Incident Wavefront Research Articles

Noise-tolerant wavefront shaping in a Hadamard basis.

Light scattering is the main limitation for optical imaging. However, light can be focused through or inside turbid media by spatially shaping the incident wavefront. Wavefront shaping is ultimately limited by the available photon budget. We developed a new 'dual reference' wavefront shaping algorithm that optimally uses the available light. Our method allows for multi-target wavefront shaping, making it suitable for transmission matrix measurements or transmitting images. We experimentally confirmed the improvement of the focus intensity compared to existing methods.

Coherent Wave Control in Complex Media with Arbitrary Wavefronts.

Wavefront shaping (WFS) has emerged as a powerful tool to control the propagation of diverse wave phenomena (light, sound, microwaves, etc.) in disordered matter for applications including imaging, communication, energy transfer, micromanipulation, and scattering anomalies. Nonetheless, in practice the necessary coherent control of multiple input channels remains a vexing problem. Here, we overcome this difficulty by doping the disordered medium with programmable meta-atoms in order to adapt it to an imposed arbitrary incoming wavefront. Besides lifting the need for carefully shaped incident wavefronts, our approach also unlocks new opportunities such as sequentially achieving different functionalities with the same arbitrary wavefront. We demonstrate our concept experimentally for electromagnetic waves using programmable metasurfaces in a chaotic cavity, with applications to focusing with the generalized Wigner-Smith operator as well as coherent perfect absorption. We expect our fundamentally new perspective on coherent wave control to facilitate the transition of intricate WFS protocols into real applications for various wave phenomena.

Multi-focal Shack–Hartmann wavefront sensing with self-interference Chinese Taiji-lenslet array

Shack–Hartmann wavefront sensor (SHWS) is a traditional method of obtaining the phase information of the incident light. As a classical method, SHWS has the merit of simple structure, good usability, real-time monitoring and wide waveband. Traditional SHWS depends mainly on a lenslet array which can split the incident wavefront and produce an array of distorted foci, which reflect the change of wavefront curvature under test. Compared to the mono-focal lenslet in SHWS, here self-interference Chinese Taiji lenslet have been introduced into the wavefront sensing in order to improve the precision of the centroid position by means of multiple foci. Wavefront sensing experiments on self-interference Taiji-lenslet array with bi- and quad-foci were sequentially carried out to verify the validity of our proposed method. More foci-splitter would bring more accuracy. Taiji lens can also be designed with amplitude modulation such as Taiji sieve, which is very suitable for wavefront measurement in the region of short wavelength, especially EUV and soft X-ray.

Improved wavefront estimation accuracy in a programmable grating array based wavefront sensor

Shack–Hartmann wavefront sensor (SHWS) is one of the popular zonal wavefront sensor that typically consists of a two-dimensional (2D) array of lenslets and a camera. Another variant of a zonal wavefront sensor is the programmable grating array based wavefront sensor (PGAWS) that replaces the lenslets array of the SHWS with a 2D array of programmable diffraction gratings and a single focusing lens to result in a 2D array of +1 order spots. The ability of a PGAWS to correctly measure the incident wavefront depends on the accuracy with which each +1 order spot centroid position in the camera plane is calculated. However, in practical applications the intensities of the +1 order spots are usually non-uniform and there is presence of higher order spots that lead to erroneous calculation of the centroid position. In the present work, an improved PGAWS is proposed and by exploiting its programmable facility the transmittance function of the grating array is defined to generate an array of uniform intensity +1 order spots with negligible contribution from unwanted higher order spots by breaking them into noise. We present proof-of-concept simulation results that illustrate the generation of uniform intensity +1 order spots and also quantify its uniformity numerically by defining a quality metric. Furthermore, the working of the proposed PGAWS is substantiated through simulation results which demonstrate its accurate wavefront estimation capability in comparison to the conventional PGAWS, in the presence of non-uniform intensity +1 order spots.

