HoloTile Framework for Phase-Only CGH

Updated 9 December 2025

HoloTile Framework is a phase-only CGH method that divides light modulation into independently synthesized tiles, enabling scalable and precise beam shaping.
It employs analytic point-spread function shaping to tailor output intensity profiles, effectively suppressing speckle and enhancing photon efficiency.
The modular architecture supports applications such as volumetric additive manufacturing, optical trapping, and high-dimensional communications.

The HoloTile Framework is a phase-only computer-generated holography (CGH) methodology that decomposes light field modulation into independently synthesized sub-holograms ("tiles") on a spatial light modulator (SLM), combined with analytic point-spread function (PSF) shaping. HoloTile provides a scalable architecture for massively parallel, speckle-suppressed, and photon-efficient light projection with tailored intensity distributions. This framework underpins a range of applications, including volumetric additive manufacturing (VAM), optical trapping, multi-wavelength imaging, and high-dimensional information transfer. Key developments include the extension to three-dimensional volumetric beamlets ("Axial HoloTile") and multi-wavelength output ("HoloTile RGB") (Glückstad et al., 2023, Madsen et al., 31 May 2024, Madsen et al., 17 Sep 2024, Madsen et al., 5 Dec 2025).

1. Architectural Principles of HoloTile CGH

The HoloTile architecture divides the SLM into an array of tiles, each displaying a synthesized sub-hologram calculated individually for a desired reconstruction. The approach fundamentally departs from monolithic CGH by factorizing the light field modulation as follows:

Tile-Based Modulation: Given an SLM of size $N \times N$ and physical pixel pitch $\ell_p$ , it is partitioned into $N_t \times N_t$ tiles with sub-holograms $h(x,y)$ of size $M \times M$ , $M \ll N$ .
Hologram Synthesis Pipeline: For a target output on an $M_{\text{x}} \times M_{\text{y}}$ grid, the sub-hologram is computed (e.g., via IFFT or optimization), then tiled across the SLM as

$\phi_{\text{total}}(x, y) = \phi_{\text{tile}}[x \bmod M, y \bmod M]$

PSF Shaping: A global phase profile $\phi_{\text{psf}}(x, y)$ is analytically designed and superimposed on the tiled pattern to define the spatial support and axial propagation of each diffracted order ("pixel") (Glückstad et al., 2023, Madsen et al., 5 Dec 2025).
Fourier Domain Output: In the Fourier (reconstruction) plane, this produces a comb of well-separated, discretized output pixels:

$(x_{mn}, y_{mn}) = (m \lambda f / \ell_s, n \lambda f / \ell_s)$

where $\ell_s$ is the physical tile size, $f$ is focal length, and $(m, n) \in \mathbb{Z}^2$ .

This framework enables non-overlapping, user-defined output pixel shapes, ultra-fast real-time updates, and inherent speckle suppression by design (Glückstad et al., 2023, Madsen et al., 17 Sep 2024).

2. Point Spread Function Shaping and Modalities

PSF shaping is central in the HoloTile framework, enabling control over both lateral and axial field attributes per output pixel:

Analytic PSF Phase Masks: The global phase mask $\phi_{\text{psf}}(x, y)$ $ϕ_{psf} (x, y)$ is engineered to produce a desired intensity profile at each pixel in the output, with canonical forms including
- Square (top-hat) pixels: uniform squares in focal plane.
- Disk-shaped pixels:
$\phi_{\rm disk}(\xi) = \beta \frac{\sqrt{\pi}}{2} \int_0^\xi \sqrt{1 - \rho^2} d\rho$ - Ring-shaped pixels (Bessel-like beams):

$\phi_{\rm ring}(\xi) = \beta \xi$ - Helico-conical (vortex) beams, Airy, or Bessel-Gaussian beams via appropriate phase encoding (Glückstad et al., 2023, Madsen et al., 31 May 2024).
Extended Depth-of-Focus (Axial HoloTile): The three-dimensional extension involves constructing each output pixel as a Bessel beamlet with long non-diffractive propagation:

$H_{\rm PSF}(r) = \exp[i \phi_{\rm ring}(r)] \quad \Longrightarrow \quad A_{\rm PSF}(r', z) \propto J_0(k r' \sin \theta_0)$

Multiplexing: Because the tile and PSF contributions factorize, PSF shaping remains fixed while target patterns (subholograms) are dynamically updated, achieving spatial and temporal control independently (Madsen et al., 31 May 2024).

