Chirality Tomography: Methods & Insights

• Chirality tomography is a suite of techniques that convert molecular handedness into structured spatial, angular, or basis-resolved observables for detailed chiral reconstructions.
• It leverages advanced methods such as orbital angular momentum probing, near-field microscopy, and electron tomography to isolate and quantify chiral signatures.
• The approach enhances sensitivity in complex media by providing linear phase responses and enabling quantitative assessments of chiroptical phenomena.

Searching arXiv for papers directly related to chirality tomography and adjacent chiral imaging methods. Chirality tomography denotes a family of measurement strategies in which handedness is not read out solely through conventional bulk chiroptical observables, but is converted into a spatially, angularly, topologically, or basis-resolved quantity from which chiral structure or chiral response can be reconstructed. In the recent literature, the term spans several distinct regimes: topological phase observables of twisted light in turbid media, orbital-angular-momentum scanning of microscopic chiral structures, force-based near-field mapping of tensorial magnetoelectric response, angular-basis measurements in electron microscopy, vector-field reconstruction of magnetic textures, and Lagrangian voxel reconstructions of helicity in turbulence (Meglinski et al., 9 Feb 2026, Xu et al., 6 May 2026, Kamandi et al., 2018, Tavabi et al., 2021, Yao et al., 2021, Noseda et al., 13 Jan 2026). The common feature is methodological rather than disciplinary: chirality is encoded into an observable that remains accessible under the dominant physical constraints of the problem.

1. Scope and definitions

The literature does not use “chirality tomography” in a single narrow sense. In some cases it refers to an actual three-dimensional reconstruction of a chiral field or vector texture, as in vector-field tomography of skyrmion bubbles or voxel-based helicity maps in turbulence (Yao et al., 2021, Noseda et al., 13 Jan 2026). In other cases it denotes a tomography-like measurement protocol in which a sample is interrogated by a family of structured probes, multiple angular channels, or multiple illumination states, and chirality is inferred from the resulting response manifold rather than from a single scalar measurement (Xu et al., 6 May 2026, Huang et al., 2019, Trigo et al., 22 Sep 2025).

This broader usage is explicit in several papers. The OAM-based characterization of photopolymerized microscopic chiral structures is described as “tomography-like” because the object is interrogated by a set of vortex beams whose ring size and twist are tuned by the topological charge $\ell$ (Xu et al., 6 May 2026). Chiral structured illumination microscopy is likewise described as not tomography in the conventional $3\text{D}$ inversion sense, but as chirality-resolved computational imaging based on multiple phases and orientations of structured optical chirality (Huang et al., 2019). A related distinction appears in Coulomb-explosion imaging, where the method is said to be “not a full tomographic reconstruction in the sense of reconstructing the entire $3\text{D}$ structure from projections,” even though it maps $3\text{D}$ molecular handedness onto a handedness-sensitive projection asymmetry (Saribal et al., 2020).

Domain	Primary observable	Reconstructed chiral quantity
Multiple-scattering optics	Azimuthal rotation of a helical wavefront; differential OAM phase	Chiral phase signature in turbid media (Meglinski et al., 9 Feb 2026)
Microscopic OAM probing	Helical dichroism versus $\ell$	Handedness-resolved OAM/structure coupling (Xu et al., 6 May 2026)
Near-field PiFM	Differential force; ARPB phase swing	Transverse and longitudinal chirality components (Kamandi et al., 2018)
Electron microscopy	$x=L_z/P_p$ from an OAM-$P_p$ spectrum	Planar chirality and orientation class (Tavabi et al., 2021)
Magnetic LTEM tomography	Reconstructed $B_x,B_y,B_z$	Bubble chirality and polarity (Yao et al., 2021)
Turbulence	Voxelwise signed-crossing average $\mathcal K$	Helicity density $\mathcal H(\mathbf x)$ (Noseda et al., 13 Jan 2026)
Chiral SIM	Structured optical chirality with FDCD	Sub-diffraction chiral-domain distribution (Huang et al., 2019)

A recurring conceptual point is that chirality need not be reduced to a single pseudoscalar. The orientation-dependent handedness framework of pseudotensors makes this explicit by replacing scalar chirality with a direction-dependent relation between a direction and a rotation, thereby giving a natural conceptual basis for orientation-resolved or basis-resolved chirality measurements (Efrati et al., 2013).

