A 0.18 cubic centimeter 3D meta-holographic zoom micro-projector

Domain: physics
Published: 2025-11-28
Editorial outcome: major_revision

Abstract
Meta-holography has become a frontier hotspot of photonics, thanks to the rapid advancement of nanofabrication. Tunable meta-holography significantly enhances information capacity and meets the growing demands of adaptive imaging, offering tremendous application prospects in fields such as optical storage, augmented and virtual realities, and biology. However, the existing meta-holography predominantly relies on 2D projection, with a small and non-adjustable image size. Here, we propose a 3D meta-holographic zoom micro-projector by integrating a high-resolution metasurface with a tailored liquid lens, and the size of the demonstrated micro-projector is only 0.18 cm3. A 3D Fourier meta-hologram generation method is proposed, which overcomes the limitation of the traditional Fourier meta-hologram in realizing 3D projection. By proposing a small-sized zoom liquid lens, the projector achieves 3D zoom projection, with the size and projection distance of the meta-holographic image extending to the decimeter scale, a feat unattainable by previous meta-holographic projection. This flexible and miniaturized 3D fingertip zoom micro-projector is anticipated to have broad applications in portable and wearable devices as well as biomedical apparatus.

Introduction
Holographic projection can be used in the fields such as display, encryption and measurement, which has important research significance1–4. Lightweight and miniaturized zoom holographic projection has become a research hotspot in the field of holography because of its high application requirements5,6. For example, in holographic near-eye display, the volume and image size of holographic projection directly determine the quality of near-eye display equipment7,8. The traditional holographic projection uses spatial light modulator (SLM) to modulate the wavefront information, and uses the lens to focus the imaging, which directly leads to a huge and complex system. In addition, there is a contradiction between zoom and near-eye miniaturization. Zoom holographic projection needs to be realized by changing the relative positions between several lenses, which makes the system more bulky. Overcoming long-standing limitations, such as shallow depth, fixed focal length, small image size, and system complexity, has been widely regarded as a critical challenge.

Metamaterials are artificial composite materials that exhibit extraordinary physical properties not found in nature, achieved through the design of artificial micro-nanostructures. These materials have been recognized as one of the top ten scientific and technological advancements globally9–12. As a specialized class of metamaterials, metasurfaces are characterized by their planar structure, ultra-thinness, high resolution and flexible design freedom13–21. In 2015, researchers combined plasmic resonant metasurface with geometric phase and realized efficient 2D holographic projection using the Gerchberg-Saxton algorithm with a system including polarized optical devices22. In 2016, a holographic projection based on Huygens metasurface was demonstrated with operation spectral bandwidth of near-infrared light, and a 5 mm image was reconstructed at a distance of 10 mm23. Subsequently, a silicon-based nano-antenna with narrow-band response was designed, enabling color holographic projection using metasurface with monolithic geometric phase control24. In this design, three types of nanoblocks were reused within a subwavelength unit to form a metamolecule, enabling the simultaneous modulation of red, green, and blue light. The reconstruction system uses three lasers with different wavelengths, and the volume of the whole system is cubic decimeter level. In 2018, researchers utilized chemical methods to control the composition of metasurface structural units, achieving dual-channel controllable meta-holographic projection. However, the chemical treatment process is slow, leading to a long response time and making it difficult to meet the demands for rapid adjustment25. In 2024, a method for multi-channel meta-holographic projection based on polarization multiplexing mechanism was proposed26. Holographic images on different planes were projected at distances from 0.3 mm to 0.6 mm, respectively. Despite significant advancements in multi-functional meta-holographic projection, the existing methods predominantly achieve multi-channel display through multiplexing. In this approach, the number of projection layers depends on the specific design of the metasurface’s multi-channel configuration, which complicates 3D projection. More critically, the projector’s large size, along with the fixed and unadjustable distance and the small reconstructed image size, remains significant limitations of the technology.

The core of miniaturization zoom projector is to have ultra-thin wavefront control ability and the ability to dynamically change the focal length27–29. In recent years, zoom lenses have been extensively developed to enable adaptive adjustment of optical systems30–34. Among these, electrowetting-based liquid lenses have garnered significant attention due to their broad focal length adjustment range and rapid response speed35–39. By incorporating liquid lenses into holographic systems, researchers can swiftly obtain the depth information of 3D objects or adjust the viewing angle of holographic display40,41. However, in electrowetting-based liquid lenses, there is a complex trade-off among interfacial tension, response time, optical power, and stability. As the size of the liquid lens decreases, the influence of liquid-liquid interfacial tension on optical power and other properties becomes increasingly dominant, imposing higher demands on the liquid material used. Currently, the design and fabrication of compact electrowetting-based liquid lens with good performance is still challenging42.

Here, we propose a 3D meta-holographic zoom micro-projector, as shown in Fig. 1. By integrating a specially designed metasurface and a liquid lens into a single cavity, we have achieved the world’s smallest 3D zoom micro-projector with dimensions of 6.5mm × 6.5mm × 4.2mm. This demonstration represents a significant advancement in meta-holography for the following reasons. First, this approach effectively realizes a large-depth 3D meta-holographic projection. A 3D object is regarded as a series of 2D layers. By incorporating the fractional Fourier transform (FRFT) into meta-holographic coding, the rotation angle of the Wigner distribution function43 can be changed, thus the depth of each layer of the 3D object is characterized and calculated, and finally a phase meta-hologram containing the depth of the 3D object is generated. The limitation that traditional Fourier-algorithm-based meta-holography can only realize 2D projection has been broken. Second, the proposed micro-projection method addresses the zoom capacity issue in traditional meta-holography. An electrowetting liquid lens with a high optical power and a small effective optical aperture of 2mm has been developed to dynamically adjust the meta-holography. By formulating special liquid materials, the size and position of holographic images can be easily adjusted over a wider range by varying the driving voltage. As shown in Fig. 1c, when the driving voltage of the liquid lens is UI and UII, there are two different projection states, and the 3D scene is reconstructed in different positions with different sizes. Consequently, using the liquid lens and the designed metasurface, the projection distance of the meta-holographic image can reach decimeter level, and the size can achieve over 5cm × 5cm. Third, our experiments demonstrate multi-wavelength zoom meta-holography with the use of the wide-band response metasurface and liquid lens. The proposed meta-holographic zoom micro-projection method is expected to find massive applications, including high-security encryption, augmented and virtual realities, wearable and biomedical devices, and automotive displays.

Results
Structure of the proposed zoom micro-projector
The proposed meta-holography-based zoom micro-projector consists of a laser (not shown in Fig. 1a, b), a transmissive metasurface, and a specially designed electrowetting liquid lens, as shown in Fig. 1c. In the design process of the metasurface, a 3D Fourier meta-hologram generation method based on FRFT is proposed to generate the 3D meta-hologram, and then the 3D meta-hologram is encoded on the sub-wavelength structures. The liquid lens is positioned behind the metasurface. Unlike traditional liquid lenses, a lightweight electrowetting liquid lens with an effective optical aperture of 2mm is developed. This lens features an extremely compact cavity size, enabling fingertip micro-projection in conjunction with the metasurface. To achieve system miniaturization, the metasurface and liquid lens are integrated into a single cavity, as shown in Fig. 1a, b. When the laser irradiates the metasurface, the holographic diffraction image passes through the liquid lens. By changing the driving voltage of the liquid lens, 3D images can be projected at different positions, with their sizes adjustable as desired.

Design of the metasurface
Leveraging the simplicity and excellent performance of geometric phase in phase modulation, a metasurface with a resolution of 2500 × 2500 using Pancharatnam-Berry (PB) geometric phase44 is designed for the proposed meta-holography. Each unit cell of the metasurface consists of a rectangular monocrystalline silicon nanorod fabricated on a sapphire substrate. L, W, and H represent the length, width, and height of the monocrystalline silicon, respectively. p is the period, and θ is the rotation angle relative to the x-axis. By adjusting the rotation angles of the unit structures, a phase shift directly proportional to twice the rotation angle is achieved, with minimal impact on the magnitude.

Specifically, for rectangular nanorod structures with C2 symmetry, the PB phase shift value is directly proportional to twice the rotation angle10. This phase modulation method leverages the geometric nature of the PB phase, enabling precise control over the phase distribution without altering the physical dimensions of the structures. More importantly, the geometric phase is wavelength-independent, allowing this phase relationship to be universally applicable for different wavelengths.

Design of the liquid lens
The designed liquid lens consists of a transparent conductive liquid and an insulating liquid encapsulated between the upper and lower electrodes, as shown in Fig. 2a. Under the effect of interfacial tension, a liquid interface is formed between the conductive liquid and the insulating liquid. Based on the electrowetting effect, the contact angle of the conductive liquid can be changed with driving voltage, and the focal length control can be achieved through voltage control (Supplementary materials S1). To ensure that the liquid lens has a high ratio of optical aperture to mechanical diameter, a straight cylindrical cavity is designed to replace the typical sloping cavity. This design reduces the thickness of the liquid lens cavity, enhancing the compactness of the meta-holographic 3D zoom projector. Additionally, to guarantee a sufficient range of optical power variation and good stability, a biphasic liquid composed of a conductive liquid without aqueous solution and an insulating liquid with low surface tension is developed. So, the proposed liquid lens offers a wide operating voltage range and a great variation in optical power.

