A Nature Research Journal. The resolution of acoustic imaging suffers from diffraction limit due to the loss of evanescent field that carries subwavelength information.
Most of the current methods for overcoming the diffraction limit in acoustics still operate in the near-field of the object. Here we demonstrate the design and experimental realization of an acoustic far-field subwavelength imaging system. Our system is based on wave vector filtering and conversion with a transmitter at the near-field and a spatially symmetrical receiver at the far-field. Furthermore, far-field imaging and edge detection of subwavelength objects are experimentally demonstrated.
The proposed system brings new possibilities for far-field subwavelength wave manipulation, which can be further applied to medical imaging, nondestructive testing, and acoustic communication. Acoustic imaging techniques have been widely used in areas such as medical ultrasonic imaging 1 , nondestructive testing 2 , and underwater sonar systems 3 , 4. Similar to other wave-based imaging techniques, the high spatial frequency information of an object is carried by evanescent waves that decay exponentially as they leave the object.
The loss of those evanescent waves in conventional imaging systems leads to the diffraction limit 5. The working wavelength of acoustic imaging is relatively large compared to imaging techniques using other wave forms e. Thus, the resolution upper bound posed by the diffraction limit has larger impact on acoustic imaging.
Various approaches have been developed to realize acoustic imaging beyond the diffraction limit 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , The near-field scanning technique 6 is one of the earliest techniques for acoustic subwavelength imaging. It requires measurements to be made in close proximity fractions of wavelength to objects in order to capture the evanescent components.
Such restriction greatly limits its application in acoustic subwavelength imaging. In the past decade, acoustic metamaterial-based lenses have demonstrated the potential in subwavelength imaging 10 , 11 , 12 , 13 , 14 , The dispersion relation and effective material properties were modified inside the metamaterials to support the propagation of evanescent waves. By coupling to acoustic metamaterial lenses in the near-field of the objects, the evanescent waves can be measured further away. Although the distance is extended by using existing acoustic metamaterials, the thermal viscous loss due to wave propagation in resonating elements is still a major factor that limits the use of metamaterial-based lenses in subwavelength imaging.
If the evanescent wave can be converted to propagating wave and propagate in free-space or empty waveguide, the propagation distance will be much less limited by thermal viscous loss and the image can be formed in the far-field of the object. One of the techniques for far-field acoustic imaging is hyperlenses 19 , 20 , which use cylindrical-shaped anisotropic metamaterials to couple and gradually compress large subwavelength wave vectors to small propagating wave vectors.
At the exit of a hyperlens, the image size is larger than the wavelength and the image can be detected in the far-field. However, due to the geometric shape, achieving higher spatial resolution of hyperlenses has a cost of smaller field of view. Another technique for acoustic far-field imaging is the time reversal technique 16 , 17 , 18 , which uses random subwavelength scattering arrays to convert evanescent waves to propagating waves in the near field, in combination with a time reversal mirror in the far-field.
However, time reversal imaging is not a direct projection based technique. Those requirements reduce the flexibility for applications. Far-field superlenses were designed in optics to realize far-field subewavelength imaging. They were designed by using gratings to convert optical evanescent waves to propagating waves 21 , The converted propagating waves were measured in far-field free space and reconstructed computationally. In order to apply gratings to imaging, the overlapping of multiple diffraction orders needs to be addressed.
In the design of optical far-field superlens, the overlapping was removed by combining the grating with a metal layer that can excite subwavelength surface plasmon to couple selected spatial frequencies to the grating. However, no counterpart of surface plasmon exists in acoustics. Thus, no such far-field superlens has been realized in acoustics yet. In this work, we propose mechanisms in acoustics to realize the functions of optical surface plasma and grating, and combine them to demonstrate an acoustic far-field subwavelength imaging system.
A resonator array denoted as filter layer of subwavelength unit cells is designed to realize the function of surface plasma in order to amplify selected subwavelength spatial frequencies. An acoustic version of binary phase grating 23 denoted as grating layer is designed to remove the incident propagating components and convert the incident subwavelength components to propagating ones.
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The combination of those two proposed structures forms the transmitter of the system, and establishes the one-to-one relationship between the subwavelength wave vectors and the propagating ones. In the proposed system, wave propagation takes place in empty waveguide with much less thermal viscous loss than in metamaterials. We show that while the transmitter still needs to be close to the object, the receiver can be many wavelengths away from the object and the distance can be flexible.
This is the reason why we call the designed system far-field lenses. Our lenses work as spatial filters that separate different subwavelength spatial frequencies and project them to the far-field. Edge detection is experimentally demonstrated as an example of far-field sub-wavelength imaging of our proposed system.
