Iterative Angular Spectrum Research Articles

Three-dimensional computer holography based on two hybrid constraint iterative angular spectrum algorithms

A method for three-dimensional holographic image calculation based on angular spectrum layering is presented, which significantly reduces the noise resulting from image overlap during hologram reconstruction. In order to enhance the reconstruction quality, we proposed a two-hybrid constraint algorithm, which employs two parallel processing frameworks to allocate multiple plane images effectively. Additionally, by applying two different hybrid constraint factors, spatial resource allocation is utilized efficiently to mitigate the impact of axial inter-layer crosstalk noise. The numerical simulations and optical experiment results demonstrated that our method has successfully improved the reconstruction quality of holograms and proved its effectiveness and feasibility.

Real-time acoustic holography with physics-reinforced contrastive learning for acoustic field reconstruction

Acoustic holography (AH) provides a promising technique for arbitrary acoustic field reconstruction, supporting many applications like robotic micro-nano manipulation, neuromodulation, volumetric imaging, and virtual reality. In AH, three-dimensional (3D) acoustic fields quantified with complex-valued acoustic pressures are reconstructed by virtue of two-dimensional (2D) acoustic holograms. Phase-only hologram (POH) is recently regarded as an energy-efficient way for AH, which is typically implemented by a dynamically programmable phased array of transducers (PATs). As a result, spatiotemporal precise acoustic field reconstruction is enabled by precise, dynamic, and individual actuation of PAT. Thus, 2D POH is required per arbitrary acoustic fields, which can be viewed as a physical inverse problem. However, solving the aforementioned physical inverse problem in numerical manners poses challenges due to its non-linear, high-dimensional, and complex coupling natures. The existing iterative algorithms like the iterative angular spectrum approach (IASA) and iterative backpropagation (IB) still suffer from speed-accuracy trade-offs. Hence, this paper explores a novel physics-iterative-reinforced deep learning method, in which frequency-argument contrastive learning is proposed facilitated by the inherent physical nature of AH, and the energy conservation law is under consideration. The experimental results demonstrate the effectiveness of the proposed method for acoustic field reconstruction, highlighting its significant potential in the domain of acoustics, and pushing forward the combination of physics into deep learning.

Three-dimensional computer-generated holography based on the hybrid iterative angular spectrum algorithm.

This paper proposes a novel three-dimensional hologram calculation method based on the angular spectrum approach, with the aim of reducing the noise generated during the hologram reconstruction process. The proposed algorithm divides the spatial domain into multiple layers and employs the angular spectrum method to propagate the image between these layers, thus avoiding the paraxial approximation. To enhance the quality of the hologram, an error iteration algorithm is utilized to alleviate the occurrence of aliasing errors when directly superimposing holograms. Moreover, constraint factors are introduced between different layers within the same region to effectively utilize spatial resources for multi-image reconstruction, thereby mitigating the noise caused by inter-layer crosstalk. The feasibility of the proposed method is demonstrated through numerical simulations and optical experiments, highlighting its potential applicability to a wide range of three-dimensional reconstruction algorithms.

Multi-plane acoustic hologram generation with a physics-enhanced neural network for micro-particle manipulation

A physics-enhanced multi-plane acoustic hologram deep neural network (PhysenNet_MPAH) approach is proposed for generating multi-plane acoustic hologram. By combining a convolutional neural network with a physical model, the PhysenNet_MPAH approach can generate high-quality acoustic holograms for holographic rendering of targeted acoustic intensity fields at multiple planes. This approach is capable of reconstructing both strong and weak-targeted multi-plane fields, with superior quality compared to traditional iterative angular spectrum approach. The reconstructed multi-plane acoustic fields are also demonstrated to be useful for three-dimensional particles manipulation, indicating potential applications in dynamic particles manipulation and volumetric display.

