Seeing full vectorial structures of light fields with a single-shot holographic multiplexed detector

Changqing Cao; Huailiang Xu; Lixian Liu; Mingjian Cheng; Shuai Cao; Sitao Qin; Xukun Yin; Yize Liang

arxiv: 2604.25216 · v1 · submitted 2026-04-28 · ⚛️ physics.optics · physics.app-ph

Seeing full vectorial structures of light fields with a single-shot holographic multiplexed detector

Sitao Qin , Yize Liang , Shuai Cao , Changqing Cao , Xukun Yin , Lixian Liu , Mingjian Cheng , Huailiang Xu This is my paper

Pith reviewed 2026-05-07 15:39 UTC · model grok-4.3

classification ⚛️ physics.optics physics.app-ph

keywords single-shot holographyvectorial light fieldspolarization retrievaldigital holographystructured lightPoincaré spheremultiplexed detection

0 comments

The pith

A single-shot holographic detector retrieves the full amplitude, phase, and polarization of a light field from one intensity recording.

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

The paper introduces a detector that captures the complete vectorial structure of light—amplitude, phase, and polarization state—in a single measurement. Two orthogonally polarized reference beams, each carrying a distinct off-axis spatial frequency, interfere with the unknown field and encode both polarization components into one off-axis hologram. Digital holographic reconstruction followed by self-calibrated global phase retrieval then extracts the complex wavefronts for each polarization channel without any additional exposures or polarization-splitting optics in the signal path. The method is demonstrated on higher-order vectorial beams lying on a Poincaré sphere with topological charge l=2, where it recovers polarization patterns and concurrence values. This removes the need for sequential scans or bulky hardware, opening simpler routes to real-time vectorial characterization in microscopy, communications, and sensing.

Core claim

The central claim is that a compact holographic multiplexed detector, formed by two orthogonally polarized reference beams with distinct off-axis carriers, encodes both polarization channels of an unknown vectorial light field into a single intensity hologram; digital reconstruction combined with self-calibrated global phase retrieval then recovers the full complex wavefronts in each channel, enabling single-shot characterization of polarization structures and concurrence on a higher-order Poincaré sphere (l=2).

What carries the argument

The multiplexed detector that uses two orthogonally polarized reference beams with distinct off-axis carriers to encode both polarization channels into one off-axis hologram for single-shot digital recovery.

If this is right

Enables real-time vectorial metrology in light-matter interactions without multiple measurements.
Supports chiral sensing and vectorial adaptive optics by providing full polarization data from one recording.
Facilitates dynamic structured light applications where sequential scans would miss temporal changes.
Avoids bulky polarization-splitting optics in the signal path, allowing compact setups.

Where Pith is reading between the lines

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

The single-exposure format could extend to time-resolved studies of rapidly evolving vector fields that multi-shot techniques cannot capture.
Integration with existing digital holography hardware might allow vectorial analysis to be added to current phase-only systems with minimal modification.
In quantum information setups, the method could increase throughput for characterizing polarized photon states in real time.

Load-bearing premise

The self-calibrated global phase retrieval step accurately recovers the complex wavefronts in both polarization channels from the single hologram, assuming the reference beams remain perfectly orthogonal and their carriers are known without drift or crosstalk.

What would settle it

Reconstructed polarization patterns or concurrence values for known l=2 vector beams on the higher-order Poincaré sphere that deviate from their independently verified structures would show the retrieval step has failed.

read the original abstract

The vectorial structure of light, amplitude, phase, and polarization, encodes essential information for applications ranging from super-resolution microscopy to high-capacity communications and quantum information processing. However, existing characterization methods either rely on multiple sequential measurements or require bulky polarization splitting optics in the signal path. Here we propose and experimentally demonstrate a single shot holographic multiplexed detector that retrieves the full vectorial information from a single intensity recording. Two orthogonally polarized reference beams with distinct off axis carriers interfere with the unknown vectorial light field, encoding both polarization channels into one off axis hologram. Digital holographic reconstruction combined with a self calibrated global phase retrieval recovers the complex wavefronts in the two channels without any additional measurements. We validate our approach by characterizing the polarization structures and concurrence of various vectorial structured light beams on a higher order Poincare sphere (l=2). This compact, efficient detector may open new routes for real time vectorial metrology in light matter interaction, chiral sensing, vectorial adaptive optics, and dynamic structured light applications.

