Introduction

Ultrasound can deliver high energy remotely by penetrating diverse materials. Creating high-resolution dynamic acoustic fields can lead to transformative opportunities for many applications, including acoustic tweezer1,2,3,4, sonodynamic therapy5,6, and nerve stimulation7. Achieving this goal requires materials/devices that can modulate acoustic waves with a high energy efficiency. Current acoustic metamaterials for wave modulation rely on tuning the medium’s effective density or modulus through architectural8,9 or composite designs10,11. Dynamically altering the architectures and the components of the metamaterial is difficult, especially when high resolution is simultaneously required. In addition, the sharp interfaces between the different components lead to significant acoustic attenuation12, prohibiting energy transmission. Traditional ultrasonic phased arrays enable dynamic control of acoustic fields, but they require bulky equipment and have a spatial resolution below 10 pixels/cm2 due to the hardware constraints3,13. Conversely, high modulation resolution can be achieved with 3D-printed acoustic holograms, but the created acoustic fields are static14,15. Approaches that leverage mechanical16,17,18,19,20 and magnetic21 controls have been attempted to create dynamic acoustic fields. However, the addressable pixel for these holograms is typically tens of square millimetres due to the limitations of the element fabrication and control, which significantly restricts the resolution of the reconstructed acoustic field. An elegant approach utilises electrochemically generated microbubbles via a semiconductor chip to locally block the acoustic wave as a way to generate dynamic acoustic holograms22,23. Although acoustic field refreshing is feasible, the mechanical bubble removal limits its refreshing rate to 1 fps. In addition, the approach relies on amplitude modulation through the interfacial impedance mismatch between the air and the surrounding medium, which intrinsically restricts its acoustic transmission efficiency. To this end, approaches employing multiplexed phase hologram were developed to dynamically reconfigure acoustic fields by either modifying the incident waves (e.g. frequency24 or orbital angular momentum25) or altering the sound speed of the medium26. However, the range of generated acoustic fields is still highly limited with the fixed hologram.

In principle, manipulating the phase profile is more attractive than manipulating the amplitude for designing acoustic holograms as it does not encounter energy loss. Acoustic waves can alter their phase as they pass through materials with different characteristics12,27. We deduce that this can present a unique opportunity for creating reconfigurable acoustic holograms utilising a polymer for which a modulus pattern can be reversibly created. The challenge lies in designing such a material with its modulus dynamically switchable yet sufficiently stable when needed. Most importantly, the material must maintain high acoustic transparency throughout the process.

Here, we report the reconfigurable dynamic acoustic holography utilising a semi-crystalline polymer for which any arbitrary acoustic phase profiles can be repeatedly encoded by laser-assisted modulus patterning (Fig. 1). Opposite to current composite metamaterials, our polymer not only is acoustically programmable but also exhibits high acoustic transparency ( > 83%) despite the coexistence of amorphous and crystalline phases. By combining our metamaterial with a partitioned piezoelectric transducer (PZT), the device allows generating dynamic acoustic fields with a high modulation resolution of 10,000 pixels/cm2 at an ultra-fast refreshing rate of 50,000 fps. These attributes result in an unprecedented opportunity to create real-time acoustic movies, suggesting many possibilities for the future.

Fig. 1: Reconfigurable dynamic acoustic holography realised with a programmable semi-crystalline polymer film and a partitioned piezoelectric transducer (PZT).
figure 1

At Step 1, target dynamic acoustic holography is optimised to simultaneously control the partitioned PZT and polymer. The semi-crystalline polymer film is laser rewritten for acoustic phase modulation, and the partitioned PZT is electrically programmed for acoustic fields multiplexing. When the semi-crystalline polymer film is projected with a laser beam in (i.), it shows that the phase profile ϕ of the transmission acoustic wave is changing from 0 to π. Further, the laser programmed polymer film is gradually recovering to its crystalline state in (ii.) and (iii.). Following the same procedure, the semi-crystalline polymer, together with the partitioned PZT, can be reprogramed (Step 2) to yield different scenarios of dynamic acoustic holography (Step 3).