The compact liquid lens, with its high ratio of optical to mechanical aperture and substantial optical power variation range, is used to adjust the depth of the meta-holographic 3D zoom projection. By tuning the driving voltage of the liquid lens, the wetting properties of the conductive and insulating liquids vary accordingly, resulting in changes in the curvature of the liquid-liquid interface and the optical power. The optical power Φ of the liquid lens can be expressed as:

Φ = 1/2 * ((2γ12 cosθ0 + CU2)Δn) / (γ12 * D) (1)

where γ12 is the interfacial tension between the conductive and insulating liquids, θ0 is the initial contact angle when no voltage is applied, C is the total capacitance per unit area of the dielectric layer coated with a hydrophobic layer, U and D are the driving voltage and effective optical aperture of the liquid lens, respectively, and Δn is the refractive index difference of the conductive and insulating liquids. The focal length f of the liquid lens can be obtained from:

f_liquidlens = 1 / Φ (2)

Principle of the 3D Fourier meta-hologram generation method based on FRFT
In the metasurface design process, a 3D Fourier meta-hologram generation method based on FRFT is proposed, as shown in Fig. 2b. The 3D object is layered according to the depth information. The FRFT and inverse Fractional Fourier transform (IFRFT) are introduced into the algorithm, with iterative constraints added in the fractional domain and spatial domain, respectively, to obtain a convergent final phase distribution and generate a 3D meta-hologram. By encoding the 3D meta-hologram on the sub-wavelength structures, a metasurface is designed and fabricated.

Different from the traditional metasurface-based holographic algorithm, the proposed 3D Fourier transform algorithm achieves 3D meta-holographic reconstruction through a transformation order (noted as a) (Supplementary material S2). Meanwhile, the position and depth of the reconstructed images are closely related to the focal length of the liquid lens, enabling efficient 3D zoom projection by adjusting the driving voltage of the liquid lens.

In detail, the 3D object is stratified based on the depth information. For each layer, a random phase distribution is introduced to generate the initial complex amplitude distribution g(x, y; za) in the spatial domain. According to the depth cues, an appropriate transformation order a is selected and the complex amplitude distribution G(u, v; za) in the fractional domain is then obtained by using FRFT:

G(u, v; za) = Fa{g(x, y; za)} = ∫∫ g(x, y; za) × exp(j2π * (x^2 + y^2 + u^2 + v^2) * cos(aπ/2) - 2(xu + yv)) / (λf_a * sin(aπ/2)) dxdy (3)

where Fa represents the FRFT with transformation order a. (x, y) and (u, v) are the position coordinates of the light field in the spatial domain and fractional domain, respectively, za is the depth of each layer. j is the imaginary number, λ is the wavelength of the incident light, and fa is the arbitrary focal length, which is related to the transformation order a. Inferred from the rotation transformation of the Wigner function, fa can be expressed as follows:

fa = f * sin(aπ/2) (4)

where f is the selected normalized focal length in the calculation process.

When the transformation order a is set to 1, the arbitrary focal length fa equals the normalized focal length. It is evident that introducing the transformation order alters the rotation angle of the Wigner function, which is crucial for extending the light field from the spatial and frequency domains into the fractional domain. This approach breaks the limitation in traditional Fourier coding, where the diffraction distance is solely determined by the focal length. Subsequently, the fractional domain constraint is applied to the complex amplitude distribution G(u, v; za), with only the phase information retained:

φ(u, v; za) = G(u, v; za) / |G(u, v; za)| (5)

where |·| denotes taking the module, and φ(u, v; za) represents the phase distribution in the fractional domain, corresponding to the phase distribution on the holographic plane. To apply the constraints in the spatial domain, the IFRFT is employed to convert φ(u, v; za) into g'(x, y; za), which represent the spatial complex amplitude information prior to applying constrains:

g'(x, y; za) = Fa^-1{φ(u, v; za)} (6)

The complex amplitude distribution g1(x, y; za) in the spatial domain is then obtained by retaining the phase distribution and replacing the original amplitude information of the 3D object A(x, y; za):

g1(x, y; za) = A * g'(x, y; za) / |g'(x, y; za)| (7)

The first iteration of the loop is completed, and g1(x, y; za) serves as the input for the next loop. This process continues until the phase distribution in the fractional domain converges to the optimal distribution, culminating in the 3D meta-hologram. The final phase distribution T can be obtained by the following equation:

T(u, v; za) = angle(G(u, v; za)) (8)

where angle(·) represents the extraction of the phase information from the complex amplitude distribution. The phase information T represents the sum of the 3D meta-hologram is recorded as a matrix (n × n), where each element corresponds to a unit cell of the metasurface. The 3D meta-hologram is encoded onto the sub-wavelength structures, meaning the metasurface is designed based on the matrix T.

Fabrication and performance tests of the micro-projector
In the proposed meta-holography-based zoom micro-projector, a laser with the wavelength of 671 nm is used as the reconstruction light to irradiate the metasurface, as shown in Fig. 3a. The distance between the metasurface and the liquid lens is 2mm. A 3D object composed of the letters ‘N’ and ‘U’ is selected as the recorded object for the metasurface, with both letters having resolutions of 2500 × 2500. The proposed 3D Fourier meta-hologram generation method is employed to generate the 3D meta-hologram, with a normalized focal length f set to 10cm. The transformation orders for the letters ‘N’ and ‘U’ are set to 1 and 0.2, respectively. The pixel pitch is 0.35 µm, and the period (p), height (H), length (L), and width (W) of the nanorod are 350 nm, 600 nm, 160 nm, and 80 nm, respectively. The scanning electron microscopy (SEM) images of the fabricated sample are shown in Fig. 3c, d.

The liquid lens is positioned directly behind the metasurface for zoom projection, operating with an effective optical aperture of 2mm and a mechanical diameter of 5mm (Supplementary material S3). During assembly, the metasurface and the liquid lens are integrated into a cavity to form a projector, with overal dimension of 6.5mm × 6.5mm × 4.2mm, as shown in Fig. 3b. A highly integrated liquid lens controller was developed to drive the liquid lens. Experimental results show that when voltages of 0 V to 70 V are applied to the liquid lens, the corresponding optical power changes from −47.54 m−1 to 18.31 m−1, as shown in Fig. 3e. The testing results demonstrate that the liquid lens exhibits fast response characteristics. When voltage is applied, the optical power can be tuned within ~68ms, as shown in Fig. 3f, g, indicating the micro-projector can dynamically adjust the projection distance in a swift manner.

Holographic reconstruction
During the generation of 3D meta-hologram, the depth difference is determined by the transformation order a (Supplementary material S4). To validate the effectiveness of the 3D Fourier meta-hologram generation method, a 3D object composed of a ‘bird’ and ‘tree’ was recorded, with a resolution of 2500 × 2500. During the meta-hologram generation, the normalized focal length f was set to 10cm, and the transformation order for the ‘bird’ (a1) was set to 1. To explore the impact of transformation order a on the depth difference, the transformation order for the ‘tree’ (a2) was varied from 0.2 to 1.8, then the depth differences varied accordingly. The 3D reconstruction results with varied depth differences are simulated in Fig. 3h–k, in which the focused ‘bird’ and ‘tree’ are shown in blue and orange boxes, respectively. As a2 gradually approaches a1, the blurriness of the ‘tree’ decreases when the ‘bird’ is in focus. Conversely, the ‘bird’ becomes less blurred when the ‘tree’ is in focus. Therefore, for a 3D object, the depth differences between layers can be represented using different transformation orders.

To validate the 3D projection capability of the proposed meta-holography-based zoom micro-projector, the liquid lens was replaced by a solid lens in the experimental system. By moving the receiving screen forward and backward, the letters ‘U’ and ‘N’ were imaged at distances of 0.5cm and 10cm, respectively, consistent with the theoretical depth. As shown in Fig. 4a, when the letter ‘N’ is in focus, the letter ‘U’ appears blurred, and vice versa.

To evaluate the zoom projection performance of the proposed micro-projector, we compared the imaging results of the letter ‘N’ at different depth planes with and without driving voltage applied to the liquid lens, as shown in Fig. 4b. The first row shows the results without the driving voltage, where the letter ‘N’ appears blurred at depths of 6cm, 12cm, 18cm and 30cm. The second row presents the results with varied driving voltages applied, demonstrating that the letter ‘N’ can be clearly projected at different depths by adjusting the driving voltage of the liquid lens (Supplementary Video 1). The size of the projected image is positively correlated with the distance of the meta-holographic projection. The micro-projection’s throw ratio (TR), defined as the ratio of projection distance to image size, and the zoom ratio (ZR), defined as the size ratio of the projected image to the metasurface, are analyzed in Supplementary material S5. In addition, based on the parameters of our designed meta-hologram, the field of view of the meta-holographic micro-projection can reach 87.5° at the wavelength of 671 nm, which has obvious advantages in the existing 3D holographic technology.

Furthermore, the 3D zoom projection was also validated, as shown in Fig. 4c, d. When the focal length of the liquid lens is 15cm, the letter ‘N’ is projected at a depth plane of 15cm, while the letter ‘U’ is focused at a depth plane of 0.7cm. As the focal length of the liquid lens decreases, the projection distance becomes closer. As shown in Fig. 4d, when the focal length of the liquid lens is 7cm, the letter ‘N’ is projected at a depth plane of 7cm, while the letter ‘U’ is focused at a depth plane of 0.3cm. Results demonstrate that the proposed meta-holographic micro-projector can readily achieve 3D zoom projection by leveraging the zoom characteristics of liquid lens.

