Phase-optimization wavefront shaping simulations in two-dimensional scattering media based on Maxwell's equations

When light propagates through complex medium, such as biological tissue and multimode fiber, refractive index inhomogeneity causes multiple scattering and distortion. This phenomenon is usually seen as obstacles for biomedical imaging, telecommunications, photodynamic therapy and so on. Thus, manipulation of the incident wavefront to compensate for the wavefront distortion due to multiple scattering has been an interdisciplinary subject of interest. Fortunately, wavefront shaping technologies have emerged to provide versatile solutions to minimize the influence of light scattering. By modulating the incident light into a special wavefront with a spatial light modulator, focusing through scattering medium is obtained. To date, several wavefront shaping techniques have been proposed, mainly including transmission matrix inversion, feedback based iterative optimization, and digital optical phase conjugation. Unlike a planar wavefront, the modulated light with special wavefront is transformed into a bright optical focus spot or a desired focus pattern after the scattering medium. Among the proposed approaches, the transmission matrix is considered as a significant tool to characterize a multiple scattering medium with the purpose of manipulating light propagation through it, which contains all the information related to the input field and the scattered output field. In this work, we experimentally measure the transmission matrix of scattering media based on self-reference interference method with a digital micromirror device. Unlike the conventional setup, which divides the incident wavefront into a signal part and reference part, in the self-reference interference method, the reference light is superimposed directly on the signal light to form a new set of input light fields. This self-reference interference method effectively improves the degree of freedom of optical field modulation. Moreover, the intensity ratio between the signal light and the reference light can be adjusted conveniently. In our experiment, this superimposed field is generated by a digital micromirror device with superpixel method. We measure the Hadamard basis and the OAM-basis transmission matrices of scattering medium, respectively. With the measured transmission matrices, single-spot, multi-spot and vortex focusing are achieved after scattering medium, verifying the accuracy of the measured transmission matrices. The strong diagonal presented in the norm of focusing operator also proves the accuracy of the measured transmission matrices. The proposed method may have potential applications in optical imaging and optical communication under scattering environment.

Controllable light delivery to the region of interest is essential to biomedical optical imaging methods like photoacoustic microscopy. It is, however, challenging beyond superficial depths in biological tissue (~1 mm beneath human skin) due to the strong scattering of light that scrambles the photon propagation paths. Recently, optical wavefront shaping has been proposed to modulate the incident light wavefront to compensate for the scattering-induced phase distortions, and consequentially, convey light optimally to a desired location behind or inside turbid media. To reach an optimum wavefront, a searching algorithm is usually required to optimize a feedback signal. In this work, we present our latest explorations, which use photoacoustic signals as the feedback to remotely and non-invasively guide the wavefront shaping process. Our method does not require direct optical access to the target region or the invasive embedding of fluorescence probes inside turbid media. Experimentally, we have demonstrated that diffuse light can be converged to the ultrasound focus by maximizing the amplitude of photoacoustic emissions from the intended absorbing site. Moreover, we show that wavefront-shaped light focusing can enhance existing optical imaging modalities like photoacoustic microscopy, in regard to signal-to-noise ratio, imaging depth, and potentially, resolution.

Optical scattering is a fundamental problem in biomedical optics and limits most optical techniques to shallow operating depths less than 1 millimeter. However, although the scattering behavior of tissue scrambles the information it contains, it does not destroy it. Therefore, if you can unscramble the scattered light, it increases the accessible imaging depths up the absorption limit of light (several centimeters deep). One such way to beat optical scattering is using wavefront shaping. Borrowing ideas from adaptive optics in astronomy and phased arrays in radar and ultrasonic imaging, the basic concept of wavefront shaping is to control the phase and amplitude of the light field in order to harness scattered light. Using wavefront shaping techniques, scattered light can be used to form focal spots or transmit information through or inside optically scattering media. Furthermore, even without correcting for scattering directly by shaping the input light field, the properties of the scattered light can be analyzed to recover information about the structure and dynamic properties of a sample using methods from diffuse optics. The main contributions of this thesis are along these two lines of research: moving wavefront shaping toward more practical applications and developing new techniques to recover useful physiological information from scattered light. This is developed through three main projects: (1) an investigation of how dynamic samples impact the scattering process and the practical implications of these dynamics on wavefront shaping systems, (2) the development of a wavefront shaping system combining light and ultrasound to focus light inside acute brain slices to improve light delivery for optogenetics, (3) a novel method to sensitively detect the dynamics of scattered light and use it to tease out information about the flow of blood within the tissue sample of interest.