Limiting the incident NA for efficient wavefront shaping through thin anisotropic scattering media

Wavefront shaping holds great potential for high-resolution imaging or light delivery either through or deep inside living tissue. However, one of the biggest barriers that must be overcome to unleash the full potential of wavefront shaping for practical biomedical applications is the fact that wavefront shaping, especially based on iterative feedback, requires lengthy measurements to obtain useful correction of the output wavefront. As biological tissues are inherently dynamic, the short decorrelation time sets a limit on the achievable wavefront shaping enhancement. Here we show that for wavefront shaping in thin anisotropic scattering media such as biological tissues, we can optimize the wavefront shaping quality by simply limiting the numerical aperture (NA) of the incident wavefront. Using the same number of controlled modes, and therefore the same wavefront measurement time, we demonstrate that the wavefront shaped focus peak to background ratio can be increased by a factor of 2.1 while the energy delivery throughput can be increased by a factor of 8.9 through 710 µm thick brain tissue by just limiting the incident NA.

Removing Phase Misalignment in the Validation of a Compact Antenna Test Range for 5G mm-Wave UE OTA Testing

Over-the-air (OTA) measurement is mandatory for 5G mm-wave wireless devices. The compact antenna test range (CATR) is the baseline method in the current version of TR 38.810 in 3rd generation partnership project (3GPP) and cellular telecommunications industry association (CTIA) millimeter-wave (mm-Wave) test plan. For CATR, both amplitude and phase variations inside the quiet zone (QZ) could affect the final OTA results significantly and hence need to be characterized carefully. Especially in the phase validation of QZ, even slight misalignments between sampling plane and incident plane wavefront due to the limited precision of the positioner or tolerance in antenna fixture could result in large phase variations, which is not the true phase property of QZ. This letter presents a method to remove the effect of the angular error due to misalignment when measuring the phase variation inside QZ. By adopting the proposed method to the measured phase data, any angular error due to misalignment with respect to the incident plane wavefront will be eliminated mathematically, leaving the true phase variations of QZ only. In the meanwhile, the proposed method can alleviate the requirements of fixture manufacture and alignment precision and reduce the test cost.

Erratum: Lamb Waves and Adaptive Beamforming for Aberration Correction in Medical Ultrasound Imaging.

In our paper titled "Lamb Waves and Adaptive Beamforming for Aberration Correction in Medical Ultrasound Imaging" [1], we mentioned that the superposition of the different symmetric (S) modes in the frequency-wavenumber (f-k) domain results in a high intensity region where its slope corresponds to the longitudinal wave speed in the slab. However, we have recently understood that this high intensity region belongs to the propagation of a wave called lateral wave or head wave [2-5]. It is generated if the longitudinal sound speed of the aberrator (i.e. the PVC slab) is larger than that of water and if the incident wavefront is curved. When the incidence angle at the interface between water and PVC is near the critical angle, the refracted wave in PVC re-radiates a small part of its energy into the fluid (i.e. the head wave). As discussed in [4], if the thickness of the waveguide is larger than the wavelength, the first arriving signal is the head wave. This is also the case in our study [1] where the ultrasound wavelength of a compressional wave in PVC was close to 1 mm, and a PVC slab with a thickness of 8 mm was used.

Experimental Realization of Optimal Energy Storage in Resonators Embedded in Scattering Media

AbstractThe ability to enhance light–matter interactions by increasing the energy stored in optical resonators is inherently dependent on the resonators' coupling to the incident wavefront. In practice, weak coupling may result from resonators' irregular shapes and/or the scrambling of waves in the surrounding scattering environment. Here, a blind and non‐invasive wavefront shaping technique providing optimal coupling to resonators is presented. The coherent control of the incident wavefront relies on the lengthening of delay times of waves efficiently exciting the resonator. Using a modal approach, the optimality of the proposed technique is proven and its limitations are quantified. The proposed concept is demonstrated in microwave experiments by injecting in situ optimal wavefronts that maximize the energy stored in high‐permittivity dielectric scatterers and extended leaky cavities embedded in a complex environment. The introduced framework is expected to find important applications in the enhancement of light–matter interactions in photonic materials as well as to enhance energy harvesting.