The object here is assumed to be acoustic scattering media with subwavelength details and is put in contact with the filter layer in the transmitter. The sound source emits continuous wave at frequency f 0 corresponding to wavenumber k 0 in air or a short pulse with center frequency f 0. P 0 is expressed as the integration of the Fourier spectrum for the scattered wave from the object, based on the principle of spatial Fourier transform The function of the filter layer is to amplify the wave components with a selected wavenumber band.
The function of the grating layer is to convert the subwavelength wave vectors emerging from the filter layer to propagating wave vectors by momentum addition. The grating is designed to only have odd diffraction orders, thus the propagating components from the filter layer, which is the zeroth order diffraction, is further suppressed. The receiver is composed of the same grating layer and the filter layer as the transmitter. By reciprocity, the receiver takes the reverse process.
The grating will also generate other higher odd order diffractions 3th order, 5th order, ….
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Other higher-order diffractions are all attenuated after passing through the filter layer at the receiver. By changing the geometric parameters, the filtering band of the filter layer and the grating constant k G of the grating layer can be adjusted to different locations in the spatial spectrum. The received signals are denoted by P 3 n respectively. The final image can be formed in two ways.
Acoustical Imaging, Volume 30
In this case, the edge image of the object that is represented by higher spatial frequencies will be obtained. System schematics and the working process of the proposed system. The whole system is composed of a transmitter and a receiver that are spatially symmetrical.
Each part is composed of a filter layer green and a grating layer blue. The propagating band can be obtained by propagating through empty waveguide. The purpose of filter layer is to couple incident waves with specific wave numbers from input to output of the layer, as a near-field spatial filter. In optics, such filtering is realized through the excitation of surface plasma in a metallic layer. However, there is no counterpart of surface plasma in acoustics yet.
We propose to realize the near-field spatial sound filtering by using two identical arrays of Helmholtz resonators HRs facing each other with distance h , forming a waveguide of height h for the wave to pass through Fig. Each HR in the arrays is built with a cavity having widths a 1 and c , and height b 1 , and a rigid tube having widths a 2 and c , and height b 2.
The array period is d 1. The resonance frequency of the HR corresponds to a wavelength that is much larger than the size of the HR itself, so we can use lumped circuit model to approximate the HRs 25 , with the cavity acting as the capacitor and the tube acting as the inductor. Model and properties of the filter layer. By changing a 1 , the filtered wave vector can be tuned.
When the incident field propagates through the waveguide, some components with specific transverse wave numbers will be coupled to the resonance mode of the HR arrays. The HRs in the array should have much smaller sizes and periods compared to the working wavelength in order to make the coupling of subwavelength components possible. The proposed system can be scaled to other sizes and working frequencies depending on different applications.
In the coordinate system shown in Fig.
It is the coupling of wave component with effective vector k e from the input to the output of the filter. Y and Z are functions of the geometric parameters of the HR arrays. This is comparable to eigenmode analysis. In realistic experiments or simulations, the arrays are of finite length and damping has to be considered, so that the transmission will not diverge.
The theoretical calculation of s 0 in Eq. Neither case considers loss. The amplification obtained in the simulation is in general smaller than that in the theoretical calculation. It is because that in the simulation the filter layer has finite numbers of HRs, which is unable to produce the resonant amplitude that approaches infinity shown in the theoretical calculation for infinite structures.
By further increasing a 1 , the filter layer can work for wave vectors larger than 3. In our designed system, a grating layer is put next to the filter layer to convert the subwavelength wave to propagating wave. A grating usually has multiple diffraction orders. The key here is to establish a one-to-one relationship between the wave vectors before and after conversion.
Observing the simulated transmission coefficients in Fig. Those unwanted propagating waves will transmit through the grating layer by the zeroth order diffraction and overlap with the subwavelength components of interest that transmit by the first order diffraction. Binary phase grating in optics is known to not have even order diffraction Thus we propose the design of an acoustic binary phase grating to eliminate the zeroth order diffraction of the propagating components. Narrow acoustic waveguide channels with cross section dimension smaller than wavelength are known to be able to generate phase delay proportional to the wave path length Based on those facts, we construct the acoustic binary phase grating in our system with a straight channel of length The width of the channels is 1.
Model and properties of the grating layer. Changing the grating period d 2 will results in different k G. The waves inside the channels and at both sides of the grating are expressed as combinations of plane wave modes. Acoustical imaging has become an indispensable tool in a variety of fields. Since its introduction, the applications have grown and cover a variety of techniques, producing significant results in fields as disparate as medicine and seismology.
Cutting-edge trends continue to be discussed worldwide. The Symposium belongs to a conference series in existence since During two well-attended workshops the applications of quantitative acoustical imaging in biology and medical applications, and in near-field imaging of materials, were discussed. Based on its cross-disciplinary aspects, the authors of the papers of AI27 present experiments, theory and construction of new instruments.
26TH INTERNATIONAL ACOUSTICAL IMAGING SYMPOSIUM
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