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The CHARA Array Polarization Model and Prospects for Spectropolarimetry

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The CHARA Array can now calibrate its instrumental polarization well enough to measure intrinsic polarization in resolved AGB stars and young stellar objects.

desk verdict A solid CHARA polarization calibration with real hardware findings, but the headline accuracy numbers are in-sample residuals and the transport-module simplification may limit transferability. read the letter →

arxiv 2509.10451 v1 pith:QP7YD2UF submitted 2025-09-12 astro-ph.IM

Linling Shuai , John D. Monnier , Benjamin R. Setterholm , Stefan Kraus , Narsireddy Anugu , Tyler Gardner , Jean-Baptiste Le Bouquin , Gail H. Schaefer This is my paper · ORCID
classification astro-ph.IM
keywords opticalinterferometryspectropolarimetryinstrumentalpolarizationcalibrationJonesmatrixCHARAArrayMIRC-XMYSTICcircumstellardust
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper aims to prove that the CHARA optical interferometer can now separate the polarizing effects of its own mirrors and instruments from the polarization of the light arriving from a star. The authors build a Jones-matrix model of the full beam train, fit it to observations of an unpolarized calibrator star, and report that after correcting for night-to-night offsets the instrumental polarization can be calibrated to about ±3.4 percent in visibility ratio and ±1.4 degrees in differential phase in the H band, and ±5.9 percent and ±2.4 degrees in the K band. These uncertainties sit below the differential polarization expected from resolved AGB dust shells and young-stellar-object disks, so the claim is that CHARA is now a viable spectropolarimetric instrument. The argument succeeds only if the model's simplifying assumption about one mirror group is valid; the paper itself flags where that assumption may fail.

What carries the argument

The central object is the product of 2×2 Jones matrices in Equation 27, which maps the sky-frame electric field to the detector's horizontal/vertical basis through a sequence of rotations and mirror matrices. Rotations account for the parallactic angle $q$, altitude $a$, azimuth $A$, the half-wave plate angle, and the fixed 39.85-degree transport rotation $\gamma$; the mirror matrices $fM_{\mathrm{AT}}$, $fM_{\mathrm{Coudé}}$, and $fM_{\mathrm{Lab}}$ each carry a fitted diattenuation $A^2$ and phase retardance $\psi$. The model's observables are flux ratios $f_H/f_V$ per telescope, visibility ratios $V_H/V_V$ per baseline, and differential phases $\Delta\psi_{H-V}$, all of which are insensitive to overall intensity fluctuations and can be fit globally across baselines and nights. This cascade is what converts raw fringe measurements into per-element instrumental polarization parameters, and inverting it would recover the sky coherency matrix of a science target.

What would settle it

Observe a second zero-polarization standard star at various hour angles and fit the same model; if the fitted lab-module parameters differ from the Upsilon Andromedae fit by more than the quoted ±0.52 percent / ±0.36 degrees, or if replacing the transport rotation $R(\gamma)$ with a full Jones matrix shifts the W2 Coudé phase by more than its ~2 degree uncertainty, the transport-module assumption — and the derived calibration accuracy — fails. A direct laboratory measurement of the diattenuation and retardance of mirrors M7–M10 at 45 degrees incidence would settle it independently.

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Extended reading notes

Core claim

Using Jones matrices, the paper models every reflection group in the CHARA path — telescope, Coudé path, transport, and lab — as products of rotations and two-parameter mirror matrices carrying a diattenuation $A^2$ and a retardance $\psi$. Fitting this model to three nights of calibrated observations of the unpolarized star Upsilon Andromedae yields per-telescope parameters for both MIRC-X (H band) and MYSTIC (K band). The fit recovers the expected roughly 4–6 percent diattenuation from multiple 45-degree aluminum reflections and identifies specific hardware anomalies: telescope W2's fixed aluminum mirror (instead of a deformable mirror) adds roughly 22–26 degrees of Coudé-path phase, and two lithium-niobate compensator plates are misaligned, producing chromatic phase slopes. After applying nightly offset corrections, the residual RMS calibration accuracy is ±3.4 percent in visibility ratio and ±1.42 degrees in differential phase for MIRC-X, and ±5.9 percent and ±2.36 degrees for MYSTIC, which the authors argue is enough to detect intrinsic polarization from spatially resolved dust structures around AGB stars and YSOs.