Most reported meta-holographic systems focus on light modulation and multi-channel holographic display based on the polarization selectivity of the metasurface. However, these systems typically achieve 3D reconstruction at a fixed depth, and the inclusion of additional lenses and other optical components complicates integration. An ideal meta-holographic 3D projection requires a continuous zoom function to access a broader depth range. Our proposed micro-projection method addresses this need by enabling continuous 3D zoom projection with a specially designed liquid lens. Additionally, the proposed 3D Fourier transform algorithm based on metasurface can achieve 3D projection without sacrificing other information like polarization and wavelength, allowing the proposed system to realize multi-functional display based on the polarization properties of the metasurface in the future. Table 1 compares the characteristics of the proposed micro-projector with those of state-of-the-art reported methods. The projected image of the liquid lens at its minimum focal length in the experiment was tested, and the minimum image size is 0.3cm, and the 3D depth is 6.7cm. Since the image size and depth are positively correlated with the focal length of the liquid lens, increasing the focal length will correspondingly enlarge the image size and 3D depth. In principle, the focal length of the liquid lens can reach infinity, but the projection energy will decrease accordingly when the focal length is too large. In the future, we will continue to explore the relationship between projection energy and distance.

Micro-projector for high-security encryption and large-capacity data storage
Metasurfaces, with their multidimensional control capabilities, offer unique advantages in optical encryption and data storage. By leveraging the flexible zoom feature of the designed liquid lens, the proposed meta-holography-based zoom micro-projector can conveniently control the size and depth of projection images, providing a novel approach for high-security encryption, as shown in Fig. 5b. Three messages ‘Help me’, ‘Thank you’, and ‘Stop’ for different users are encrypted into unique patterns ‘moon’, ‘heart’, and ‘thunder’ located at different depths with parameters a1, a2, and a3, respectively. A 3D meta-hologram with 2500 × 2500 resolution and 0.35 μm pixel pitch is generated by using the proposed 3D Fourier meta-hologram generation method, serving as encryption key I. Simultaneously, the corresponding driving voltages required to project each pattern clearly onto a screen at a fixed distance are pre-calculated based on their depth information, forming encryption Key II. As shown in Fig. 5b, when applying different driving voltages Un (decrypting from an) to the liquid lens, the corresponding patterns are clearly projected onto the receiving screen, with the patterns of other channels being blurred. Consequently, the three messages are successfully decrypted as ‘Help me’, ‘Thank you’, and ‘Stop’, respectively. Notably, successful decryption requires precise alignment of the screen distance, the meta-hologram structure, and the liquid lens driving voltage (Supplementary material S7). Compared to single encryption process, this way significantly enhances information security. Additionally, with a volume of just 0.18cm3, our proposed micro-projector offers greater portability and concealment for encryption.

Moreover, the meta-hologram is generated by the proposed 3D Fourier transform meta-hologram generation method, which effectively enables multi-plane 3D projection by adjusting the transformation order a. By setting different transformation orders, information can be stored across multiple plane channels, highlighting the potential of our micro-projector for large-capacity data storage. In the future, integrating polarization-controlled or wavelength-controlled structures could further expand data storage capacity.

