Wavefront Imaging Research Articles

Differences in Image Quality after Three Laser Keratorefractive Procedures for Myopia.

Psychophysical estimates of spatial and depth vision have been shown to be better after bilateral ReLEx small-incision lenticule extraction (SMILE) refractive surgery for myopia, relative to photorefractive keratectomy (PRK) and femtosecond laser-assisted in situ keratomileusis (FS-LASIK). The present study provides the optical basis for these findings using computational image quality analysis. This study aimed to compare longitudinal changes in higher-order wavefront aberrations and image quality before and after bilateral PRK, FS-LASIK, and SMILE refractive procedures for correcting myopia. Wavefront aberrations and image quality of both the eyes of 106 subjects (n = 40 for FS-LASIK and SMILE and n = 26 for PRK) were determined pre-operatively and at 1-week, 1-month, 3-month, and 6-month post-operative intervals using computational through-focus analysis for a 6-mm pupil diameter. Image quality was quantified in terms of its peak value and its interocular difference, residual defocus that was needed to achieve peak image quality (best focus), and the depth of focus. The increase in root mean squared deviations of higher-order aberrations post-operatively was lesser after SMILE (1-month visit median [25th to 75th interquartile range], 0.34 μm (0.28 to 0.39 μm]) than after PRK (0.80 μm [0.74 to 0.87 μm]) and FS-LASIK (0.74 μm [0.59 to 0.83 μm]; P ≤ .001), all relative to pre-operative values (0.20 μm [0.15 to 0.30 μm]). The peak image quality dropped and its interocular difference increased, best focus shifted myopically by 0.5 to 0.75 D, and depth of focus widened significantly after PRK and FS-LASIK surgeries, all relative to pre-operative values (P < .001). All these changes were negligible but statistically significant in a minority of instances after SMILE surgery (P ≥ .01). Although all three refractive surgeries correct myopia, the image quality and its similarity between eyes are better and closer to pre-operative values after SMILE, compared with FS-LASIK and PRK. These results can be explained from the underlying increase in higher-order wavefront aberrations experienced by the eye post-operatively.

Nonlinear Wavefront Shaping and Imaging in Nonlinear Photonic Crystals with a Generalized Quasi-Multivalue-Encoding Method

Nonlinear Wavefront Shaping and Imaging in Nonlinear Photonic Crystals with a Generalized Quasi-Multivalue-Encoding Method

Cross-iteration multi-step optimization strategy for three-dimensional intensity position correction in phase diverse phase retrieval.

Parameters mismatching between the real optical system and phase retrieval model undermines wavefront reconstruction accuracy. The three-dimensional intensity position is corrected in phase retrieval, which is traditionally separated from lateral position correction and axial position correction. In this paper, we propose a three-dimensional intensity position correction method for phase diverse phase retrieval with the cross-iteration nonlinear optimization strategy. The intensity position is optimized via the coarse optimization method at first, then the intensity position is cross-optimized in the iterative wavefront reconstruction process with the exact optimization method. The analytic gradients about the three-dimensional intensity position are derived. The cross-iteration optimization strategy avoids the interference between the incomplete position correction and wavefront reconstruction during the iterative process. The accuracy and robustness of the proposed method are verified both numerically and experimentally. The proposed method achieves robust and accurate intensity position correction and wavefront reconstruction, which is available for wavefront measurement and phase imaging.

