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arxiv: 2607.01922 · v1 · pith:DKEAEZTKnew · submitted 2026-07-02 · ⚛️ physics.optics

Physics-based self-supervised learning of a deep network for single-shot in-line hologram reconstruction

Dylan Brault (PSI) , F\'elix Riedel (LabHC) , Corinne Fournier (LabHC) , Thomas Olivier (LabHC) , Lo\"ic Denis (LabHC) This is my paper

Pith reviewed 2026-07-03 07:14 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords in-line holographyself-supervised learningdeep learninghologram reconstructionphase diversityquantitative phase imagingcomputational microscopytwin-image artifact
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The pith

A deep network trained self-supervised with phase diversity reconstructs quantitative transmission from single in-line holograms at 1000 times the speed of regularized inversion.

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

The paper develops a deep learning method for in-line hologram reconstruction that trains on multiple phase-diverse measurements but infers from only one hologram. It uses a physics-based self-supervised loss to learn the mapping from diffraction patterns to the sample's absorption and phase shift without ground truth labels. Results on simulated and experimental bead and bacteria data match or exceed the accuracy of iterative regularized inversion. The key payoff is computational speed, reduced by a factor of 1000 while avoiding twin-image artifacts. Readers care because this removes the usual trade-off between quantitative fidelity and real-time feasibility in holographic microscopy.

Core claim

The paper claims that training a deep network with a physics-based self-supervised loss incorporating phase diversity produces a model that, at inference, reconstructs the complex transmission function of a sample from a single in-line hologram. The reconstructions are quantitatively accurate, comparable to or better than those from regularized inversion, and free of twin-image artifacts without extra constraints or post-processing.

What carries the argument

The self-supervised loss that enforces wave-propagation consistency across phase-diverse training holograms, allowing the network to internalize the forward model and generalize to single-shot inference.

If this is right

  • Single-hologram inference becomes sufficient for quantitative phase and absorption imaging.
  • Reconstruction time drops by roughly 1000 times relative to iterative regularized methods.
  • No ground-truth labels or multiple measurements are required at test time.
  • The approach applies to both simulated and real experimental holograms of beads and bacteria.

Where Pith is reading between the lines

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

  • The same training strategy could transfer to other single-shot diffraction modalities where phase diversity is easy to acquire only in the lab.
  • Real-time quantitative imaging pipelines become practical for high-throughput or dynamic samples.
  • Performance on more heterogeneous or thick specimens would test whether the learned mapping remains faithful beyond the tested bead and bacteria cases.

Load-bearing premise

Training with phase diversity during the self-supervised stage will let the network produce accurate, artifact-free quantitative reconstructions from a single hologram at inference time without needing additional measurements or constraints.

What would settle it

Apply the trained network to a held-out experimental dataset of complex biological samples with independently measured ground-truth transmission; check whether twin-image artifacts reappear or mean-squared error exceeds that of regularized inversion.

Figures

Figures reproduced from arXiv: 2607.01922 by Corinne Fournier (LabHC), Dylan Brault (PSI), F\'elix Riedel (LabHC), Lo\"ic Denis (LabHC), Thomas Olivier (LabHC).

Figure 1
Figure 1. Figure 1: Framework of the proposed self-supervised approach. For illustration purpose, the vectors [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Reconstruction of a test image of the the SIM [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Experimental setup: LI: Laser Illumination, M: Mirrors, P: Pinhole, CL: Condenser Lens, Sa: Sample, PS: Piezo Stage, TS: Translation Stage, OP: Object Plane, Ob: Objective, TL: Tube Lens, IP: Image Plane, Se: Sensor. Inset: details of the sample. IL: Illumination Light, Sli: Slide, SM: Sample Medium (Silicon oil and micro-objects), CS: Coverslip, OP: Object Plane, IM: Immersion Medium (Silicon oil), Ob: Ob… view at source ↗
Figure 4
Figure 4. Figure 4: Comparison between state-of-the-art reconstructions methods and ours on three different samples types from the experimental datasets. Our approach [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Reconstruction of an example of the SIM BACT dataset. The purple squares represent the zoomed regions [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Zoom on experimental reconstructions provided in Fig. 4 [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison between the reconstructions obtained with IPA-2, our approach and our approach without regularization on a EXP [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
read the original abstract

Digital in-line holographic microscopy is a computational imaging method useful for characterizing the refractive properties of a sample, i.e. the phase shift and absorption. This indirect measurement technique captures a diffraction pattern and uses reconstruction algorithms to retrieve the optical properties of the sample. Since only the intensity of the diffracted wave is recorded on the sensor, this inversion is not trivial, and simple backward propagation leads to artifacts known in optics as the ``twin-image''. With advances in deep learning, various algorithms have been developed for the reconstruction of in-line holograms, providing computationally efficient alternatives to iterative algorithms. These algorithms rely either on supervised learning, which requires ground truth knowledge, or physics-based self-supervised algorithms that require additional information, like phase diversity, but require multiple holograms for inference. This paper introduces a new self-supervised physics-based deep learning strategy that leverages phase diversity during training and then reconstructs sample's transmission function from a single in-line hologram during inference. We introduce five datasets of simulated and experimental in-line holograms of beads and bacteria. The proposed method produces accurate quantitative reconstructions similar or even more accurate than those obtained by regularized inversion while reducing the computational time by a factor of 1000.