Load-bearing premise

The model assumes the mirrors that route the beam from each telescope into the lab (M7 through M10) only rotate the polarization direction and do not dim one polarization component or delay it relative to the other; if they do either, the fitted telescope parameters and quoted accuracies are biased.

Editorial extensions

If this is right

  • CHARA data can now be calibrated for H- and K-band differential polarization without assuming the instrument is polarization-free.
  • Resolved observations of AGB stars and YSO inner disks can recover local intrinsic polarization in the 10–30 percent range, well above the reported 3–6 percent visibility-ratio uncertainty.
  • The W2 fixed-mirror anomaly identified in the 2022 data should disappear after the May 2024 deformable-mirror upgrade, improving polarization symmetry across the array.
  • Adopting a unified calibration matrix and routine calibrator–science–calibrator observing should reduce the remaining correlated night-to-night errors.
  • Calibrated differential visibilities open the door to polarized aperture-synthesis imaging of circumstellar dust, for example with existing reconstruction tools.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the transport module is later shown to have real diattenuation or retardance, the quoted calibration accuracies are optimistic, but the fix is straightforward: replace the rotation $R(\gamma)$ with a full Jones matrix and re-fit the same calibrator data.
  • The identified lithium-niobate plate misalignments suggest a hardware remedy — retune the plates to the primary visibility maximum — that could flatten the chromatic phase slopes without additional modeling.
  • The roughly 3 percent flux-ratio accuracy will keep net-polarization measurements of faint sources out of reach; the competitive science channel is polarized differential visibility, not total polarization.
  • The same Jones-matrix calibration framework, with adjusted rotation angles and mirror groupings, could be adapted to other long-baseline arrays that lack field rotators.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper presents a Jones-matrix model of the polarization transfer function of the CHARA Array, spanning the telescope optics, Coudé path, transport mirrors, delay lines, and the MIRC-X and MYSTIC beam combiners. The model is fit to three nights of observations of the unpolarized standard star υ Andromedae, yielding per-telescope diattenuation and retardance parameters for grouped mirror sets (fMAT, fMCoudé, fMLab), a detection of a large Coudé-path phase shift for telescope W2 (attributed to a fixed aluminum M4 mirror), and evidence for misaligned LiNbO3 compensator plates on S1 and W2. The paper reports post-fit calibration accuracies of ±3.4% in visibility ratio and ±1.4° in differential phase for MIRC-X, and ±5.9% and ±2.4° for MYSTIC, and concludes that CHARA can now deliver high-accuracy spectropolarimetric measurements of resolved sources such as AGB stars and YSOs.

Significance. If the calibration accuracy claim holds, this work would be an important step toward routine long-baseline near-infrared spectropolarimetry, enabling resolved studies of dust scattering in AGB envelopes and YSO inner disks. The paper has clear strengths: the Jones-formalism framework is standard and clearly presented; the model successfully identifies specific hardware anomalies (the W2 fixed mirror and LiNbO3 plate misalignments) that are plausible and partly corroborated by independent hardware knowledge; and the authors release the fitting code as the mircxpol package, which supports reproducibility. The main weakness is that the headline accuracy numbers are in-sample residual scatters from a fit to a single unpolarized target, with systematic error terms tuned to force reduced chi-square near unity, and with an admitted simplification of the transport module. The central capability claim therefore rests on internal consistency rather than independent validation.