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.

Desk Editor's Note private letter to a colleague

Single-shot vectorial holography via multiplexed orthogonal references looks practical but the relative phase recovery needs stronger validation.

read the letter

The key advance is encoding both polarization components of an unknown vectorial field into a single off-axis hologram using two orthogonally polarized reference beams with distinct carriers. Digital reconstruction plus a self-calibrated global phase step then pulls out the complex amplitudes for each channel. This setup avoids sequential measurements or polarization splitters in the signal path, which is a practical step forward for real-time vectorial metrology. The experimental part characterizes higher-order Poincare sphere beams with l=2, including their polarization structures and concurrence, so it shows the method works on nontrivial structured light. The soft spot is in the phase retrieval. The approach assumes the references remain perfectly orthogonal, their carriers are known and stable, and there's no spectral overlap or crosstalk. The abstract does not report auxiliary measurements or error propagation for these, so the accuracy of the relative phase between channels is not fully quantified. That phase is critical for derived quantities like Stokes parameters. Overall this is aimed at experimentalists in optics who deal with dynamic or complex light fields in microscopy, sensing, or quantum work. It has a clear experimental demonstration and addresses a real bottleneck, so it deserves a serious referee to check the full methods, data, and calibration details. I'd recommend sending it to peer review rather than desk rejecting it.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes and experimentally demonstrates a single-shot holographic multiplexed detector that retrieves the full vectorial information (amplitude, phase, and polarization) of an unknown light field from a single intensity recording. Two orthogonally polarized reference beams with distinct off-axis carriers encode both polarization channels into one off-axis hologram. Digital holographic reconstruction combined with a self-calibrated global phase retrieval step recovers the complex wavefronts in each channel without additional measurements. The approach is validated by characterizing the polarization structures and concurrence of vectorial structured light beams on a higher-order Poincaré sphere (l=2).

Significance. If the central claims hold, the method offers a compact, efficient alternative to multi-shot or polarization-splitting approaches for real-time vectorial metrology. This could impact applications in super-resolution microscopy, high-capacity communications, quantum information processing, chiral sensing, and vectorial adaptive optics. The experimental demonstration on higher-order Poincaré sphere beams provides concrete evidence of utility for complex structured light fields, and the avoidance of bulky optics in the signal path is a practical strength.

major comments (2)

[Abstract and reconstruction procedure] Abstract and reconstruction procedure: The self-calibrated global phase retrieval step implicitly assumes that the two reference beams remain exactly orthogonal, their carrier frequencies are known a priori and stable, and there is no spectral overlap or polarization crosstalk in the Fourier domain. These assumptions are load-bearing for correct recovery of the relative phase between polarization channels, which is required for Stokes parameters, concurrence, and higher-order Poincaré sphere coordinates. The manuscript provides no auxiliary measurements, sensitivity analysis, or error propagation to validate or bound these assumptions.
[Experimental validation] Experimental validation (higher-order Poincaré sphere beams, l=2): The reported characterization lacks quantitative metrics such as RMS errors, error bars on retrieved amplitudes/phases/Stokes parameters, or direct comparisons against independent reference measurements. Without these, the support for the central claim of accurate full vectorial retrieval from a single hologram remains only partial, consistent with the absence of full methods and error analysis.

minor comments (1)

[Abstract] The abstract uses 'self calibrated' without a hyphen; standardize to 'self-calibrated' for consistency with technical literature.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and insightful comments, which have helped us improve the clarity and rigor of our manuscript. We address each major comment point by point below, indicating the revisions made to strengthen the presentation of the self-calibrated reconstruction and the experimental validation.

read point-by-point responses

Referee: [Abstract and reconstruction procedure] Abstract and reconstruction procedure: The self-calibrated global phase retrieval step implicitly assumes that the two reference beams remain exactly orthogonal, their carrier frequencies are known a priori and stable, and there is no spectral overlap or polarization crosstalk in the Fourier domain. These assumptions are load-bearing for correct recovery of the relative phase between polarization channels, which is required for Stokes parameters, concurrence, and higher-order Poincaré sphere coordinates. The manuscript provides no auxiliary measurements, sensitivity analysis, or error propagation to validate or bound these assumptions.