Phase holograms for the three-dimensional patterning of microparticles in a traveling wave field

Acoustic fields can generate radiation forces that can align particles in patterns. Forces from standing waves pattern particles in three dimensions (3-D) at either nodal or anti-nodal regions. These patterns can be utilized to form 3-D microstructures for applications in tissue engineering or fabrication of layered materials. However, standing waves require more than one transducer or a reflector, which can complicate implementation. Here, we developed a method to suspend and align microspheres using a traveling wave from a single transducer. Acoustic fields were shaped to align polyethylene microspheres mimicking tissue cells in parallel planes along the axis of the transducer. A Bessel-like beam was developed using diffraction theory and an iterative angular spectrum approach were used to design phase holograms to shape pressure fields. Gor’kov potential was used to calculate radiation forces while minimizing the axial forces to create a stable trap. The resulting pressure fields and particle patterns matched predictions with a similarity index >0.92, where 1 is a perfect match. The transverse radiation force was ten times each microsphere’s weight and comparable to the standing wave radiation forces. Next steps are in vivo implementation of cell patterning for tissue engineering. [Work supported by NIH K25-DK132416 and P01-DK043881.]

Phase holograms for the three-dimensional patterning of unconstrained microparticles

Acoustic radiation forces can remotely manipulate particles. Forces from a standing wave field align microscale particles along the nodal or anti-nodal locations of the field to form three-dimensional (3D) patterns. These patterns can be used to form 3D microstructures for tissue engineering applications. However, standing wave generation requires more than one transducer or a reflector, which is challenging to implement in vivo. Here, a method is developed and validated to manipulate microspheres using a travelling wave from a single transducer. Diffraction theory and an iterative angular spectrum approach are employed to design phase holograms to shape the acoustic field. The field replicates a standing wave and aligns polyethylene microspheres in water, which are analogous to cells in vivo, at pressure nodes. Using Gor’kov potential to calculate the radiation forces on the microspheres, axial forces are minimized, and transverse forces are maximized to create stable particle patterns. Pressure fields from the phase holograms and resulting particle aggregation patterns match predictions with a feature similarity index > 0.92, where 1 is a perfect match. The resulting radiation forces are comparable to those produced from a standing wave, which suggests opportunities for in vivo implementation of cell patterning toward tissue engineering applications.

Deep Learning-Based Framework for Fast and Accurate Acoustic Hologram Generation.

Acoustic holography has been gaining attention for various applications, such as noncontact particle manipulation, noninvasive neuromodulation, and medical imaging. However, only a few studies on how to generate acoustic holograms have been conducted, and even conventional acoustic hologram algorithms show limited performance in the fast and accurate generation of acoustic holograms, thus hindering the development of novel applications. We here propose a deep learning-based framework to achieve fast and accurate acoustic hologram generation. The framework has an autoencoder-like architecture; thus, the unsupervised training is realized without any ground truth. For the framework, we demonstrate a newly developed hologram generator network, the holographic ultrasound generation network (HU-Net), which is suitable for unsupervised learning of hologram generation, and a novel loss function that is devised for energy-efficient holograms. Furthermore, for considering various hologram devices (i.e., ultrasound transducers), we propose a physical constraint (PC) layer. Simulation and experimental studies were carried out for two different hologram devices, such as a 3-D printed lens, attached to a single element transducer, and a 2-D ultrasound array. The proposed framework was compared with the iterative angular spectrum approach (IASA) and the state-of-the-art (SOTA) iterative optimization method, Diff-PAT. In the simulation study, our framework showed a few hundred times faster generation speed, along with comparable or even better reconstruction quality, than those of IASA and Diff-PAT. In the experimental study, the framework was validated with 3-D printed lenses fabricated based on different methods, and the physical effect of the lenses on the reconstruction quality was discussed. The outcomes of the proposed framework in various cases (i.e., hologram generator networks, loss functions, and hologram devices) suggest that our framework may become a very useful alternative tool for other existing acoustic hologram applications, and it can expand novel medical applications.

Planar focusing lens for enhanced far-field ultrasonic imaging.

This paper presents a far-field enhanced-resolution underwater ultrasonic imaging on the basis of a single-slit structured planar focusing lens. The iterative angular spectrum approach was employed to optimize the planar focusing lens from a designated focal pattern, characterized by focal length and full width at half maxima. Numerical simulations and experimental investigations were conducted on different target objects. Compared to the conventional method, both results showed that the performance of far-field ultrasonic imaging was comprehensively enhanced with the proposed planar focusing lens, in terms of resolving capability, working distance, operational bandwidth, and robustness. The single-slit structured planar focusing lens is cost effective and easy to fabricate, which would greatly benefit ultrasonic imaging and drive new applications of ultrasound in various scenarios.