Mitigating the ill-posedness of first-arrival traveltime tomography using slopes: application to the eastern Nankai Trough (Japan) OBS data set

SUMMARYFirst-arrival traveltime tomography is one of the most used velocity model building techniques especially in sparse wide-angle acquisitions for deep crustal seismic imaging cases. Relying on the inversion of a picked attribute, the absolute traveltimes, the approach is ill-posed in terms of non-uniqueness of the solution. The latter is remedied by proper regularization or the introduction of prior information. Indeed, since traveltime kernels are vulnerable to the velocity–depth ambiguity, the inversion is stabilized by the introduction of complementary data like reflections and explicit reflectors in the velocity models. Here, we propose to supplement first-arrival traveltimes by their slopes, in other words the horizontal component of the slowness vectors at the sources and/or receivers. Slopes are a crucial attribute in state of the art scattering-based or reflection-based tomographic methods like slope tomography or wavefront tomography where the differential information is needed in order to locate the scattering events position or to parametrize the wavefront. The optional but valuable injection of slopes as an objective measure in first-arrival traveltime tomography stabilizes the problem by constraining the emergence angle or in turn implicitly the turning point depth of the rays. We explain why slopes have a tremendous added value in such a tomographic problem and highlight its remedial effect in cases where the medium is unevenly illuminated. We also show that the contribution of slopes become even more significant when the acquisition is sparse as it is generally the case with ocean-bottom seismometer surveys. The inferred models from such an extended time-attributes tomography will be used as initial guesses in a full-waveform inversion workflow context. The proposed strategy is benchmarked in 2-D media against a dip section of the SEG/EAGE overthrust model and then followed by a revisit of ocean bottom seismometers data from the eastern-Nankai subduction margin as a real deep crustal case study.

Characteristics of wavefront correction using stacked liquid lens based on electrowetting-on-dielectric

A stacked liquid lens based on electrowetting-on-dielectric (EWOD) is designed to analyze the ability of correcting the distorted wavefront caused by curvature, tilt, and piston. The model of the stacked liquid lens is constructed by COMSOL software which is used to simulate the change of liquid interface with different voltage combinations, and the change range of the interface. The correction ability of the stacked liquid lens at a certain point in the wavefront is assessed from wavefront image and point spread function (PSF) is got by ZEMAX software. The results show that different types of distorted wavefront can be compensated via the stacked liquid lens. The peak-to-valley (PV) value decreases from 19.7853 to 0.18, and the root mean square (RMS) value is down from 5.6638 to 0.0355. Concurrently, the Strehl ratio (SR) increased from near 0 to 0.962. The related research results have broad prospects in the field of wavefront correction.

Ptychographic wavefront characterization for single-particle imaging at x-ray lasers

A well-characterized wavefront is important for many x-ray free-electron laser (XFEL) experiments, especially for single-particle imaging (SPI), where individual biomolecules randomly sample a nanometer region of highly focused femtosecond pulses. We demonstrate high-resolution multiple-plane wavefront imaging of an ensemble of XFEL pulses, focused by Kirkpatrick–Baez mirrors, based on mixed-state ptychography, an approach letting us infer and reduce experimental sources of instability. From the recovered wavefront profiles, we show that while local photon fluence correction is crucial and possible for SPI, a small diversity of phase tilts likely has no impact. Our detailed characterization will aid interpretation of data from past and future SPI experiments and provides a basis for further improvements to experimental design and reconstruction algorithms.

Geometric layout optimization of a large aperture thin elliptical mirror’s axial and lateral support

For passive support of large aperture telescopes, geometric layout optimization of the support structure is one of the most critical tasks because it determines the deformation of the mirror under gravity, which affects the wavefront aberration and image quality of the system. Due to a lack of symmetry, the optimization of an elliptical mirror support can be much more complex compared with circular mirrors. We optimize the geometric layout of axial and lateral support for the tertiary mirror of the Thirty Meter Telescope (TMT). Based on a theoretical analysis of the whiffletree principle, a parametric model of axial support is established based on the multi-point constraint equation. The mirror deformation SlopeRMS of the tertiary mirror under vertical gravity is used as the optimization target of the support points. The axial support point position is optimized by means of a simulated annealing algorithm and a mirror-deformed post-processing script written in Python. The TMT tertiary mirror lateral support also uses the whiffletree structure, and its in-plane layout affects the system's resonant modal frequency and the maximum load at each point. According to the dynamic equation and the static principle, the lateral support optimization model is established. The first-order resonant frequency and maximum load of the support point are the objective function. Through optimization of the axial and lateral support, the overall mirror distortion of the system is improved.

