a static corona output by a global 3D MHD Coronal Model, which provides density, temperature, and Alfvén speed in the undisturbed coronal medium (before the eruption). We then compare the propagation of the computed wave front with the observed wave in EUV images (PROBA2/SWAP, SDO/AIA). Lastly, we use the frequency drift of the type II radio bursts to track the propagating shock wave, compare it with the simulated wave front at the same instant, and identify the wave vectors that best match the plasma density deduced from the radio emission. We apply this methodology for two EUV waves observed during SOL2017-04-03T14:20:00 and SOL2017-09-12T07:25:00. Results. The simulated wave front displays a good qualitative match with the observations for both events. Type II radio burst emission sources are tracked on the wave front all along its propagation. The wave vectors at the ray-path points that are characterized as sources of the type II radio burst emission are quasi-perpendicular to the magnetic field. Conclusions. We show that a simple ray-tracing model of the EUV wave is able to reproduce the observations and to provide insight into the physics of such waves. We provide supporting evidence that they are likely fast-mode MHD waves. We also narrow down the source region of the radio burst emission and show that different parts of the wave front are responsible for the type II radio burst emission at different times of the eruptive event.

Experimental study and numerical simulation of dam reservoir sediment release

In this research, experimental and numerical modelling of three-phase air, water, and sediment transport flow, due to the opening of a sluice gate was conducted in two scenarios, i.e., with and without a triangular obstacle. Numerical simulation was conducted using the Navier-Stokes equations with the aid of the volume of fluid method (VOF) to track the free surface of the fluid. For the experimental model, a glass-enclosed flume with 150 × 30 × 50 cm dimensions was used. The experiment was performed for an initial height of the water column at 20 cm and 10 cm sediment column. To evaluate the numerical model's performance, the simulation results were compared with the experimental observations using the average relative error %. The amount of relative error between experimental observations and numerical simulations, for the position and height of the wave flow for the three-phase air, water, and sediment flow, were obtained as 2.64% and 4.51% for the position and height of the water wave, and 2.23% and 2.82% for the position and height of the sediment transport, respectively, for the ‘without obstacle’ scenario, and 3.77% and 5.25% for the position and height of the water wave, and 2% and 7.23% for the position and height of the sediment transport, respectively, for the ‘with obstacle’ scenario. The findings of the study indicate the appropriate performance of the numerical model in the simulation of water and sediment wavefront advance, and also its weakness in the estimation of wave height.

Average gradient of Zernike polynomials over polygons.

Wavefront estimation from slope sensor data is often achieved by fitting measured slopes with Zernike polynomial derivatives averaged over the sampling subapertures. Here we discuss how the calculation of these average derivatives can be reduced to one-dimensional integrals of the Zernike polynomials, rather than their derivatives, along the perimeter of each subaperture. We then use this result to derive closed-form expressions for the average Zernike polynomial derivatives over polygonal areas, only requiring evaluation of polynomials at the polygon vertices. Finally, these expressions are applied to simulated Shack-Hartmann wavefront sensors with 7 and 23 fully illuminated lenslets across a circular pupil, with their accuracy and calculation time compared against commonly used integration methods.

Three-dimensional finite element modelling and dynamic response analysis of track-embankment-ground system subjected to high-speed train moving loads

A finite element approach is presented to examine ground vibration characteristics under various moving loads in a homogeneous half-space. Four loading modes including single load, double load, four-load, and twenty-load were simulated in a finite element analysis to observe their influence on ground vibrations. Four load moving speeds of 60, 80, 100, and 120 m/s were adopted to investigate the influence of train speed to the ground vibrations. The results demonstrated that the loading mode in a finite element analysis is reliable for train-induced vibration simulations. Additionally, a three-dimensional finite element model (3D FEM) was developed to investigate the dynamic responses of a track-ballast-embankment-ground system subjected to moving loads induced by high-speed trains. Results showed that vibration attenuations and breaks exist in the simulated wave fronts transiting through different medium materials. These tendencies are a result of the difference in the Rayleigh wave speeds of the medium materials relative to the speed of the moving train. The vibration waves induced by train loading were greatly influenced by the weakening effect of sloping surfaces on the ballast and embankment. Moreover, these tendencies were significant when the vibration waves are at medium and high frequency levels. The vibration waves reflected by the sloping surface were trapped and dissipated within the track-ballast-embankment-ground system. Thus, the vibration amplitude outside the embankment was significantly reduced.

