Diffractive Volumetric Displays

• Diffractive volumetric displays are 3D visualization systems that use engineered diffractive optical elements and spatial light modulators to reconstruct light fields in volume.
• They employ techniques like multi-plane diffractive coding, phase retrieval algorithms, and hybrid SLM–metasurface setups to achieve wide field of view and dynamic imaging.
• Design trade-offs center on balancing resolution, efficiency, and fabrication constraints, with performance metrics including voxel size, diffraction efficiency, and angular coverage.

Diffractive volumetric displays are three-dimensional visualization systems that utilize micro- and nano-structured diffractive optical elements (DOEs), metasurfaces, or programmable spatial light modulators (SLMs) to reconstruct optical fields spatially distributed in volume. These systems leverage the principles of optical diffraction, wavefront shaping, and holography to overcome conventional limitations in display etendue, field of view (FOV), and volumetric resolution. Diffractive volumetric displays encompass several architectures, including hybrid meta-projectors, multi-plane diffractive coding, direct laser-generated plasma volumetrics, faceted Fresnel element arrays, and diffractive screens designed for continuous parallax. The following provides a comprehensive technical overview of the prevailing methodologies, principles, system metrics, and ongoing research directions.

1. Fundamental Principles of Diffractive Volumetric Imaging

Diffractive volumetric displays operationalize phase modulation and diffraction to steer and shape light fields across three spatial dimensions. Typically, phase-only modulation is performed using SLMs or engineered metasurfaces. Scalar diffraction mathematics—encompassing the Fresnel and angular spectrum approximations—serves as the foundation. The field at an output plane or point is calculated by propagating the modulated wavefront using integrals or fast Fourier transforms (FFTs):

$$U(x',y';Z) = \frac{e^{i k Z}}{i\lambda Z} \iint U_h(x,y)\exp\left[i\frac{k}{2Z}\left((x'-x)^2+(y'-y)^2\right)\right]\;dx\,dy$$

where $U_h(x,y) = A_0\exp[i\,\phi_h(x,y)]$ is the modulated field on the SLM or DOE, and $\phi_h(x,y)$ is the programmed phase profile (Ochiai et al., 2015).

Metasurfaces, composed of subwavelength elements (e.g., TiO₂ nanopillars, pmeta=249.3 nm), enable large diffraction angles by engineering local grating laws ($\sin\theta_m = m\lambda/\Lambda$) and deterministic phase profiles ($\phi_\text{meta}(x,y)$). Layered DOEs and multi-plane encoding via phase retrieval algorithms (Gerchberg–Saxton, Optimal-Rotation-Angle, iterative Fourier methods) enhance volumetric addressability and reduce cross-talk (Li et al., 27 Nov 2025, Isil et al., 23 Dec 2025, Song et al., 2019).

2. Display Architectures and Computational Encoding

2.1 Hybrid SLM–Metasurface Projectors

The meta-projector approach combines a conventional SLM with a fixed, FOV-expanding metasurface placed at the optical image plane. The SLM phase pattern is telescopically demagnified, resulting in each SLM pixel overlapping multiple metasurface elements ("pixel-interpolation-assisted", N/M ratio). The composite phase ($\phi_{\text{interp}}(x,y)$) generates a wide-diffraction angle cone ($160^\circ \times 160^\circ$, NA ≈ 0.985). Gerchberg–Saxton-style iterative updating enables volumetric rendering by time-multiplexing or encoding multiple planes (Li et al., 27 Nov 2025).

2.2 Digital Encoder + Diffractive Decoder Systems

Recent systems deploy a Fourier-based digital encoder, which accepts multiple target image slices (axial planes), extracts spatial/frequency features, and outputs a unified phase map (Φ_enc(x,y)) to an SLM. This encoded wavefront is then decoded by a passive multi-layer diffractive stack (each layer with optimized phase profile φ_l(x,y)), producing high-axial-resolution, simultaneous multi-plane projections (up to 28 slices in a snapshot). End-to-end optimization leverages deep learning to mitigate cross-talk and balance efficiency (Isil et al., 23 Dec 2025).

2.3 Direct-Write Femtosecond Laser Volumetrics

With focused femtosecond lasers and a programmable hologram plane, volumetric "voxel" graphics are directly generated in air by plasma luminescence. SLM CGH encoding enables parallel voxel addressing; galvo-mirror scanning and varifocal lensing expand the traversable workspace. The CGH is iteratively refined (e.g., ORA algorithm) for uniform intensity at target 3D positions (Ochiai et al., 2015).

2.4 Faceted Fresnel DOEs and Diffractive Screens

Passive 3D visualization is achievable via arrays of Fresnel-type DOEs, fabricated in matrixed facets, each steering incident light to reconstruct a 3D image view at a predetermined depth. Each facet’s phase profile combines lensing and blazed grating components, optimized through iterative Fourier algorithms (M-IFTA with soft phase quantization) for high-efficiency multi-view parallax (Song et al., 2019). Diffractive screens, such as the Lunazzi–Diamand system, use motor-tilted mirrors and holographic screens to position vectorial elements, encoding z-depth via spectral dispersion (Lunazzi et al., 2011).

3. Computational Procedures and Optimization Algorithms

The generation of volumetric diffractive patterns relies on phase-retrieval and wavefront optimization techniques.