Adaptable transfer-matrix method for fixed-energy finite-width beams

This work presents a novel methodology to analytically solve the stationary Schrödinger equation in presence of a couple of two-dimensional semi-infinite rectangular potential barriers, when the incident wave is a finite-width monoenergetic wave packet. Such methodology does not depend at all on the incident wavefront of the packet and is based on the transfer-matrix method, but unlike the latter, our transfer matrix is built partly in real space and partly in Fourier space. A spectrum of angular plane waves is used to represent the incident, reflected and transmitted beams. As a particular case, we study the transmission of Hermite-Gaussian wave packets through the barrier system. A detailed analysis of the transmission coefficient is carried out as a function of both the parameters of the incident beam (which in turn are directly related to the shape of the incident packet) and the parameters of the barriers. We also briefly discuss the behavior of the probability density of three transmitted beams.

Photonic nanojet generation under converging and diverging beams

In practical applications of the photonic nanojet (PNJ), a microscope objective can be used to illuminate a microsphere. Under such conditions, it is difficult to determine the absolute position of the sphere with respect to the focal point of the incident beam. A small change in the axial position of the sphere can change the form of the incident wavefront from diverging to converging and will significantly influence the evolution of PNJ. In our paper, we report a systematic study of the PNJ properties, including the effective focal length and the full-width at half maximum (FWHM) by changing the source curvature. We treat the cases of diverging and converging wavefronts with different NAs (from 0.1 to 0.8) and sphere diameters (from 1.6 λ to 33 λ ). We demonstrate that for a diverging source curvature, the effective focal length and FWHM of the PNJ increase as a function source NA for all the sphere diameters. By further increase of the source NA, for a NA of 0.8, the PNJ can be found only for sphere diameters less than 16 λ (refractive index n = 1.5 ). At larger diameters, the microsphere behaves like a diffractive–refractive lens, collimating the light and showing aberrations. For the converging source, the effective focal length and FWHM tend to decrease as a function of source NA, the PNJ localizing inside the sphere for N A > 0.2 . Also, the PNJ shows similar behavior with respect to the NA of a converging source and sphere refractive index under plane wave illumination. Finally, we compare our theoretical 2D simulation results with 3D sphere geometries for diameters of 1.6 λ and 8.3 λ ; we find similar behavior for converging and diverging source wavefront curvatures.

Метод формирования единственного сфокусированного порядка дифракции при помощи бинарных амплитудных дифракционных элементов без пространственной несущей

The method of synthesis of self-focusing amplitude DOE without the carrier spatial frequency working in divergent beams and forming single focused diffraction order which can occupy whole DOE reconstruction field because there is no necessity for spatial separation of diffraction orders, which is the case with holograms, is presented. Synthesis was carried out in two stages. The first one was carried out by the iteration algorithm similar to Gerchberg-Saxton algorithm, with those differences that synthesizable DOE is an amplitude one and incident wave front is divergent. Then the method of direct search with random trajectory was applied. As a result for binary amplitude DOE synthesis error of 6% and diffraction efficiency of 6% was achieved. Results of experimental DOE implementation using DMD are presented.

On the reflection of time-domain acoustic spherical waves by a sinusoidal diffraction grating

This work reports on some results obtained from numerical simulations of time-domain acoustic wave propagation in the presence of a periodically rough interface. Emphasis is put on the structure of the reflected signals in the presence of a sinusoidal grating. More specifically, we investigate the effect of the frequency bandwidth of the emitted signal and the effect of the incident wavefront sphericity on the signals reflected from the rough interface and associated with the different diffraction orders.