2. Topological phase tomography with twisted light

A central optical formulation converts molecular chirality into a topological phase observable carried by Laguerre–Gaussian beams with orbital angular momentum (Meglinski et al., 9 Feb 2026). In this setting, the chiral refractive-index difference is defined as

$3\text{D}$0

and the measured OAM-related phase shift is written as

$3\text{D}$1

with

$3\text{D}$2

The achiral background is therefore independent of the OAM sign, while the chiral contribution reverses sign with $3\text{D}$3. The physical mechanism is spin–orbit interaction in a chiral medium: circular birefringence is converted into an azimuthal rotation of the helical wavefront, and molecular handedness appears as the sign of that rotation (Meglinski et al., 9 Feb 2026).

This formulation is significant because the observable is not conventional polarization rotation. The authors contrast it explicitly with circular dichroism and optical rotatory dispersion, which are rapidly degraded in turbid media and generally require ballistic or quasi-ballistic propagation. By contrast, the OAM topology survives statistically under strong multiple scattering, so that the local phase is scrambled into speckle while the ensemble-averaged azimuthal phase gradient remains accessible. The reported regime includes scattering strengths at which conventional beams are fully depolarized, including $3\text{D}$4 (Meglinski et al., 9 Feb 2026).

The differential measurement with conjugate charges isolates the chiral term: $3\text{D}$5 According to the paper, this subtraction cancels bulk refractive-index changes, scattering-induced path-length variations, depolarization, and other achiral phase delays, while doubling the chiral amplitude. Opposite enantiomers, specifically $3\text{D}$6-glucose and $3\text{D}$7-glucose, produce mirror-symmetric phase maps and opposite signs of azimuthal rotation even after multiple scattering. Quantitatively, the phase response remains linear from $3\text{D}$8 to $3\text{D}$9 mg/dl, the slope is preserved across two orders of magnitude in scattering strength, and the phase sensitivity reaches refractive-index changes of order $3\text{D}$0 (Meglinski et al., 9 Feb 2026).

This work gives one of the clearest literal routes from chirality sensing to chirality tomography in scattering media. The paper states that mapping spatially varying chirality and reconstructing chiral concentration distributions in turbid samples becomes plausible when opposite OAM handedness is used as a differential probe. This suggests a tomographic program in which multiple views or scanning are combined with topological phase retrieval to move beyond ballistic-photon chiroptics (Meglinski et al., 9 Feb 2026).

3. OAM scanning and microscale helical dichroism

A second optical lineage uses orbital angular momentum not primarily as a transport-robust phase carrier but as a geometrically matched probe of microscopic chiral structures (Xu et al., 6 May 2026). The field is written as

$3\text{D}$1

so the handedness of the probe is set by the sign of $3\text{D}$2, while the ring radius grows approximately with $3\text{D}$3. This allows the probe to be size-matched to a target microstructure. When the beam’s spatial twist and transverse scale overlap well with the chiral geometry, the structure responds differently to $3\text{D}$4 and $3\text{D}$5; the paper identifies this OAM analogue of circular dichroism as helical dichroism (Xu et al., 6 May 2026).

The platform combines DMD-based maskless photolithography, capillarity-induced self-assembly, and LC-SLM beam generation. Chiral polymer microstructures of deterministic handedness are fabricated from rectangular motifs projected through an Olympus $3\text{D}$6 objective onto a $3\text{D}$7m-thick acrylate resin film, then characterized with vortex beams generated by a phase-only LC-SLM using a standard $3\text{D}$8 nm laser. For simple spiral micropillar assemblies with characteristic diameter $3\text{D}$9m, the HD spectra are nearly mirror-symmetric for opposite enantiomers, the HD peaks are about $3\text{D}$0, and the maxima occur around $3\text{D}$1–$3\text{D}$2, where the vortex ring diameter matches the structure size. The achiral control gives essentially zero HD across the scanned range (Xu et al., 6 May 2026).

