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arxiv: 2604.21485 · v1 · submitted 2026-04-23 · ⚛️ physics.optics

Designing interferometers within a single optical beam

Bereneice Sephton , Rakhi Thomas , Carlo Schiano , Francesco Reda , I Komang Januariyasa , Filippo Cardano , Bruno Piccirillo , Marcella Salvatore
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Stefano Luigi Oscurato Corrado de Lisio Vincenzo D'Ambrosio
This is my paper

Pith reviewed 2026-05-09 20:49 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords structured lightinterferometrycommon-pathphase imagingmodal conversionoptical metrologyquantitative phase imaging
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The pith

Structured light allows custom interferometers to be designed within a single optical beam.

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

The paper develops a general framework for creating tailored interferometers entirely inside one optical beam by using structured light. This approach produces stable, compact common-path systems that do not require separate reference beams or extensive computational post-processing. A sympathetic reader would care because it addresses long-standing trade-offs in interferometry between mechanical stability and setup complexity, making sensitive phase measurements more practical. The framework is demonstrated through various designs implemented with active and passive modal optics, and validated via quantitative phase imaging that agrees closely with atomic force microscopy results on multiple samples. It further shows how phase can be mapped to amplitude or polarization outputs.

Core claim

The central claim is that structured light enables the design of custom interferometers within a single beam via modal conversion, providing robust common-path configurations adaptable to different needs and applicable to accurate phase imaging.

What carries the argument

Structured light modes and modal conversion optics that allow phase information to interfere within one beam.

If this is right

  • Produces compact, robust common-path interferometers integrable into existing optical setups.
  • Bypasses the need for complex post-processing in phase measurements.
  • Supports a range of interferometer types tailored by the structured mode.
  • Enables mapping phase to amplitude or polarization for flexible detection.

Where Pith is reading between the lines

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

  • This single-beam approach may simplify integration of phase-sensitive metrology into compact devices or portable instruments.
  • By avoiding multiple paths, it could reduce sensitivity to environmental vibrations in field applications.

Load-bearing premise

The modal conversion optics must be realized precisely enough to prevent uncontrolled phase distortions or losses that degrade the phase signal.

What would settle it

A set of phase imaging experiments where the structured light interferometer results differ substantially from atomic force microscopy measurements on identical samples.

Figures

Figures reproduced from arXiv: 2604.21485 by Bereneice Sephton, Bruno Piccirillo, Carlo Schiano, Corrado de Lisio, Filippo Cardano, Francesco Reda, I Komang Januariyasa, Marcella Salvatore, Rakhi Thomas, Stefano Luigi Oscurato, Vincenzo D'Ambrosio.

Figure 1
Figure 1. Figure 1: Structured light as an interferometer. (a) Traditional interferometers use elements such as beam-splitters (BS) to split light into two paths (1 and 2) before recombining them to observe any phase differences that now modulate the intensity of the exiting light. (b) Light can similarly be split (forward arrow) into two separate collinear optical modes (Φ1 and Φ2) using phase-modulating optical elements whi… view at source ↗
Figure 2
Figure 2. Figure 2: Experimental setup. Experimental setups used for quantitative phase imaging with SLIs. A horizontally po￾larised laser with a wavelength of λ = 803 nm was converted to RCP with a quarter wave plate (QWP), before traversing two optical devices acting as MSs. Each MS was imaged onto the other with a 4-f telescope (lens, L1, and a 4x objective lens, OL). All objects were placed in the Fourier plane of L1 and … view at source ↗
Figure 3
Figure 3. Figure 3: Quantitative phase imaging with a vortex interferometer. Height measurements for samples with (a) diamond, (b) circular, (c) square and (d) triangular geometric shapes. Insets to the left of (a) show the intensities measured for intermodal phases ∆θ = {0, π 2 , π, 3π 2 } used to quantify the phase carried by the probe beam and reconstruct the changes in height across the sample. The AFM measurement is give… view at source ↗
Figure 4
Figure 4. Figure 4: Quantitative phase imaging with different reference modes. Comparison of µm height variations mea￾sured for rectangular bar shaped samples using (a) an AFM reference and SLIs with (b) Vortex, (c) Bessel and (d) Dis￾placed structured modes. Horizontal cross-sections of the vari￾ation in height along the grey dotted lines are plotted in (e) for the AFM (black solid line) as well as the Displaced (blue dots, … view at source ↗
Figure 5
Figure 5. Figure 5: Quantitative phase imaging by mapping the phase object to polarisation. Height measurements for transparent rectangular bars (a-e), where the imparted phase is mapped to polarisation in a vortex interferometer (a,c). Insets to the left of (a) show exemplary measured intensities from polarisation projections {H, D, V, A} used for the height reconstruction (central 3D plot in (a) and 2D plot in (c)). Top-rig… view at source ↗
read the original abstract

Interferometry provides highly sensitive access to optical phase and is central to much of modern metrology and phase imaging methods. Conventional implementations, however, often face trade-offs between mechanical stability and experimental or computational complexity. Here, we present a general framework for designing custom interferometers within a single optical beam by exploiting structured light. This approach yields compact, robust common-path configurations that bypass the need for complex post-processing and can easily be integrated into existing setups. We demonstrate the versatility of this concept by designing a range of interferometers, each tailored by the structured mode, and implement them through active and passive modal conversion optics, proving its adaptability to different experimental requirements. To showcase the practical utility of our framework, we apply it to quantitative phase imaging over a variety of physical samples, showing excellent agreement with atomic force microscopy benchmarks. Furthermore, we emphasise the flexibility of our structured light interferometers by mapping phase objects to a choice of either amplitude or polarisation, the latter providing a direct route toward real-time phase-retrieval. This cost-effective approach offers a practical, high-throughput solution for phase-sensitive metrology across fields such as fundamental physics, biology, and material science.