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Results

Acoustically transparent and programmable semi-crystalline polymer

Amorphous and semi-crystalline polymers are potential candidates as they can reversibly alter their moduli upon heating or cooling across their thermal transition temperatures. However, for an amorphous polymer, its high-temperature modulus cannot be stabilised without continuous heating. By contrast, the high-temperature modulus of a semi-crystalline polymer can remain stable for a certain period even after cooling, due to the hysteresis of the crystallisation process28. In principle, this can open up an opportunity to create dynamically switchable yet stable modulus patterns. The dilemma is that a semi-crystalline polymer generally consists of two phases (an amorphous phase and a crystalline phase), much like a composite. For currently known composite metamaterials, an incident acoustic wave is reflected when it encounters the sharp interface between the two components (Fig. 2a), resulting in multiple scattering and significant loss in the transmitted energy29,30, contrary to our goal.

Fig. 2: Programming the modulus and sound velocity of the PCL film.
figure 2

a Schematic illustration of the role of interfaces in controlling sound propagation. b Sound velocity and transmission efficiency of the PCL film upon temperature sweep. c Localised melting of the crystalline PCL film via laser heating, with grey and black colours denoting the crystalline and melt states, respectively. d The reversible sound velocity change during the repeated laser ON-OFF cycling, with the PCL film immersed in water fixed at 20 °C. The blue regions are the hysteretic process of the PCL, with the low-speed can be maintained for about 3 minutes e Surface topography showing the resolution of the laser writing, measured by an interferometer (see details in Supplementary Note 3). f Photographs showing the reconfigurability of the modulus pattern by altering the laser writing path.

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Our semi-crystalline polymer is a crosslinked poly(ε-caprolactone) (PCL) containing a photo-thermal dye (Sudan Black, 1.5%). The chemical structure of the PCL network is optimised to ensure a stable crystalline state at ambient temperature yet can be quickly melted upon laser writing (Supplementary Note 1). Unlike classical acoustic metamaterials, our semi-crystalline polymer in its crystalline state is acoustically transparent with transmittance higher than 75% across a broadband from 0.9 MHz to 140 MHz (Supplementary Fig. 1), despite the coexistence of the amorphous and crystalline phases. For comparison, a polymer composite, even at a low particle loading of 5.0 vol% tungsten, has drastically lower energy transmittance, especially at frequencies above 10 MHz (Supplementary Fig. 1). Our semi-crystalline polymer has a crystallinity of 30.9%, which can be viewed as a composite with 30.9 vol% of rigid crystalline fillers in its amorphous matrix. The fact that it can maintain broadband high acoustic transparency even at such a high “filler” loading is therefore unexpected. We attribute this to the unique gradient interface, that is, an interfacial gradient amorphous layer exists and acts as a bridge between the rigid crystalline phase and the soft amorphous phase31,32,33,34,35,36. With this gradient interface37,38, waves can transmit directly through the rigid crystalline particles, resulting in minimum energy loss regardless of the sound frequency (Fig. 2a). The surprising acoustic transparency, especially for high frequencies, makes it particularly useful for high resolution detection/stimulation.

We focus hereafter on a frequency of 2.25 MHz, at which the acoustic transmissions of the PCL in both its crystalline and amorphous states exceed 83% (Fig. 2b). This ensures the high transparency required for designing high-performance acoustic holograms. The measured sound velocity of our PCL changes from 1880 m/s in its crystalline to 1520 m/s in its amorphous states (Fig. 2b and Supplementary Fig. 2), consistent with the prediction using the equivalent medium theory. With the sound velocity, the calculated PCL film thickness required for binary phase modulation (π phase difference) between the crystalline and melt states under 2.25 MHz is determined as 1.75 mm, which is used in this study. However, it is worth noting that other frequencies beyond 2.25 MHz would also be applicable by varying the thickness of PCL film (see details in Supplementary Note 2).

When illuminated by a focused infrared-laser beam (1064 nm, 20 W, beam size: 80 μm), the photo-thermal effect induces localised melting of the PCL film. As the laser scans across the PCL surface at a speed of 60 mm/s, an initial modulus pattern is created (Fig. 2c). During this process, as the laser moves away from a scanned spot, the PCL undergoes natural cooling. However, polymer crystallisation is a hysteretic process, namely, the melt state can persist for a certain period before crystallisation occurs upon natural cooling. As shown in Fig. 2d, the sound velocity is rapidly reduced when the laser is on. As the laser is moved away, however, the sound velocity does not immediately change. Instead, the sound velocity remained at its reduced level for at least 3 minutes (the light blue regions in Fig. 2d) before ascending to reach the equilibrium high velocity. This is critical as it allows creating a stable modulus pattern through repeated rewriting along the same path. An optimal laser rewriting speed of 150 mm/s was chosen to ensure the stability of the modulus pattern without compromising the resolution. The resolution of the modulus pattern (Fig. 2e), which corresponds to the acoustic modulation resolution, is 100 µm or 10,000 pixels/cm2. This resolution is primarily limited by the laser beam size (80 µm), with minor heat diffusion occurring beyond the laser spots. Under these conditions, the modulus pattern can be well maintained for as long as needed (Supplementary Note 4). By contrast, if sufficient time is allowed for the crystallisation of the entire sample, the modulus pattern is erased, and a new modulus pattern can be created (Fig. 2f) with a different laser writing path. This enables repeatedly programming and reprogramming the modulus pattern in an on-demand manner.