The paper explicitly casts this as tomography-like because the object is not interrogated by a single beam but by a family of helical probes. The resulting data do not directly reconstruct a volumetric density, but they resolve how the optical response changes with sign and magnitude of $3\text{D}$3, thereby producing a handedness-resolved map of OAM/structure coupling. This is reinforced by the FDTD validation based on full $3\text{D}$4 geometries reconstructed from high-resolution SEM images: opposite-signed HD for opposite enantiomers, near-zero achiral response, and maxima at the size-matching condition are reproduced in simulation (Xu et al., 6 May 2026).

The same structured-light logic appears in other chiroptical methods that are not explicitly framed as OAM tomography but have similar inferential structure. Synthetic chiral light, for example, distinguishes local handedness, global chirality, and polarization of chirality, and uses the spatial organization of local chirality to encode molecular chirality either into total harmonic yield or into the direction of harmonic emission (Rego et al., 2022). This suggests that chirality tomography can be understood more generally as a controlled transfer of handedness into a structured optical observable.

4. Spatially resolved chiral microscopy

Near-field and super-resolution implementations emphasize that chirality tomography can also mean spatially resolving which component of a chiral response is present and where. In photo-induced force microscopy, the sample’s handedness is encoded in the magnetoelectric polarizability tensor

$3\text{D}$5

and an achiral tip acts as the force transducer (Kamandi et al., 2018). Circularly polarized illumination probes transverse chirality through the differential force

$3\text{D}$6

whereas longitudinal chirality requires a superposition of azimuthally and radially polarized beams with pure longitudinal on-axis fields. The measurable quantity in that case is the force swing as the phase $3\text{D}$7 between APB and RPB is varied: $3\text{D}$8 The practical consequence is a near-field route to distinguishing transverse and longitudinal chirality components with sub-$3\text{D}$9-nm spatial resolution (Kamandi et al., 2018).

Chiral structured illumination microscopy translates the same logic into a wide-field, far-field modality (Huang et al., 2019). The absorption rate is written as

$\ell$0

or equivalently

$\ell$1

with

$\ell$2

The method engineers a sinusoidal optical-chirality pattern

$\ell$3

while keeping the electric energy density uniform, and then detects fluorescence-detected circular dichroism. For each of three pattern orientations, three phase shifts are used, giving nine raw images. The $\ell$4th-order electric-background term is discarded during reconstruction, and the $\ell$5 orders are phase-corrected and recombined. The theoretical demonstration uses $\ell$6 nm, $\ell$7, $\ell$8, and yields a resolution of about $\ell$9 nm (Huang et al., 2019).

A precursor to these explicitly chirality-resolved microscopies is polarization tomography of planar chiral plasmonic nanostructures (Drezet et al., 2010). There the full Mueller matrix of an isolated left- or right-handed spiral groove around a subwavelength hole is reconstructed, showing that the output polarization states trace circles on the Poincaré sphere whose planes do not pass through the origin. The fitted Jones matrices satisfy $x=L_z/P_p$0, and the left- and right-handed structures yield mirror-related signs of the overlap $x=L_z/P_p$1, establishing a polarization-tomographic signature of planar optical chirality without conventional optical activity (Drezet et al., 2010).

5. Basis-transform and vector-field reconstructions

In electron microscopy, chirality tomography is formulated as a direct measurement of a quantum observable associated with planar handedness (Tavabi et al., 2021). The key quantity is the planar chirality operator

$x=L_z/P_p$2

defined in a log-polar basis in which $x=L_z/P_p$3 is orbital angular momentum and $x=L_z/P_p$4 is logarithmic radial momentum. An electron OAM sorter performs the conformal mapping

$x=L_z/P_p$5

after which ordinary diffraction yields an OAM-$x=L_z/P_p$6 spectrum. Applied to a virtual-protein hologram in the context of the EspB protein, the two opposite orientations are distinguished by the sign of $x=L_z/P_p$7: one orientation gives $x=L_z/P_p$8, the opposite orientation gives $x=L_z/P_p$9, and a non-chiral reference gives $P_p$0 (Tavabi et al., 2021). The paper emphasizes that the observable is best measured in focus and positions the method as a way to resolve upside-down ambiguities in cryo-EM.

