pith. sign in

arxiv: 1907.06081 · v3 · pith:QYWYANICnew · submitted 2019-07-13 · ⚛️ physics.optics · eess.IV

Preliminary study on the modal decomposition of Hermite Gaussian beams via deep learning

Yi An , Tianyue Hou , Jun Li , Liangjin Huang , Jinyong Leng , Lijia Yang , Pu Zhou This is my paper

Pith reviewed 2026-05-24 21:46 UTC · model grok-4.3

classification ⚛️ physics.optics eess.IV
keywords Hermite-Gaussian beamsmodal decompositiondeep learningbeam characterizationintensity imagingoptical modes
0
0 comments X

The pith

A deep neural network recovers both the power content and phases of Hermite-Gaussian beams from a single intensity image.

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

The paper shows that deep learning can perform modal decomposition on Hermite-Gaussian beams. It takes one beam intensity photograph as input and returns the fraction of power in each mode plus the relative phases between them. This replaces slower or more hardware-intensive traditional decomposition techniques. A reader would care because the approach is described as fast, low-cost, and suitable for practical optical work such as beam shaping and resonator diagnostics.

Core claim

The authors demonstrate for the first time a deep learning method for modal decomposition of Hermite-Gaussian beams. The network is trained on simulated intensity patterns of mode superpositions and, when given a single experimental intensity image, outputs the modal power coefficients together with phase information. The method is presented as a fast, economical, and robust route to beam characterization that supports applications in beam shaping, quality assessment, and studies of resonator perturbations.

What carries the argument

A deep neural network trained to map single-shot intensity images of Hermite-Gaussian mode mixtures directly to modal power coefficients and relative phases.

If this is right

  • Provides modal power and phase data in a single camera exposure instead of multiple sequential measurements.
  • Supports real-time monitoring during beam shaping or resonator experiments.
  • Reduces equipment needs for routine Hermite-Gaussian beam analysis.
  • Yields phase information without separate interferometric setups.

Where Pith is reading between the lines

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

  • The same network architecture might be retrained for other complete mode bases such as Laguerre-Gaussian beams.
  • If the simulation-to-experiment transfer holds, laboratories could replace specialized mode analyzers with an ordinary camera plus the trained model.
  • Higher-order or aberrated beams not represented in the training set would provide a direct test of generalization limits.

Load-bearing premise

A network trained exclusively on simulated intensity patterns will give accurate modal coefficients and phases when shown real camera images of actual Hermite-Gaussian beams.

What would settle it

Capture experimental intensity images of known Hermite-Gaussian mode combinations and check whether the network's predicted coefficients and phases match independent measurements made with conventional modal decomposition on the same beams.

Figures

Figures reproduced from arXiv: 1907.06081 by Jinyong Leng, Jun Li, Liangjin Huang, Lijia Yang, Pu Zhou, Tianyue Hou, Yi An.

Figure 1
Figure 1. Figure 1: The intensity profiles of the former sixth HG modes. HG modes make up a complete and orthonormal basis so that an arbitrary transverse field U can be expanded into a superposition of these modes[16] 00 ( , ) ( , ), mn i mn mn mn mn mn U x y c HG x y c e    == ==  (2) 2 00 1, [ , ] mn mn mn      ==  =  − (3) where 2  mn denotes the modal weights while  mn is the modal phases. Since only the… view at source ↗
read the original abstract

The Hermite-Gaussian (HG) modes make up a complete and orthonormal basis, which have been extensively used to describe optical fields. Here, we demonstrate, for the first time to our knowledge, deep learning-based modal decomposition (MD) of HG beams. This method offers a fast, economical and robust way to acquire both the power content and phase information through a single-shot beam intensity image, which will be beneficial for the beam shaping, beam quality assessment, studies of resonator perturbations, and other further research on the HG beams.

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 presents a preliminary simulation-based study demonstrating the use of a convolutional neural network for modal decomposition of Hermite-Gaussian beams. It claims that the trained network can extract both modal power coefficients and relative phases from a single-shot intensity image, offering a fast and robust alternative to conventional methods.