Reconfigurable acoustic holography

Figure 3a illustrates the steps for generating a PCL-based acoustic phase hologram. For an exemplary target acoustic ring image, an iterative angular spectrum approach (IASA)14 is employed to design the binary phase profile for acoustic wave modulation. Experimentally, the modulus pattern corresponding to this phase profile is encoded onto a PCL film immersed in ambient water, which enables the successful reconstruction of the target acoustic ring. More specifically, as an incident plane wave emitted by an acoustic transducer penetrates through the patterned PCL film, the transmitted wavefront is spatially modulated to the desired phase distribution via interference. When propagating forward, an acoustic field is constructed at a target plane due to acoustic interference, exhibiting maximal pressures at specific locations consistent with the original ring (Fig. 3b). The acoustic transmission phase delay between the crystalline domain and amorphous domain exactly matches π, which is key to the PCL-based binary phase modulation (Supplementary Note 5). The acoustic pressure distribution (Supplementary Note 6) can be further reflected as a ripple pattern on water surface to directly visualise the acoustic field.

Fig. 3: Design principle of reconfigurable acoustic holography.
figure 3

a Process for generating an acoustic phase hologram, and the binary mechanism for modulating the acoustic wave. A phase delay of π occurs between the transmission wave when propagating through crystalline and amorphous PCL. b Simulated results showing the evolution of acoustic interference along the wave propagation path. c Modulus patterns rewritten on the same PCL film. d Simulated and experimental ripple patterns based on the reconstructed acoustic fields. The distance between the target plane and the PCL film was fixed at 20 mm. All the scale bars are 10 mm.

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Unless otherwise specified, we use surface ripple patterns hereafter for visualising the acoustic fields. Accordingly, a generated acoustic pattern can be well maintained for at least 9 hours as long as laser is scanned continuously along the same path (Supplementary Fig. 3). By contrast, when reprogramming is desired, the modulus pattern is erased by natural cooling and a new modulus pattern is created by laser rewriting on the same PCL film (Fig. 3c). This allows reconstruction of different arbitrary acoustic fields (Fig. 3d) consistent with the simulated results (details of the simulation are provided in Supplementary Note 7). A movie capturing real-time reconfiguration of the acoustic field is provided in Supplementary Movie 1.

Dynamic acoustic holography with partitioned PZT

Although Fig. 3d shows the feasibility of creating dynamic acoustic holography, the refreshing rate is inherently limited by the natural cooling time (around 13 min) required for a full heating/cooling cycle (Supplementary Note 8). To achieve an ultra-high refreshing rate, we resort to use partitioned PZT, which allows switching the amplitude of the transducer sources between 0 (OFF) and 1 (ON) with an electrically controlled field-programmable gate array. The device enables operating an 8×8 source array within a highly compact setup (see Supplementary Fig. 4). Then, the source setup is coupled with the programmable PCL via an optically transparent acoustic reflector to form an integrated acousto-optic system (Supplementary Fig. 5). The entire setup provides unprecedented flexibility in manipulating the phase of an acoustic field at a high spatial resolution and refreshing rate. To facilitate this, we also developed an algorithm that converts a target acoustic field into desired binary phase maps using a deep learning-assisted neural network approach (see Methods, Supplementary Fig. 6, Supplementary Notes 9 and 10), which determines both the modulus pattern of the PCL film and the switch matrix of the partitioned PZT (Fig. 4a).