The XFaster Power Spectrum and Likelihood Estimator for the Analysis of Cosmic Microwave Background Maps

Abstract We present the XFaster analysis package, a fast, iterative angular power spectrum estimator based on a diagonal approximation to the quadratic Fisher matrix estimator. It uses Monte Carlo simulations to compute noise biases and filter transfer functions and is thus a hybrid of both Monte Carlo and quadratic estimator methods. In contrast to conventional pseudo-C ℓ –based methods, the algorithm described here requires a minimal number of simulations and does not require them to be precisely representative of the data to estimate accurate covariance matrices for the bandpowers. The formalism works with polarization-sensitive observations and also data sets with identical, partially overlapping, or independent survey regions. The method was first implemented for the analysis of BOOMERanG data and also used as part of the Planck analysis. Here we describe the full, publicly available analysis package, written in Python, as developed for the analysis of data from the 2015 flight of the Spider instrument. The package includes extensions for self-consistently estimating null spectra and estimating fits for Galactic foreground contributions. We show results from the extensive validation of XFaster using simulations and its application to the Spider data set.

Holographic mirrors for spatial ultrasound modulation in contactless acoustic energy transfer systems

This work introduces and investigates a flat acoustic mirror capable of efficiently manipulating a wavefront and creating an arbitrary pressure pattern in a target plane using the sound reflection phenomenon. The mirror is a metallic holographic lens that performs as a spatial ultrasound modulator by introducing a relative phase shift to the reflected wavefront. The phase-shifting lens is designed using an iterative angular spectrum algorithm and 3D-printed from powdered aluminum through direct metal laser melting. The lens's capabilities to construct diffraction-limited complex pressure patterns under water are tested numerically and experimentally. The proposed holographic mirror design can drive immense improvements in applications involving contactless acoustic energy transfer, which is investigated in this Letter.

Non-planar holographic lens for mild hyperthermia in a broad area

High intensity focused ultrasound (HIFU) has been used as a non-invasive tool for thermal ablation treatments. Typically, HIFU can ablate a small region (2 × 10 mm2) depending on the frequency and transducer dimensions. Cavitation-induced bubbles or injected microbubbles have been shown to enhance tissue heating during HIFU at lower acoustic intensities. The formed lesion is limited to the focal region, necessitating prolonged time of treatment to expose the entire target. To solve this problem, we designed a non-planar diffraction lens that mounts onto the surface of a 900kHz focused transducer (64 mm diameter and 62 mm focus) to enlarge the focal region. The lens was designed with an iterative angular spectrum approach to achieve a lateral beamwidth of 8 mm while maintaining a similar axial beamwidth. The focal beam size (transverse × axial) increased from 2.5 × 15.8 mm2 to 8 × 20 mm2 which also resulted in a corresponding increase in thermal lesion. We plan to expand this work to matrix phased arrays for application to mild hyperthermia for enhanced drug delivery.

Multiplexed acoustic holography using an iterative angular spectrum approach

Technological advancements have enhanced the capability of acoustic holography over the years. A major drawback for current techniques is the lack of ability of multiplexing, which has limited their potentials in ultrasound imaging and acoustofluidics. In this work, we propose an algorithm based on an iterative angular spectrum approach to overcome this limit. An optimized phase distribution at the source plane can be obtained which can project multiple acoustic projections at various distances and frequencies. As such, the acoustic fields at the image planes are encoded onto the same source plane and this facilitates the design of 3D printed acoustic kinoforms integrated on a single element transducer. The parameters including the frequency and projection distance to obtain the best performance are tested. The algorithm can be used in conjunction with other optimization strategies to fine tune pressure fields and further improve the image quality. The results are expected to be useful in medical ultrasound and acoustofluidics where complex acoustic field projection is needed.

Three-Dimensional (3D) Printing Implemented by Computer-Generated Holograms for Generation of 3D Layered Images in Optical Near Field

Photocurable three-dimensional (3D) printing is a stepwise layer-by-layer fabrication process widely used in the manufacture of highly specialized objects. Current 3D printing techniques are easily implemented; however, the build rate is slow and the surface quality is less than ideal. Holographic 3D display (3DHD) technology makes it possible to reform planar wavefronts into a 3D intensity distribution, which appears as a 3D image in space. This paper examined the application of holographic imaging technology to 3D printing based on photocurable polymers. The proposed system uses a 3DHD diffractive optics system based on a liquid-crystal-on-silicon spatial light modulator (LCoS-SLM), wherein a 3D layered image is created in the optical near field, based on a computer-generated hologram (CGH) optimized using the iterative angular spectrum algorithm (IASA) and a circular IASA. From a single CGH, multiple 2D sliced images are created in space to form a 3D optical image used to initiate the photopolymerization of photocurable resin to form 3D objects. In experiments, the proposed 3D printing system was used to create five polymer objects with a maximum axial length of 25 mm and minimum feature width of 149 μm. The phase-only CGH reformed the incident light into a distribution of optical intensity with high diffraction efficiency suitable for photocuring. Despite limitations pertaining to fabrication area and axial complexity in this initial study, the proposed method demonstrated high light efficiency, high resolution in the lateral direction, rapid fabrication, and good object continuity.