The scattering effect of turbid media can lead to optical wavefront distortion. Focusing light through turbid media can be achieved using wavefront shaping techniques. Intelligent optimization algorithms and neural network algorithms are two powerful types of algorithms in the field of wavefront shaping but have their advantages and disadvantages. In this paper, we propose a new hybrid algorithm that combines the particle swarm optimization algorithm (PSO) and single-layer neural network (SLNN) to achieve the complementary advantages of both. A small number of training sets are used to train the SLNN to obtain preliminary focusing results, after which the PSO continues to optimize to the global optimum. The hybrid algorithm achieves faster convergence and higher enhancement than the PSO, while reducing the size of training samples required for SLNN training. SLNN trained with 1700 training sets can speed up the convergence of the PSO by about 50% and boost the final enhancement by about 24%. This hybrid algorithm will be of great significance in fields such as biomedicine and particle manipulation.

The shape of the radio wavefront of extensive air showers as measured with LOFAR

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.

NONREGULAR REFLECTION OF A RING SHOCK FROM THE AXIS OF SYMMETRY E. M. Barkhudarov, M. O. Mdivnishvili, I. V. Sokolov, M. I. Taktakishvili, and V. E. Terekhin UDC 533.6.011.72 INTRODUCTION The convergence of one-dimensional spherical or cylindrical shock waves is accompanied by an unbounded increase in the flow parameters as the shock wave approaches the center (axis) of s w~netry (unbounded c%unulation) [i, 2]. The cumulation effect is also char- acteristic of nonone-dimensional convergent axisymmetric shock waves. It has been shown experimentally that a ring shock wave is amplified as it moves towards the axis [3]. A theoretical analysis of the problem within the framework of Whitham's method indicates that the cumulation of the ring shock is unbounded [4] in the absence of lower azimuthal harmonics of the perturbation of the shape of the shock front [5]. Here we investigate the pattern of the flow that develops after the arrival of the ring shock at the center of the ring. The principal result is the formation of a Mach shock wave observed on reflection of the ring wave from the axis of symmetry at small values of the axial coordinate z, reckoned from the center of the ring, nonregular reflection being predicted at arbi- trarily small distances from the center. As shown theoretically [6], the nonregular reflection of the ring shock at small values of z is due to the increase in the angle of inclination of the incident wave front to the axis in accelerated convergence. This conclusion is consistent with the well- known hypothesis of Courant and Friedrichs [7] to the effect that in any case an axisym- metric ("conical") convergent shock wave undergoes nonregular reflection as distinct from a plane wave, which may be regularly reflected. This hypothesis was recently [8] proved for a conical shock wave in a perfect gas. I. The shock wave investigated was created, as in [3], as a result of the surface breakdown of a large number (~i00) of spark gaps on the inner surface of a ring facing the axis of symmetry. The radius and thickness of the ring were R K = 5 cm and h = 1 cm, respectively. The energy introduced into the discharge E ~ 1.2 kJ. The average value of the Mach number of the shock wave traveling towards the axis was M 0 ~ 2. The shock wave was visualized by the shadow method using a laser light source with illumination in a direction perpendicular to the axis of the ring. The sequence of shadowgrams shown in Fig. 1 was obtained for different realizations of the process by varying the time delay of the laser radiation pulse. The space scale and the time in- tervals between the photographs are indicated in the figure. The coordinates correspond- ing to the position of the Mach wave on the axis are equal to: z I = 1.4 cm, z= = 2.5 cm, z 3 = 4 cm. The source of the ring shock is on the left. In the shadowgrams the formation of the discontinuity configuration typical of Mach reflection (Fig. 2) is clearly visible. In Fig. 2 the letters AI denote the incident wave, AR the reflected wave, AM the Mach wave, and AE the contact discontinuity. In the first shadowgram because of the poor spatial resolution the Mach wave is not visible, but the strong distortion of the incident wave front near the axis as a result of the acceleration of the wave during cumulation is obvious. In Fig. 3 we have plotted the experimental values of the radius r M (curve 2) and the Mach wave velocity M M (curve 3) together with the value of the angle v (curve 4) between the incident wave front and the axis of symmetry measured at the point A (see Fig. 2). If there were no cumulation effect, the angle v would be given by the expression ~,=arctg