Design of online damage images detection system for large-aperture mirrors of high power laser facility based on wavefront coding technology

The laser transport system of the high power laser facility is mainly composed of large-aperture laser transport mirrors (TMs). Obtaining the high-resolution online damage images during the operation, which is of great significance for operating safely of the mirrors and the facility. Based on wavefront coding, pan-tilt scanning and image stitching technologies, an online laser-damage images detection system is designed, and it can achieve high-precision detection of surface characteristics of large-aperture laser transport mirrors. The preliminary simulation proves that the system can solve the depth of field matching problem caused by pan-tilt tilt imaging and achieve higher resolution.

Refractive Index Measurement of Corneal-Shaped Hydrogel Material and Elasmobranch Corneas by Shack–Hartmann Wavefront Sensor System

The biocompatible hydrogel materials are used for the fabrication of artificial cornea. The refractive index of the hydrogel material can affect the optical quality of the artificial cornea. It is challenging to measure the refractive index of the hydrogel material because it is between solid and liquid status during the fabrication processes. In this work, we propose using the Shack-Hartmann wavefront sensor system to measure the wavefront images and to calculate the corresponding aberrations of optical material. The wavefront aberrations can be used to estimate the refractive index of the optical material. To prove the concept, the standard N-BK7 bi-convex lenses with focal lengths of 100 and 150 mm at wavelengths 780, 532, and 450 nm have been measured, and the results show that the relative errors of the average measured refractive indices are about 0.1%-0.17%. We used this proposed method to measure the refractive index of the P407-DA hydrogel material. We found that the average measured refractive indices of the P407-DA hydrogel material are 1.3175, 1.3516, and 1.3645 at wavelengths 780, 532, and 450 nm, respectively. Compared with the refractive index of human cornea, the P407-DA hydrogel can be used as the artificial cornea material. The Cauchy dispersion formula can be used to calculate the Abbe number of the P407-DA hydrogel material, which is about 11, lower than the human cornea's Abbe number. It means that the P407-DA hydrogel material has higher chromatic dispersion than the human cornea material. Moreover, the elasmobranch (shark) corneas, which are known as the suitable material for xenotransplantation, are measured by the Shack-Hartmann wavefront sensor system. The ABBE refractometer (ATAGO DR-M4) is used to measure the flat P407-DA hydrogel sample and it is found that the refractive index is slightly different when compared with the measured results by the Shack-Hartmann wavefront sensor system. The refractive indices of other biocompatible hydrogels poly(acrylic acid) (PAA) and poly(2-hydroxyethyl methacrylate) (PHEMA) are also measured by our proposed method, and it is found that the refractive index of P407-DA is more suitable for designing corneal samples than other hydrogels. It is found that the refractive indices of the elasmobranch corneas are similar to the P407-DA material. Our proposed method to measure the refractive index of hydrogel material using the Shack-Hartmann wavefront sensor system is useful. It is a non-contact, minimally invasive, and time-efficient method for shaped structures. The results can be used as a guide for developing better biocompatible material for artificial cornea.

Defocused Image Deep Learning Designed for Wavefront Reconstruction in Tomographic Pupil Image Sensors