Method of inverting wavefront phase from far-field spot based on deep learning

In the adaptive optics system, the accuracy and robustness of wavefront sensor greatly affect the ability of aberration detection and closed-loop correction. In the condition of the nonuniformity of amplitude distributions or insufficient of beacon light energy, it will cause accuracy decrease of Hartmann wavefront sensing due to the lack of sub-aperture light. Meanwhile, the real-time performance of the wavefront sensing-free adaptive system based on far-field spot inversion cannot meet the practical requirements. The method of the wavefront inversion based on deep learning is to directly obtain aberrations by inputting the far-field light intensity image, which can be used as an effective supplement to the adaptive optical system. Through numerical simulation, this paper proved that the deep residual neural network could directly predict the Zernike coefficient of the wavefront phase through the far-field spot. And experimental demonstrated the corrected residual RMS between input and reconstructed wavefront phase was 0.08 waves, the average computation time was less than 2 ms by GPU acceleration. This method can predict the Zernike coefficient of incident wavefront distortion more accurately, and has a good aberration correction capability, suitable for measuring and correcting the main components of wavefront distortion in traditional adaptive optics method, or providing a good initial wavefront estimation for optimized adaptive optics.

Geometric treatment of the radiation captured by the Large Millimeter Telescope (LMT/GTM) and ronchigrams at the caustic region for a static source

The aim of the present work is to determine the reflected light rays, wavefronts, caustic and the ronchigram associated with the reflection phenomenon of a plane wave on a parabolic mirror, in particular on the parabolic antenna of the Large Millimeter Telescope (LMT/GTM). The results presented here are general in the sense that the incident plane wavefront has an arbitrary direction , determined by the angles α and β. We present numerical results for two different cases: () and (). From these results we find that in general the caustic is a surface with a stable singularity of a hyperbolic umbilic type. For these cases we compute the distribution of the reflected light rays at some representative planes, determined by the form and dimensions of the caustic, then assuming that the ronchigrating is placed at those representative planes we compute the associated ronchigram. These results are important because they could describe the behavior of the light emitted by a static pointlike source located far away in the Universe.

Disruption and recovery of reaction–diffusion wavefronts interacting with concave, fractal, and soft obstacles

In a recent publication (Smith et al., 2019), we documented the distinct recovery of reaction–diffusion wavefronts disrupted by hard convex obstacles. Here, we extend that work to include concave, spiral, fractal, random, and soft obstacles. Curvature dependent wavefront velocities ultimately restore the wavefronts, with perturbations that decay as power-law functions of time. But concave, spiral, and fractal obstacles can sustain wavefronts locally for long times. Soft obstacles with variable diffusivity, either intrinsically or due to light sensitivity, can enforce one-way propagation and, appropriately configured, can locally and indefinitely sustain incident wavefronts, creating clocks or repeaters, beating hearts for these excitable systems.

An all-photonic focal-plane wavefront sensor

Adaptive optics (AO) is critical in astronomy, optical communications and remote sensing to deal with the rapid blurring caused by the Earth’s turbulent atmosphere. But current AO systems are limited by their wavefront sensors, which need to be in an optical plane non-common to the science image and are insensitive to certain wavefront-error modes. Here we present a wavefront sensor based on a photonic lantern fibre-mode-converter and deep learning, which can be placed at the same focal plane as the science image, and is optimal for single-mode fibre injection. By measuring the intensities of an array of single-mode outputs, both phase and amplitude information on the incident wavefront can be reconstructed. We demonstrate the concept with simulations and an experimental realisation wherein Zernike wavefront errors are recovered from focal-plane measurements to a precision of 5.1 × 10−3 π radians root-mean-squared-error.

Spatial ultrasonic wavefront characterization using a laser parametric curve scanning method