Methods
Metasurface fabrication
The sample fabrication is performed using silicon on sapphire (SOS) material through a conventional electron beam lithography technique. Firstly, the substrate is cleaned with sequential immersion in N-Methyl-2-pyrrolidone, isopropyl alcohol, and deionized water. Next, a 100nm-thick layer of hydrogen silsesquioxane is deposited on the substrate via spin-coating, and subsequently baked on a hot plate at 100°C for one minute. To enhance the conductivity and reduce electron accumulation, a conductive adhesive layer (AR-PC 5092) is applied by spin-coating. The nano-brick structures are then patterned by electron beam exposure. Following exposure, the development process involves immersing the samples in a 2.38% NMD-3 solution for two minutes. Finally, the structures are transferred from the resist to the SOS material using inductively coupled plasma etching.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript reports an intriguing fingertip zoom micro-projector that integrates a metasurface hologram with a tailored liquid lens. The 3D zoom projection of holographic images can reach up to the decimetre scale. The liquid lens allows for the adjustment of the viewing angle of holographic images. This integration is expected tohave broad applications in portableand wearable devices and biomedical fields. Although I find the demonstrated wearable micro-project interesting and potentially applicable in biomedical contexts, the current manuscript lacks the conceptual novelty expected for a publication in Nature Communications. I have several majorconcerns regarding someclaims in thismanuscript:\n1. The authors claim the use of a 3D Fourier transform for the hologram calculation. However, Equations 3 and 6 suggest that they used 2D Fourier holography instead of 3D.\n2. Even though a 3D Fourier transform allows the consideration of the entire image space in 3D, the computational cost is orders of magnitude higher than that of a 2D Fourier transform. For instance, the authors only considered information from two planes with an image resolution of 2500 by 2500 by 2. Therefore, this is not true 3D holography but rather arepresentation with information from only two layers?\n3. It is unclear how the liquid lens works and adjusts image depth. The authors only presented a schematic design of the liquid lens chamber in Fig. 2a, but its functionality is not clearly explained. This integration with a metasurface hologram represents thekey innovation ofthispaper,yet it lacks essential information.\n4. Whatdoes \"dimensional information\" mean?\n5. Whyis optical power expressed in m^-1 in line279?\n6. Another major concern is the comparison of this approach with the state-of-the-art metasurface holograms. Table 1 does not include all relevant results. In particular, previous papers dealing with full-space light-field displays with large image sizes have notbeen included:\nNatureCommunications,DOI: 10.1038/s41467-022-32117-2\nNaturePhotonics,DOI: 10.1038/s41566-024-01450-x\n7. In the introduction, the manuscript states, \"By incorporating liquid lenses into holographic systems, researchers can swiftly obtain the depth information of 3D objects or adjust the viewing angle of holographic display [32-33].\" However, reference 33does notdeal with liquidlenses.", "reviewer_2": "In this manuscript authors report a miniaturized holographic zoom projector realized by developing a high resolution metasurface and a tailored liquid lens. 3D fractional Fourier transformation is used to calculate the optical field of 3D objects using layer based propagation method. Dimensions of the projector, excluding illumination source and optics, are 6.5 mm × 6.5 mm × 4.2 mm and dimensions of the projected image 5cm x 5cm. Experiments show that depth and size of reconstructed image can be adjusted by changing voltage supplied to the liquid lens. Authors need to address following points in the manuscript:\n1. In the title words “---fingertip zoom micro projector”, creates confusion therefore title should be revised to make it more informative.\n2. Please provide field of view (FOV) of the developed projector and how much FOV and zoom is desirable for the intended application.\n3. Authors demonstrated 3D effect by considering two layers. Please discuss how much object depth can be supported by this projector and it’s limitations, if any.\n4. In the text authors describe polarization engineering. It is important to describe it’s mathematical background and how this concept is actually used in the design and fabrication of the metasurfaces reported in this manuscript. Otherwise, it is just a simple statement, which is known in the literature. Also explain why preservation of polarization is important in this case.\n5. Authors claim “---our experiments demonstrate color meta-holography across different wavelengths” and “---color zoom meta-holography” but in actual the system create image of different color in different image plane. So this claim is not valid as in any single plane system will generate significant chromatic aberrations, which is unacceptable.\n6. It will be beneficial for the readers if authors can explain how their 3D field calculation is different from the well-known layer based CGH generation method.\n7. Generally, projectors are required to project dynamic images, so will a particular fabricated metasurface be suitable for updating the 3D images or each time a new metasurface is required. In this case the projector may not serve the purpose in many applications, for example, AR/VR displays.\n8. The application of “high-security encryption” is demonstrated through an SLM instead by using the metasurface. What is resolution, pixel pitch of SLM and how it is correlated with metasurfaces? Further, this example seems misfit in the manuscript.\nThus, the manuscript has demonstrated small sized zoom projection optics for monochromatic images but presently it is not suitable for color 3D images. Also, only static 3D images can be projected and not the 3D dynamic images, which are required for most of the applications including AR/VR displays."}, "author_response": "As detailed below, we have revised our manuscript in response to the reviewers’ comments. The original reviewers’ comments are shown in black color, whereas for ease of communication, our answers are provided in blue. Our revisions have also been marked in themain textand supplementary information files usingblue.\nReviewer#1\nThis manuscript reports an intriguing fingertip zoom micro-projector that integrates a\nmetasurface hologram with a tailored liquid lens. The 3D zoom projection of\nholographic images can reach up to the decimetre scale. The liquid lens allows for the\nadjustment of the viewing angle of holographic images. This integration is expected\ntohave broad applications in portableand wearable devices and biomedical fields.\nAlthough I find the demonstrated wearable micro-project interesting and\npotentially applicable in biomedical contexts, the current manuscript lacks the\nconceptual novelty expected for a publication in Nature Communications. I have\nseveral majorconcerns regarding someclaims in thismanuscript:\nResponse: We thank the reviewer for acknowledging the general interest and broad\napplication potential of our work. We also appreciate the constructive suggestions\nhighlighting areas for improvement.\nWe acknowledge that the original manuscript overemphasized the device-level\naspects, which may have diluted the core conceptional innovations. In response to the\nreview’s comments, we have re-structed and condensed the manuscript to more\nclearly articulate the novelty of our algorithm and methodology, and have revised the\ntitle accordingly. We have also reprocessed and experimentally validated the\nmeta-hologram used for encryption to further demonstrate the practical advantages of\nourproposed micro-projector.\nIn particular the following conceptual novelties have been highlighted in the\nrevised manuscript:\nMeta-holographic projection represents a frontier in information display.\nOvercoming long-standing limitations, such as shallow depth, fixed focal length,\nsmall image size and system complexity, has been widely regarded as a critical\nchallenge. Our work addresses these issues through the development of a highly\ncompact (0.18 cubic centimeter) 3D meta-holographic zoom micro-projector, with\nfourkey innovations:\n1) Volumetric meta-holography via fractional Fourier transform. We treat a 3D\nobject as a sequence of 2D layers, each encoded using the fractional Fourier\ntransform. This enables accurate depth encoding across the object volume,\nsurpassing theshallowreconstruction depth ofFourier-based holography.\n2) Zoom capability through electrowetting liquid lens integration. We introduce a\ncompact, high-optical-power liquid lens (2 mm in aperture) with voltage-tuned\nliquid formulation, achieving dynamic and wide-range modulation of image\nsize and position. This allows projection distances at decimeter scale and\nimage sizes exceeding 5 × 5 cm² - approximately two orders of magnitude\nlarger than thestate-of-the-art.\n3) World’s smallest zoom meta-holographic projector. By monolithically\nintegrating the metasurface and liquid lens, we achieve 3D projection with\nzoom function in an ultra-compact form factor (~0.18 cm³), which, to our\nknowledge, has never been achieved before.\n4) Validated application potential. We performed new experiment to demonstrate\nhigh-security holographic encryption, and highlight the broad applicability in\nAR/VR,biomedical devices, wearables, and automotivedisplays.\nBased onthe reviewer’s suggestion, we have conducted comprehensive revisions,\nsupplemented additional experiments, and clairfied and innovated the concepts. We\nhopetherevised manuscript canaddress theconcerns ofthereviewer.\n1. The authors claim the use of a 3D Fourier transform for the hologram calculation.\nHowever, Equations 3 and 6 suggest that they used 2D Fourier holography instead of\n3D.\nResponse: Thanks for the reviewer’s valuable suggestion. We apologize for the\nunclear expression. In the initial submission, considering the length limit of the\nmanuscript, we simplified the explanation of the algorithm, which unfortunately\nresulted in anincomplete explanationofthe process ofthe3Dholography.\nTo clarify, our method performs layered processing to compute the hologram of\nthe 3D object. The object is decomposed into a series of 2D layers, each located at a\nspecific depth. For each 2D layer, the fractional Fourier transform (FRFT) is used to\nintroduce fractional transform order a, so that each 2D layer can be reconstructed at\nthe corresponding depth. By setting different orders a for different 2D layers, the\ncorresponding phase information of each layer can be obtained, which are then\nsuperimposed to generate the complete 3D hologram. This approach goes beyond a\nsimple extension of the traditional 2D Fourier transform, it leverages FRFT to enable\ntruevolumetricrecording and reconstructionof3D objects.\nIn response to the reviewer’s suggestions, we have revised the manuscript to\nprovide a more rigorous and comprehensiveexplanation of the algorithm. Specifically,\nwe have redefined the mathematical formalism in Eqs. (3)-(8), introducing z to\na\nrepresent the layer-specific depth, and using (x, y; z ) and (u, v; z ) to clearly denote\na a\nthe coordinates of the object points, thus completely distinguishing the proposed 3D\nFourier algorithm based on FRFT from the traditional 2D Fourier transform. We have\nalso updated Fig. 2b, Eqs. (3)-(8), and the corresponding explanatory text in\nparagraphs onPages 8and 9to enhance clarity.\nWe hope these revisions can fully address the reviewer’s concern and better\nreflect thenovelty and rigor ofourproposed algorithm.\n2. Even though a 3D Fourier transform allows the consideration of the entire image\nspace in 3D, the computational cost is orders of magnitude higher than that of a 2D\nFourier transform. For instance, the authors only considered information from two\nplanes with an image resolution of 2500 by 2500 by 2. Therefore, this is not true 3D\nholography but rather arepresentation with information from only two layers?\nResponse: We thank the reviewer for the valuable suggestions, which are very\nhelpful for improvingthequality of ourmanuscript.