Mathematical modelling methods have several limitations when addressing complex physics whose calculations require considerable amount of time. This is the case of adaptive optics, a series of techniques used to process and improve the resolution of astronomical images acquired from ground-based telescopes due to the aberrations introduced by the atmosphere. Usually, with adaptive optics the wavefront is measured with sensors and then reconstructed and corrected by means of a deformable mirror. An improvement in the reconstruction of the wavefront is presented in this work, using convolutional neural networks (CNN) for data obtained from the Tomographic Pupil Image Wavefront Sensor (TPI-WFS). The TPI-WFS is a modified curvature sensor, designed for measuring atmospheric turbulences with defocused wavefront images. CNNs are well-known techniques for its capacity to model and predict complex systems. The results obtained from the presented reconstructor, named Convolutional Neural Networks in Defocused Pupil Images (CRONOS), are compared with the results of Wave-Front Reconstruction (WFR) software, initially developed for the TPI-WFS measurements, based on the least-squares fit. The performance of both reconstruction techniques is tested for 153 Zernike modes and with simulated noise. In general, CRONOS showed better performance than the reconstruction from WFR in most of the turbulent profiles, with significant improvements found for the most turbulent profiles; overall, obtaining around 7% of improvements in wavefront restoration, and 18% of improvements in Strehl.

Compensating atmospheric turbulence with CNNs for defocused pupil image wavefront sensors

Abstract Adaptive optics are techniques used for processing the spatial resolution of astronomical images taken from large ground-based telescopes. In this work, computational results are presented for a modified curvature sensor, the tomographic pupil image wavefront sensor (TPI-WFS), which measures the turbulence of the atmosphere, expressed in terms of an expansion over Zernike polynomials. Convolutional neural networks (CNN) are presented as an alternative to the TPI-WFS reconstruction. This technique is a machine learning model of the family of artificial neural networks, which are widely known for its performance as modeling and prediction technique in complex systems. Results obtained from the reconstruction of the networks are compared with the TPI-WFS reconstruction by estimating errors and optical measurements (root mean square error, mean structural similarity and Strehl ratio). The reconstructed wavefronts from both techniques are compared for wavefronts of 153 Zernike modes. For this case, a detailed comparison and grid search to find the most suitable neural network is performed, searching between multi-layer perceptron, CNN and recurrent networks topologies. In general, the best network was a CNN trained for TPI-WFS reconstruction, achieving better performance than the reconstruction software from TPI-WFS in most of the turbulent profiles, but the most significant improvements were found for higher turbulent profiles that have the lowest r0 values.

When There Is No Offset: A Demonstration of Seismic Diffraction Imaging and Depth‐Velocity Model Building in the Southern Aegean Sea

AbstractA vast majority of marine geological research is based on academic seismic data collected with single‐channel systems or short‐offset multichannel seismic cables, which often lack reflection moveout for conventional velocity analysis. Consequently, our understanding of Earth processes often relies on seismic time sections, which hampers quantitative analysis in terms of depth, formation thicknesses, or dip angles of faults. In order to overcome these limitations, we present a robust diffraction extraction scheme that models and adaptively subtracts the reflected wavefield from the data. We use diffractions to estimate insightful wavefront attributes and perform wavefront tomography to obtain laterally resolved seismic velocity information in depth. Using diffraction focusing as a quality control tool, we perform an interpretation‐driven refinement to derive a geologically plausible depth‐velocity model. In a final step, we perform depth migration to arrive at a spatial reconstruction of the shallow crust. Further, we focus the diffracted wavefield to demonstrate how these diffraction images can be used as physics‐guided attribute maps to support the identification of faults and unconformities. We demonstrate the potential of this processing scheme by its application to a seismic line from the Santorini Amorgos Tectonic Zone, located on the Hellenic Volcanic Arc, which is notorious for its catastrophic volcanic eruptions, earthquakes, and tsunamis. The resulting depth image allows a refined fault pattern delineation and, for the first time, a quantitative analysis of the basin stratigraphy. We conclude that diffraction‐based data analysis has a high potential, especially when the acquisition geometry of seismic data does not allow conventional velocity analysis.

Reconstruction and analysis of wavefront with irregular-shaped aperture based on deep learning

Convolutional neural networks (CNNs) have been successfully applied to solve optical problems. In this paper, a method is proposed for the reconstruction and analysis of a wavefront with an irregular-shaped aperture based on deep learning, for which a U-type CNN (U-net) was used to reconstruct the wavefront image. The data generated by the simulation contain several types of wavefront images with irregularly shaped apertures for training the U-net. The results indicate that modal wavefront reconstruction of irregular-shaped apertures is feasible based on deep learning; it will be very helpful for the reconstruction and analysis of wavefronts in real time applications, and the method is robust.