major comments (4)
  1. [§6.1, Fig. 8, Abstract] The quoted calibration accuracies (±3.4% visibility ratio, ±1.4° differential phase for MIRC-X; ±5.9%, ±2.4° for MYSTIC) are the RMS residuals from fitting Eq. (27) to the same υ And dataset, after tuning the systematic error terms σ_flux,sys, σ_vis,sys, and σ_phase,sys so that each observable's reduced chi-square approaches unity. This makes the residuals in-sample scatter, not an independent accuracy estimate: the tuned error terms can absorb model deficiencies, so the near-Gaussian histograms in Fig. 8 partly reflect the fitting construction. Please provide an out-of-sample test, for example fitting two nights and testing the third, or observing an independent unpolarized calibrator and reporting its residuals without re-tuning the systematic terms, before the abstract-level accuracy claim is made.
  2. [§3.2, Eq. (27), §6.4] The Transport module (mirrors M8–M10) is modeled as a pure rotation R(γ=39.85°) with no diattenuation or retardance. Section 6.4 explicitly concedes that 'residual systematic deviations in the differential phase data suggest that unmodeled transport module effects may be present' and that M7–M10 diattenuation/retardance would create off-diagonal Jones elements absent from Eq. (27). If the transport module does introduce such effects, the fitted fMAT, fMCoudé, and fMLab parameters become effective parameters that absorb orientation-dependent transport effects, and the residual RMS measured on υ And at specific hour angles may not bound the calibration error for a science target observed at different parallactic angles. Please quantify the sensitivity to this assumption, for example by re-fitting with a full fMtrans Jones matrix and comparing the calibrated residuals, or by clearly qualifying the accuracy claim as conditional on the transport-module simplification.
  3. [§4.1] The manuscript excludes data with differential-phase uncertainties exceeding 10° and, for October 21, observations at HA ≤ −4.9 hr are excluded from the fit due to 'anomalous behavior' while being retained in the figures. Because the model is fit to this single unpolarized target, these post-hoc exclusions can bias the derived instrumental parameters and the residual statistics used for the calibration-accuracy claim. Please report the effect of including the excluded data (or justify the cut with an objective, reproducible criterion) and state how the quoted accuracies change when the exclusions are lifted.
  4. [§6.2 and §6.1, Fig. 8] Night-to-night correlated errors are removed by subtracting each night's mean parameter offset across wavelengths, which reduces the scatter in diattenuation from ±3.70% to ±0.52% and in phase from ±1.47° to ±0.36°. The manuscript does not state clearly whether the Figure 8 residual histograms and the abstract calibration accuracies include this nightly-offset correction, nor how a future science observation would receive the same correction without a suitable same-night calibrator. Please clarify this and, if the quoted numbers are post-correction, also report the raw per-night accuracies before the empirical offset subtraction.
minor comments (5)
  1. [Abstract] The sentence 'the differential intrinsic polarization of spatially resolved sources, such as AGB stars and YSOs, typically greater than these instrumental uncertainties' is missing a verb; it should read '... is typically greater than ...'.
  2. [Eq. (6)] The notation ⟨E_m + E_n⟩² is ambiguous; the expression should be written as ⟨|E_m + E_n|²⟩ to make the ensemble average and the modulus explicit.
  3. [§5, Eq. (27)] The scalar factors f and e^{iφ} in Eq. (27) are introduced but not explicitly defined in the adjacent text; please define them as the net transmission and common phase of the beam path, respectively.
  4. [Reference list] The citation 'Gardner et al. 2025' appears in the text without a full bibliographic entry; please add the complete reference.
  5. [Figures 22–24] The y-axis labels in the MYSTIC differential-phase figures are rendered as 'H V(deg)' rather than 'Δψ(H−V) (deg)'; please correct the axis labels for consistency with Figures 4, 20, and 21.

Circularity Check

1 steps flagged · score 6.0 of 10

Quoted 'calibration accuracy' is the RMS residual of the same fit after tuning systematic errors to chi-squared=1; the claim reduces to the fit, not an independent test.