\nCompared with 2D objects, 3D objects contain more information, so the\ncalculation cost of 3D holograms is higher than that of 2D holograms. In traditional\n2D Fourier meta-hologram generation process, the phase distribution is generated and\noptimized iteratively in both the frequency and spatial domains to obtain the\nmeta-hologram. In contrast, our proposed 3D Fourier meta-hologram algorithm based\non FRFT introduce depth-resolved encoding by decomposing the 3D object into\nmultiple 2D layers, each defined as a specific depth z . The phase distribution of each\na\nlayer needs to be iterated and optimized, and the final hologram of the 3D object is\nobtained by superimposing the corresponding phase information of each layer.\nTherefore, thecalculation cost is positively correlated with thenumber ofdepth layers.\nHowever, for each layer, the phase optimization typically converges within 50\niterations, ensuring theoverall computation remains efficient and manageable.\nIn the original manuscript, we used a two-layer object ‘N’ and ‘U’ in Figure 2b to\ndemonstrate the principle of the algorithm. In the revised manuscript, we have\nextended this to include experimental verification of a three-layer object for\nmeta-holographic encryption, as shown in Fig. R1 (Fig. 5b in the revised manuscript).\nAdditionally, in the original supplementary material S1, the reconstruction results of\n3Dobject with four different depth layers were verified bysimulation.\nFigureR1.Demonstration ofthe high-security encryption withthree layers of object.\nTo further verify the effectiveness and scalability of the proposed method for 3D\nmeta-holographic reconstruction, we have conducted additional simulation using\nmore complex 3D objects with increased depth layers, as shown in Fig. R2 (Fig. S3 in\ntherevised Supplementary materials).\nFor a 3D object composed of nine letters ‘abcdefghi’ in different depth layers, the\ndepths are characterized as a =0.80, a =0.85, a =0.90, a =0.95, a =1.00, a =1.05,\n1 2 3 4 5 6\na =1.10, a =1.15, and a =1.20, respectively. Furthermore, for a 3D object composed\n7 8 9\nof twelve zodiac constellations ‘Aries’, ‘Taurus’, ‘Gemini’, ‘Cancer’, ‘Leo’, ‘Virgo’,\n‘Libra’, ‘Scorpio’, ‘Sagittarius’, ‘Capricorn’, ‘Aquarius’, and ‘Pisces’ in different\ndepth layers, characterized as a =0.79, a =0.82, a =0.85, a =0.90, a =0.95, a =1.00,\n1 2 3 4 5 6\na =1.05, a =1.10, a =1.15, a =1.18, a =1.21, and a =1.24, respectively. In both\n7 8 9 10 11 12\ncases, all components were successfully reconstructed at theirrespectivedepths.\nThe extended simulation results verify the robustness and flexibility of the\nproposed 3D Fourier meta-hologram algorithm in coding complex 3D objects. The\nnew results and discussions have been added in the revised manuscript according to\nthe reviewer’s suggestions. (Please see Fig. 2b, Fig. 5b, the paragraphs below Fig. 5b,\nand Supplementary materials S2)\nFigureR2.3D Fourier meta-holographic reconstruction results in different z-depths.\naReconstructed images at different depths fora 3Dobject layered in ninedifferent\ndepths. b Reconstructed images at different depths fora 3Dobject layered in twelve\ndifferent depths.\n3. It is unclear how the liquid lens works and adjusts image depth. The authors only\npresented a schematic design of the liquid lens chamber in Fig. 2a, but its\nfunctionality is not clearly explained. This integration with a metasurface hologram\nrepresents thekey innovation ofthispaper,yet it lacks essential information.\nResponse:Wethank thereviewer forthe valuablesuggestions.\nThe proposed liquid lens is driven by the electrowetting effect, and the dynamic\nfocal length tuning can be enabled through voltage modulation. This tunability allows\ntheadjustment ofimage depth inmeta-holographic projection.\nAs shown in Fig. R3a (Fig. S1a in the revised Supplementary materials), the\nliquid lens consists of a transparent conductive liquid and an insulating liquid\nencapsulated between the upper and lower electrodes. The upper electrode is coated\nwith a dielectric layer and ahydrophobic layer. Under the effect of interface tension, a\nliquid interface is formed between the conductive liquid and the insulating liquid. At\nequilibrium (no voltage), a stable contact angle θ forms at the liquid-electrode\n0\ninterface, governed bytheinterfacial tensions. It can bederived that:\n \ncos  13 23 , (R1)\n0 \n12\nwhere γ represents the interface tension between the upper electrode and insulating\n23\nliquid, γ represents the interface tension between the insulating liquid and\n12\nconductive liquid, γ represents the interface tension between the upper electrode and\n13\nconductiveliquid, θ is theinitialcontact angle.\ntheproposed liquid lens without applied voltage. b Workingstateof theproposed\nliquid lens with an applied voltage.\nWhen a voltage is applied to the liquid lens (Fig. R3b and Fig. S1b in the revised\nSupplementary materials), charge accumulation occurs at the interface of the upper\nelectrode and the liquids, forming a microscopic electric field force, which causes\nchanges in thecontact angle:\nU2\ncos cos  0 , (R2)\n1 0 2d\n12\nwhere ε is the relative dielectric constant of the dielectric layer, ε is the absolute\n0\ndielectric constant, U is the driving voltage, d is the thickness of the dielectric layer,\nθ is the contact angle under the control of electrowetting. The curvature radius R of\n1\ntheliquidinterface changes accordingly:\nd D\nR 12 , (R3)\n2d cos U2\n12 0 0\nwhere D is the optical diameter of the liquid lens. Thus, the focal length f of the liquid\nlens can beobtained:\nd D\nf  12 ,\n（2d cos U2）n\n12 0 0\nwhere ∆nis therefractiveindex difference oftheconductive andinsulatingliquids.\nWhen the liquid lens is used in the meta-holographic reproduction, the\nrelationship between the imaging depth z and the focal length f of the liquid lens can\nbedescribed as follows:\na a\nz  f sin tan . (R5)\n 2   4 \nTherefore, the imaging depth can be adjusted by controlling the applied voltage of the\nliquidlens.\nThe above dynamic tuning principle has been added in the revised manuscript.\nFig. 2a has also been revised according to the reviewer’s suggestions. (Please see Fig.\n2a, theparagraph above Fig.2and Supplementary materials S1)\n4. Whatdoes \"dimensional information\" mean?\nResponse: We thank the reviewer’s question. The ‘dimensional information’ in the\noriginal manuscript refers to other information of the light field beyond the depth\ndimension, such as the polarization state and wavelength of light. Considering this\nphrasing may have ledto confusion,we have deleted thisexpression and use thename\nof the actual parameter directly instead. (Please see the fourth paragraph in Section 1,\nthe paragraph below Eq. (2), the paragraph above Table 1, and the paragraph below\nFig.5b)\n5. Whyis optical power expressed in m^-1 in line279?\nResponse: Thanks for the reviewer’s valuable question. In general, the unit of optical\npower is diopter, which is abbreviated as D. The optical power (Φ) of the lens can be\nexpressed as [John Wiley & Sons,Inc. 1991]:\n1/ f', (R6)\nwhere f’ is the focal length of the lens with a unit of meter (m). Therefore the unit of\noptical power ism^-1.\n6. Another major concern is the comparison of this approach with the state-of-the-art\nmetasurface holograms. Table 1 does not include all relevant results. In particular,\nprevious papers dealing with full-space light-field displays with large image sizes\nhave notbeen included:\nNatureCommunications,DOI: 10.1038/s41467-022-32117-2\nNaturePhotonics,DOI: 10.1038/s41566-024-01450-x\nResponse: We thank the reviewer for the valuable suggestion. In recent years, 3D\nmeta-holography has seen significant achievement in field of view, image depth,\nimage size and so on, which promotes the further advancement and practical\napplications of meta-holography. In response to the reviewer’s recommendation, we\nhave incorporated several relevant and excellent studies of meta-holography [Nat.\nCommun. 16, 2699, 2025; Adv. Photon. 6(6), 066002, 2024; Adv. Opt. Mater. 13,\n2402872,2025;PhotoniX 5,27,2024; Nat.Mater. 24,535-543, 2025] inSection 1.\nWe are also very grateful to the reviewer for recommending two highly relevant\nreferences. The first [Nat. Commun. 13,5920, 2022] presents a metasurface-based flat\nstructured light projector capable of producing dense dot or line patterns in full space,\nenabling multi-type illumination. The second [Nat. Photon. 18, 848-855, 2024]\nrealizes a differentiable framework with first-order optimization to design structured\nlight fields via metasurfaces. Both works demonstrate notable improvements in\nviewing angle, image size, and depth, and reflect the promise of metasurface-enabled\nimaging. Thesereferences have been addedin therevised manuscript as Refs. 45-46.\nWhile these contributions are impressive, our work differs fundamentally in\nprinciple and approach. Rather than structured light projection, our proposed method\nreconstructs the 3D wavefront information of the object based on holography, using\nthe principles of interference and diffraction. The principles and technical methods\nusedare fundamentally different. Specifically:\n1. By introducing the method of 3DFourier hologram generation based on FRFT,\n3D meta-holography can be achieved without sacrificing other information\nlikepolarizationstateand wavelength ofthelight.\n2. Based on the designed zoom liquid lens, our proposed meta-holographic\nmicro-projector can realize the zoom function in milliseconds, and we can\nflexibly adjust the imaging depth and size, further increasing the depth range\nand expanding theinformation capacity.\n3. By integrating the designed liquid lens and metasurface, the size of the\nmicro-projector can be reduced to a millimeter level, but the imaging size and\ndepth range can reach thedecimeter level.\nThese discussions and comparisons have been added in the revised manuscript\naccording to the reviewer’s suggestions. The suggested reference have been added\nwith other relevant new references (Please see Refs. [17]-[21], Refs. [45]-[46], Table\n1 and the paragraphs above Table 1). We are very grateful for the valuable\nsuggestions, and we also plan to combine the proposed method with the interesting\nmetasurface structurein theabove references in ourfuture exploration.\n7. In the introduction, the manuscript states, \"By incorporating liquid lenses into\nholographic systems, researchers can swiftly obtain the depth information of 3D\nobjects or adjust the viewing angle of holographic display [32-33].\" However,\nreference 33does notdeal with liquidlenses.\nResponse: We sincerely thank the reviewer for the attention to details. We apologize\nfor the oversight. The reference has been carefully corrected and checked throughout\nthe entire manuscript. In addition, we have added some more relevant and excellent\nstudiesof meta-holography. (Please seeRefs. [15]-[21],Ref. [41])\nReviewer#2\nIn this manuscript authors report a miniaturized holographic zoom projector realized\nby developing a high resolution metasurface and a tailored liquid lens. 3D fractional\nFourier transformation is used to calculate the optical field of 3D objects using layer\nbased propagation method. Dimensions of the projector, excluding illumination\nsource and optics, are 6.5 mm × 6.5 mm × 4.2 mm and dimensions of the projected\nimage 5cm × 5cm. Experiments show that depth and size of reconstructed image can\nbe adjusted by changing voltage supplied to the liquid lens. Authors need to address\nfollowing pointsin themanuscript:\nResponse: We sincerely thank the reviewer’s time in reviewing our manuscript and\ntheconstructive comments provided.\n1. In the title words “---fingertip zoom micro projector”, creates confusion therefore\ntitleshould berevised tomake itmoreinformative.\nResponse: We thank the reviewer for the valuable suggestions, and we apologize\nfor the unclear expression. Our work proposes a 0.18 cubic centimeter 3D\nmeta-holographic zoom micro-projector. By integrating specially designed\nmetasurface and liquid lens into a single cavity to achieve large image size and zoom\nfunction in meta-holography, we have achieved the world’s smallest 3D zoom\nmicro-projector with a size of only 6.5 mm × 6.5 mm × 4.2 mm. To better highlight\nthe novelty and technical significance, we have revised the title to be more\ninformative as “A 0.18 cubic centimeter 3D meta-holographic zoom micro-projector”.\nAccordingly, the manuscript has been reorganized and streamlined to more clearly\narticulate the core contributions, as suggested. (Please see the revised title, the\nAbstract, thelast paragraph ofSection 1and theDiscussion, respectively)\n2. Please provide field of view (FOV) of the developed projector and how much FOV\nand zoomis desirable forthe intended application.