Explicit PSF engineering eliminates spatial frequency overlap between neighboring output pixels, removing the main origin of speckle-noise in Fourier holography.

3. Mathematical Models and Algorithmic Workflow

The mathematical and computational workflow in HoloTile-based systems proceeds as follows:

Phase Map Construction: Each tile $t$ carries a phase pattern

$\phi_t(x, y) = k_x^{(t)} x + k_y^{(t)} y + \phi_{\text{PSF}}(x, y) - \frac{k}{2f}(x^2 + y^2) \;\; (\bmod 2\pi)$

where $(k_x^{(t)}, k_y^{(t)})$ regulate the tile's Fourier order, and $\phi_{\text{PSF}}$ sets the PSF type (Madsen et al., 5 Dec 2025).

Tomographic Dose Accumulation (for VAM):

$D(x, y, z) = \int_0^{2\pi} I_\theta(x, y, z)\, d\theta$

where $I_\theta$ is the light intensity for a given rotation angle in a rotating tomographic system.

Optimization and Projection: Voxelized 3D targets are transformed via Radon/sinogram projections, optimized for dose control, mapped tile-by-tile to SLM patterns, and synchronized with system dynamics (e.g., rotating vials in additive manufacturing) (Madsen et al., 5 Dec 2025).
Pseudocode Sketch:

mesh = load_STL(...)
voxels = voxelize(mesh, dx)
sinogram = RadonTransform(voxels, angles)
warped = prewarp_for_refraction(sinogram)
optimized = optimize_projections(warped)
for angle, proj in optimized:
  H = zeros(SLM_size)
  for tile in tiles:
    (kx, ky) = steering_vector(tile, proj)
    phi_tile = kx*x + ky*y + alpha*sqrt(x**2+y**2) - k*(x**2+y**2)/(2*f)
    H[tile.region] = wrap_mod_2pi(phi_tile)
  display_SLM(H)
  wait_for_rotation(angle)

(Madsen et al., 5 Dec 2025)

SGD Optimization (RGB/Multi-wavelength): Phase patterns for each channel are optimized by minimizing the squared error versus target pixel intensities, with gradient-based update and per-channel PSF/tile scaling (Madsen et al., 17 Sep 2024).

4. Photon Efficiency, System Performance, and Speckle Suppression

HoloTile offers substantial advantages in speed, fidelity, and optical efficiency.

Parameter	Conventional Fourier CGH	HoloTile Framework
Speckle Contrast	10–25%	<2–5% (typically)
Image SSIM (full-color)	0.80–0.90	≥0.98
Compute time/CGH (large)	100–200 ms (FFT)	8–20 ms (tiling/SGD, GPU)
Refresh Rate	<10 Hz	60–180 Hz (full-color possible)
Diffraction Efficiency	<50%	>90% (phase-only, no filtering)
Pixel Sampling	Continuous, speckled	Discretized, pseudo-digital

Phase-Only SLM Use: Phase-only modulation ensures nearly all photons contribute to desired output, a major improvement over amplitude masks or grayscale DMD projection (Madsen et al., 5 Dec 2025).
Lensless Configurations: Digital lens phases can eliminate the need for physical relay optics, permitting highly compact setups and removing sources of loss/scatter (Madsen et al., 5 Dec 2025, Madsen et al., 31 May 2024).
Speckle Suppression: Non-overlapping PSF design removes random phase interference, observed to reduce speckle contrast by a factor of 5–10 compared to AWGS-optimized holography (Glückstad et al., 2023).
Computational Efficiency: Tiling reduces complexity from $O(N^2 \log N)$ to $O((N/M)^2 M^2 \log M)$ per sub-hologram, enabling real-time CGH even on standard hardware (Madsen et al., 17 Sep 2024).
RGB and Broadband Support: Multi-wavelength operation is achieved by independently rescaling tile parameters and phase masks, with demonstrated full-color, single-shot reconstructions (Madsen et al., 17 Sep 2024).

