Polarization effects on high contrast imaging: measurements on THD2 Bench

Celia Desgrange; Iva Laginja; Pierre Baudoz; Rapha\"el Galicher

REVIEW 3 major objections 4 minor 20 references

Polarization effects on high contrast imaging: measurements on THD2 Bench

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A deformable mirror on the THD2 bench creates a polarization-dependent beam shift of several hundred nanometers, about ten times larger than predicted, degrading coronagraph contrast.

desk verdict A convincing weak-measurement demonstration that a deformable mirror introduces large polarization-dependent beam shifts, despite an imperfectly validated drift model. read the letter →

arxiv 2411.13746 v1 pith:A5NXKVRT submitted 2024-11-20 astro-ph.IM

Pierre Baudoz , Celia Desgrange , Raphaël Galicher , Iva Laginja This is my paper · ORCID

classification astro-ph.IM

keywords effectsbenchpolarizationhighbeaminstrumentsopticalthd2

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

The THD2 bench at Paris Observatory is a testbed for high-contrast imaging, a technique used to photograph planets around other stars. The authors noticed that when they changed the polarization of the light entering the camera, the image of a star moved slightly, which could ruin the performance of a coronagraph, a device that blocks starlight to reveal faint planets. They suspected the shift was caused by polarization-dependent beam shifts upon reflection, known as the Goos-Hänchen and Imbert-Fedorov effects. Using a 'weak measurement' scheme with nearly crossed polarizers, they amplified these tiny shifts and measured beam positions with a center-of-gravity algorithm. They recorded shifts of several hundred nanometers between horizontal and vertical polarization states. The largest contribution came from a deformable mirror, DM2, even though it has a small angle of incidence and a simple aluminum coating. This shift is about ten times larger than the theoretical predictions for metallic mirrors, and the origin is not fully understood. The authors propose two explanations: the mirror coating may not be what was specified, or micrometer-scale surface structures on the mirror may act like a metasurface. The result matters for future space missions that aim to image Earth-like planets at contrasts of one part in ten billion. If deformable mirrors introduce polarization-dependent shifts, they could become a limiting factor that must be characterized and corrected.

Extended reading notes

Core claim

The paper claims: "We showed that a Boston Micromachine deformable mirror located in the pupil on our bench (DM2) introduces a differential polarization shift between the PSF related to vertical and horizontal states." The measured shift is about 555 nm horizontally and 340 nm vertically for DM2 alone, which is more than ten times larger than the predicted Goos-Hänchen and Imbert-Fedorov shifts for the whole bench, and it degrades coronagraph contrast when the analyzer is rotated away from the optimized polarization state.

Load-bearing premise

The data-reduction model in Sect. 3.2 (Eq. 10: a 360-degree sinusoidal prism term plus a linear temporal drift plus a constant) fully captures all non-polarization beam motion during a measurement series. Any unmodeled systematic motion is absorbed into the fitted amplification function (Eq. 9) and would directly bias every reported shift in Table 2, including the conclusion that DM2 is the dominant contributor. The paper provides no independent validation of this drift model, and the authors explicitly call the linear drift assumption an empirical approximation.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Dear X,

The headline result is real and worth knowing: a Boston Micromachine DM on the THD2 bench shifts the beam by several hundred nanometers depending on polarization, an order of magnitude above Goos-Hänchen and Imbert-Fedorov predictions. Applying weak measurement to a full optical bench is new in this context, and the paper has internal controls that support the finding: configurations without DM2 show small shifts, configurations with DM2 consistently show large ones. The writing is honest and the limitations are stated clearly.

The main soft spot is the drift model. To isolate the weak-measurement amplification, they fit and subtract a 360° prismatic term plus a linear drift (Eq. 10), then fit the 1/(ω−ω⊥) amplification. The drift term is openly declared an empirical approximation, and there are no residual plots, no reversed scan orders, and no independent drift monitor. A residual ordered motion could be amplified by the second fit. That said, the control measurements (20 nm with no mirror, 32–60 nm for FM2 alone) show the pipeline does not generate spurious large shifts without DM2. The DM2 shift is ~500 nm with 70–130 nm errors; even a few tens of nm of unmodeled drift would not erase the discrepancy with theory.

The bigger gap is that DM1 was never measured, so the claim that DM2 is the dominant contributor is provisional, as the authors say. The physical origin is unexplained; two hypotheses are offered, but the theory section and measurement section sit uneasily together. The paper does not try to force them into agreement, which is fine for a measurement paper.