Computing 3D Phase-Type Holograms Based on Deep Learning Method

Computer holography is a technology that use a mathematical model of optical holography to generate digital holograms. It has wide and promising applications in various areas, especially holographic display. However, traditional computational algorithms for generation of phase-type holograms based on iterative optimization have a built-in tradeoff between the calculating speed and accuracy, which severely limits the performance of computational holograms in advanced applications. Recently, several deep learning based computational methods for generating holograms have gained more and more attention. In this paper, a convolutional neural network for generation of multi-plane holograms and its training strategy is proposed using a multi-plane iterative angular spectrum algorithm (ASM). The well-trained network indicates an excellent ability to generate phase-only holograms for multi-plane input images and to reconstruct correct images in the corresponding depth plane. Numerical simulations and optical reconstructions show that the accuracy of this method is almost the same with traditional iterative methods but the computational time decreases dramatically. The result images show a high quality through analysis of the image performance indicators, e.g., peak signal-to-noise ratio (PSNR), structural similarity (SSIM) and contrast ratio. Finally, the effectiveness of the proposed method is verified through experimental investigations.

Acoustic Hole-Hologram for Ultrasonic Focusing With High Sensitivity

Acoustic hologram enable the capability in the acoustic pattern control and drive many applications of ultrasound. However, hologram has not been applied to ultrasound imaging because the medical application of acoustic holograms is limited owing to the sound reflection and scattering at the acoustic holographic surface and its internal attenuation. In this study, we propose an acoustic holographic computing method and present a disc-shaped hologram with a central hole comparing with a conventional hologram using the iterative angular spectrum approach. The results show that the transducer with hole hologram achieves the required focusing effect with the full width at half maximum about <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.5\lambda $ </tex-math></inline-formula> , high sensitivity increased by 92.7%, and a low two-way insertion loss with −15.8 dB compared to conventional hologram. Pulse-echo and ultrasonic imaging are achieved by a transducer with two holograms which shows new applications of acoustic hologram in ultrasound.

Comparison of balanced direct search and iterative angular spectrum approaches for designing acoustic holography structure

There are many pure phase methods for designing acoustical holography structures in the known literature. Different methods may have different characteristics and lead to different results, but few researchers put these methods together for comparison. So we have no idea which method should be taken when dealing with a specific optimization case. This paper investigated the characteristics of three different PM methods, one is the direct search method taking suitable objective function and another two are the conventional IASA methods but with different restricts in image plane, one called ISREL relaxes the whole background pressure constraints and one called ISRES restricts the whole background pressure to zero. We find that DS is a balanced method in terms of various metrics evaluating target pattern and background noise. Finally, the ability of particle manipulation of DS was verified experimentally by designing a holography structure projecting a circle with a non-uniform phase gradient. In a word, it provides a specific comparison between the two mainstream methods DS and IASA by two optimization cases. On one hand, it gives us a clear view of the characteristics of these methods in designing acoustic holography; On the other hand, we know that DS may be a preferred algoritm for most optimization cases owing to its balanced characteristic regardless of time costs.

Characterizing the physical limitations of phase-only metasurface design for acoustic holograms

Numerous recent studies have shown that acoustic metasurfaces (AMS) can be used to control reflected or transmitted wave fronts. Acoustic holograms have commonly been created by designing a metasurface that applies local phase changes to a wave front to construct arbitrary pressure fields at one or more image planes. The hologram design process typically features iterative methods, such as the Iterative Angular Spectrum approach. However, metasurfaces that apply phase-only modulation are restricted in the quality of the pressure field reconstruction that can be achieved, especially when attempting to create different holograms at different planes for a single-frequency incident wave. The control of magnitude and phase by an AMS is of significant interest because it enables one to completely define an entire reflected or transmitted wave field in a 3-D region. In the present work, the physical limitations in simultaneously reconstructing multiple single-frequency holograms at different planes via phase-only metasurface design are examined. Methods for overcoming these limitations, including both amplitude and phase control by an acoustic metasurface, are also investigated. Comparisons between simulation and experiment are made for a multi-image reflective hologram system. [S.N.L. is managed and operated by NTESS under DOE NNSA Contract No. DE-NA0003525.]