Recent efforts have extended fluid dynamic modeling to include low-electrical-conductivity (wavelike) electromagnetic field effects in plasmas. Here, we present results of a new study to explore and illustrate the capability of resolving such effects in the development of plasma instabilities. Recent work[1, 2] has explored the development of an efficient numerical procedure for simulating the coupled fluid dynamic and full electromagnetic (Maxwell) equations. This system of equations is more general than the resistive magnetohydrodynamic (MHD) model. The physical advantage to this system is that the inclusion of the displacement current and charge separation effects extends fluid dynamic modeling of plasmas to include regions of extremely low (or zero) electrical conductivity, where the electromagnetic fields possess a wave nature. Capturing the correct physical behavior of plasma instabilities in the limit of extremely low electrical conductivity is of significance for modern aerospace applications, including energy bypass arrangements for scramjet propulsion using magnetohydrodynamic augmentation, due to the extremely low electrical conductivity of the aerospace environment. The results depicted in this paper illustrate the potential for the numerical method realized in Ref. 1 to effectively resolve this behavior in cases where the MHD approximation may not be valid due to an exceedingly low electrical conductivity. A new study was initiated to explore more fully the capabilities to resolve regions of both low and high electrical conductivity using this numerical scheme. The problem selected for this study was the classic MHD KelvinHelmholtz instability. The initial and boundary conditions are provided in Ref. 2. A periodic box is initialized with two fluids of different density moving in opposite directions. An initial small perturbation is applied to the interfaces between the fluids, seeding an instability. A 256x256 grid size using a Roe solver for the coupled system of Navier-Stokes and full Maxwell equations was used, as detailed in [1, 2]. Three cases were explored: Case A was assigned a zero electrical conductivity, σ = 0 (purely hydrodynamic), Case B was given a small electrical conductivity of σ = 1, and Case C was given a very high conductivity of σ = 10 6 . Case A provides a hydrodynamic benchmark. Case B permits an investigation of a simulation that includes the effects of electromagnetic wave propagation in the plasma evolution. Case C effectively realizes the magnetohydrodynamic approximation. Results for the simulations are presented in a unique fashion in Fig. 1. For each subfigure, three spacetime isosurfaces of the density (blue, green and orange corresponding to the color range) have been depicted. Isosurfaces are the same for all three presented subfigures. Time flows from right (initial conditions) to left (final solution). For Case A, the fluid achieves a highly chaotic solution. The propagation of the initial disturbance at the interfaces between the two fluids is clear, as well as their development into a highly turbulent flow. Case B possesses an extremely low electrical conductivity, and therefore is not subject to the magnetic diffusion approximation of MHD. In fact, electromagnetic wave propagation was visible in this solution. The presence of a finite electrical conductivity provides some diffusion, but it does not match very well to the MHD prediction. However, the conductivity is large enough to abate the low-wavelength instabilities somewhat, and provide stability to the flow. Case C realizes the magnetohydrodynamic limit, where the magnetic field tends to stabilize the flow and strongly suppresses low-wavelength instabilities. A much more organized series of flow structures evolve through time to the final state. The magnetic field is effectively “frozen” to the fluid with such a large electrical conductivity, and the field strongly diffuses with little wave propagation.

When light propagates in a turbid medium, multiple scattering prevents it from reaching depths much greater than the mean free path. This limited propagation presents a problem for many fields where optical energy delivery through scattering media is critical, such as energy conversion in dye-sensitized solar cells, light-based medical techniques, or white LEDs. In this work we show that wavefront shaping techniques can significantly increase the delivery of optical energy through strongly scattering media.

Wavefront shaping techniques are being actively developed to achieve optical focusing through and inside opaque scattering media. These techniques promise to revolutionize biophotonics by enabling deep-tissue non-invasive optical imaging, optogenetics, optical tweezing, and light-based therapy. Among the existing wavefront shaping techniques, optical time-reversal-based techniques determine the optimum wavefront globally based on the principle of time reversal, without the need to perform time-consuming iterations to optimize each mode in sequence. In all previous optical time-reversal-based wavefront shaping experiments, Nyquist sampling criterion was followed so that the scattered light field was well-sampled during wavefront measurement and wavefront reconstruction. In this work, we overturn this conventional practice by demonstrating that a high-quality optical focus can still be achieved even when the scattered light field is under-sampled. Even more strikingly, we show both theoretically and experimentally that the focus achieved by the under-sampling scheme can be one order of magnitude brighter than that achieved by the well-sampling schemes used in previous works, where 3×3 to 5×5 pixels sampled one speckle grain on average. Moreover, since neighboring pixels were uncorrelated in feedback-based wavefront shaping, introducing the concept of sub-Nyquist sampling in time-reversal-based wavefront shaping makes the optimal phase maps obtained using these two different methods consistent. We anticipate that this newly explored under-sampling scheme will transform the understanding of optical time reversal and boost the performance of optical imaging, manipulation, and communication through opaque scattering media.