Citations look solid, including the relevant van Holstein et al. beam-shift paper, and the method is described well enough to reproduce. I would send this to a referee, asking for residual plots or an independent drift check and a careful sign-convention statement.

Best

Referee Report

3 major / 4 minor

Summary. The paper reports polarization-dependent beam shifts on the THD2 high-contrast imaging bench. It first shows that the dark-hole contrast degrades when the analyzer is rotated away from the polarization state used for wavefront control, and reproduces the morphology with a ~800 nm tip-tilt. It then computes expected Goos-Hänchen and Imbert-Fedorov shifts for the bench mirrors using analytical expressions from Aiello et al., obtaining total shifts of order tens of nanometers. To measure such small shifts, the authors use a weak-measurement scheme with crossed polarizer/analyzer, record centroid positions versus analyzer angle, subtract a fitted 360° sinusoidal prism term and a linear temporal drift, and fit the residual with an amplification function 1/(ω−ω⊥). Table 2 reports shifts of several hundred nanometers for configurations containing DM2 (about 555 nm horizontal and 340 nm vertical for DM2 alone), far exceeding the theoretical predictions, and the paper concludes that DM2 introduces a dominant differential polarization shift.

Significance. If the quantitative result is robust, the paper is relevant to high-contrast instrument polarization error budgets: it identifies a specific pupil-plane deformable mirror as the dominant source of differential polarization shifts, and it demonstrates a bench-level impact on a FQPM coronagraph. The paper also provides a useful explicit comparison between analytical GH/IF predictions and measurements on a complete optical bench. The main strength is the use of weak measurement to amplify subpixel beam shifts; the main weakness is that the central quantitative claim depends on an empirically fitted drift model whose systematic error is not characterized.

major comments (3)

[Section 3.2, Eq. (10)] The data-reduction model f(ω,t) = a sin(ω+φ1) + bω(t) + d1 is load-bearing for every value in Table 2, but it is not independently validated. The authors explicitly call the linear drift an empirical approximation, and the amplification fit of Eq. (9) is applied to the residuals after subtracting this model. Any unmodeled ordered motion, such as a slowly nonlinear mechanical drift or a vibration mode with an angular signature, can project onto 1/(ω−ω⊥) over the fitted interval and bias the extracted coefficient q, which is then reported as the physical shift. This is especially concerning because DM2 is the only component with a large measured shift, so a systematic at the level of tens of nanometers could change the central conclusion. The paper should show residual plots after the first fit, repeat measurements with reversed or scrambled analyzer angle order, or provide an independent drift monitor (for example, an idle analyzer position) to demonstrate that the model is adequate.
[Section 3.2, Table 2] The reported 1σ RMS values (70 to 130 nm for the largest shifts) appear to be fit uncertainties from the inverse-function linear fit, but they do not include the uncertainty introduced by the first-stage subtraction of Eq. (10) or by the choice of fitting intervals. The fitted interval is changed by defect size (|ω−ω⊥| between 0.1° and 1° for small defects, 0.5° and 15° for large defects), yet there is no stability test of q against the interval bounds or against alternative drift models. Without this, the statistical significance of the 555 nm and 340 nm DM2 shifts is established only under the assumption that the residual noise is white, which is precisely the assumption in question.
[Section 2.3, Table 1] The theoretical predictions in Table 1 assume that all mirrors are silver-coated, but the text notes that the DMs are aluminum-coated, and DM2 is the component later identified as the anomalous contributor. No calculation is shown for the GH/IF shifts of an aluminum-coated mirror at the DM2 incidence angle (6.55°), so the statement that the measured shifts are 'more than ten times smaller' than the predictions is not quantitatively established for the actual coating of DM2. The authors should provide predictions using the appropriate aluminum permittivity, or explicitly justify why the silver coating approximation is valid for the comparison.

minor comments (4)

[Section 3.2, Eq. (10)] The parameter list below Eq. (10) contains a typo: it reads 'a, d1 b, d1 are parameters of the fit', which should presumably be 'a, φ1, b, d1 are parameters of the fit'.
[Table 2] The table layout is difficult to parse: the column labels, wavelength entries, and the H/V pairs are not clearly aligned in the text, and it is not immediately clear which wavelength and optical configuration correspond to each measured value. Please reformat the table and clarify in the caption whether the quoted 1σ RMS values include any systematic component.
[Figures 8–10] The figures would benefit from explicit axis labels and error bars on the centroid positions, and from residual plots after subtracting Eq. (10), so the reader can assess whether the drift model leaves any structure as a function of angle.
[Section 2.2] The predicted angular shifts depend on the beam waist w0 in Eq. (2), but the value used for Table 1 is only vaguely described as the FWHM of the beam at the focal plane. Please state the numerical value of w0 and discuss how the truncated, non-Gaussian bench beam affects the predicted shifts.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the measured polarization shifts are extracted with an independent weak-measurement calibration and compared with theoretically computed GH/IF values that are not fitted to the data.