Fig. 4: Dynamic acoustic holography controlled by partitioned PZT.
figure 4

a Schematic illustration of the realisation of a complex-amplitude acoustic holography via the combination of the partitioned PZT and the modulus pattern, which controls the amplitude and phase profiles, respectively. b ON-OFF state of the switch matrices, simulated acoustic fields, and the experimentally displayed ripple patterns demonstrating real-time control of various digital numbers. The modulus pattern remains unchanged throughout the process. c Design process for an acoustic movie depicting a flying bird (Step 1), in which the modulus pattern of PCL film was optically reprogrammed (Step 2). d Switch matrices, simulated acoustic fields, and ripple patterns of the bird with different gestures. The distance between the target plane and the PCL film was fixed at 15 mm. All the scale bars are 10 mm.

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With the aforementioned hardware and algorithm, we proceed to illustrate the holographic display of acoustic 7-segments (Supplementary Note 11). Using the optimised modulus pattern, Fig. 4b shows the dynamic evolution of the acoustic field by electrically controlling the switch matrix of the partitioned PZT. The corresponding live actions are provided in Supplementary Movie 2. Beyond the digit numbers, it is also feasible to switch between more complex acoustic images. At the design level, electrical switching of the partitioned PZT companied with a specific merged phase/modulus pattern enables generating consecutive images of a bird (Fig. 4c and Supplementary Note 12). This is experimentally realised in Fig. 4d, showing the rapid switching of ripple patterns mimicking closely the wing flapping of a flying bird. An acoustic movie showing the real-time bird flying at different speeds is provided in Supplementary Movie 3, highlighting the versatility of our dynamic acoustic holography. Here, the refreshing rate of our device is mainly determined by the electrical-switching rate of the partitioned PZT, which operates at the nanosecond scale. Indeed, we show experimentally a maximal achievable refreshing rate of 50,000 fps by monitoring rapid switching of two focal points on water surface (Supplementary Fig. 7 and Supplementary Movie 4). This corresponds to a response time of 20 µs, mainly limited by the recovery time of the water surface ripple. We note that the distance between the acoustic plane and the PCL film hologram in Fig. 4 is 15 mm whereas it is 20 mm in Fig. 3. This suggests that, in addition to controlling the acoustic field as desired, the distance can also be designated on demand.

Potential applications of reconfigurable dynamic acoustic holography

Our ability to generate high-resolution dynamic acoustic holography without compromising its acoustic energy can lead to many opportunities for engineering/medical applications. To demonstrate this, we focus on two exemplary cases that explore remote delivery of localised mechanical forces and thermal energy, respectively. In the first case, the partitioned PZT is in an all-ON state, and we illustrate the remote manipulation of micro-particles via acoustic mechanical forces generated solely by phase modulation. Micro-particles (polydimethylsiloxane, 10-250 µm) with positive acoustic contrast were initially suspended in water. Further, when the micro-particles were exposed to an acoustic field (Fig. 5a), the acoustic radiation force pushed them towards regions of high acoustic pressure, which can be theoretically calculated from the acoustic field distribution (Supplementary Fig. 8). Experimentally, the modulus pattern of PCL film can be repeatedly reprogrammed to generate drastically different yet designable acoustic radiation forces that enable precise control of particle trapping (Fig. 5b). A video showing the live capture of micro-particles is provided in Supplementary Movie 5. We emphasise that the above results were obtained in an optically opaque environment, with a black film blocking light penetration from the wave-side (Fig. 5a). This highlights the unique penetration capability of acoustic tweezers beyond optical counterpart, which can only operate under optically transparent conditions.

Fig. 5: Illustration of potential applications of dynamic acoustic holography.
figure 5

a Schematic illustration of particle trapping, where trapped particles are patterned along the upper window of the cavity under the effect of the acoustic radiation force FARF, gravity force FG and Buoyancy force FB. b Repeated particle trapping into distinct patterns using PCL film with different reprogrammed modulus patterns. c Schematic illustration of remote acoustic heat writing through a biological tissue via dynamic acoustic holography, with the yellow region is the heating trajectory. d Schematic of the experimental setup for remote acoustic heating. e Acoustic heating efficiency as the wave penetrates through the biological tissue (10 mm thick beef steak). f Snapshots of the thermal images captured by an infrared camera, showing real-time heat writing of a “Z” letter by switching the partitioned PZT. The distance between the target plane and the PCL film is fixed at 12 mm. All the scale bars are 10 mm.