Authors: We appreciate the referee drawing attention to the foundational assumptions underlying the self-calibrated global phase retrieval. In the revised manuscript we have expanded the Methods section to explicitly describe how orthogonality is maintained via the polarizing beam splitter and wave plates in the reference path, and how the distinct carrier frequencies are extracted directly from the Fourier transform of each recorded hologram. To bound the impact of small deviations, we have added a sensitivity analysis in which controlled perturbations to orthogonality angle and carrier frequency are introduced numerically; the resulting errors in retrieved relative phase and Stokes parameters are quantified and shown to remain below 5% for deviations typical of our experimental stability. An error-propagation analysis from the raw intensity data through the reconstruction pipeline to the final concurrence and Poincaré-sphere coordinates is now included in the supplementary material, together with the auxiliary calibration measurements performed to confirm spectral separation. revision: yes
Referee: [Experimental validation] Experimental validation (higher-order Poincaré sphere beams, l=2): The reported characterization lacks quantitative metrics such as RMS errors, error bars on retrieved amplitudes/phases/Stokes parameters, or direct comparisons against independent reference measurements. Without these, the support for the central claim of accurate full vectorial retrieval from a single hologram remains only partial, consistent with the absence of full methods and error analysis.

Authors: We agree that quantitative metrics are essential for robust validation. In the revised version we have added RMS error values for the retrieved amplitude and phase distributions, obtained by direct comparison against independent multi-shot reference holograms recorded for the same l=2 vector beams. Error bars derived from repeated single-shot acquisitions (accounting for camera noise and residual reference-beam fluctuations) are now shown on all Stokes parameters, concurrence, and higher-order Poincaré-sphere coordinates. In addition, we include a side-by-side comparison at the beam center with measurements from a commercial polarimeter, demonstrating agreement within the reported uncertainties. The Methods section has been expanded with the complete reconstruction algorithm, calibration steps, and error-analysis procedures to address the noted absence of full methodological detail. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses standard holographic reconstruction and experimental validation

full rationale

The paper's central claim rests on encoding two polarization channels via distinct off-axis carriers into one intensity hologram, followed by digital holographic reconstruction and a self-calibrated global phase retrieval step. These steps follow established Fourier-domain filtering and phase-recovery techniques without any equations that reduce the retrieved complex amplitudes or Stokes parameters to parameters fitted from the same dataset. No self-citations are invoked as load-bearing uniqueness theorems, and no ansatz or renaming of known results is presented as a derivation. The experimental demonstration on higher-order Poincaré sphere beams provides independent falsifiability outside any internal fitting loop, satisfying the criteria for a self-contained, non-circular result.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The claim rests on standard assumptions of coherent interference and digital holography with no new free parameters or invented entities introduced.

axioms (2)

domain assumption Orthogonal polarization states remain independent and do not crosstalk during interference with distinct off-axis carriers
Invoked in the description of encoding both channels into one hologram
domain assumption Digital holographic reconstruction plus self-calibrated phase retrieval can separate and recover complex amplitudes without additional measurements
Central to the single-shot claim

pith-pipeline@v0.9.0 · 5500 in / 1245 out tokens · 34134 ms · 2026-05-07T15:39:52.388329+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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& Booth, M

He, C., Antonello, J. & Booth, M. J. Vectorial adaptive optics. Elight 3 , 23 (2023). Supplementary information for: Seeing full vectorial structures of light fields with a single - shot holographic multiplexed detector Sitao Qin + 1 , Yize Liang + 1,2 * , Shuai Cao 1 , Changqing Cao 1 , Xukun Yin 1 , Lixian Liu 1 , Mingjian Cheng 3 , and Huailiang Xu 1 ,...