Photoacoustic guided wavefront shaping using digital micromirror devices

Controlling light propagation intentionally through turbid media such as ground glass or biological tissue has been demonstrated for many useful applications. Due to random scattering effect, one of the important goals is to draw a desired shape behind turbid media with a swift and precise method. Feedback wavefront shaping method which is known as a very effective approach to focus the light, is restricted by slow optimization process for obtaining multiple spots. Here we propose a technique to implement feedback wavefront shaping with optical memory effect and optical 4f system to speedy move focus spot and form shapes in 3D space behind scattering media. Starting with only one optimization process to achieve a focusing spot, the advantages of the optical configuration and full digital control allow us to move the focus spot with high quality at the speed of SLM frame rate. Multiple focusing spots can be achieved simultaneously by combining multiple phase patterns on a single SLM. By inheriting the phase patterns in the initial focusing process, we can enhance the intensity of the focusing spot at the edge of memory effect in with 50% reduction in optimization time. With a new focusing spot, we have two partially overlapped memory effect regions, expanding our 3D scanning range. With fast wavefront shaping devices, our proposed technique could potentially find appealing applications with biological tissues.

We begin our study of edge diffraction with the simplest case, namely, plane wave diffraction at a half-plane. The exact solution to this problem was derived in elsewhere and we shall now proceed to discuss the solution in detail. When a plane wave is normally incident upon a half-plane (i.e. the incident wavefront is parallel to the edge) and has a field component in the z-direction, then the exact solution for the z-component at any field point (p, φ) can be written in the compact form.

The problem of scattering of a plane acoustic wave by a fluid sphere was addressed by V. C. Anderson [J. Acoust. Soc. Am. 22, 426 (1950)]. This wave was assumed to be homogeneous, without amplitude variation over the wave front. The problem of scattering of a plane wave partially insonifying a rigid sphere was addressed by G. C. Gaunaurd [IEEE J. Oceanic Eng. 10, 213 (1985)], but in the Kirchhoff approximation. Here, the problem of scattering of an inhomogeneous plane acoustic wave by a fluid sphere is addressed. A general analytical solution is given. A particular solution is described for a monochromatic plane wave whose amplitude on the surface of a sphere of radius r=a, with center at the origin, is exp[ika cos θ−2αa cos2(θ/2)], where k is the wavenumber, θ is measured relative to the direction of propagation, and α is the absorption coefficient. Both the scattered and internal fields are evaluated for a range of parameter values of k, α, r, and θ, and compared against the Anderson solution for a homogeneous plane wave. It is believed that H. Medwin would have appreciated the unexpressed direction of this work: modeling of sonar interactions with marine animals.

Wavefront shaping based on optoacoustic (photoacoustic) feedback has recently emerged as a promising tool to control the light distribution in optically-scattering media. In this approach, the phase of a short-pulsed light beam is spatially-modulated to create constructive light interference (focusing) at specific locations in the speckle pattern of the scattered wavefield. The optoacoustic signals generated by light absorption provide a convenient feedback mechanism to optimize the phase mask of the spatial light modulator in order to achieve the desired light intensity distribution. The optimization procedure can be done by directly considering the acquired signals or the reconstructed images of the light absorption distribution. Recently, our group has introduced a volumetric (three-dimensional) optoacoustic wavefront shaping platform that enables monitoring the distribution of light absorption in an entire volume with frame rates of tens of Hz. With this approach, it is possible to simultaneously control the volumetric light distribution through turbid media. Experiments performed with absorbing microparticles distributed in a three-dimensional region showcase the feasibility of enhancing the light intensity at specific points, where the size of particles is also essential to maximize the signal enhancement. The advantages provided by optoacoustic imaging in terms of spatial and temporal resolution anticipate new capabilities of wavefront shaping techniques in biomedical optics.