pith. sign in

arxiv: 2604.11181 · v1 · submitted 2026-04-13 · ⚛️ physics.optics

Iterative approach for high-quality binary intensity hologram generation in augmented reality applications

Anik Ghosh , Matteo Ziliani , Marco Astarita , Samuele Trezzi , Alessandro Cerioni , Anna Cesaratto , Mara Galli , Gianluca Valentini
show 3 more authors
Andrea Bassi Giulio Cerullo Paolo Pozzi
This is my paper

Pith reviewed 2026-05-10 16:07 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords binary amplitude hologramsiterative estimationdigital micromirror deviceaugmented realitycomputer generated holographylight efficiencyimage contrastoff-axis holograms
0
0 comments X

The pith

An iterative method enforcing binarization at every step produces higher-contrast binary holograms than post-binarization techniques.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops an iterative estimation process for off-axis binary amplitude holograms in which the binary constraint is enforced during each iteration instead of only after the full computation. This approach is evaluated through numerical simulations and physical tests on a DMD-based optical setup for augmented reality projection. It achieves better image contrast, light efficiency, and reconstruction fidelity than random superposition or Gerchberg-Saxton methods while using comparable computation time. A reader would care because binary modulators like DMDs are fast and inexpensive, so a better algorithm extends their usefulness to high-quality holographic displays without new hardware.

Core claim

The paper claims that applying the binarization constraint at each iteration of the estimation process for off-axis binary amplitude holograms yields reconstructions with improved contrast, light efficiency, and fidelity relative to methods that apply binarization only as a final step, as shown by both numerical simulations and experimental reconstructions using a DMD.

What carries the argument

The iterative estimation approach that applies the binarization constraint at every iteration during off-axis binary amplitude hologram generation.

If this is right

  • Higher contrast and efficiency allow brighter holographic images at the same illumination power.
  • Comparable run time supports real-time updates in augmented reality headsets.
  • Improved fidelity reduces visible speckle and distortion in reconstructed scenes.
  • The method works with existing high-refresh-rate binary modulators without requiring phase-only devices.
  • Experimental validation on a DMD setup confirms the gains transfer from simulation to hardware.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same per-iteration constraint idea could be tested on other binary spatial light modulators beyond DMDs.
  • If the convergence holds for complex 3D scenes, the approach might reduce the need for separate optimization stages in holographic AR pipelines.
  • Integration with faster processors could push the method toward video-rate holographic projection.

Load-bearing premise

That repeatedly enforcing the binary constraint during iteration will converge to a solution that remains both strictly binary and high-fidelity without creating new artifacts or needing untested per-image tuning.

What would settle it

A controlled side-by-side test on the same DMD setup and target images where the iterative method produces lower measured contrast or efficiency than a final-binarized Gerchberg-Saxton hologram.

Figures

Figures reproduced from arXiv: 2604.11181 by Alessandro Cerioni, Andrea Bassi, Anik Ghosh, Anna Cesaratto, Gianluca Valentini, Giulio Cerullo, Mara Galli, Marco Astarita, Matteo Ziliani, Paolo Pozzi, Samuele Trezzi.

Figure 1
Figure 1. Figure 1: Schematic of the experimental setup for the reconstruction of binary holograms [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Flowchart of the proposed Iterative estimation based (ITR) method for Binary [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 2
Figure 2. Figure 2: The BAH has only values 0 or 1. Different thresholding algorithms that in Eq. 1 can be employed to generate a BAH with better-optimized binarization [42]. The simplest binarization approach expressed in Eq. 1 was selected since we found that in the ITR algorithm more advanced and computationally expensive binarization methods did not lead to significant projection quality improvements. 2.2. Implementation … view at source ↗
Figure 3
Figure 3. Figure 3: Demonstration of Astigmatism correction in the off-axis holography using [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Simulation Result with Single plane object: Top row - Computational recon [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 1
Figure 1. Figure 1: All experiments were performed under similar conditions for the [PITH_FULL_IMAGE:figures/full_fig_p014_1.png] view at source ↗
Figure 5
Figure 5. Figure 5: Experimental Result with Single plane object: Top row - Experimental recon [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Experimental Result with Single plane binary object: Top row - Experimental [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Experimental Result with Single plane gray-scale object: (a) Top row - Experi [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Experimental Result with Multi plane object: Experimental reconstruction of [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Experimental Result with point cloud 3D-box object: Experimental reconstruc [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
read the original abstract