• Gerchberg–Saxton Iteration: Up-samples SLM phase to match metasurface grid, synthesizes composite phase, forward FFT computes far-field, inverse FFT reconstructs, subtracts fixed metasurface phase, and down-samples for iterative correction (Li et al., 27 Nov 2025).
• Modified Iterative Fourier Transform (M-IFTA): Enforces amplitude constraints, back-and-forth propagation, and soft quantization toward discrete phase levels for fabrication compatibility (Song et al., 2019).
• Optimal-Rotation-Angle (ORA): Maximizes intensity uniformity across volume by updating SLM phase per the voxel’s propagated field (Ochiai et al., 2015).
• End-to-end Deep Learning Optimization: Trains encoder and diffractive decoder jointly, incorporating losses for reconstruction fidelity, cross-talk suppression, efficiency maximization, and alignment robustness. Auto-differentiation is employed for gradient updates (Isil et al., 23 Dec 2025).

4. Quantitative Performance Metrics and Trade-Offs

Key metrics include angular FOV, spatial resolution, efficiency, volumetric fidelity, speed, and observer bandwidth:

Display Type	Field of View / Volume	Resolution	Efficiency
Meta-Projector (Li et al., 27 Nov 2025)	160°×160°, 60 Hz, NA≈0.985	~15.85 µm at 95.1 mm	~45.1%
Diffractive Decoder (Isil et al., 23 Dec 2025)	4–28 axial planes, Δz ≈λ	256×256–600×600 px	Tunable: 0.0005–35%
Femtosecond Plasma (Ochiai et al., 2015)	1–8 cm³, up to 200,000 vox/s	~5–10 µm focal spots	<70% (CGH), serial
Fresnel FDOE (Song et al., 2019)	20° × 8 mm eye-box	2.7 mm facet, 1.5 µm	~46% (signal image)
Diffractive Screen (Lunazzi et al., 2011)	65×35 cm screen, ~24 cm cube	≈5 mm voxel	<9% (total optical)

Trade-offs arise between pixel pitch and angular coverage, brightness and diffraction efficiency, volumetric multiplexing versus lateral resolution, bandwidth (for RGB), and speed versus volumetric density. High numerical apertures yield shallow depth-of-field—requiring multi-plane encoding or varifocal tuning to reconstruct substantial volumes.

5. Optical and Device Engineering Considerations

System stability, alignment tolerance (up to ±400 µm for meta-projector (Li et al., 27 Nov 2025)), and fabrication constraints (phase quantization, etch depth for DOEs, SLM damage thresholds) critically influence practical deployments. The pixel-interpolation approach enables large FOV and etendue expansion but demands achromatic metasurface designs for multi-wavelength display. Passive diffractive stacks must balance inter-layer distances, lateral pixel count, and axial resolution to mitigate cross-talk.

Implementation often requires off-the-shelf SLMs (HOLOEYE PLUTO, LUNA), state-specific photoresist coated glass substrates, and maskless photolithography for patterned DOEs. For femtosecond plasma volumetrics, safety is governed by exposure durations, skin and ocular protection, and power density thresholds.

6. Applications, Extension Strategies, and Research Directions

Diffractive volumetric displays underpin next-generation holographic television, AR/VR interfaces with true focus cues, photonic computing, optical trapping, and secure 3D image rendering.

• Multi-plane switching via time-sequential SLM updates and varifocal elements enables dynamic volumetric display.
• Spatial or angular interleaving (multiplexed hologram coding) assigns distinct phase patterns to depth channels, guided by metasurface steering.
• Continuous-depth generation is plausible using angle-coded holograms with anisotropic dispersion engineering.
• Passive stacked DOEs may be extended by multi-layer encoding or time/wavelength multiplexing, with consideration of resultant resolution and efficiency loss (Song et al., 2019).
• Deep learning-optimized diffractive decoders support dynamic axial reconfiguration and are experimentally validated for snapshot volumetric projection (Isil et al., 23 Dec 2025).

Future directions include RGB/achromatic metasurfaces, parallelized phase retrieval, hybrid metalens–metasurface stacks, SLMs with >120 Hz refresh for real-time volumetrics, and integration with eye-tracking for foveated rendering to reduce computational spatial-bandwidth product requirements. Research continues to define optimal architectures under constraints of device manufacturing, system complexity, and cross-domain application needs.

7. Comparative Analysis and Limitations

Each diffractive volumetric architecture possesses specific constraints:

• Meta-projectors and decoders achieve high FOV and axial density, contingent on SLM speed, metasurface chromatic correction, and phase optimization (Li et al., 27 Nov 2025, Isil et al., 23 Dec 2025).
• Femtosecond plasma displays offer unique direct-write capabilities but are hardware-limited in SLM frame rate and workspace volume (Ochiai et al., 2015).
• Passive DOE arrays excel in efficiency and compactness, but volumetric scaling diminishes per-plane brightness and multiplies fabrication complexity (Song et al., 2019).
• White-light diffractive screens afford multi-observer, no-accessory parallax but are limited in brightness (<9% efficiency), spatial resolution (~5 mm), and update speed (Lunazzi et al., 2011).

Continuous parallax, dynamic volumetric refresh, and multi-plane fidelity remain active areas of optimization; trade-offs in optical design, phase quantization, and encoding algorithms underscore system engineering. Extensions to full-color, fast-refresh, and scalable volumetric imaging continue to draw interdisciplinary interest spanning photonics, display technology, and computational imaging.