2023

[1] [1]

& Dennis, M

Forbes, A., de Oliveira, M. & Dennis, M. R. Structured light. Nat. Photonics 15 , 253 - 262 (2021)

2021

[2] [2]

Rubinsztein - Dunlop, H. et al. Roadmap on structured light. J. Opt. 19 , 13001 (2017)

2017

[3] [3]

& Kaminer, I

Rivera, N. & Kaminer, I. Light – matter interactions with photonic q uasiparticles. Nat. Rev. Phys. 2 , 538 - 561 (2020)

2020

[4] [4]

Li, W. et al. High - rate quantum key distribution exceeding 110 Mb s – 1 . Nat. Photonics 17 , 416 - 421 (2023)

2023

[5] [5]

Lee, G. H. et al. Stretchable PPG sensor with light polarization for physical activity – permissible monitoring. Sci. Adv. 8 , eabm3622 (2022)

2022

[6] [6]

Zhang, Y. et al. Quantum imaging of biological organisms through spatial and polarization entanglement. Sci. Ad v. 10 , eadk1495 (2024)

2024

[7] [7]

& Forbes, A

Singh, S. & Forbes, A. Progress in Structured Light with Nonlinear Optics Download Full Article View Full Article. Progress in Electromagnetics Research . 185 , 1 - 16 (2026)

2026

[8] [8]

Cylindrical vector beams: from mathematical concepts to applications

Zhan, Q. Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt. Photonics 1 , 1 - 57 (2009)

2009

[9] [9]

Liang, Y. et al. Spatiotemporal vectorial structured light that dynamically varies on higher - order Poincaré sphere. Opt. Express 32 , 28413 - 28428 (2024)

2024

[10] [10]

Shen, Y. et al. Optical skyrmion s and other topological quasiparticles of light. Nat. Photonics 18 , 15 - 25 (2024)

2024

[11] [11]

& Romanato, F

Vogliardi, A., Ruffato, G., Bonaldo, D., Dal Zilio, S. & Romanato, F. Azimuthally - variant perfect vector beams for the control of arbitrary phase and polarization ring pa tterns. Light: Science & Applications . 14 , 183 (2025)

2025

[12] [12]

Zhou, C. et al. Optical vectorial - mode parity Hall effect: a case study with cylindrical vector beams. Nat. Commun. 15 , 4022 (2024)

2024

[13] [13]

Dai, S. et al. Tomography of complex coherence - polarization matrix of random vector light for phase image encoding. ACS Photonics 12 , 6182 - 6190 (2025)

2025

[14] [14]

& Diaspro, A

Vicidomini, G., Bianchini, P. & Diaspro, A. STED super - resolved microscopy. Nat. Methods 15 , 173 - 182 (2018)

2018

[15] [15]

& Hajizadeh, F

Moradi, H., Shahabadi, V., Madadi, E., Karimi, E. & Hajizadeh, F. Efficient optical trapping with cylindrical vector beams. Opt. Express 27 , 7266 - 7276 (2019)

2019

[16] [16]

& Rosales - Guzmán, C

Yang, Y., Ren, Y., Chen, M., Arita , Y. & Rosales - Guzmán, C. Optical trapping with structured light: a review. Adv. Photon . 3 , 34001 (2021)

2021

[17] [17]

Nape, I. et al. Revealing the invariance of vectorial structured light in complex media. Nat. Photonics 16 , 538 - 546 (2022)

2022

[18] [18]

Guo, Z. et al. Top ological robustness of classical and quantum optical skyrmions in atmospheric turbulence. Nat. Commun. 17 , 2085 (2026)

2085

[19] [19]

& Jing, J

Wang, X., Wei, Y., Zhang, K., Pan, X. & Jing, J. Direct generation of massive vector - mode entanglement from a polarization - insensitive optical amplifier. Sci. Adv. 12 , eaec0001 (2026)

2026

[20] [20]

Aharonovich, I., Crozier, K. B. & Neshev, D. Programmable integrate d quantum photonics. Nat. Photonics 20 , 254 - 265 (2026)

2026

[21] [21]

& Liang, Y

Wang, J. & Liang, Y. Generation and detection of structured light: a review. Front. Physics 9 , 688284 (2021)