\nResponse: We are very grateful for the reviewer’s valuable suggestions. The FOV is\nan important parameter of 3D meta-holography. In conventional holographic 3D\nreconstruction, it is usually limited by the pixel size of the hologram, and the viewing\nangle is relatively small [Light Sci. Appl. 3, e213, 2014]. For the conventional\nholographic technology with holograms loading onto a spatial light modulator, the\nFOV is limited to ~8°. Based on the parameters of our designed meta-hologram, the\nFOV can reach 87.5°, representing a 11-times improvement over existing\ntechnologies.Although the current FOV can satisfy viewing requirement, achieving a\nFOV above 100° is our next goal. In addition, in the original supplementary materials\nS4, the throw ratio and the zoom ratio of our proposed meta-holographic\nmicro-projector have been analyzed. The throw ratio can reach 0.52, and the zoom\nratio can theoretically reach 131.5:1, which can meet the application requirements.\nWe have added the discussions in the revised manuscript. (Please see the second\nparagraph belowFig. 4,and Supplementary materials S5)\n3. Authors demonstrated 3D effect by considering two layers. Please discuss how\nmuch object depthcan be supported bythisprojector and it’s limitations, ifany.\nResponse: We thank the reviewer for the valuable suggestions. In the original\nmanuscript, we used a 3D object composed of two letters ‘N’ and ‘U’ positioned at\ndifferent layers is selected to demonstrate the feasibility of our proposed\nzoom-enabled meta-holographic micro-projector. The core of our method lies in\nintroducing the Fractional Fourier transform and its inverse to construct a 3D Fourier\nmeta-hologram algorithm capable of handling volumetirc 3D objects with depths up\nto twice the focal length. By layering the 3D object and characterizing the depth of\neachlayer with different orders a,we obtain a 3Dmeta-hologram, and encode itinto a\nmetasurface. In the original supplementary material S1, the reconstruction results of\n3Dobject with four different depth layers were verified bysimulation.\nFigureR4.3D Fourier meta-holographic reconstruction results in different z-spaces.\naReconstructed images at different depths fora 3Dobject layered in ninedifferent\ndepths. b Reconstructed images at different depths fora 3Dobject layered in twelve\ndifferent depths.\nIn the experimental verification of meta-holographic encryption, the object with\nthree layers has been reconstructed in the revised manuscript, as shown in Fig. 5b in\nthe revised manuscript. In addition, to further verify the effectiveness and advantages\nofthe proposed method, 3Dobjects with more depth layers are simulated, as shownin\nFig. R4 (Fig. S3 in the revised Supplementary materials). Firstly, nine letters\n‘abcdefghi’ are chosen as the 3D object. Each letter is situated at different depths, and\nis characterized by different transformation order a. As shown in Fig. R4a, letters\n‘a’-‘i’ are individually reconstructed at their respective depths. Furthermore, another\n3D object consisting of twelve constellations located at different depth is chosen as\nthe recorded object. Each constellation is characterized by a different transformation\norder a. As shown in Fig. R4b, these constellations are reconstructed at their own\nrespective depths. The results from the simulation affirm the feasibility of the\nproposed 3D Fourier meta-hologram algorithm in encoding complex 3D objects with\nmultipledepth layers.\nTheoretically, the proposed method permits an unlimited number of the depth\nlayers. However, as the layer increases, the 3D object’s information density will be\nenlarged, and the crosstalk between each layer will increase, resulting in progressive\ndegradation of the reconstruction quality. In order to maintain the reconstruction\nquality, it is necessary to improve the resolution of the metasurface. However, the\nfabrication of high-resolution metasurfaces is highly challenging during processing.\nConsequently, a balance between the number of depth layers, the metasurface\nresolution, and production costs is necessary. We have added these new results and\ndiscussions in the revised manuscript. (Please see Fig. 5b, the paragraphs below Fig.\n5b,and Supplementary materials S2)\n4. In the text authors describe polarization engineering. It is important to describe it’s\nmathematical background and how this concept is actually used in the design and\nfabrication of the metasurfaces reported in this manuscript. Otherwise, it is just a\nsimple statement, which is known in the literature. Also explain why preservation of\npolarizationis important in thiscase.\nResponse:Weare very grateful tothe reviewer’s valuable suggestions.\nIn our metasurface design, the broadband response is achieved through phase\nmodulation that is independent of wavelength. This behavior arises from the\nPancharatnam-Berry (PB) geometric phase, which is introduced via circularly\npolarized stateconversion.\nIn the original manuscript, we included a detailed explanation of polarization\nstate conversion to clarify the origin of the PB phase. However, as the current work\ndoes not implement polarization multiplexing in the meta-hologram reconstruction\nand polarization engineering is not the key highlight of our manuscript, we have\nremoved the related discussion on polarization engineering to enhance the clarity as\nperthe reviewer’s suggestion.(Please see thethirdparagraph inSection 2)\n5. Authors claim “---our experiments demonstrate color meta-holography across\ndifferent wavelengths” and “---color zoom meta-holography” but in actual the system\ncreate image of different color in different image plane. So this claim is not valid as in\nany single plane system will generate significant chromatic aberrations, which is\nunacceptable.\nResponse: We thank the reviewer for the valuable suggestions, and we are sorry for\nthe unclear expression. The designed metasurface has a broadband response, which\nenables us to verify its holographic reconstruction effect at multiple wavelengths.\nAccording to the reviewer’s suggestions, we have revised the expression of the\noriginal manuscript to‘multi-wavelength meta-holography’.\nIn addition, while the reconstruction depth is determined solely by the focal\nlength of the liquid lens, the reconstructed image size is influenced by both the focal\nlength and the wavelength.As such, by adjusting the lens’s focal length, we can align\nthe image planes of different colors to the same depth, effectively eliminating axial\nchromatic aberration. However, magnification chromatic aberration remains. We note\nthat this challenge could potentially be addressed in future by employing multiple\nliquid lenses to achieve chromatic-aberration-free color zoom holography. However,\nthat is beyond the scope ofthe current work.These clarifications and discussions have\nbeen added to the revised manuscript. (Please see Fig. 5, the paragraph above Fig. 5\nand Supplementary materials S6)\n6. It will be beneficial for the readers if authors can explain how their 3D field\ncalculationis different from thewell-known layer based CGHgeneration method.\nResponse: We thank the reviewer for the thoughtful question. We have carefully\nreviewed the relevant literature and clarified how our proposed method for 3D\nmeta-hologram generation differs fundamentally from existing layer based CGH\ngeneration methods.\nA recent 2024 study [Nat. Commun. 15, 8242, 2024] employed a 3D\nmeta-hologram generation method based on Fresnel diffraction where each layer’s\nphase distribution is calculated by using a near-field angular spectral diffraction\ntechnique. This method is inherently limited by the pixel pitch and the\nunder-sampling operation in the discrete sampling process. In contrast, our approach\nis based on the fractional Fourier transform, which is suitable for far-field diffraction,\nmaking it ideal for large-depth 3D meta-holography. In our proposed method, the\ndepth information of 3D object is represented by using transformation orders a. The\ndepth range can be extended to 0-2 times of the focal length f, and the depth and\nposition of the reconstructed images is related to a and f, which can be flexibly\nadjusted.\nIn another study from 2021 [Nat. Commun. 12, 3631, 2021], the researchers used\nfar-field Fourier diffraction to realize meta-holographic reconstruction with images in\ndifferent depth layers. The amplitude and polarization information of the far-field is\nencoded simultaneously into the metasurface, thus images can be reconstructed in\ndifferent depths bychanging thepolarization states oftheincident light.\nOur proposed method is fundamentally different. In our proposed method, a 3D\nobject is regarded as a series of 2D layers with different depths, and the 3D\nmeta-hologram is generated by superimposing the phase information of all 2D layers.\nIn the design of metasurface, only phase information is considered, while polarization\ninformation and intensity information are notinvolved.\nCompared with the existing layer based CGH generation methods, our proposed\nmethod has different principle and calculation strategies, underscore the novelty and\nadvantages of our approach. Our method can provide calculations for more depth\nplanes, and the reconstruction results are related to the lens focal length, allowing for\nflexibledepth control.\nThese discussions have been added in the revised manuscript according to the\nreviewer’s suggestions. (Please see the second paragraph below Table 1, and\nSupplementary materials S2)\n7. Generally, projectors are required to project dynamic images, so will a particular\nfabricated metasurface be suitable for updating the 3D images or each time a new\nmetasurface is required. In this case the projector may not serve the purpose in many\napplications, for example,AR/VRdisplays.\nResponse: Thank you for the valuable suggestions. In 3D meta-holography, dynamic\nmeta-holographic projection is an important research direction and hotspot. While\nsignificant advances have been made in developing addressable metasurfaces,\nrealizing dynamic 3D meta-holography remains highly challenging due to the\nimmense data demands and current limitations in real-time metasurface refreshing\ntechnologies.\nRecent works have laid important groundwork in 2D dynamic meta-holography.\nFor instance, in 2020 [Nat. Electron. 3, 785-793, 2020], a large-scale programmable\nmetasurface composed of CMOS-based chip arrays demonstrated amplitude and\nphase modulation with ~25 dB amplitude modulation depth. This\nelectronic-control-based metasurface provides a solution for dynamic 2D holographic\nprojection. In 2024[Opto-Electron. Adv. 7, 230108, 2024], a bitwise meta-holography\nwith pre-designed sub-pattern multiple distinct channels allowed efficient dynamic\nrefreshing of pre-set 2D images. In 2025[Nano Lett. 25, 890-897, 2025], dual-channel\ndynamic modulation was realized using electrochemically deposited conducting\npolymers.\nWhile these advances represent significant progress, they remain limited to\ndynamic switching between pre-set 2D patterns. In addition, due to the huge amount\nof information of 3D objects and the fact that the technology of real-time refreshing\nmetasurface has yet been broken through. Dynamic 3D meta-holography has not been\nrealizedso far.\nOur work, in contrast, addresses a different but equally vital frontier by achieving\nzoom functionality in 3D meta-holography. We integrate a high-transmission\nmetasurface with a compact, tunable liquid lens to enable real-time image size and\ndepth adjustment, within an ultra-compact 0.18 cm³ form factor. While our aim is not\nto create a commercial projector, this design marks a meaningful step toward\nhigh-performance, miniaturized 3Dmeta-holographic systems.\nFollowing the reviewer’s advice, we have revised and condensed the description\nof our innovations and clarified their distinction from dynamic metasurface research.\nAlthough dynamic metasurface is not the focus of the current work, we elucidate our\nvision to combine the proposed zoom micro-projector with future developments in\ndynamically tunable metasurfaces, which could open new possibilities for real-time\n3Dholography in applications such asAR/VR,encryption, and data storage.