Simulation study on X-ray phase contrast imaging with dual-phase gratings.

Two phase gratings in an X-ray grating interferometers can solve several technical challenges for clinical use of X-ray phase contrast. In this work, we adapt and evaluate this setup design to clinical X-ray sources and detectors in a simulation study. For a given set of gratings, we optimize the remaining parameter space of a dual-phase grating setup using a numerical wave front simulation. The simulation results are validated with experimentally obtained visibility measurements on a setup with a microfocus tube and a clinical X-ray detector. We then confirm by simulation that the Lau condition for the [Formula: see text] grating also holds for two phase gratings. Furthermore, we use a [Formula: see text] grating with a fixed period to search for periods of matching phase grating configurations. Simulated and experimental visibilities agree very well. We show that the Lau condition for a dual-phase grating setup requires the interference patterns of the first phase grating to constructively overlay at the second phase grating. Furthermore, a total of three setup variants for given [Formula: see text] periods were designed with the simulation, resulting in visibilities between 4.5 and 9.1%. Dual-phase gratings can be used and optimized for a medical X-ray source and detector. The obtained visibilities are somewhat lower than for other Talbot-Lau interferometers and are a tradeoff between setup length and spatial resolution (or additional phase stepping, respectively). However, these disadvantage appears minor compared to the overall better photon statistics, and the fact that dual-phase grating setups can be expected to scale to higher X-ray energies.

Point spread function reconstruction for single-conjugate adaptive optics on extremely large telescopes

Modern ground-based telescopes like the planned extremely large telescope (ELT) depend heavily on adaptive optics (AO) systems to correct for atmospheric turbulence. Even though AO correction is used, the quality of astronomical images still is degraded due to the time delay stemming from the wavefront sensor integration time and temporal response of the deformable mirror(s) (DM). This results in a blur, which can be mathematically described by a convolution of the true image with the point spread function (PSF). We present an algorithm for single-conjugate adaptive optics PSF reconstruction adapted to the needs of ELTs in a storage efficient way. In particular, the classical PSF reconstruction algorithm is changed in several points to give a more accurate estimate for the post-AO PSF. Bilinear splines are used as basis functions to minimize the computational effort. Results obtained in an end-to-end simulation tool show qualitatively good reconstruction of the PSF compared with the PSF calculated directly from the simulated incoming wavefront. Furthermore, the used algorithm has a reasonable runtime and memory consumption.

Reciprocal space mapping and strain scanning using X-ray diffraction microscopy

Dark-field X-ray microscopy is a new full-field imaging technique for nondestructively mapping the structure of deeply embedded crystalline elements in three dimensions. Placing an objective in the diffracted beam generates a magnified projection image of a local volume. By placing a detector in the back focal plane, high-resolution reciprocal space maps are generated for the local volume. Geometrical optics is used to provide analytical expressions for the resolution and range of the reciprocal space maps and the associated field of view in the sample plane. To understand the effects of coherence a comparison is made with wavefront simulations using the fractional Fourier transform. Reciprocal space mapping is demonstrated experimentally at an X-ray energy of 15.6 keV. The resolution function exhibits suppressed streaks and an FWHM resolution in all directions of ΔQ/Q = 4 × 10−5 or better. It is demonstrated by simulations that scanning a square aperture in the back focal plane enables strain mapping with no loss in resolution to be combined with a spatial resolution of 100 nm.

Orthonormal vector general polynomials derived from the Cartesian gradient of the orthonormal Zernike-based polynomials.