  1. fitted input called prediction [Abstract; Section 6.1 (Systematic errors and Calibration accuracy); Section 6.2 (Correlated errors)]
    "These values are tuned such that the reduced chi-squared for each observable approaches unity... We achieve a root-mean-square (RMS) calibration accuracy of approximately ±2.5% for the flux ratio, ±3.4% for the visibility ratio, and ±1.42 deg for the differential phase with MIRC-X; and ±4.6%, ±5.9%, and ±2.4 deg, respectively, with MYSTIC."

    The quoted 'calibration accuracy' figures are not independent predictions or external checks: they are the RMS residuals of the same Jones-model fit to upsilon And data on the same three nights. Section 6.1 first tunes empirical systematic-error terms (e.g., sigma_phase,sys = 1.829 deg for MIRC-X) so that the reduced chi-squared for each observable approaches unity; Section 6.2 then subtracts per-night mean parameter offsets. With the error floor tuned to absorb the residual scatter, the normalized residual variance is forced to one, so the reported RMS (3.4% visibility ratio, 1.42 deg differential phase, etc.) is, by construction, a restatement of the injected systematic floor rather than a measured calibration accuracy.

full rationale

The main circularity is that the headline accuracy numbers are in-sample residuals. Section 6.1 tunes empirical systematic errors until each reduced chi-squared equals one, Section 6.2 subtracts nightly mean offsets, and the remaining RMS scatter is then presented as 'calibration accuracy' in the Abstract and Summary. By construction the normalized residual variance is forced to unity, so the quoted RMS is a restatement of the tuned noise floor, not an independent estimate of calibration error; this is the 'fitted input called prediction' pattern, and the capability claim rests on it. The model does contain genuine independent content: the hour-angle dependence of flux ratio, visibility ratio, and differential phase is fit with a parametric Jones model, and the LiNbO3 plate slope comparison (Figure 7) is an independent prediction using laboratory alignment angles and Sellmeier indices rather than fitted parameters. These features keep the circularity partial rather than total. The transport-module simplification (Section 3.2 treating M7-M10 as a pure rotation, with Section 6.4 admitting 'residual systematic deviations in the differential phase data suggest that unmodeled transport module effects may be present') is a serious limitation that weakens the accuracy claim, but it is a correctness risk, not a definitional circularity. Self-citations such as Setterholm et al. (2020) supply the model ansatz, but the fit to upsilon And data, not the citations, carries the result. Overall: the central accuracy claim reduces in part to the fit that produced it, so the circularity score is 6.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced. The paper characterizes existing hardware and softwares. The main modeling burden is a set of per-telescope complex mirror-group parameters plus empirical systematic-error terms that are tuned to make the fit statistically consistent.