\nThese above discussions have been added in the revised manuscript. (Please see\ntheparagraphs inDiscussion, Refs. [47]-[49])\n8. The application of “high-security encryption” is demonstrated through an SLM\ninstead by using the metasurface. What is resolution, pixel pitch of SLM and how it is\ncorrelated withmetasurfaces? Further,thisexampleseems misfitinthe manuscript.\nResponse:Wethank the reviewer for the valuable suggestions, which are very helpful\ntous.\nIn the original manuscript, we have used an SLM to load holograms instead of\nmetasurface as key I, and employed liquid lens to control the reconstruction distance\nfor preliminary verification of high-security encryption. According to the reviewer’s\nsuggestion, to further verify the application potential of the proposed zoom\nmeta-holographic micro-projector in ‘high-security encryption’, we conducted new\nexperiments by redesigning and processing a new meta-hologram to replace the\noriginal SLM, as shown in Fig. R5(Fig. 5bintherevised manuscript).\nFigureR5.Demonstrationof thehigh-security encryption with three layers of\nobject.\nFirstly, distinct messages for different users were encrypted into unique patterns\nlocated at different depths, respectively, and assigned corresponding transformation\norders. With the parameters, a 3D meta-hologram with 2,500×2,500 resolution and\n0.35 μm pixel pitch was generated by using the proposed 3D Fourier transform\nalgorithm, serving as encryption keyI.\nSimultaneously, the corresponding driving voltages required to project each\npattern clearly onto a screen placed at a fixed distance (6 cm) were pre-calculated\nbased ontheir depthinformation, forming encryption Key II.\nAs shown in Fig. R6a-c (now Fig. S9 in the revised Supplementary Materials),\nwhen both keys are correctly matched, each pattern can be clearly projected onto the\nreceiving screen, respectively.Then, themessages are successfully decrypted. Notably,\nsuccessful decryption requires precise alignment of the screen distance, the\nmeta-hologram structure, and the liquid lens driving voltage, which significantly\nenhances information security.\nFigureR6.Verification ofthehigh-security encryption. aEncryption process from\ntheplaintextmessages totheencrypted patterns. bKey Iand key II oftheencryption.\nc Resultscaptured from thereceiving screen placed at the depth of6cm with key I\nand key II. d Results captured from the receivingscreen placed at adepth of 12cm\nwithkey Iand key II.\nTo further validate the potential of our zoom meta-holographic micro-projector in\nhigh-security encryption, we conducted new experiments, presented in Fig. R6 (Fig.\nS9 in the revised supplementary materials). During the encryption process, three\nplaintexts ‘Help me’, ‘Thank you’, and ‘Stop’ for different users are encrypted into\n‘moon’, ‘heart’, and ‘thunder’, respectively, as shown in Fig. R6a. These three\npatterns located at different depths with a =1.0, a =0.9, and a =0.8 are chosen,\n1 2 3\nrespectively, to represent the depths. By using our proposed 3D Fourier transform\nalgorithm, a single 3D meta-hologram with resolution of 2,500×2,500 and pixel pitch\nof 0.35 μm is generated, which is considered as key I for the encryption. Assuming\nthat the receiving screen is placed at the depth of 6 cm, we pre-calculate the driving\nvoltages of the liquid lens for each pattern to be clearly projected on the receiving\nscreen. The correspondence between the transformation order and the driving voltage\nis considered as key II, as shown in Fig. R6b. Then, optical experiments are\nconducted. By changing the driving voltage of the liquid lens, the projection results\non the receiving screen can be captured. Three patterns ‘moon’, ‘heart’, and ‘thunder’\nare projected clearly with the corresponding driving voltages with a receiving screen\nplaced at 6 cm, as shown in Fig. R6c. And then, they can be decrypted to messages\n‘Help me’, ‘Thank you’, and ‘Stop’correctly. When the receiving screen is moved to\nan incorrect depth of 12 cm, different from key II, the patterns cannot be projected\ncorrectly onthescreen, as shown in Fig.R6d.\nThese results confirm that successful decryption is only possible when the\nhologram, liquid lens voltage, and screen position precisely match, highlighting the\nsystem’s robustness and security.\nThe new experimental results and discussions above have been added into the\nrevised manuscript. (Please see Fig. 5b, the paragraphs below Fig. 5b, and\nSupplementary materials S7)\nThus, the manuscript has demonstrated small sized zoom projection optics for\nmonochromatic images but presently it is not suitable for color 3D images.Also, only\nstatic 3D images can be projected and not the 3D dynamic images, which are required\nformost oftheapplications includingAR/VRdisplays.\nResponse:Wethank again for thereviewer’s thorough and thoughtful review, andthe\nconstructive suggestions. In response, we have substantially revised and reorganized\nthe manuscript, clarified the conceptual contributions, and updated the title to better\nreflect the core innovations. Additionally, new meta-holograms used for encryption\nhave been produced, and new experimental results have been included to provide\nstrong evidence tosupport theclaims of themanuscript.\nMeta-holography has emerged as a vibrant and transformative frontier in\nphotonics. Among the most sought-after goals in this field is the realization of a\ncompact 3D projection system capable of large image size, deep reconstruction depth,\nand dynamic zoom functionality. These capabilities are essential for practical\napplications such as AR/VR, where ultra-thin wavefront control and tunable focal\nlength are prerequisites. Our work addresses these critical challenges by introducing a\n3D zoom meta-holographic micro-projector that combines a wideband metasurface\nwitha tunableelectrowetting liquid lens.\nWe need to emphases dynamic image projection is an interesting future topic but\nis beyond thescope ofthecurrent manuscript.\nOurwork introduces four main innovations:\n1) Deep 3D meta-holography via fractional Fourier transform. A 3D object is\nregarded as a series of 2D layers. By introducing fractional Fourier transform into the\nmeta-holographiccoding of each layer, the depth information across theentire volume\nof the object is characterized and encoded, circumventing the limitations of\nconventional Fourier-based holography, which is largely restricted to 2D or shallow\n3Dprojections.\n2) Zoom functionality with millimeter-scale optical hardware. For the first time,\nan electrowetting liquid lens with a high optical power and a small effective optical\naperture of 2 mm has been proposed. By tailoring the liquid formulation and voltage\ncontrol, we achieve dynamic, wide-range tunability of image size and position.\nConsequently, using the liquid lens and the designed metasurface, the projection\ndistance of the meta-holographic image can reach decimeter level, and the size can\nachieve over 5cm ×5cm area, which is ~100 times larger than state-of-the-art.\n3) The world’s smallest 3D zoom meta-holographic projector. By integrating\nspecially designed metasurface and liquid lens into a single cavity to achieve large\nimage size and zoom function in meta-holography, the volume of the micro-projector\nis limited to ~0.18 cm3. To our knowledge, this is the smallest reported 3D\nzoom-capablemeta-holographic projection device.\n4)Application in high-security encryption.Todemonstrate a compelling use case,\nwe redesigned and experimentally validated a meta-hologram for multilayer,\ndepth-dependent information encryption. Successful decryption requires precise\ncoordination of the metasurface, focal depth, and liquid lens voltage, highlighting the\nplatform’s utility insecure communication.\nWeacknowledge that dynamic meta-holography remains a critical and unresolved\nchallenge in the field. Most current approaches are limited to pre-defined 2D patterns\nand fall short of achieving real-time volumetric refresh capabilities. A truly dynamic\n3D meta-holographic imaging system inherently requires two core components: (1) a\ndynamic projection system capable of tunable image depth and size, and (2) an\nupdatablemeta-hologram capable ofreal-timewavefront modulation.\nThis manuscript specifically addresses the first of these two challenges. By\nintegrating a high-optical-power electrowetting liquid lens with a compact, broadband\nmetasurface, we demonstrate a reconfigurable projection system that enables\ncontinuous zooming and depth-tunable 3D meta-holographic reconstruction. This\nzoom-enabled architecture allows the projected image to be dynamically resized and\nrepositioned in real-time, which is a substantial step forward in the path toward\ndynamic meta-holography. To our knowledge, this is the first time such a highly\nintegrated system has been realized with decimeter-scale image projection from a\nsub-cm³ device.\nThe second challenge, developing an updatable or reprogrammable metasurface\ncapable of high-speed modulation of phase information, remains an important avenue\nfor future research. While this manuscript does not directly address that component,\nour current system lays a robust foundation for future integration with dynamically\ntunablemetasurfaces as thosetechnologies mature.\nIn summary, this work makes a significant and timely contribution by solving a\ncore bottleneck in dynamic 3D meta-holography, the development of a reconfigurable\nprojection system with integrated zoom functionality. It is our belief that the\nmodularity and compactness of our system will facilitate future integration with\nprogrammable metasurface platforms, enabling the full realization of real-time\ndynamicvolumetricmeta-holography.\nWe have revised the manuscript, supplemented the experiment, and further\nhighlighted the innovation and the concepts. We hope that the conceptual clarity, new\nexperiments, and expanded discussion provided in the revised manuscript fully\naddress the reviewer’s concerns and clearly convey the scientific and practical\nsignificance ofour work."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I believe this revision has significantly enhanced the technical soundness of the manuscript and strengthened its standing on the international stage. While it does not introduce a novel physical concept, I leave the final decision to the editor. In my view, it is acceptable for publication if the journal does not consider physical novelty a critical criterion. From a technical and application perspective, the manuscript merits a strong publication.", "reviewer_2": "The authors have improved the manuscript and addressed many aspects of the manuscript in it revised version. The following points still require improvement for the manuscript to become publishable in Nature Communications:\n• The authors claim that “A 3D Fourier transform method based on metasurface is proposed to calculate the meta-hologram of 3D object----” but the method of Fractional Fourier Transform is well known in the literature and authors only implemented it for calculations in this work. Thus authors should modify their claim accordingly.\n• In Fig 1(c), u=60V and u=40V is shown two times. It will be good to explain it in more details.\n• Please elaborate the statement “By simply adjusting the driving voltage of the liquid lens, magnification chromatic aberration can be easily eliminated, leading to high quality imaging.” As magnification and focal length for different wavelengths will be different, then how simple adjustment will compensate the chromatic aberrations. Also clarify whether both lateral and transverse aberrations can be compensated?\n• Figure 4 shows results corresponding to zoom effect and not the 3D effect. Please clarify.\n• Please discuss the pixel pitch in image plane of reconstructed image obtained using the Fractional Fourier Transformation. Is it constant or vary with reconstruction distance?\n• Please quantify or show experimentally cross talk effect of images reconstructed at different depth planes of a 3D object. It is important to generate good quality reconstructed image of a continuous 3D object."}, "author_response": "As detailed below, we have revised our manuscript in response to the reviewers’ comments. The original reviewers’ comments are shown in black color, whereas for ease of communication, our answers are provided in blue. Our revisions have also been marked in themain textand supplementary information files usingblue.