Ultrasonic wavefield imaging (UWI) provides insightful spatial information about ultrasonic wave propagation in planar (2-D) space for nondestructive evaluation and structural health monitoring (NDE-SHM) applications. In all materials, the wavefronts of the incident and reflected waves propagate with unique patterns that may be represented by parametrized polar curves in 2-D geometric space. In this paper, a spatial ultrasonic wavefront characterization method based on a parametric curve laser scan is proposed to characterize the spatial ultrasonic wavefront for both isotropic and anisotropic materials. Three parametric curves (circular, hyperbolic, and cyclic-harmonic curves) were considered. Two wavefront characterization process were carried out, namely (i) deciding the parametric equation of the closed-form geometric plane curve via UWI, and (ii) measuring and updating the ultrasound via laser ultrasonic interrogation system (LUIS) and quantifying the values(s) of the predicted parametric curve equation using a temporal cross-correlation technique. The proposed method was tested on pristine aluminum and cross-ply CFRP plates to characterize the spatial incident and reflected wavefronts of the plates. The non-fiber direction region (105°⩽ϕS⩽165°) and the fiber direction region (165°⩽ϕS⩽195°) of the cross-ply CFRP plate were considered in the test. The laser circle scan and the laser cyclic-harmonic curve scan showed the ability to characterize the incident wavefronts of the S0 and A0 modes in the aluminum plate and the CFRP plate, respectively, followed by the laser hyperbolic curve scan. With the promising results obtained in the proposed method, the integration of the parametric curve scanning method into LUIS may provide a new approach to damage detection and useful information for ultrasonic algorithm design in NDE-SHM applications.

Design of binary-phase diffusers for a compressed sensing snapshot spectral imaging system with two cameras.

We propose designs of pupil-domain optical diffusers for a snapshot spectral imaging system using binary-phase encoding. The suggested designs enable the creation of point-spread functions with defined optical response, having profiles that are dependent on incident wavefront wavelength. This efficient combination of dispersive and diffusive optical responses enables us to perform snapshot spectral imaging using compressed sensing algorithms while keeping a high optical throughput alongside a simple fabrication process. Experimental results are reported.

High-Efficiency, Wideband GRIN Lenses With Intrinsically Matched Unit Cells

We present an automated design procedure for the rapid realization of wideband millimeter-wave lens antennas. The design method is based upon the creation of a library of matched unit-cells which comprise wideband impedance matching sections on either side of a phase-delaying core section. The phase accumulation and impedance match of each unit-cell is characterized over frequency and incident angle. The lens is divided into rings, each of which is assigned an optimal unit-cell based on incident angle and required local phase correction given that the lens must collimate the incident wavefront. A unit-cell library for a given realizable permittivity range, lens thickness, and unit-cell stack-up can be used to design a wide variety of flat wideband lenses for various diameters, feed elements, and focal distances. A demonstration GRIN lens antenna is designed, fabricated, and measured in both far-field and near-field chambers. The antenna functions as intended from 14 GHz to 40 GHz and is therefore suitable for all proposed 5G MMW bands, Ku- and Ka-band fixed satellite services. The use of intrinsically matched unit-cells results in aperture efficiency ranging from 31% to 72% over the 2.9:1 bandwidth which is the highest aperture efficiency demonstrated across such a wide operating band.

Metasurface Generation of Paired Accelerating and Rotating Optical Beams for Passive Ranging and Scene Reconstruction

Depth measurements are vital for many emerging technologies with applications in augmented reality, robotics, gesture detection, and facial recognition. These applications, however, demand compact and low-power systems beyond the capabilities of many state-of-the-art depth cameras. While active illumination techniques can enable precise scene reconstruction, they increase power consumption, and systems that employ stereo require extended form factors to separate viewpoints. Here, we exploit a single, spatially multiplexed aperture of nanoscatterers to demonstrate a solution that replicates the functionality of a high-performance depth camera typically comprising a spatial light modulator, polarizer, and multiple lenses. Using cylindrical nanoscatterers that can arbitrarily modify the phase of an incident wavefront, we passively encode two complementary optical responses to depth information in a scene. The designed optical metasurfaces simultaneously generate a focused accelerating beam and a focused rotating beam that exploit wavefront propagation-invariance to produce paired, adjacent images with a single camera snapshot. Compared to conventional depth from defocus methods, this technique enhances both the depth precision and depth of field at the same time. By decoding the captured data in software, our system produces a fully reconstructed image and transverse depth map, providing an optically passive ranging solution. In our reconstruction algorithm, we account for the field curvature of our metasurface by calculating the change in Gouy phase over the field of view, enabling a fractional ranging error of 1.7%. We demonstrate a precise, visible wavelength, and polarization-insensitive metasurface depth camera with a compact 2 mm2 aperture.