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In the second case, we demonstrate real-time acoustic heating via remote penetration of biological tissues. As schematically illustrated in Fig. 5c, after phase-modulated by the patterned PCL film, the acoustic wave can further penetrate through the biological tissue. This allows generating thermal heating at specific locations. By sequentially altering the switch matrices applied to the partitioned PZT, the heating path can be real-time controlled to follow a designated route, effectively achieving an acoustic heat-writing effect. This is experimentally verified with the setup illustrated in Fig. 5d. As depicted in Fig. 5e, the acoustic energy was concentrated at the focal spot on a thermo-chromic sheet after passing through the tissue, inducing a temperature rise of 21 °C within 10 seconds. The high heating efficiency is attributed to our acoustic modulation method that mechanistically incurs trivial energy loss through the acoustically transparent PCL film. By electrically controlling the partitioned PZT at a desired refreshing rate, the images in Fig. 5f show sequential heat writing, with the real-time heating path following the writing order of the ‘Z’ letter as captured in Supplementary Movie 6. By changing the modulus pattern and switch matrices, drastically different heat-writing paths can be yet generated (Supplementary Fig. 9).

Discussion

Our freedom and flexibility to control acoustic fields offer unusual benefits for many future applications that require remote, real-time and lossless delivery of energies through biological or other soft barriers. In particular, the unique penetration capability surpasses other physical systems, such as optical tweezers, which can only work in an optically transparent environment. The spatial resolution and precision it offers may open up opportunities in various fields, including microfluidics39,40, micro-assembly6,41,42, 3D-printing43, tissue engineering44 and medical treatments (e.g. tumour therapy2,3,4,7 and deep brain stimulation45,46). The two key components, the programmable polymer film and the partitioned PZT, can be integrated into a highly compact system. However, the laser scanning system is relatively bulky and not easily integrated into the same package. Meanwhile, the laser scanning-based thermal writing is relatively inefficient for modulus patterning. This restriction could be addressed by exploiting advanced and non-volatile programmable materials, such as slow crystallising polymers, which are capable of one-step patterning with structured light projection or electrical heating and therefore greatly facilitate the practical applications. On a broader basis, the discovery of acoustic transparency in the programmable polymer, especially the role of the gradient interfaces, inspires future work on developing smart materials for unique acoustic applications.

Methods

Materials

Ethylene glycol, ε-caprolactone (ε-CL), and pentaerythritol tetra(3-mercaptopropionate) (PTME) were received from TCI. 2-isocyanate ethyl acrylate was acquired from Bide Pharmatech. Stannous octanoate was obtained from Aladdin. Dibutyltin dilaurate (DBTDL), 2,2-dimethoxy-2-phenylacetophenone (DMPA), and Sudan Black were purchased from Macklin. Polydimethylsiloxane (PDMS) particles were synthesised from suspension polymerisation of Sylgard 184 (Dow Corning) with a 1:10 ratio of the curing agent and the base in water containing 1 wt% Pluronic F-127 under 8000 rpm, vigorously stirring at 50 °C for 6 hours. The particles sifted by a 100-mesh screen were used for the acoustic trapping. All chemicals were used as received.

Synthesis of polycaprolactone (PCL) and PCL diacrylate (PCLDA)

PCL was synthesised through the ring-opening polymerisation of ε-CL47. Its molecular weight (Mn = 2000, 5000, and 10000) was controlled by varying the molar ratio between ε-CL and ethylene glycol (initiator). To synthesise PCLDA, weighted PCL and 2-isocyanatoethyl acrylate (molar ratio = 1:2.1) were dissolved in toluene. After DBTDL (catalyst, 1%) was added, the mixture was maintained at 80 °C for 6 hours. White powders were obtained after participating in methanol, followed by vacuum drying at room temperature overnight.

Synthesis of crosslinked PCL film

Weighted PCLDA and PTME (crosslinker) at a stoichiometric balance between the acrylate and the thiol groups and 1% DMPA (photo-initiator) were dissolved in dimethylformamide to form a 47% solution. After degassing, the precursor was poured into a glass cell sandwiched with a PDMS spacer (thickness: 2.1 mm) between two glass slides. After UV exposed (Uvitron Intelliray 600, 66 mW/cm2, 265-700 nm) for 180 seconds, the obtained film was soaked in 1.5% DMF solution of Sudan Black (the photothermal agent) for 24 hours. After vacuum dried at 80 °C overnight, a PCL film with approximately 3% Sudan Black and a thickness of 1.75 mm was obtained.