Significance. If the sim-to-real generalization holds and the network proves accurate on experimental data, the method could enable efficient single-shot beam characterization useful for resonator studies and beam shaping. The current results are limited to ideal simulated patterns, so the practical significance remains prospective rather than demonstrated.

major comments (2)
  1. [Results] Results section: All reported performance metrics derive from noise-free, perfectly aligned simulated HG superpositions; no tests with sensor noise, misalignment, wavefront aberrations, or real camera images are shown, which directly undermines the abstract claim of a 'robust' practical method.
  2. [Methods] Methods section: The manuscript provides no information on the training/validation split, network architecture details (layers, activation functions, hyperparameters), or quantitative error metrics (e.g., MAE on held-out modal coefficients) on unseen simulated data, preventing assessment of whether the learned mapping is reliable.
minor comments (2)
  1. [Title/Abstract] The title uses 'Preliminary study' but the abstract asserts a general practical method; this mismatch should be clarified for consistency.
  2. [Figures] Figure captions and axis labels lack units or normalization details for the intensity images and coefficient outputs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our preliminary simulation study. We agree that the work is limited in scope and will revise the manuscript to address the methodological omissions and to better contextualize the results and claims.

read point-by-point responses

  1. Referee: [Results] Results section: All reported performance metrics derive from noise-free, perfectly aligned simulated HG superpositions; no tests with sensor noise, misalignment, wavefront aberrations, or real camera images are shown, which directly undermines the abstract claim of a 'robust' practical method.

    Authors: We agree that all presented results are from ideal simulated patterns and that this limits the demonstrated practicality. As the title indicates, this is a preliminary study focused on establishing the feasibility of the DL approach in simulation. The word 'robust' in the abstract was meant to highlight the method's conceptual advantages (single-shot, fast inference) rather than proven experimental resilience. In revision we will (i) add a Limitations subsection explicitly stating the simulation-only scope, (ii) tone down the abstract claim to 'potentially robust', and (iii) include a short additional experiment with additive Gaussian noise on the simulated images to provide an initial indication of noise tolerance. Full experimental validation with real camera data remains future work. revision: partial

  2. Referee: [Methods] Methods section: The manuscript provides no information on the training/validation split, network architecture details (layers, activation functions, hyperparameters), or quantitative error metrics (e.g., MAE on held-out modal coefficients) on unseen simulated data, preventing assessment of whether the learned mapping is reliable.

    Authors: We apologize for these omissions. The revised Methods section will explicitly state the training/validation/test split ratios, provide the full CNN architecture (number of layers, filter sizes, activation functions), list all hyperparameters (learning rate, batch size, optimizer, epochs), and report quantitative metrics including mean absolute error (MAE) and root-mean-square error on the modal coefficients for a held-out simulated test set. These additions will allow readers to evaluate the reliability of the learned mapping. revision: yes

Circularity Check

0 steps flagged

No circularity; standard supervised DL mapping from simulated intensities to coefficients

full rationale

The paper presents a CNN trained on simulated HG mode superpositions to regress modal coefficients and phases from intensity images. This is a conventional supervised learning setup with no self-referential equations, fitted parameters renamed as predictions, or load-bearing self-citations that reduce the claimed decomposition to its own inputs by construction. The method learns an external mapping rather than deriving results tautologically from the same data or prior self-work.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no equations, training details, or dataset description, so the ledger cannot be populated with concrete free parameters, axioms, or invented entities.

pith-pipeline@v0.9.0 · 5627 in / 1070 out tokens · 14647 ms · 2026-05-24T21:46:59.613343+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

27 extracted references · 27 canonical work pages · 1 internal anchor

  1. [1]

    They are related to orbital angular momentum (OAM) beams[3], optical communications[4] and quantum information processing[5]

    Introduction Hermite-Gaussian (HG) [1] and Laguerre–Gaussian (LG) beams[2], usually generated from the solid-state lasers, are gaining increasing interest in both fundamental and applied research fields. They are related to orbital angular momentum (OAM) beams[3], optical communications[4] and quantum information processing[5]. Recent years, much attentio...

    work page

  2. [2]