Design, fabrication, and characterization of broad beam transducers for fragmenting large renal calculi with burst wave lithotripsy.

Burst wave lithotripsy (BWL) is a technology for comminuting urinary stones. A BWL transducer's requirements of high-pressure output, limited acoustic window, specific focal depth, and frequency to produce fragments of passable size constrain focal beamwidth. However, BWL is most effective with a beam wider than the stone. To produce a broad-beam, an iterative angular spectrum approach was used to calculate a phase screen that was realized with a rapid prototyped lens. The technique did not accurately replicate a target beam profile when an axisymmetric profile was chosen. Adding asymmetric weighting functions to the target profile achieved appropriate beamwidth. Lenses were designed to create a spherically focused narrow-beam (6 mm) and a broad-beam (11 mm) with a 350-kHz transducer and 84-mm focal depth. Both lenses were used to fragment artificial stones (11 mm long) in a water bath, and fragmentation rates were compared. The linearly simulated and measured broad beamwidths that were 12 mm and 11 mm, respectively, with a 2-mm-wide null at center. The broad-beam and the narrow-beam lenses fragmented 44 ± 9% and 16 ± 4% (p = 0.007, N = 3) of a stone by weight, respectively, in the same duration at the same peak negative pressure. The method broadened the focus and improved the BWL rate of fragmentation of large stones.

Acoustic holograms in contactless ultrasonic power transfer systems: Modeling and experiment

Contactless ultrasonic acoustic energy transfer (UAET) is a new technology that eliminates risks or impracticalities associated with wired electrical connections or batteries that need to be replaced on a regular basis. This technology, which is based on the reception of acoustic waves at ultrasonic frequencies by piezoelectric receivers, can be used to wirelessly charge low-power electronics. The execution and efficiency of this technology can be significantly enhanced through patterning and focusing of the transmitted acoustic energy in space to simultaneously power distributed sensors or devices. This work investigates the use of an acoustic hologram to create a multifocal pressure pattern in a plane where target receivers are located at specific focal points or regions. First, a phase-shifting hologram is designed using an iterative angular spectrum approach. Then, a multi-physics acoustic-electro-elastic model is presented for an axially vibrating cylindrical transmitter used to power multiple piezoelectric receivers, in conjunction with the hologram. Experiments are also performed to show the capability of an acoustic hologram to selectively power an array of the receivers. Both analytical and experimental results show a dramatic enhancement of power transfer to receivers exposed to a multi-focal pressure pattern created by the hologram. As a case study, a bi-focal receiver setup is investigated where one receiver is targeted. The UAET simulation predicts a doubling of the power transfer to the targeted receiver, which is verified by the proof-of-concept experiment. The effects of system parameters such as input frequency and hologram aperture size are also reported.

Design of a transducer for fragmenting large kidney stones using burst wave lithotripsy

Burst wave lithotripsy (BWL) is a potential noninvasive treatment for breaking kidney stones. BWL requirements of high-pressure output, limited aperture for acoustic window, and specific focal length and frequency constrain the focal beam width. However, BWL is most effective only on stones smaller than the beam width. We tested a porous piezoelectric material (PZ36) to increase the output power and designed acoustic lenses that broaden the beam. A weighted iterative angular spectrum approach was used to calculate the source phase distribution needed to generate desired cross sectional focal beam profiles each of 12 mm width. The phase calculations were then 3D printed as holographic lenses placed over a circular aperture of 80-mm diameter, 350 kHz PZ36 to produce the desired beam at 85 mm depth. The difference in simulated beam width and that measured by hydrophone was &amp;lt;1 mm, and the structural-similarity index value was greater than 0.65. The differences in structures were due not to shape and size of the 6-dB contours but to amplitude distribution within the contour. In conclusion, this design approach combined with 3D printing provide a way to tailor focal beam profiles for lithotripsy transducers. [The work was supported by NIDDK P01-DK043881 and K01-DK104854.]