Acoustic hologram generated via laser writing

Laser scanning was performed on the crystalline PCL film using a focused infrared-beam (1064 nm, 20 W, beam spot: 80 μm) from a laser marking machine (GH-SMART, HUAGONG, China). The laser scanning path was controlled by a PC according to the designed binary phase pattern (.DWG file) derived from the target acoustic image. Given that the thermal heat required for maintaining the PCL modulus was significantly lower than that needed for PCL melting, a hybrid laser scanning strategy was proposed for stable acoustic hologram generation. This strategy involved slow-speed laser writing (60 mm/s) to generate the initial modulus pattern, followed by fast-speed laser writing (150 mm/s) to maintain the modulus pattern over extended periods.

Integration of the acousto-optic system

An 8 × 8 partitioned piezoelectric transducer (PZT) was fabricated following traditional process of electron deposition, coupling layer deposition, assembling, backing layer filling, and wiring. A piezoelectric sheet was pre-treated with the deposition of electrons on one side (2 MHz, 50 × 50 × 1 mm3). The sheet was then divided into a square array with 6×6 mm2 elements which were wired with a flexible circuit board. Next, the integrated acousto-optic system was built by assembling the partitioned PZT and PCL film. The incident plane wave generated by the partitioned PZT propagated to the PCL film, which was simultaneously irradiated by a laser beam for modulus patterning and maintenance. The partitioned PZT is electrically-controlled by the field programmable gate array (STM32F407 series, ST, Italy). The sinusoidal signal (2.25 MHz, 15 V peak to peak) from the signal generator (CST-8077PR, Keysight, USA) and the power amplifier (ATA-1372A, Aigtek, China) was fed to excite the transducer. Next, the control circuit was connected to the PC and power supply (QJ3005N, Qiujing, CHINA) for switching the incident wavefront and powering, respectively.

Characterisations

Melting transition temperatures were determined using a differential scanning calorimetry (DSC Q200, TA Instruments, USA) with a ramping rate of 3 °C min-1. Dependence of the modulus on temperature was tested using a dynamic mechanical analyser (DMA Q800, TA Instruments, USA), with a ramping rate of 1 °C min-1 and frequency of 1 Hz. The size of PDMS particles was measured using a laser particle analyser (LS13320, Beckman Coulter, USA, size range of 0.017–2000 μm). The surface morphology originated from laser writing was measured using an optical profilometer (NT9100, Veeco, USA).

Crystallinity measurements

The crystallinity of the PCL films (10 × 20 × 1.8 mm3) was measured using the in-suit X-Ray Diffractometer (In-suit XRD, D8 ADVANCE, Bruker, USA) between −20 °C and 95 °C. The temperature interval was set as 5 °C from 40 °C and 65 °C and 10 °C for the rest. During the measurements, the PCL films with different molecular weight (Mn = 2000, 5000, and 10000) were heated to a target temperature, which was then stabilised for 2 min before performing the X-ray scanning. Thereafter, the X-ray beam was scanned from 10° to 60° with a step size of 0.12 ° s-1, with the temperature maintained during the whole process. After that, the temperature was raised for next measurement until the end.

Acoustic property measurements

An immersion ultrasonic testing system was utilised to simultaneously measure the sound velocity and transmission efficiency of the PCL film. The testing system consists of an ultrasonic transducer (V328-SU15MHz, V390-SU50MHz, V3346-SU100MHz, Olympus, Japan), which generate incident ultrasonic waves onto the PCL film and capture the reflected echo waves. The system was immersed in a water tank set at temperatures between 10 °C and 65 °C. A sinusoidal pulse signal was input to the exciting transducer from the signal generator (5900PR, Olympus, Japan). The transmitted and reflected ultrasonic waves were received by the transducers and recorded with an oscilloscope (MS07032B, Keysight, USA).

Acoustic fields measurements

The acoustic field distribution was reconstructed by scanning a hydrophone (NH1000, Precise Acoustic, UK) fixed on a 6-DOF robotic arm (IRB1200, ABB, Switzerland). The hydrophone was raster scanned across the image plane, and the acoustic pressure was recorded at each point.

Finite-element simulation

Finite-element analysis was performed using COMSOL Multiphysics 5.5TM to simulate modulus pattern-based acoustic phase modulation with the Acoustic-Structure Multiphysics module in the frequency domain. Specific material properties, including density, Poisson’s ratio and Young’s modulus, were assigned to both the crystalline PCL and melted PCL elements.