    The intensity profiles of the former sixth HG modes are illustrated in Fig

    Method 2.1 The basics of modal decomposition HG beams can be generated from l aser resonators with rectangular geometry and the field distribution of HG mod es can be expressed as[21] 22 2 0 0 0 0 1 2 2 2( , ) ( ) ( )exp( )2 ! ! mn m n mn xyHG x y H x H yw w w m n w+ +=− (1) where w0 denotes waist radius of the fundamental mode HG 00 and Hl is Hermite po...

    work page

  3. [3]

    In every training epoch, 50000 beam intensity images with a resolution of 128 ×128 are randomly generated to train the CNN

    Results and discussion We take the former sixth HG modes as an example to verify the principle of our s cheme. In every training epoch, 50000 beam intensity images with a resolution of 128 ×128 are randomly generated to train the CNN. The training is on a desktop computer w ith an Intel Core i7 -8700 CPU and GTX 1080 GPU and the learning rate is set as 0....

    work page

  4. [4]

    Our approach only requires a single -shot beam image, so that greatly reduce the operation efforts and consuming time

    Conclusion In this paper, we have proposed the modal decomposition of HG beams via deep learning for the first time, which is demonstrated through 6 -mode simulated beam intensity im ages. Our approach only requires a single -shot beam image, so that greatly reduce the operation efforts and consuming time. With a trained CNN, both the modal weights and ph...

    work page

  5. [5]

    Hermite–Gaussian functions of complex argument as optical-beam eigenfunctions,

    A. Siegman, "Hermite–Gaussian functions of complex argument as optical-beam eigenfunctions," JOSA 63, 1093-1094 (1973)

    work page 1973

  6. [6]

    Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes,

    L. Allen, M. W. Beijersbergen, R. Spreeuw, and J. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Physical Review A 45, 8185 (1992)

    work page 1992

  7. [7]

    Orbital angular momentum: origins, behavior and applications,

    A. M. Yao and M. J. Padgett, "Orbital angular momentum: origins, behavior and applications," Advances in Optics and Photonics 3, 161-204 (2011)

    work page 2011

  8. [8]

    Terabit free-space data transmission employing orbital angular momentum multiplexing,

    J. Wang, J.-Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, and M. Tur, "Terabit free-space data transmission employing orbital angular momentum multiplexing," Nature photonics 6, 488 (2012)

    work page 2012

  9. [9]

    Entanglement of the orbital angular momentum states of photons,

    A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature 412, 313- 316 (2001)

    work page 2001

  10. [10]

    High-Power Higher Order Hermite–Gaussian and Laguerre–Gaussian Beams From Vertical External Cavity Surface Emitting Lasers,

    M. L. Lukowski, J. T. Meyer, C. Hessenius, E. M. Wright, and M. Fallahi, "High-Power Higher Order Hermite–Gaussian and Laguerre–Gaussian Beams From Vertical External Cavity Surface Emitting Lasers," IEEE Journal of Selected Topics in Quantum Electronics 25, 1-6 (2019)

    work page 2019

  11. [11]

    Creation and detection of optical modes with spatial light modulators,

    A. Forbes, A. Dudley, and M. McLaren, "Creation and detection of optical modes with spatial light modulators," Advances in Optics and Photonics 8, 200-227 (2016)

    work page 2016

  12. [12]

    Controllable conversion between Hermite Gaussian and Laguerre Gaussian modes due to cross phase,

    G. Liang and Q. Wang, "Controllable conversion between Hermite Gaussian and Laguerre Gaussian modes due to cross phase," Opt. Express 27, 10684-10691 (2019)

    work page 2019

  13. [13]

    Hermite–Gaussian mode sorter,

    Y. Zhou, J. Zhao, Z. Shi, S. M. H. Rafsanjani, M. Mirhosseini, Z. Zhu, A. E. Willner, and R. W. Boyd, "Hermite–Gaussian mode sorter," Opt. Lett. 43, 5263-5266 (2018)

    work page 2018

  14. [14]

    Spatial mode multiplexing/demultiplexing by Gouy phase interferometry,

    J. Liñ ares, X. Prieto-Blanco, C. Montero-Orille, and V. Moreno, "Spatial mode multiplexing/demultiplexing by Gouy phase interferometry," Opt. Lett. 42, 93-96 (2017)

    work page 2017

  15. [15]