free parameters (5)
  • fMAT complex values (diattenuation and phase for the Array Telescope group, per telescope) = A^2_AT around 1.00 to 1.04 (MIRC-X) and 1.00 to 1.05 (MYSTIC); psi_AT from -3.85 to 0.77 degrees
    Fitted per telescope to Upsilon And flux, visibility, and phase data in Section 5.
  • fMCoudé complex values (Coude path group M4 to M7) = A^2 about 1.02 to 1.09; psi up to -26 degrees for W2
    Fitted per telescope; the W2 fixed mirror drives the large phase value.
  • fMLab complex values (delay lines and lab group M11 to M18) = A^2 about 1.0 to 1.23; psi up to 65.7 degrees for W2 (MYSTIC)
    Fitted per telescope and treated as time-invariant in Section 5.
  • Fifteen visibility normalization scaling coefficients = Not listed in the text
    Fitted to account for per-baseline visibility normalization in Section 5.
  • Systematic error terms (sigma_sys) for flux ratio, visibility ratio, and differential phase for MIRC-X and MYSTIC = MIRC-X: 0.013, 0.017, 1.829 deg; MYSTIC: 0.018, 0.006, 1.972 deg
    Tuned in Section 6.1 so that the reduced chi-square for each observable approaches unity.
assumptions (5)
  • domain assumption The calibrator Upsilon Andromedae is unpolarized, with Stokes vector (1,0,0,0).
    All observed polarization is attributed to the instrument. Literature values are low (Piirola 1977 gives p = 0.011% ± 0.014%), but no in-run measurement verifies this assumption.
  • ad hoc to paper The Transport module (mirrors M8 to M10) is a pure rotation R(gamma = 39.85 degrees) with no diattenuation or retardance.
    Assumed in Equation 27 and Section 3.2 to simplify the model. Section 6.4 acknowledges residuals likely arise from this simplification.
  • ad hoc to paper Mirror groups with no significant rotational impact can be lumped into single diagonal Jones matrices (M1 to M3, M4 to M7, M11 to M18).
    This is a modeling simplification stated in Section 3.2; relative orientations within each group are assumed negligible.
  • standard math Reflections are described by diagonal diattenuation and phase in the S/P basis, with rotations only at specified interfaces.
    Standard Jones formalism for reflections (Born and Wolf 1999); the approximation is that mirrors do not mix S and P polarization states.
  • ad hoc to paper Night-to-night instrumental changes can be removed by subtracting each night's mean parameter offset.
    Empirical correction in Section 6.2: 'applied a nightly correction by subtracting the mean parameter value across wavelengths from each night's dataset'; no physical model is given for the drift.

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Pith. "Pith review of The CHARA Array Polarization Model and Prospects for Spectropolarimetry." pith.science (2026). https://pith.science/paper/QP7YD2UF

@misc{pith2026250910451,
  author       = {Pith},
  title        = {Pith review of: The CHARA Array Polarization Model and Prospects for Spectropolarimetry},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QP7YD2UF}},
  note         = {Machine review of arXiv:2509.10451}
}
abstract

Polarimetric data provide key insights into infrared emission mechanisms in the inner disks of YSOs and the details of dust formation around AGB stars. While polarization measurements are well-established in radio interferometry, they remain challenging at visible and near-infrared due to the significant time-variable birefringence introduced by the complex optical beamtrain. In this study, we characterize instrumental polarization effects within the optical path of the CHARA Array, focusing on the H-band MIRC-X and K-band MYSTIC beam combiners. Using Jones matrix formalism, we developed a comprehensive model describing diattenuation and retardance across the array. By applying this model to an unpolarized calibrator, we derived the instrumental parameters for both MIRC-X and MYSTIC. Our results show differential diattenuation consistent with >= 97% reflectivity per aluminum-coated surface at 45 deg incidence. The differential retardance exhibits small wavelength-dependent variations, in some cases larger than we expected. Notably, telescope W2 exhibits a significantly larger phase shift in the Coude path, attributable to a fixed aluminum mirror (M4) used in place of deformable mirrors present on the other telescopes during the observing run. We also identify misalignments in the LiNbO_3 birefringent compensator plates on S1 (MIRC-X) and W2 (MYSTIC). After correcting for night-to-night offsets, we achieve calibration accuracies of $\pm$ 3.4% in visibility ratio and $\pm$ 1.4 deg in differential phase for MIRC-X, and $\pm$ 5.9% and $\pm$ 2.4 deg, respectively, for MYSTIC. Given that the differential intrinsic polarization of spatially resolved sources, such as AGB stars and YSOs, typically greater than these instrumental uncertainties, our results demonstrate that CHARA is now capable of achieving high-accuracy measurements of intrinsic polarization in astrophysical targets.

Figures

Figures reproduced from arXiv: 2509.10451 by the authors.