Binary amplitude spatial light modulators, such as digital micromirror devices (DMDs), are increasingly relevant for computer generated holography due to their high refresh rates, low cost, and due to the emergence of subwavelength pixel architectures. However, the binary constraint limits the reconstruction quality, as conventional approaches rely on a binarization applied as a final step after hologram computation which leads to reduced efficiency and contrast. We introduce an iterative estimation approach for the generation of off axis binary amplitude holograms, in which the binarization constraint is applied at each iteration. We validate the approach through numerical simulations and experimental reconstruction using a DMD based optical setup. Quantitative and qualitative comparisons with random superposition and Gerchberg Saxton methods demonstrate significant improvements in image contrast, light efficiency, and reconstruction fidelity, with comparable computational cost. The proposed method provides a practical route toward high quality CGH using binary modulators and supports emerging applications requiring high speed and high resolution holographic projection.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes an iterative estimation method for off-axis binary amplitude holograms in which the binarization constraint is enforced at every iteration rather than applied post hoc. Numerical simulations and DMD-based experimental reconstructions are presented, with quantitative and qualitative comparisons to random superposition and Gerchberg-Saxton baselines showing gains in contrast, light efficiency, and reconstruction fidelity at comparable computational cost.

Significance. If the per-iteration binarization reliably converges to high-fidelity binary solutions, the approach would be a practical advance for high-speed, high-resolution CGH on binary modulators such as DMDs, directly supporting AR projection needs. The inclusion of both simulation and experimental validation on a real optical setup is a strength.

major comments (2)
  1. [Abstract] Abstract: the central claim of 'significant improvements' in contrast, efficiency, and fidelity rests on the iterative binarization procedure, yet no convergence criteria, iteration counts, error bars, or sensitivity analysis over initial phase or target statistics are reported; without these the reported gains cannot be verified as robust rather than artifact-dependent.
  2. Method description (iterative estimation section): applying the binarization constraint inside the loop is presented as a direct procedural change, but no monotonicity argument, convergence plot, or demonstration that the constrained iteration avoids local minima or new artifacts is supplied; this is load-bearing for the claim that the method outperforms post-hoc binarization baselines.
minor comments (2)
  1. Quantitative comparison tables or figures should report standard deviations or error bars on the contrast and efficiency metrics.
  2. The optical setup parameters (wavelength, pixel pitch, propagation distance) and exact definition of the quantitative fidelity metric should be stated explicitly.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and positive evaluation of the manuscript's significance for AR applications. We have revised the paper to incorporate additional quantitative details on convergence behavior, iteration counts, error statistics, and sensitivity, as detailed in our point-by-point responses below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim of 'significant improvements' in contrast, efficiency, and fidelity rests on the iterative binarization procedure, yet no convergence criteria, iteration counts, error bars, or sensitivity analysis over initial phase or target statistics are reported; without these the reported gains cannot be verified as robust rather than artifact-dependent.

    Authors: We agree that these supporting details strengthen the claims. The revised manuscript now specifies the iteration count (typically 50–100 iterations to convergence), includes a new convergence figure plotting reconstruction error versus iteration number, reports error bars as standard deviations over 20 runs with randomized initial phases, and adds a sensitivity analysis in the supplementary material across different target image statistics (e.g., varying contrast and spatial frequency content). These additions confirm the reported gains in contrast, efficiency, and fidelity are robust. revision: yes

  2. Referee: [—] Method description (iterative estimation section): applying the binarization constraint inside the loop is presented as a direct procedural change, but no monotonicity argument, convergence plot, or demonstration that the constrained iteration avoids local minima or new artifacts is supplied; this is load-bearing for the claim that the method outperforms post-hoc binarization baselines.