    Wavefront reconstruction by modal decomposition,

    C. Schulze, D. Naidoo, D. Flamm, O. Schmidt, A. Forbes, and M. Duparre, "Wavefront reconstruction by modal decomposition," Opt. Express 20, 19714-19725 (2012)

    work page 2012

  16. [16]

    Measurement of the orbital angular momentum density of light by modal decomposition,

    C. Schulze, A. Dudley, D. Flamm, M. Duparre, and A. Forbes, "Measurement of the orbital angular momentum density of light by modal decomposition," New Journal of Physics 15, 073025 (2013)

    work page 2013

  17. [17]

    Deep learning enabled superfast and accurate M2 evaluation for fiber beams,

    Y. An, J. Li, L. Huang, J. Leng, L. Yang, and P. Zhou, "Deep learning enabled superfast and accurate M2 evaluation for fiber beams," Opt. Express 27, 18683-18694 (2019)

    work page 2019

  18. [18]

    Coherence theoretic algorithm to determine the transverse-mode structure of lasers,

    J. Turunen, E. Tervonen, and A. T. Friberg, "Coherence theoretic algorithm to determine the transverse-mode structure of lasers," Opt. Lett. 14, 627-629 (1989)

    work page 1989

  19. [19]

    Transverse laser-mode structure determination from spatial coherence measurements: experimental results,

    E. Tervonen, J. Turunen, and A. T. Friberg, "Transverse laser-mode structure determination from spatial coherence measurements: experimental results," Applied Physics B 49, 409-414 (1989)

    work page 1989

  20. [20]

    Real-time determination of laser beam quality by modal decomposition,

    O. A. Schmidt, C. Schulze, D. Flamm, R. Brü ning, T. Kaiser, S. Schrö ter, and M. Duparré , "Real-time determination of laser beam quality by modal decomposition," Opt. Express 19, 6741-6748 (2011)

    work page 2011

  21. [21]

    Intensity-based modal decomposition of optical beams in terms of Hermite–Gaussian functions,

    X. Xue, H. Wei, and A. G. Kirk, "Intensity-based modal decomposition of optical beams in terms of Hermite–Gaussian functions," JOSA A 17, 1086-1091 (2000)

    work page 2000

  22. [22]

    Transverse mode analysis of a laser beam by near- and far-field intensity measurements,

    A. Cutolo, T. Isernia, I. Izzo, R. Pierri, and L. Zeni, "Transverse mode analysis of a laser beam by near- and far-field intensity measurements," Appl. Opt. 34, 7974-7978 (1995)

    work page 1995

  23. [23]

    Mode analysis with a spatial light modulator as a correlation filter,

    D. Flamm, D. Naidoo, C. Schulze, A. Forbes, and M. Duparré , "Mode analysis with a spatial light modulator as a correlation filter," Opt. Lett. 37, 2478-2480 (2012)

    work page 2012

  24. [24]

    Imagenet classification with deep convolutional neural networks,

    A. Krizhevsky, I. Sutskever, and G. E. Hinton, "Imagenet classification with deep convolutional neural networks," in Advances in neural information processing systems, 2012), 1097-1105

    work page 2012

  25. [25]

    Laser beams and resonators,

    H. Kogelnik and T. Li, "Laser beams and resonators," Appl. Opt. 5, 1550-1567 (1966)

    work page 1966

  26. [26]

    Learning to decompose the modes in few-mode fibers with deep convolutional neural network,

    Y. An, L. Huang, J. Li, J. Leng, L. Yang, and P. Zhou, "Learning to decompose the modes in few-mode fibers with deep convolutional neural network," Opt. Express 27, 10127-10137 (2019)

    work page 2019

  27. [27]

    Very Deep Convolutional Networks for Large-Scale Image Recognition

    K. Simonyan and A. Zisserman, "Very deep convolutional networks for large-scale image recognition," arXiv preprint arXiv:1409.1556 (2014)

    work page internal anchor Pith review Pith/arXiv arXiv 2014