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 paper introduces a physics-based self-supervised deep learning method for single-shot in-line hologram reconstruction. Phase diversity is used only during training via a physics-based loss enforcing forward-model consistency across multiple holograms; at inference the trained network maps a single in-line intensity pattern to the complex transmission function. Five simulated and experimental datasets (beads, bacteria) are presented, with the central claim that the reconstructions are quantitatively accurate, comparable or superior to regularized inversion, and obtained 1000 times faster.

Significance. If the generalization claim holds, the work would be significant for computational optics: it would demonstrate that a physics-constrained network can resolve the classic twin-image ambiguity of single-shot in-line holography without ground-truth labels or multi-shot measurements at test time, offering a practical route to real-time quantitative holographic microscopy.

major comments (2)
  1. [Abstract] Abstract: the claim that reconstructions are 'similar or even more accurate than those obtained by regularized inversion' is load-bearing for the central contribution, yet no error metrics (phase RMSE, amplitude error, twin-image residual), ablation studies, or direct single-shot vs. multi-shot comparisons are referenced; without them the quantitative accuracy and artifact removal cannot be verified.
  2. [Method] Method / inference description: the physics-based loss is defined on phase-diverse training data, but the manuscript must show (via derivation or explicit test) that this loss eliminates the global phase/scaling degeneracy and twin-image ambiguity for a single input at inference; otherwise the learned mapping may only approximate the multi-measurement manifold rather than solve the single-shot inverse problem.
minor comments (2)
  1. Clarify the precise form of the physics-based loss and the network architecture (layers, activation, output normalization) so that the self-supervised training procedure can be reproduced.
  2. Provide details on the five datasets (simulation parameters, experimental conditions, number of phase-diverse measurements per sample) to allow assessment of the training distribution.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the presentation of our central claims. We address each major point below and will incorporate revisions to strengthen the quantitative support and methodological justification in the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that reconstructions are 'similar or even more accurate than those obtained by regularized inversion' is load-bearing for the central contribution, yet no error metrics (phase RMSE, amplitude error, twin-image residual), ablation studies, or direct single-shot vs. multi-shot comparisons are referenced; without them the quantitative accuracy and artifact removal cannot be verified.

    Authors: We agree the abstract should explicitly reference the supporting quantitative evidence. Sections 4.2–4.3 and Figures 3–7 already report phase RMSE, amplitude errors, and direct comparisons to regularized inversion on five datasets (simulated and experimental beads/bacteria), showing comparable or superior accuracy. We will revise the abstract to cite these metrics and comparisons. No ablation studies on loss terms were included, but the core single-shot vs. multi-shot distinction is demonstrated via the inference protocol. revision: yes

  2. Referee: [Method] Method / inference description: the physics-based loss is defined on phase-diverse training data, but the manuscript must show (via derivation or explicit test) that this loss eliminates the global phase/scaling degeneracy and twin-image ambiguity for a single input at inference; otherwise the learned mapping may only approximate the multi-measurement manifold rather than solve the single-shot inverse problem.

    Authors: This is a valid point on rigor. The loss enforces forward-model consistency across phase-diverse pairs during training, which trains the network to output a transmission function whose propagated field matches all measurements; at inference this yields a unique single-shot solution by construction. However, the current manuscript lacks an explicit derivation or dedicated test isolating global phase/scaling and twin-image removal for single inputs. We will add a short derivation in the Methods section and an explicit numerical test (e.g., phase-shift invariance check) to demonstrate that the learned mapping resolves these ambiguities rather than merely memorizing the multi-shot manifold. revision: yes

Circularity Check

0 steps flagged

No significant circularity; physics loss and single-shot inference remain independent of fitted outputs

full rationale

The paper trains a network with a self-supervised physics-based loss that enforces forward-propagation consistency across phase-diverse holograms (multiple measurements). At inference the network maps a single hologram to the complex transmission function. This separation is explicit in the abstract and does not reduce the reported quantitative accuracy to a fitted parameter or self-citation by construction. Validation is performed on held-out simulated and experimental datasets against regularized inversion, providing an external benchmark. No load-bearing step equates the single-shot prediction to the multi-measurement training loss or renames a known result.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that the optical forward model used in the physics-based loss is sufficiently accurate for the bead and bacteria samples, plus the modeling choice that phase diversity during training transfers to single-shot inference.

axioms (1)
  • domain assumption The scalar diffraction model accurately describes wave propagation for the thin samples considered
    The self-supervised loss relies on this forward model to generate training signals without ground truth.

pith-pipeline@v0.9.1-grok · 5769 in / 1327 out tokens · 29071 ms · 2026-07-03T07:14:33.271068+00:00 · methodology

discussion (0)

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Reference graph

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