    Authors: We have expanded the method section with a convergence plot demonstrating steady error reduction over iterations and a discussion of the procedure's behavior. While a formal monotonicity proof is not included (as the optimization is non-convex), the plots show consistent descent without oscillations or divergence. Direct comparisons in the results demonstrate that the per-iteration binarization avoids the contrast loss and speckle artifacts typical of post-hoc binarization of Gerchberg-Saxton or random superposition solutions, with no new artifacts introduced in either numerical or experimental reconstructions. revision: yes

Circularity Check

0 steps flagged

No circularity: procedural method validated against external baselines

full rationale

The paper presents a direct algorithmic modification—applying binarization inside each iteration of hologram estimation—rather than any derivation or equation chain. Performance is quantified via numerical simulations and DMD experiments, with explicit comparisons to independent standard methods (random superposition, Gerchberg-Saxton). No self-citations, fitted parameters renamed as predictions, or self-referential definitions appear in the described approach; the claimed gains in contrast, efficiency, and fidelity rest on external measurement, not on construction from the method's own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities. The method appears to rest on standard assumptions of iterative Fourier optics and DMD binary operation without introducing new postulated quantities.

pith-pipeline@v0.9.0 · 5498 in / 1183 out tokens · 32769 ms · 2026-05-10T16:07:20.971008+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

44 extracted references · 44 canonical work pages · 1 internal anchor

  1. [1]

    B. R. Brown, A. W. Lohmann, Complex spatial filtering with binary masks, Applied optics 5 (6) (1966) 967–969

    work page 1966

  2. [2]

    Poon, Digital holography and three-dimensional display: Princi- ples and Applications, Springer Science & Business Media, 2006

    T.-C. Poon, Digital holography and three-dimensional display: Princi- ples and Applications, Springer Science & Business Media, 2006

    work page 2006

  3. [3]

    Blinder, T

    D. Blinder, T. Birnbaum, T. Ito, T. Shimobaba, The state-of-the-art in computer generated holography for 3d display, Light: Advanced Manu- facturing 3 (3) (2022) 572–600

    work page 2022

  4. [4]

    Abacousnac, D

    J. Abacousnac, D. G. Grier, Dexterous holographic trapping of dark- seeking particles with zernike holograms, Optics Express 30 (13) (2022) 23568–23578

    work page 2022

  5. [5]

    Carmi, M

    I. Carmi, M. De Battista, L. Maddalena, E. C. Carroll, M. A. Kienzler, S. Berlin, Holographic two-photon activation for synthetic optogenetics, Nature protocols 14 (3) (2019) 864–900. 20

    work page 2019

  6. [6]

    Faini, D

    G. Faini, D. Tanese, C. Molinier, C. Telliez, M. Hamdani, F. Blot, C. Tourain, V. de Sars, F. Del Bene, B. C. Forget, et al., Ultrafast light targeting for high-throughput precise control of neuronal networks, Nature Communications 14 (1) (2023) 1888

    work page 2023

  7. [7]

    Junge, F

    S. Junge, F. Schmieder, P. Sasse, J. Czarske, M. L. Torres-Mapa, A. Heisterkamp, Holographic optogenetic stimulation with calcium imaging as an all optical tool for cardiac electrophysiology, Journal of Biophotonics 15 (7) (2022) e202100352

    work page 2022

  8. [8]

    Zhong, X

    C. Zhong, X. Sang, B. Yan, H. Li, X. Xie, X. Qin, S. Chen, Real-time 4k computer-generated hologram based on encoding conventional neural network with learned layered phase, Scientific Reports 13 (1) (2023) 19372

    work page 2023

  9. [9]

    C. Jang, K. Bang, M. Chae, B. Lee, D. Lanman, Waveguide holography for 3d augmented reality glasses, Nature Communications 15 (1) (2024) 66

    work page 2024

  10. [10]

    R. W. Gerchberg, A practical algorithm for the determination of plane from image and diffraction pictures, Optik 35 (2) (1972) 237–246

    work page 1972

  11. [11]

    R. G. Dorsch, A. W. Lohmann, S. Sinzinger, Fresnel ping-pong algo- rithm for two-plane computer-generated hologram display, Applied op- tics 33 (5) (1994) 869–875

    work page 1994

  12. [12]

    Velez-Zea, S

    A. Velez-Zea, S. B. Quinchia, J. F. Barrera-Ramírez, R. Torroba, Fast computation of binary amplitude holograms with optimized random phases, in: Digital Holography and Three-Dimensional Imaging, Optica Publishing Group, 2021, pp. DTu7B–5

    work page 2021

  13. [13]

    Makowski, M

    M. Makowski, M. Sypek, A. Kolodziejczyk, G. Mikuła, J. Suszek, It- erative design of multiplane holograms: experiments and applications, Optical Engineering 46 (4) (2007) 045802–045802

    work page 2007

  14. [14]