Vector-field tomography of magnetic textures uses a more literal three-dimensional reconstruction (Yao et al., 2021). For skyrmion bubbles in centrosymmetric Mn–Ni–Ga, multi-angle Lorentz TEM tilt series are recorded around two orthogonal axes, with under-focus, in-focus, and over-focus images processed by the transport-of-intensity equation,

$P_p$1

The reconstructed $P_p$2 and $P_p$3 components are combined with the divergence-free condition $P_p$4 to recover $P_p$5. This is necessary because different $P_p$6 spin states can produce the same projected LTEM contrast. The reconstruction distinguishes the four chirality types $P_p$7, where chirality depends on both polarity and vorticity, and shows that bubbles can flip chirality while preserving polarity (Yao et al., 2021).

Both methods share a structural feature: chirality is not inferred from direct image appearance alone. Instead it is encoded in a transformed representation—an OAM-$P_p$8 spectrum in one case, a full $P_p$9 induction field in the other—from which handedness can be identified without the projection ambiguities that affect conventional imaging (Tavabi et al., 2021, Yao et al., 2021).

6. Helicity tomography, partial tomography, and methodological limits

The most explicit field-reconstruction use of the term appears in turbulence, where chirality tomography is defined as a Lagrangian, voxel-based reconstruction of a three-dimensional helicity field from particle trajectories alone (Noseda et al., 13 Jan 2026). Starting from helicity,

$B_x,B_y,B_z$0

the method exploits the topological meaning of helicity via trajectory linking. For each voxel and projection direction, the normalized signed-crossing average is

$B_x,B_y,B_z$1

and averaging over $B_x,B_y,B_z$2 projections yields

$B_x,B_y,B_z$3

Empirically, $B_x,B_y,B_z$4 is linearly related to the coarse-grained dimensionless helicity $B_x,B_y,B_z$5, with $B_x,B_y,B_z$6; in the Taylor–Green results, $B_x,B_y,B_z$7. Using $B_x,B_y,B_z$8 particles, $B_x,B_y,B_z$9 cubic voxels, and $\mathcal K$0, the voxelwise correlation between $\mathcal K$1 and $\mathcal K$2 is reported as $\mathcal K$3 (Noseda et al., 13 Jan 2026).

The same paper is also unusually explicit about limitations. The proportionality between $\mathcal K$4 and $\mathcal K$5 remains robust across different voxel geometries and different values of particle inertia, but it is not held in laminar or time-modulated flows. In synthetic laminar flow, $\mathcal K$6 saturates toward a binary response rather than remaining a linear proxy, and for time-modulated helicity the relation can become hysteretic when the averaging window is comparable to the modulation period (Noseda et al., 13 Jan 2026). This is an important corrective to the assumption that any handed trajectory ensemble automatically yields a universal tomographic helicity estimator.

Several other papers make analogous boundary statements. The Stokes-parameter method for spherical chiral objects introduces a non-forward “Stokes Chirality Measure” that is concentration- and path-length-independent and can identify which enantiomer predominates in a mixture, but it is described as a “partial chirality tomography”: it reconstructs effective chiral dipolar response parameters rather than the full internal geometry of the object (Trigo et al., 22 Sep 2025). The Coulomb-explosion method for aligned gas-phase molecules is handedness-sensitive and linear in enantiomeric excess through the asymmetry

$\mathcal K$7

yet the paper explicitly states that it is not a full tomographic reconstruction (Saribal et al., 2020). Similar caveats apply to OAM scanning of microstructures and to chiral SIM, both of which are tomography-like but not general $\mathcal K$8 inversion procedures (Xu et al., 6 May 2026, Huang et al., 2019).

A broader implication is that “chirality tomography” is best treated as a family of inverse or quasi-inverse strategies for recovering chirality-resolved information under modality-specific constraints. In some systems the target is a literal $\mathcal K$9 field; in others it is a basis-resolved chirality observable, a response tensor component, or a spatial map of chiral contrast. The methodological pluralism is not accidental: it follows from the fact that chirality appears as molecular handedness, magnetoelectric coupling, planar roto-scale symmetry, vorticity–polarity combinations, or helicity density depending on the underlying physics (Efrati et al., 2013, Rego et al., 2022, Martínez-Romeu et al., 28 May 2026).