The concept of orthonormal vector circle polynomials is revisited by deriving a set from the Cartesian gradient of Zernike polynomials in a unit circle using a matrix-based approach. The heart of this model is a closed-form matrix equation of the gradient of Zernike circle polynomials expressed as a linear combination of lower-order Zernike circle polynomials related through a gradient matrix. This is a sparse matrix whose elements are two-dimensional standard basis transverse Euclidean vectors. Using the outer product form of the Cholesky decomposition, the gradient matrix is used to calculate a new matrix, which we used to express the Cartesian gradient of the Zernike circle polynomials as a linear combination of orthonormal vector circle polynomials. Since this new matrix is singular, the orthonormal vector polynomials are recovered by reducing the matrix to its row echelon form using the Gauss-Jordan elimination method. We extend the model to derive orthonormal vector general polynomials, which are orthonormal in a general pupil by performing a similarity transformation on the gradient matrix to give its equivalent in the general pupil. The outer form of the Gram-Schmidt procedure and the Gauss-Jordan elimination method are then applied to the general pupil to generate the orthonormal vector general polynomials from the gradient of the orthonormal Zernike-based polynomials. The performance of the model is demonstrated with a simulated wavefront in a square pupil inscribed in a unit circle.

Measurement range of Talbot wavefront sensor

The possibilities of wavefront curvature measuring by the Talbot sensor are theoretically and experimentally investigated. The analytic expressions for measurement range are obtained. Operation of the wavefront sensor is illustrated with computer simulated spherical wavefront propagation through the two-dimensional periodic mask of the sensor system. The measurement range of the Talbot wavefront sensor is compared with the range of the Shack–Harmann wavefront sensor.

Pseudononlinear ultrasound simulation approach for reverberation clutter.

Multipath scattering, or reverberation, takes a substantial toll on image quality in many clinical exams. We have suggested a model-based solution to this problem, which we refer to as aperture domain model image reconstruction (ADMIRE). For ADMIRE to work well, it must be trained with precisely characterized data. To solve this specific problem and the general problem of efficiently simulating reverberation, we propose an approach to simulate reverberation with linear simulation tools. Our simulation method defines total propagation time, first scattering site, and a final scattering site. We use a linear simulation package, such as Field II, to simulate scattering from the final site and then shift the simulated wavefront later in time based on the total propagation time and the geometry of the first scattering site. We validate our simulations using theoretical descriptions of clutter in the literature and data acquired from ex vivo tissue. We found that ex vivo tissue clutter had a mean speckle SNR of [Formula: see text], which we could simulate with about 2 scatterers per resolution cell. Axial clutter distributions drawn from an exponential distribution with a mean of 5mm and at least 0.5 scatters per resolution cell resulted in clutter that was statistically indistinguishable from the van Cittert-Zernike behavior predicted by literature.

Phase shifting in the spatial frequency domain

We present a simple mathematical method for phase shifting that overcomes some phase shift errors and limitations of commonly used methods. The method is used to generate a sequence of phase-shifted interferograms from a single interferogram. The generated interferograms are employed to reconstruct the wavefront aberrations, as an application. The approach yields results with only very small deviations compared to both simulated wavefront aberrations, including the first 25 Zernike polynomials (0.05%) and those measured with a Shack-Hartmann sensor (0.5%).

Numerical modeling of the proposed WFIRST-AFTA coronagraphs and their predicted performances

The WFIRST-AFTA 2.37 m telescope will provide the opportunity to host a coronagraph for the imaging and spectroscopy of planets and disks in the next decade. The telescope, however, is not ideal, given its obscured aperture. Only recently have coronagraph designs been thoroughly investigated that can efficiently work with this configuration. Three coronagraph designs, the hybrid Lyot, shaped pupil, and phase-induced amplitude apodization complex mask coronagraph have been selected for further development by the Astrophysics Focused Telescope Asset project. Real-world testbed demonstrations of these have just begun, so for now, the most reliable means of evaluating their potential performance comes from numerical modeling incorporating diffraction propagation, realistic system models, and simulated wavefront sensing and control. Here, we present the methods of performance evaluation and results for the current coronagraph designs.