Deep Learning-Assisted Metasurface Design for Megapixel Acoustic Holograms | Applied Physics Review

Holography is a promising technique for wave field reconstruction. It has many applications such as volume display.¹ ultra-high density data storage,² optical³ or acoustic^Four tweezers, optical^Five or acoustic imaging,⁶ acoustic suspension,^6,7 and biomedical engineering,^8,9 Acoustic holography, as one of the representative holographic technologies, has attracted a great deal of attention from scientists and engineers in various fields. Conventional acoustic holography uses an active phased array, which requires many transducers with cumbersome phase-shifting circuits. Recently, his two-dimensional equivalent of metamaterials with subwavelength microstructures, metasurfaces, has emerged as a promising holographic technique in both fields of optics.^Ten and acoustics.^{11, 12} Metasurfaces can reduce system complexity as only a single source transducer is required to achieve the desired scattered field based on phase modulation (PM) or phase amplitude modulation (PAM). PM method was applied by Melde other.⁷ and thank you other.¹³ Designed a metasurface-based hologram for acoustic holographic imaging in 2016, subsequently designed by Bakhtiari-Nejad. other.¹⁴ Generate multifocal pressure patterns with water-based ultrasound. PAM technology can be achieved through the elaborate design of composite elements containing two parts that independently modulate phase and amplitude.^11,15 Tian and others,¹⁶ Vermillion and others,¹⁷ and fan other.¹⁸ We used this strategy to design a transmission type¹⁶ and reflex^17,18 Metasurface-based holograms for acoustic imaging. Although controlling both amplitude and phase provides more freedom, the design of metasurface-based holograms using decoupling (or quasi-decoupling) PAMs is sensitive to the configuration and size of their microstructures, increasing accuracy. and may lack flexibility.The difference is Mr. Zhang other.¹⁹ introduced a modified weighted Gerchberg-Saxton algorithm to design monolithic acoustic holograms with PAM in mind. Images of nine focal patterns and the letter ‘U’ were displayed by a 2 MHz transducer attached to the hologram with the designed thickness profile.brown²⁰ used two phase holograms to modulate both the phase and amplitude of an incident sound wave to experimentally generate the letters ‘UCL’. The hologram thickness profile was designed using an optimization technique. The PAM technique was also applied to the design of multiple acoustic metasurface-based holograms.^21,22 In general, PAM can provide a larger design space than PM for metasurface-based holograms. One difficulty, however, is finding a set of functional elements that can simultaneously modulate phase and amplitude. This problem is even more pronounced when many factors are involved.

Several studies on metasurface-based holography have been reported, but their advantages have not been fully exploited due to limitations in resolution and PAM accuracy of the proposed metasurfaces. Intuitively, the number of metasurface elements (pixels), which defines the metasurface resolution, is critical for obtaining high-resolution complex holographic imaging. As an example, we show a holographic image (Figure 1) of a quick response code (QR code) containing 100 words. [as shown in Fig. 1(a)] by metasurfaces with different numbers of elements. The images are displayed as sound pressure distributions and detailed calculations are shown in Fig. S3 in Supplementary Text S2.In addition, the image is [Fig. 1(f)] with a metasurface of 500 × 500 elements [Fig. 1(d)] While recognizable (that is, the QR code image can be scanned and converted to the expected characters), the image is [Fig. 1(e)] 120 × 120 by metasurface [Fig. 1(c)] Unrecognizable. As the number of words increases, more metasurface elements are required, as shown in Fig. 1(b). In other words, high-quality metasurface-based holograms require a huge number of elements with accurate PAM. This can be understood by considering the following facts. On the other hand, compiling more words into binary images requires higher resolution (as shown in Fig. S4 in Supplementary Text S2). On the other hand, to realize a binary holographic image, N. ×N.Pixels mean that we need to increase the number of elements in the acoustic metasurface to render more complex images. Therefore, as the number of metasurface elements increases, so does the number of words recognizable by metasurface-based holography. Although a positive correlation exists between the number of metasurface elements and recognizable word length, there is no explicit relationship (such as formulas or limits) that can be found based on current data. Please be careful.

However, it is usually more difficult to have a large number of elements while achieving high accuracy. Traditional approaches either cannot achieve this or require a very cumbersome design process. For example, optimization methods have been successfully applied to the inverse design of acoustic metasurfaces.^23,24 However, designing thousands of elements typically requires significant computing resources and time costs. Recently, deep learning (DL), a type of machine learning method based on artificial neural networks,^{twenty five} has been applied to the design of optical metasurfaces,^26–29 acoustic metasurface,^30–33 non-photonic devices,³⁴ It is even possible to generate holographic images.^35,36 However, data-driven models of inverse problems remain largely unsolved in terms of efficiency and functionality, especially in the context of megapixel-resolution acoustic metasurface-based holography. For example, simultaneous control of amplitude and phase is rarely studied in DL-based models.³⁷ Other inverse design approaches are also inefficient and fail to achieve rapid design of large numbers of elements with target responses.

On the other hand, the potential of metasurface-based holography has not yet been fully realized. In general, information loss during reconstruction is mainly caused by limited metasurface size, sound field discretization, and diffraction limit. If the metasurface is not large enough, the image quality may suffer due to imperfect information. When the holographic data is discretized, the holographic image is inevitably suboptimal compared to the holographic image from continuous data. Additionally, the inherent diffraction limit can limit the resulting image resolution. To facilitate the application of metasurface-based holograms, the ability to rapidly construct unit cells using a unique PAM and compensate for information loss during metasurface design is desired.

In this paper, we propose a DL-based high-definition acoustic metasurface optimization method for achieving high-quality holographic reconstruction. The power of this approach is demonstrated by megapixel images showing that deep neural network (DNN) techniques combined with genetic algorithms (GA) can accelerate the convergence of element inverse design. This enables him to design millions of highly customized elements using PAM’s high precision in a matter of hours. The element topology exhibits dual anisotropic features that can accommodate fully controllable phase and amplitude requirements.³⁸ An iterative algorithm for phase-amplitude distribution optimization was developed to more efficiently use millions of bi-anisotropic elements. Several demonstrations are shown to show how DL can assist in the rapid custom design of acoustic metasurface-based holograms. In addition to the aforementioned hologram of his QR code image showing how the number of pixels affects the performance of the hologram, to discuss the appropriate spatial relationship between the hologram and the image, the Tianjin University logo A design for imaging is also presented (include. focal length, metasurface size and resolution). Finally, a 2000 × 2000 metasurface-based hologram for a high-quality megapixel image of the Mona Lisa portrait was designed by the proposed method and the Mona Lisa portrait reconstructed by the three-dimensional (3D) printed metasurface. are experimentally demonstrated.