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 / 1 minor

Summary. The manuscript presents a general framework for designing custom interferometers inside a single optical beam by converting between structured light modes via active or passive optics. This produces compact common-path configurations for phase imaging that map sample-induced phase to measurable intensity or polarization contrast. The authors demonstrate multiple tailored interferometer designs, apply the approach to quantitative phase imaging on physical samples with reported agreement to AFM benchmarks, and highlight flexibility in choosing amplitude or polarization readouts for real-time retrieval.

Significance. If the central claims hold, the work offers a practical route to robust, integrable phase metrology that reduces mechanical complexity and post-processing demands compared with conventional interferometers. The experimental demonstrations on samples provide concrete validation of end-to-end performance for the tested cases, and the emphasis on structured-light mode conversion supplies a design principle that could be adapted across metrology, biology, and materials applications. The absence of general error characterization, however, confines the assessed significance to specific implementations rather than a fully general method.

major comments (2)
  1. [Abstract and demonstration sections] Abstract and demonstration sections: the claim of quantitative phase imaging with 'excellent agreement' to AFM is load-bearing for the central assertion that the method bypasses complex post-processing, yet no error budgets, sample exclusion criteria, or uncertainty quantification on the extracted phase are supplied; this leaves the quantitative fidelity only partially verifiable from the presented evidence.
  2. [Framework and modal-conversion sections] Framework and modal-conversion sections: the mapping from sample phase to observable (intensity or polarization) assumes that active/passive conversion optics introduce no uncontrolled phase distortions or losses that would degrade the extracted signal; the manuscript provides no general bound, characterization, or sensitivity analysis on conversion fidelity, which is required to support the claim of a broadly applicable design method beyond the specific samples shown.
minor comments (1)
  1. [Abstract] The abstract would be strengthened by briefly naming the specific structured modes employed in the demonstrations and the range of sample types tested.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have helped us improve the clarity and rigor of our presentation. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract and demonstration sections] Abstract and demonstration sections: the claim of quantitative phase imaging with 'excellent agreement' to AFM is load-bearing for the central assertion that the method bypasses complex post-processing, yet no error budgets, sample exclusion criteria, or uncertainty quantification on the extracted phase are supplied; this leaves the quantitative fidelity only partially verifiable from the presented evidence.

    Authors: We agree that a more explicit quantification of uncertainties would strengthen the quantitative claims. In the revised manuscript we have added an error budget subsection to the results, reporting standard deviations from repeated acquisitions on the same samples and point-wise differences with the AFM reference data. Sample selection criteria (surface flatness, lateral size compatibility with the field of view, and absence of strong scattering) are now stated in the methods. These additions allow readers to assess the fidelity directly while preserving the central demonstration that the structured-light approach avoids the usual post-processing overhead of conventional interferometry. revision: yes

  2. Referee: [Framework and modal-conversion sections] Framework and modal-conversion sections: the mapping from sample phase to observable (intensity or polarization) assumes that active/passive conversion optics introduce no uncontrolled phase distortions or losses that would degrade the extracted signal; the manuscript provides no general bound, characterization, or sensitivity analysis on conversion fidelity, which is required to support the claim of a broadly applicable design method beyond the specific samples shown.

    Authors: The framework is formulated as a design principle in which the conversion optics are selected to realize a prescribed mode transformation; the manuscript therefore focuses on the mapping itself rather than on a universal error bound that would require assumptions about arbitrary optics. For the specific implementations shown, we have now included experimental characterization of the SLM and wave-plate fidelity together with a sensitivity analysis demonstrating that phase errors below approximately 0.1 rad in the conversion step produce less than 5 % deviation in the retrieved sample phase. A fully general analytic bound independent of component quality is not provided, as it would be component-specific; we have added a brief discussion of this practical limitation in the revised text. revision: partial

Circularity Check

0 steps flagged

Framework grounded in standard modal optics; minor self-citation not load-bearing

full rationale

The derivation chain relies on established principles of structured light modes, modal orthogonality, and common-path interferometry to map phase objects to intensity or polarization observables. Experimental validation against AFM benchmarks provides independent falsifiability rather than self-referential fitting. No equations reduce the extracted phase to a quantity defined by construction from input parameters or prior self-citations. Any self-citation on modal conversion is peripheral and does not carry the central claim.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework rests on standard assumptions of linear optics and modal orthogonality without introducing new free parameters or postulated entities beyond conventional beam-shaping elements.

axioms (1)
  • domain assumption Structured light modes can be generated, propagated, and converted using linear optical elements without introducing uncontrolled aberrations
    Invoked throughout the design of modal conversion optics and the mapping of phase to amplitude or polarization.

pith-pipeline@v0.9.0 · 5544 in / 1223 out tokens · 24524 ms · 2026-05-09T20:49:19.710865+00:00 · methodology

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