Full optical characterization of single nanoparticles using quantitative phase imaging

This paper introduces a procedure aimed to quantitatively measure the optical properties of nanoparticles, namely the complex polarizability and the extinction, scattering, and absorption cross sections, simultaneously. The method is based on the processing of intensity and wavefront images of a light beam illuminating the nanoparticle of interest. Intensity and wavefront measurements are carried out using quadriwave lateral shearing interferometry, a quantitative phase imaging technique with high spatial resolution and sensitivity. The method does not require any preknowledge on the particle and involves a single interferogram image acquisition. The full determination of the actual optical properties of nanoparticles is of particular interest in plasmonics and nanophotonics for the active search and characterization of new materials, e.g., aimed to replace noble metals in future applications of nanoplasmonics with less-lossy or refractory materials.

Recent Advances and Challenges of Waveform‐Based Seismic Location Methods at Multiple Scales

AbstractSource locations provide fundamental information on earthquakes and lay the foundation for seismic monitoring at all scales. Seismic source location as a classical inverse problem has experienced significant methodological progress during the past century. Unlike the conventional traveltime‐based location methods that mainly utilize kinematic information, a new category of waveform‐based methods, including partial waveform stacking, time reverse imaging, wavefront tomography, and full waveform inversion, adapted from migration or stacking techniques in exploration seismology has emerged. Waveform‐based methods have shown promising results in characterizing weak seismic events at multiple scales, especially for abundant microearthquakes induced by hydraulic fracturing in unconventional and geothermal reservoirs or foreshock and aftershock activity potentially preceding tectonic earthquakes. This review presents a comprehensive summary of the current status of waveform‐based location methods, through elaboration of the methodological principles, categorization, and connections, as well as illustration of the applications to natural and induced/triggered seismicity, ranging from laboratory acoustic emission to field hydraulic fracturing‐induced seismicity, regional tectonic, and volcanic earthquakes. Taking into account recent developments in instrumentation and the increasing availability of more powerful computational resources, we highlight recent accomplishments and prevailing challenges of different waveform‐based location methods and what they promise to offer in the near future.

High-contrast imaging based on wavefront shaping to improve low signal-to-noise ratio photoacoustic signals using superpixel method**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFB1104500), the Beijing Natural Science Foundation, China (Grant No. 7182091), the National Natural Science Foundation of China (Grant No. 21627813), and the Research Projects on Biomedical Transformation of China-Japan Friendship Hospital

Photoacoustic (PA) imaging has drawn tremendous research interest for various applications in biomedicine and experienced exponential growth over the past decade. Since the scattering effect of biological tissue on ultrasound is two- to three-orders magnitude weaker than that of light, photoacoustic imaging can effectively improve the imaging depth. However, as the depth of imaging further increases, the incident light is seriously affected by scattering that the generated photoacoustic signal is very weak and the signal-to-noise ratio (SNR) is quite low. Low SNR signals can reduce imaging quality and even cause imaging failure. In this paper, we proposed a new wavefront shaping and imaging method of low SNR photoacoustic signal using digital micromirror device (DMD) based superpixel method. We combined the superpixel method with DMD to modulate the phase and amplitude of the incident light, and the genetic algorithm (GA) was used as the wavefront shaping algorithm. The enhancement of the photoacoustic signal reached 10.46. Then we performed scanning imaging by moving the absorber with the translation stage. A clear image with contrast of 8.57 was obtained while imaging with original photoacoustic signals could not be achieved. The proposed method opens new perspectives for imaging with weak photoacoustic signals.