2021

[22] [22]

& Forbes, A

Ndagano, B., Sroor , H., McLaren, M., Rosales - Guzmán, C. & Forbes, A. Beam quality measure for vector beams. Opt. Lett. 41 , 3407 - 3410 (2016)

2016

[23] [23]

& Rosales Guzmán, C

Shen, Y. & Rosales Guzmán, C. Nonseparable states of light: from quantum to classical. Laser Photonics Rev. 16 , 2100533 (2022). 2

2022

[24] [24]

Zhen, W. et al. Reconfiguring optical skyrmion topology in free space. Optica . 13 , 188 - 194 (2026)

2026

[25] [25]

Sheppard, C. J. Jones and Stokes parameters for polarization in three dimensions. Phys. Rev. A . 90 , 23809 (2014)

2014

[26] [26]

Azzam, R. M. Stokes - vector and M ueller - matrix polarimetry. J. Opt. Soc. Am. A 33 , 1396 - 1408 (2016)

2016

[27] [27]

Ge, M. et al. Accurate single - shot full - Stokes detection enabled by heterogeneous grain orientations in polycrystalline films. Nat. Commun. 16 , 5603 (2025)

2025

[28] [28]

Polarization basis for vortex beams

Gori, F. Polarization basis for vortex beams. J. Opt. Soc. Am. A 18 , 1612 - 1617 (2001)

2001

[29] [29]

Yao, J. et al. Generation of arbitrary vector vortex beam using a single Q‐plate. Laser Photon ics Rev. 19 , 2402290 (2025)

2025

[30] [30]

& Dudley, A

Singh, K., Tabebordbar, N., Forbes, A. & Dudley, A. Digital Stokes polarimetry and its application to structured light: tutorial. J. Opt. Soc. Am. A 37 , C33 - C44 (2020)

2020

[31] [31]

Manthalkar, A. et al. All - digital Stokes polarimetry with a digital micromirror device. Opt. Lett. 45 , 2319 - 2322 (2020)

2020

[32] [32]

Chen, Q. et al. Manipulating perovskite structural asymmetry for high - performing self - powered full - stokes polarimetry. Sci. Adv. 11 , eads6123 (2025)

2025

[33] [33]

Wu, X. et al. Wavelength - insensitive snapshot Stokes polarimetric imaging based on cascaded metasurfac es. Adv. Photon ics 7 , 16008 (2025)

2025

[34] [34]

I., López - Mariscal, C

Perez - Garcia, B., Hernández - Aranda, R. I., López - Mariscal, C. & Gutiérrez - Vega, J. C. Morphological transformation of generalized spirally polarized beams by anisotropic media and its experimental characterization. O pt. Express 27 , 33412 - 33426 (2019)

2019

[35] [35]

Liang, Y. et al. Coherent detector for the non - separability measurement of vectorial structured light. Light: Science & Applications . 14 , 343 (2025)

2025

[36] [36]

Liu, H. et al. Real‐Time Jones Matrix Synthesis by Compact Pol arization Inline Holographic Microscopy. Laser Photon ics Rev. 18 , 2301261 (2024)

2024

[37] [37]

T., Micó, V., Trusiak, M., Kuś , A

Shaked, N. T., Micó, V., Trusiak, M., Kuś , A. & Mirsky, S. K. Off - axis digital holographic multiplexing for rapid wavefront acquisition and processing. Adv. Opt. Photonics 12 , 556 - 611 (2020)

2020

[38] [38]

Liang, Y. et al. Reconfigurable structured light generation and its coupling to air – core fiber. Adv . Photonics Nexus 2 , 36015 (2023)

2023

[39] [39]

& Booth, M

He, C., Antonello, J. & Booth, M. J. Vectorial adaptive optics. Elight 3 , 23 (2023). Supplementary information for: Seeing full vectorial structures of light fields with a single - shot holographic multiplexed detector Sitao Qin + 1 , Yize Liang + 1,2 * , Shuai Cao 1 , Changqing Cao 1 , Xukun Yin 1 , Lixian Liu 1 , Mingjian Cheng 3 , and Huailiang Xu 1 ,...

2023