Derivation of binary amplitude and phase modulus patterns

A deep learning-based iterative angular spectrum approach (DL-based IASA) was developed to simultaneously optimise the incident wavefront and the phase modulation pattern. The proposed algorithm is composed of two steps, namely the physical-assisted neural network (PANN) and the multiplane IASA. Firstly, the 8×8 binary amplitudes Ai (i = 1, 2, …, n) at the transducer plane were optimised in accordance with multi-frame images Ii (i = 1, 2, …, n) based on the deep-learning network and acoustic propagating model. Then, the merged binary phase ϕ at the hologram plane was computed using the multi-plane IASA. The computation involved propagating the incident wavefront with amplitude profile Ai from the transducer plane to the image plane and back. The binary phase profile ϕ was iteratively optimised until the respective acoustic fields converged to the target images Ii. The constraints for each plane were defined as follows. At the transducer plane, the plane incident wave was assumed to be unity in amplitude and zero in phase. At the hologram plane, the amplitude coefficients of the PCL film at its melting and crystalline states were set as 1 and 1.1, respectively.

For clarity, the specific designing steps for the amplitude profiles Ai and the merged phase profile ϕ are outlined as follows:

Step 1: Optimisation of incident plane wavefront via PANN48

Firstly, U-Net + + was chosen as the generating network model with a depth of five layers. Then, a random noise image was input to yield optimised Ai and ϕ. During each iteration, the acoustic fields Ii (i = 1, 2, …, n) at the image plane were reconstructed using the optimised Ai and ϕ via an angular spectrum approach. Therefore, mean square error (MSE) was calculated to assess the error between the reconstructed fields Ii and the target fields \({\bar{{{{\bf{I}}}}}}_{i}\). The loss function was obtained as \({{{{\mathcal{l}}}}}_{{{{\rm{loss}}}}}={\sum }_{i={{\mathrm{1,2}}},\cdots,n}{{{\rm{MSE}}}}\left({{{{\bf{I}}}}}_{i},{\bar{{{{\bf{I}}}}}}_{i}\right)\), and the Adam optimiser was adopted to minimise the \({{{{\mathcal{l}}}}}_{{{{\rm{loss}}}}}\) to derive the amplitude profiles Ai and the merged phase profile ϕ'. Notably, the phase profile ϕ' was continuous at this stage, and the optimised amplitude profiles at the transducer plane were average pooled to 8 × 8 matrices to match the array size of partitioned PZT transducer (see Supplementary Note 9 for more details).

Step 2: Calculation of merged phase profile via multi-plane IASA

The merged binary phase profile ϕ for the PCL film was further calculated by considering the conjugation of the multiplexed incident waves during the forward- and backward-propagations. Herein, the amplitude profiles Ai optimised in Step 1 were assumed as a fixed condition at the transducer plane, and therefore the acoustic fileds at the hologram plane can be calculated as \({{{{\bf{I}}}}}_{b(i)}^{{\prime} }={{{{\bf{A}}}}}_{i}{e}^{{{{\rm{j}}}}{{{\bf{k}}}}D}\). Meanwhile, the optimised phase profile ϕ' from Step 1 was set as the initial condition for the iterative calculation of the binary phase profile ϕ. During each iteration, the acoustic fields at the image planes were calculated as \({{{{\bf{I}}}}}_{c(i)}^{{\prime} }={{{{\bf{A}}}}}_{i}{e}^{{{{\rm{j}}}}{{{\bf{k}}}}D+{{{\boldsymbol{\phi }}}}+{{{\rm{j}}}}{{{\bf{k}}}}d}\), which were then renewed as \({{{{\bf{I}}}}}_{c\left(i\right)}={{{{\bf{A}}}}}_{i}\) arg\(({{{{\bf{I}}}}}_{c(i)}^{{\prime} })\) by replacing the phase profile and backward-propagating to the hologram plane. Finally, the merged phase profile can be obtained by considering the fixed acoustic field \({{{{\bf{I}}}}}_{b(i)}^{{\prime} }\) at the phase modulation plane, as \({{{\mathbf{\phi }}}}=\,{{\arg }}\,\left({\sum }_{i={1,2},\ldots,{n}}{{{{\bf{I}}}}}_{c\left(i\right)}{e}^{-{{{\rm{j}}}}{{{\bf{k}}}}d}*\right.\) conj\(\left.({{{{\bf{I}}}}}_{b(i)}^{{\prime} })\right)\). In this step, the renewed phase profile ϕ was binarised in each iteration.