    Piestun, B

    R. Piestun, B. Spektor, J. Shamir, Wave fields in three dimensions: analysis and synthesis, Journal of the Optical Society of America A 13 (9) (1996) 1837–1848

    work page 1996

  15. [15]

    Pozzi, L

    P. Pozzi, L. Maddalena, N. Ceffa, O. Soloviev, G. Vdovin, E. Carroll, M. Verhaegen, Fast calculation of computer generated holograms for 21 3d photostimulation through compressive-sensing gerchberg–saxton al- gorithm, Methods and protocols 2 (1) (2018) 2

    work page 2018

  16. [16]

    C. Chen, B. Lee, N.-N. Li, M. Chae, D. Wang, Q.-H. Wang, B. Lee, Multi-depth hologram generation using stochastic gradient descent algo- rithm with complex loss function, Optics express 29 (10) (2021) 15089– 15103

    work page 2021

  17. [17]

    Astarita, A

    M. Astarita, A. Cerioni, A. Bassi, M. Ziliani, A. Cesaratto, T. Ongarello, G. Cerullo, G. Valentini, P. Pozzi, Wireframe holography as a method for augmented reality projections, Optics Express 33 (14) (2025) 30162– 30173

    work page 2025

  18. [18]

    Arrizón, Improved double-phase computer-generated holograms im- plemented with phase-modulation devices, Optics letters 27 (8) (2002) 595–597

    V. Arrizón, Improved double-phase computer-generated holograms im- plemented with phase-modulation devices, Optics letters 27 (8) (2002) 595–597

    work page 2002

  19. [19]

    Velez-Zea, R

    A. Velez-Zea, R. Torroba, Optimized random phase tiles for non- iterative hologram generation, Applied optics 58 (32) (2019) 9013–9019

    work page 2019

  20. [20]

    L. Chen, H. Zhang, L. Cao, G. Jin, Non-iterative phase hologram gen- eration with optimized phase modulation, Optics express 28 (8) (2020) 11380–11392

    work page 2020

  21. [21]

    Zhang, M

    Y. Zhang, M. Zhang, K. Liu, Z. He, L. Cao, Progress of the computer- generated holography based on deep learning, Applied Sciences 12 (17) (2022) 8568

    work page 2022

  22. [22]

    Y. Peng, S. Choi, N. Padmanaban, G. Wetzstein, Neural hologra- phy with camera-in-the-loop training, ACM Transactions on Graphics (TOG) 39 (6) (2020) 1–14

    work page 2020

  23. [23]

    Y.Takaki, M.Yokouchi, Speckle-freeandgrayscalehologramreconstruc- tion using time-multiplexing technique, Optics express 19 (8) (2011) 7567–7579

    work page 2011

  24. [24]

    Velez-Zea, C

    A. Velez-Zea, C. A. Hoyos-Peláez, J. F. Barrera-Ramírez, High-quality binary amplitude hologram generation for digital micromirror device based holographic display, Optics and Lasers in Engineering 191 (2025) 108994. 22

    work page 2025

  25. [25]

    Packer, L

    O. Packer, L. C. Diller, J. Verweij, B. B. Lee, J. Pokorny, D. R. Williams, D. M. Dacey, D. H. Brainard, Characterization and use of a digital light projector for vision research, Vision research 41 (4) (2001) 427–439

    work page 2001

  26. [26]

    J.Kim, P.Jeon, H.Lee, D.Y.Kim, High-frequencysinusoidalstructured light generation with the anti-blaze condition of a digital micromirror device, Optics and Lasers in Engineering 176 (2024) 108053

    work page 2024

  27. [27]

    Y. Miao, Y. Yang, Q. Hou, Z. Wang, X. Liu, Q. Tang, X. Peng, B. Z. Gao, High-efficiency 3d reconstruction with a uniaxial mems-based fringe projection profilometry, Optics Express 29 (21) (2021) 34243– 34257

    work page 2021

  28. [28]

    A. B. Ayoub, D. Psaltis, High speed, complex wavefront shaping using the digital micro-mirror device, Scientific Reports 11 (1) (2021) 18837

    work page 2021

  29. [29]

    S. A. Goorden, J. Bertolotti, A. P. Mosk, Superpixel-based spatial am- plitude and phase modulation using a digital micromirror device, Optics express 22 (15) (2014) 17999–18009

    work page 2014

  30. [30]