5. Experimental Demonstrations and Performance Metrics

Experimental verifications span diverse beam-shaping and manufacturing applications:

Volumetric Additive Manufacturing (Lensless HoloVAM): The HoloTile framework enables direct, high-fidelity volumetric photopolymerization with near-unity optical throughput and sub-100 ms update cycles. Geometry complexity is limited only by the voxelization and SLM resolution, with typical photon efficiency exceeding 90% (Madsen et al., 5 Dec 2025).
Axial HoloTile: Experiments confirm >95–100% diffraction efficiency for Bessel-like beamlet projections over >10 mm axial depth, with central lobe diameter variation <10% and intensity fluctuations below ±5%, even at extended depths (Madsen et al., 31 May 2024).
HoloTile RGB: Single-shot, speckle-free, full-color holography at 60 Hz full-speed has been demonstrated with mean-squared error per channel ≤0.005 and pixel uniformity error <3% (Madsen et al., 17 Sep 2024).
Optical Trapping: Generation of >100 ring-shaped or vortex traps in parallel with <0.05 speckle contrast and dynamic update rates >100 Hz (Glückstad et al., 2023).

6. Applications, Limitations, and Future Directions

Applications

Volumetric Additive Manufacturing: High-contrast, lossless, and programmable curing in single-shot or rapid tomographic VAM processes (Madsen et al., 5 Dec 2025, Madsen et al., 31 May 2024).
Optical Tweezers: Parallel, aberration-corrected, speckle-suppressed ring/vortex traps for micromanipulation (Glückstad et al., 2023).
Quantum and Classical Communications: High-dimensional OAM beam multiplexing with minimal intermodal crosstalk (Glückstad et al., 2023).
Biophotonics and Optogenetics: Uniform, pixel-defined two-photon excitation patterns (Glückstad et al., 2023).
Full-Color and Multi-wavelength Projection: Discretized RGB/UV/IR holography for AR/VR and microscope imaging (Madsen et al., 17 Sep 2024).

Limitations and Research Directions

Coherence and Chromaticity: Current implementations require coherent, monochromatic sources; chromatic phase dispersion must be managed for polychromatic or ultrafast sources (Glückstad et al., 2023).
Resolution Trade-offs: Increasing non-diffractive beamlet length (Bessel core) requires more tiles, imposing a trade-off between propagation length, subhologram resolution, and overall SLM pixel count (Madsen et al., 31 May 2024).
System Aberrations: Residual aberrations (e.g., SLM non-uniformity, resin refractive index gradients) require analytic or ML-based compensation (Glückstad et al., 2023).
SLM and DMD Refresh Rates: Maximum dynamic update speed is bounded by modulator technology; DMD-based architectures offer higher frame rates but at binary phase resolution (Madsen et al., 31 May 2024).
Extensible Modalities: Ongoing work includes generalized PSF design for complex volumetric patterns, temporal multiplexing (multi-plane projections), and combined amplitude-phase encoding via GPC (Glückstad et al., 2023).

7. Representative Implementations and System Parameters

Component	Typical Value/Model
SLM	HoloEye GAEA-4K, 10 μm pitch, 1920–2160 px/side
Laser Source	He–Ne (633 nm), diode (450–638 nm), linewidth <1 MHz
PSF Forms	Square, disk, ring, vortex, Bessel, Airy, etc.
Update Rates	60–180 Hz (SLM), >1 kHz (DMD, binary)
Diffraction Efficiency	>90% (phase-only, no filtering)
Computational (per hologram)	8–25 ms (GPU, 2160×2160 px, full RGB)

These parameters enable deployment across biophotonic, manufacturing, display, and quantum optical platforms.

HoloTile CGH unifies tile-based phase modulation and analytic PSF engineering into a modular, computationally efficient, and experimentally robust toolkit for high-fidelity, high-throughput, and speckle-suppressed holographic beam shaping and volumetric light projection (Glückstad et al., 2023, Madsen et al., 31 May 2024, Madsen et al., 17 Sep 2024, Madsen et al., 5 Dec 2025).