Jacobi–Fourier phase mask for wavefront coding

In this work we propose Jacobi–Fourier phase masks for wavefront coding-based imaging systems. The optical properties of the phase mask is study in detail and numerical simulation are shown. Pixel size and noise are taken into account for the deconvolution of images. Numerical simulations indicate that overall performance is better than of the well-known and commonly used trefoil phase.

A diagnostic system toward high-resolution measurement of wavefront profile

Analysis of wavefront is vital in the process of the inertial confinement fusion (ICF), but there is lack of accurate method to achieve the wavefront image with a high resolution of up to the picosecond (ps) level. The two-dimensional imaging velocity interferometer system for any reflectors (2D-VISAR) can only realize two-dimensional images with a temporal resolution in a nanosecond scale or one two-dimensional image, leading to the difficulties in recovering the high-speed changing process. Although the line-imaging VISAR with a streak camera has a higher temporal resolution of 5 ps, it hardly offers two-dimensional images. In this study, we design a diagnostic system by coupling the line-imaging VISAR and compressed sensing theory to recover the wavefront profile, by which both the two-dimensional and high-temporal resolution wavefront are obtained. A series of original fringe images are firstly processed, and then acquiring data and reconstructing images are simulated, which results in corresponding reconstructed fringe images. The deviation of the resulting images is evaluated to be below 2.1% for the reconstructed shock wave velocities compared to the original shock wave velocities, much lower than the initial velocity, suggesting that the wavefront profile change is successfully recovered, which indicates the diagnostic system for more accurate measurements of the wavefront profile is feasible. This new system is expected to be applied in the field of implosion to provide more extensive information.

Development of novel Moving Wave Front image processing algorithm and microstructural quantification of Tungsten Heavy Alloy

Tungsten Heavy Alloy (WHA) is used in various aerospace applications. This alloy has a two-phase microstructure with a contiguous matrix dispersed with nearly spherical tungsten particles. The properties of this alloy depend on microstructural parameters such as tungsten particle size, tungsten-matrix and tungsten-tungsten interface. In this work, a novel Moving Wave Front (MWF) image processing algorithm was proposed for automatic detection of the interface boundary between coalesced tungsten particles. MWF algorithm was used to measure the size and orientation of the tungsten-tungsten interface from a two-dimensional montage of backscattered Scanning Electron Microscope images. The bivariate size-orientation distribution was measured for undeformed and deformed samples. The obtained distribution in 2D was used to estimate three dimensional size-orientation distribution. The evolution of the tungsten-tungsten interface in 3D was studied as a function of thermo-mechanical deformation. A characteristic evolution of the 3D size and orientation of the tungsten-tungsten interface with deformation was observed.

Source localization and joint velocity model building using wavefront attributes

SUMMARYThe localization of passive seismic sources in form of microseismic tremors as well as large-scale earthquakes is a key issue in seismology. While most previous studies are assuming fairly good knowledge of the underlying velocity model, we propose an automatic spatial localization and joint velocity model building scheme that is independent of detailed a priori information. The first step is a coherence analysis, estimating so-called wavefront attributes to locally describe the wavefield in terms of slopes and curvatures. In a similar fashion, we also obtain an initial guess of the source excitation times of the recorded events. The wavefront attributes constitute the input for wavefront tomography which represents the next step of the workflow and allows for a refinement of the previously evaluated source excitation times while simultaneously approximating the velocity distribution. In a last step, we use the final estimate of the velocity distribution and compute the respective image function by reverse time modelling to gain the source locations. This paper introduces the theoretical concept of our proposed approach for the general 3-D case. We analyse the feasibility of our strategy and the influences of different acquisition settings by means of a synthetic 2-D data example. In a final 3-D field data example we use the workflow to localize a deep earthquake without relying on a given velocity model. The approach can deal with high levels of noise and low signal amplitudes, respectively, as well as sparse geophone sampling. The workflow generally delivers good approximations of the long-wavelength velocity variations along with accurate source locations.