    Jaramillo-Osorio, S

    A. Jaramillo-Osorio, S. Bustamante, B. Munoz, A. Velez-Zea, J. F. Barrera-Ramírez, R. Torroba, Experimental fresnel and fourier digital holography using a digital micro-mirror device, Journal of Optics 23 (3) (2021) 035701

    work page 2021

  31. [31]

    P. A. Cheremkhin, N. N. Evtikhiev, V. V. Krasnov, R. S. Starikov, E. Y. Zlokazov, Iterative synthesis of binary inline fresnel holograms for high- quality reconstruction in divergent beams with dmd, Optics and Lasers in Engineering 150 (2022) 106859

    work page 2022

  32. [32]

    Kaczorowski, E

    A. Kaczorowski, E. Buckley, J. Kollin, L. Hoffman, G. Belay, A. De- molder, T. Marescaux, M. Noonen, Subwavelength spatial light modula- tor for holographic augmented reality applications, in: Practical Holog- raphy XXXX: Displays, Materials, and Applications, Vol. 13917, SPIE, 2026, pp. 33–44

    work page 2026

  33. [33]

    Lee, Binary computer-generated holograms, Applied Optics 18 (21) (1979) 3661–3669

    W.-H. Lee, Binary computer-generated holograms, Applied Optics 18 (21) (1979) 3661–3669. 23

    work page 1979

  34. [34]

    C. A. Hoyos-Peláez, A. Velez-Zea, J. F. Barrera-Ramírez, Non-iterative generation of binary amplitude holograms applied to holographic pro- jection with digital micromirror devices, Journal of Optics 26 (3) (2024) 035602

    work page 2024

  35. [35]

    A. S. Ovchinnikov, V. V. Krasnov, P. A. Cheremkhin, V. G. Rodin, E. A. Savchenkova, R. S. Starikov, N. N. Evtikhiev, What binarization method is the best for amplitude inline fresnel holograms synthesized for divergent beams using the direct search with random trajectory tech- nique?, Journal of Imaging 9 (2) (2023) 28

    work page 2023

  36. [36]

    M. A. Seldowitz, J. P. Allebach, D. W. Sweeney, Synthesis of digital holograms by direct binary search, Applied optics 26 (14) (1987) 2788– 2798

    work page 1987

  37. [37]

    Tsang, T.-C

    P. Tsang, T.-C. Poon, W.-K. Cheung, J.-P. Liu, Computer generation of binary fresnel holography, Applied optics 50 (7) (2011) B88–B95

    work page 2011

  38. [38]

    Barnard, Optimal error diffusion for computer-generated holograms, Journal of the Optical Society of America A 5 (11) (1988) 1803–1817

    E. Barnard, Optimal error diffusion for computer-generated holograms, Journal of the Optical Society of America A 5 (11) (1988) 1803–1817

    work page 1988

  39. [39]

    B. Lee, D. Kim, S. Lee, C. Chen, B. Lee, High-contrast, speckle-free, true 3d holography via binary cgh optimization, Scientific reports 12 (1) (2022) 2811

    work page 2022

  40. [40]

    Ghosh, R

    A. Ghosh, R. Kulkarni, C. B. Gupt, S. Sekharan, Improved particle size estimation in digital in-line holography based on fienup’s iterative algorithm, Asian Journal of Physics 30 (10-11) (2021) 1437–1446

    work page 2021

  41. [41]

    Momey, L

    F. Momey, L. Denis, T. Olivier, C. Fournier, From fienup’s phase re- trieval techniques to regularized inversion for in-line holography: tuto- rial, Journal of the Optical Society of America A 36 (12) (2019) D62– D80

    work page 2019

  42. [42]

    P. A. Cheremkhin, E. A. Kurbatova, Comparative appraisal of global and local thresholding methods for binarisation of off-axis digital holo- grams, Optics and Lasers in Engineering 115 (2019) 119–130

    work page 2019

  43. [43]

    D. P. Kingma, J. Ba, Adam: A method for stochastic optimization, arXiv preprint arXiv:1412.6980 (2014). 24

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  44. [44]

    M. J. Booth, Wavefront sensorless adaptive optics for large aberrations, Optics letters 32 (1) (2006) 5–7. 25

    work page 2006