\nReviewer#1\nI believe this revision has significantly enhanced the technical soundness of the\nmanuscript and strengthened its standing on the international stage. While it does not\nintroduce a novel physical concept, I leave the final decision tothe editor. In my view,\nit is acceptable for publication if the journal does not consider physical novelty a\ncritical criterion. From a technical and application perspective, the manuscript merits\nastrong publication.\nResponse: We sincerely thank the reviewer’s time in reviewing our manuscript and\nweare very grateful for thepositivecomments provided.\nReviewer#2\nThe authors have improved the manuscript and addressed many aspects of the\nmanuscript in it revised version. The following points still require improvement for\nthemanuscript to become publishablein Nature Communications:\nResponse: We sincerely thank the reviewer for the constructive and valuable\nfeedback, which helps us further strengthen ourmanuscript.\n1. The authors claim that “A 3D Fourier transform method based on metasurface is\nproposed to calculate the meta-hologram of 3D object----” but the method of\nFractional Fourier Transform is well known in the literature and authors only\nimplemented it for calculations in this work. Thus authors should modify their claim\naccordingly.\nResponse: We sincerely thank the reviewer for the valuable suggestions. We fully\nagreethat theFractional FourierTransform (FRFT)is well established inthe literature.\nOur contribution is not the introduction of FRFT itself, but rather its novel application\ntothe generation of3Dmeta-holograms.\nIn our approach, the 3D object is decomposed into a series of 2D layers, each\npositioned at a defined depth. For each 2D layer, we apply the FRFT with a specific\nfractional transform order a, which enables the corresponding reconstruction at its\nrespective depth. By assigning different transform orders a to different layers, we\nextract the appropriate phase information of each layer and then coherently\nsuperimpose them to generate the complete 3D hologram. This approach goes beyond\na simple extension of the traditional 2D Fourier transform, as it leverages FRFT to\nenable truedepthrecording and accurate reconstruction of3Dobjects.\nAs requested by the reviewer, to reflect this more precisely, we have revised our\nwording throughout the manuscript. Specifically, we now describe our method as “a\n3D Fourier meta-hologram generation method based on FRFT” and emphasize that\nour innovation lies in its layered processing framework for 3D holographic\nreconstruction. The revisions have been incorporated into the abstract, the first\nparagraph of Section 2, the first paragraph below Eq. (2), the second paragraph above\nFig.3,thefirst paragraph above Fig.4,and theparagraphs belowFig. 5.\n2. In Fig. 1(c), u=60V and u=40V is shown two times. It will be good to explain it in\nmoredetails.\nResponse: We are very grateful for the reviewer’s insightful suggestion. In Fig. 1(c),\nour aim was to illustrate the 3D zoom capability of the proposed micro-projector\nusing a recorded 3D object composed of two depth planes (a “tree” and a “bird”). In\nthe original manuscript, “U=60 V” and “U=40 V” were used to indicate two distinct\nprojection states of the proposed micro-projector.We recognize that this labeling may\nhave caused ambiguity.\nTo improve clarity, we have revised the figure and its description. In the updated\nversion, the driving voltage of the liquid lens are denoted as U and U , which\nI II\ncorrespond to projection states I and II, respectively. Projection state I (U)\nI\nreconstructs the 3D scene at a closer distance, while projection state II (U )\nII\nreconstructs it at a farther distance. Under different driving voltages, the reconstructed\ndepth and size of the 3D images differ, thereby demonstrating the zooming function.\nThese clarifications have been incorporated into the revised manuscript according to\nthereviewer’s suggestions. (Pleasesee Fig. 1andthelast paragraph ofSection 1).\n3. Please elaborate the statement “By simply adjusting the driving voltage of the\nliquid lens, magnification chromatic aberration can be easily eliminated, leading to\nhigh quality imaging.” As magnification and focal length for different wavelengths\nwill be different, then how simple adjustment will compensate the chromatic\naberrations. Also clarify whether both lateral and transverse aberrations can be\ncompensated?\nResponse: We sincerely thank the reviewer for raising this important point and\napologize for the lack of clarity in our original description. At different wavelengths,\nthe proposed micro-projector can suppress either magnification chromatic aberration\nor axial chromatic aberration by adjusting the focal length of the liquid lens, but it\ncannot eliminate both simultaneously. The reconstruction depth depends on the focal\nlength of the liquid lens (Eq. (S5) in the supplementary material), whereas the\nreconstructed image size is determined by both the focal length and wavelength (Eq.\n(S8)).\nToaddress thereviewer’s specific question:\n- Axial chromatic aberration can be eliminated by tuning the driving voltage of\nthe liquid lens such that the focal length remains constant across different\nwavelengths, thereby fixing the reconstruction depth. As shown in Fig. S8 of\nthe supplementary material, this removes axial chromatic aberration. However,\nthe projected image size varies with wavelength, leaving magnification\nchromatic aberration unresolved. Moreover, lateral and transverse aberrations\npersist to varying degrees, since the reconstructed image is scaled uniformly\naround the optical axis.\n- Magnification chromatic aberration can instead be compensated by tuning the\nliquid lens focal length to offset the influence of wavelength-dependent\nchanges. Nevertheless, this approach requires different focal lengths for each\nwavelength, which shifts the reconstructed images to different depth planes,\nthereby inducing axial chromatic aberration.\nIn summary, the current system allows selective elimination of either axial or\nmagnification chromatic aberration by adjusting the driving voltage of the liquid lens,\nbut not both simultaneously.As the reviewer rightly notes, full achromatic correction\nremains a challenge. Achromatic meta-holography is widely recognized as a critical\nstep for advancing this field. Our future work will focus on achieving achromatic\nmeta-holographic zoom micro-projector with multiple micro liquid lenses. We have\nadded these clarifications and discussions to the revised manuscript. Please see the\nfirst paragraph above Fig. 5,and Supplementary materials S6.\n4. Figure 4 shows results corresponding to zoom effect and not the 3D effect. Please\nclarify.\nResponse: We are very grateful to the reviewer’s valuable suggestions. Specifically,\nFig. 4a presents the 3D reconstruction results obtained using a solid lens with a fixed\nfocal length of 10 cm instead of the liquid lens, thereby validating the 3D projection\ncapability of the proposed micro-projector. Fig. 4b illustrates the zoom projection\nresults of the letter ‘N’ at different depth planes, both with and without a driving\nvoltage applied to the liquid lens, demonstrating the zoom functionality of the\nproposed micro-projector. Figs. 4c-d show two sets of the 3D zoom projection results\nunder different driving voltages, further confirming the 3D zoom capability of the\nproposed micro-projector.\nIn order to improve clarity, the title of Fig. 4 has been revised to “3D zoom\nreconstruction results of the micro-projector” in the revised manuscript. In addition,\nthe subheadings of Fig. 4c and Fig. 4d have been consolidated into a single, clearer\ndescription: “3D zoom projection results when the focal length of the liquid lens is\nchangedfrom 15cm to7cm”.\n5. Please discuss the pixel pitch in image plane of reconstructed image obtained using\nthe Fractional Fourier Transformation. Is it constant or vary with reconstruction\ndistance?\nResponse: We thank the reviewer for the valuable suggestions. Taking the x-direction\nas an example, the relationship between the pixel pitch (dx’) in the image plane and\nthe reconstruction depth (z) can be derived from Eqs. (S6) - (S8) in supplementary\nmaterial, and isdescribed as:\nzsin  a \n2\ndx'  ,\nndutan\n a \n4\nwhere n and du denote the number of the pixels and the pixel pitch of the metasurface\nalong the x direction, respectively. For the designed metasurface, n=2500, du=0.35\nμm. λ is the wavelength of the laser. a is the transformation order, which is fixed for\neachdepth plane ofthe3Dobject.\nTherefore, for a fabricated metasurface, the pixel pitch in the image plane varies\nwith the reconstruction distance. More specifically, it increases directly proportional\nto the reconstruction depth. We have these clarifications in Supplementary materials\nS5.\n6. Please quantify or show experimentally cross talk effect of images reconstructed at\ndifferent depth planes of a 3D object. It is important to generate good quality\nreconstructed image ofacontinuous 3D object.\nResponse: We thank the reviewer for the thoughtful question. In 3D holography, the\ndivision of an object into multiple depth inevitably increases computational\ncomplexity and introduces crosstalk between different layers. To quantitatively\nanalyze this effect, we employed a test 3D object consisting of four different depth\nplanes, “pentagon”, “rhombus”, “triangle”, and “square” with adjacent planes\npartially overlapped.The corresponding fractional orders were set to 1.0, 1.2, 1.3, and\n1.4 respectively. Using our proposed method, we redesigned and re-fabricated a\nmetasurface for verification. The meta-holographic reconstruction results are shown\nin Figs. R1a-d. As expected, when one pattern is in focus, the other patterns appear\nout of focus and manifest as noise around the primary image, which degrades the\nviewing quality.\nAs the reviewer mentioned, it is very important to generate high-quality\nreconstructed images of continuous 3D objects. We have also been working on the\nelimination of meta-holographic crosstalk in order to achieve high-quality\nreconstructed images. To address this, we further optimize the meta-holographic\ngeneration algorithm by using noise homogenization and spectral shift methods, and\nthe simulation results are shown in Figs. R1e-h. By adding appropriate spectral shifts\ntodifferent depth planes, the noise caused by out-of-focus patterns can be dispersed to\nareas far away from the focused images, thus reducing interference and improving\nimage quality. However, this improved crosstalk elimination algorithm imposes\nconstrains onboththeresolution and focal length setting ofthe3Dobjects, and we are\nactively studying thesedependencies.\nIn our manuscript, our primary focus is on demonstrating an ultra-compact\nzoomable 3D meta-holographic projection system with four key innovations: 1)\nEnabling deep 3D meta-holography via fractional Fourier transform. 2) Introducing\nzoom functionality via electrowetting liquid lens integration. 3) Achieving, to our\nknowledge, the world’s smallest zoom micro-projector. 4) Opening pathways to\nmassive practical applications including high-security encryption, AR/VR, wearable\nand biomedical device and automotive displays. Within this scope, we did not\nimplementthe crosstalk-elimination algorithmin theprototype system.\nThat said, we fully agree with the reviewer that achieving crosstalk-free\nmeta-holography is a critical goal for advancing high-quality 3D reconstruction. We\nhave therefore expanded the manuscript to discuss crosstalk more thoroughly and to\noutline how future research will refine the 3D Fourier meta-hologram generation\nmethod to achieve continuous, crosstalk-free 3D imaging. These details have been\nadded to the revised manuscript (Please see the third paragraph below Fig. 5 and the\nrevised Supplementary materials S2).\nFigure R1. Crosstalk analysis of the proposed method. a-d Reconstruction results\nof a 3D object with four different depth layers. e-h Crosstalk-free reconstruction\nresults of a 3D object with four different depth layers (the patterns in the yellow\ndashed boxes are in focus)."}, {"round": 3, "reviewer_comments": {"reviewer_2": "The authors have suitably addressed all the comments in the re-revised manuscript."}, "author_response": "Response: We sincerely thank the reviewer’s time in reviewing our manuscript\nand we are very grateful for the positive comments provided."}]

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