Figure 1
Figure 1. Schematic layout of the CHARA light path, from telescopes to the beam combiners. Not to scale. Note that the M4 mirror in telescope W2 was a fixed aluminum mirror during the time of observations. It has been replaced with a deformable mirror since May 10th, 2024. length, each telescope’s beam is routed through a sys￾tem of vacuum tubes referred as the Pipes of Pan (PoP). Each CHARA beam can be adjusted remotely by c… view at source ↗
Figure 2
Figure 2. Measured flux ratio (fH/fV ) and model from Section 5 as a function of hour angle for each telescope, observed by MIRC-X on October 22th, 2022. Different colors correspond to different wavelengths. The flux ratio (fH/fV ) exhibits strong variation around the zenith, where the hour angle equals 0. remains nearly constant before and after zenith (hour angle = 0) but exhibits significant variations near the zenith. Thi… view at source ↗
Figure 3
Figure 3. Measured visibility ratio between the horizontal and vertical components (VH/VV ) and model from Section 5 as a function of hour angle for each beam, observed by MIRC-X on October 22th, 2022. Different colors represent different wavelengths. The visibility ratio between the horizontal and vertical directions (VH/VV ) remains close to unity [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (21 more)
Figure 4
Figure 4. Figure 4: Measured differential phase (∆ψ(H−V )|mn) and the model from Section 5 as a function of hour angle for each beam, observed by MIRC-X on October 22th, 2022. Different colors indicate different wavelengths. The differential phase (∆ψ(H−V )|mn) exhibits intermittent fluct…
Figure 5
Figure 5. Figure 5: The diattenuation A 2 and phase shift ψ of the three mirror groups MfAT, MfCoud´e, and MfLab for MIRC-X. The error bars are based on υ And observed data collected on October 19th, 21st, and 22nd, 2022. Different colors represent different telescopes. 5.3. Delay lines a…
Figure 6
Figure 6. Figure 6: The diattenuation A 2 and phase shift ψ of the three mirror groups MfAT, MfCoud´e, and MfLab for MYSTIC. The error bars are based on υ And observed data collected on October 19th, 21st, and 22nd, 2022. Different colors represent different telescopes. beam is equipped w…
Figure 7
Figure 7. Figure 7: The differential phase delay ∆ϕ as a function of wavelength for MIRC-X (left) and MYSTIC (right). The observed phase delay for different nights (Oct 19, 21, and 22) is compared against the predicted values for a model of a mismatched LiNbO3 plate (black dashed line). w…
Figure 8
Figure 8. Figure 8: Histogram of residuals for normalized visibility ratio, differential phase, and flux ratio for both MIRC-X (top row) and MYSTIC (bottom row). Each subplot shows the distribution of residuals between the observed data and the best-fit model. Vertical dashed lines indica…
Figure 9
Figure 9. Figure 9: Heatmap showing the median reduced chi-square (∆χ 2 ν) differences between the global and Individual models across all wavelengths. The x-axis represents the reduced ∆χ 2 ν for: normalized visibility ratio ∆χ 2 ν(VH/VV ), differen￾tial phase ∆χ 2 ν(δψH−V ), and flux ra…
Figure 10
Figure 10. Figure 10: Measured flux ratio (fH/fV ) and model from Section 5 as a function of hour angle for each beam, observed by MIRC-X on October 19th, 2022. Different colors represent different wavelengths. 0.8 0.9 1.0 1.1 fH = fV E1 W2 W1 6 4 2 0 2 4 Hour Angle (hr) 0.8 0.9 1.0 1.1 fH…
Figure 11
Figure 11. Figure 11: Measured flux ratio (fH/fV ) and model from Section 5 as a function of hour angle for each beam, observed by MIRC-X on October 21th, 2022. Different colors represent different wavelengths. The first three data points (HA ≤ −4.9 hr) are excluded from the fit [PITH_FUL…
Figure 12
Figure 12. Figure 12: Measured flux ratio (fH/fV ) and model from Section 5 as a function of hour angle for each beam, observed by MYSTIC on October 19th, 2022. Different colors represent different wavelengths. 0.9 1.0 1.1 1.2 1.3 fH = fV E1 W2 W1 6 4 2 0 2 4 Hour Angle (hr) 0.9 1.0 1.1 1.…
Figure 13
Figure 13. Figure 13: Measured flux ratio (fH/fV ) and model from Section 5 as a function of hour angle for each beam, observed by MYSTIC on October 21th, 2022. Different colors represent different wavelengths. The first three data points (HA ≤ −4.9 hr) are excluded from the fit [PITH_FUL…
Figure 14
Figure 14. Figure 14: Measured flux ratio (fH/fV ) and model from Section 5 as a function of hour angle for each beam, observed by MYSTIC on October 22th, 2022. Different colors represent different wavelengths. Benisty, M., Natta, A., Isella, A., et al. 2010, A&A, 511, A74, doi: 10.1051/00…
Figure 15
Figure 15. Figure 15: Measured visibility ratio (VH/VV ) and model from Section 5 as a function of hour angle for each beam, observed by MIRC-X on October 19th, 2022. Different colors represent different wavelengths [PITH_FULL_IMAGE:figures/full_fig_p026_15.png]
Figure 16
Figure 16. Figure 16: Measured visibility ratio (VH/VV ) and model from Section 5 as a function of hour angle for each beam, observed by MIRC-X on October 21th, 2022. Different colors represent different wavelengths. The first three data points (HA ≤ −4.9 hr) are excluded from the fit [PI…
Figure 17
Figure 17. Figure 17: Measured visibility ratio (VH/VV ) and model from Section 5 as a function of hour angle for each beam, observed by MYSTIC on October 19th, 2022. Different colors represent different wavelengths [PITH_FULL_IMAGE:figures/full_fig_p028_17.png]
Figure 18
Figure 18. Figure 18: Measured visibility ratio (VH/VV ) and model from Section 5 as a function of hour angle for each beam, observed by MYSTIC on October 21th, 2022. Different colors represent different wavelengths. The first three data points (HA ≤ −4.9 hr) are excluded from the fit [PI…
Figure 19
Figure 19. Figure 19: Measured visibility ratio (VH/VV ) and model from Section 5 as a function of hour angle for each beam, observed by MYSTIC on October 22th, 2022. Different colors represent different wavelengths [PITH_FULL_IMAGE:figures/full_fig_p030_19.png]
Figure 20
Figure 20. Figure 20: Measured differential phase (δΦH−V ) and model from Section 5 as a function of hour angle for each beam, observed by MIRC-X on October 19th, 2022. Different colors represent different wavelengths [PITH_FULL_IMAGE:figures/full_fig_p031_20.png]
Figure 21
Figure 21. Figure 21: Measured differential phase (δΦH−V ) and model from Section 5 as a function of hour angle for each beam, observed by MIRC-X on October 21th, 2022. Different colors represent different wavelengths. The first three data points (HA ≤ −4.9 hr) are excluded from the fit […
Figure 22
Figure 22. Figure 22: Measured differential phase (δΦH−V ) and model from Section 5 as a function of hour angle for each beam, observed by MYSTIC on October 19th, 2022. Different colors represent different wavelengths [PITH_FULL_IMAGE:figures/full_fig_p033_22.png]
Figure 23
Figure 23. Figure 23: Measured differential phase (δΦH−V ) and model from Section 5 as a function of hour angle for each beam, observed by MYSTIC on October 21th, 2022. Different colors represent different wavelengths. The first three data points (HA ≤ −4.9 hr) are excluded from the fit […
Figure 24
Figure 24. Figure 24: Measured differential phase(δΦH−V ) and model from Section 5 as a function of hour angle for each beam, observed by MYSTIC on October 22th, 2022. Different colors represent different wavelengths [PITH_FULL_IMAGE:figures/full_fig_p035_24.png]

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.