full rationale

The paper's central claim, that DM2 introduces a differential polarization shift, rests on direct weak-measurement data reduction (Eqs. 9 and 10) rather than on a theory-derived quantity that is fed back into the measurement. The fitted coefficient q in Eq. 9 is the reported shift in nm after centroid tracking; it is not defined in terms of the GH/IF prediction. The theoretical values in Table 1 are computed independently from external analytic expressions (Aiello et al.) and tabulated silver permittivities, with no free parameters adjusted to match the measurements. Indeed, the paper explicitly reports that the measured shifts are more than ten times larger than the predicted GH/IF values, which is the opposite of forcing theory to equal data. The only empirical modeling is the 360-degree sinusoidal plus linear-drift subtraction in Eq. 10, which the authors describe as an approximation; any inadequacy there is a systematic-error risk, not a circular step. Self-citations (Potier et al. 2020 for the dark-hole procedure, Mazoyer et al. 2014 for DM surface metrology) support standard experimental methods and do not carry the polarization-shift conclusion. No load-bearing premise reduces to its own input, and no renamed known result is presented as a new derivation.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. Its central claim rests on data-reduction fit parameters (prism amplitude, drift slope, amplification constants, cross-polarization angle) and on modeling assumptions about beam shape and mirror coatings that the authors explicitly state.

free parameters (8)

cross-polarization angle omega_perp = determined by transmission minimum (precision 0.01 deg)
Defines the singularity in the amplification function g(omega) = q/(omega - omega_perp) + d2; an error in omega_perp scales the extracted shifts and is not propagated into the stated uncertainties.
prism amplitude a = fitted per series (numeric value not reported)
Eq. 10: amplitude of the 360-degree periodic sinusoidal term attributed to the polarizer substrate rotation.
prism phase phi1 = fitted
Eq. 10: phase of the prismatic rotation term.
drift slope b = fitted
Eq. 10: linear temporal drift coefficient; assumed proportional to time.
mean position d1 = fitted
Eq. 10: offset of the beam position.
amplification coefficient q = fitted
Eq. 9: strength of the weak-measurement amplification, fitted to the inverse function to extract shifts.
amplification offset d2 = fitted
Eq. 9: constant offset in the amplification fit.
beam waist w0 = assumed equal to beam FWHM at focal plane
Sect. 2.3: used in theoretical GH/IF angular-shift expressions even though the THD2 beam is a truncated Gaussian.

assumptions (5)

standard math Fresnel reflection coefficients and Snell's law describe reflection at dielectric and metal interfaces.
Used in Sect. 2.2 to derive the Goos-Hänchen and Imbert-Fedorov coefficient expressions.
domain assumption The THD2 beam can be approximated as Gaussian with waist equal to the FWHM at the focal plane.
Sect. 2.3: The authors state the beam is actually a truncated Gaussian, but they apply Gaussian formulas for all predicted shifts.
domain assumption All reflecting surfaces can be modeled as bulk silver with tabulated permittivities, ignoring protective layers and aluminum coatings on the deformable mirrors.
Sect. 2.3: The authors list this simplification before computing Table 1; the DM2 shift is later explained by deviating from this assumption.
ad hoc to paper Temporal drift of the beam is linear with time during each measurement series.
Sect. 3.2: The authors call this an empirical approximation that is subtracted from the data.
ad hoc to paper Rotation of the analyzer produces a sinusoidal beam motion with exactly 360-degree period.
Sect. 3.2, Eq. 10: Used to remove the prismatic effect of the non-parallel polarizer substrate.

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Cite this review

Pith. "Pith review of Polarization effects on high contrast imaging: measurements on THD2 Bench." pith.science (2026). https://pith.science/paper/A5NXKVRT

@misc{pith2026241113746,
  author       = {Pith},
  title        = {Pith review of: Polarization effects on high contrast imaging: measurements on THD2 Bench},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/A5NXKVRT}},
  note         = {Machine review of arXiv:2411.13746}
}

abstract

The spectroscopic study of mature giant planets and low mass planets (Neptune-like, Earth-like) requires instruments capable of achieving very high contrasts ($10^{-10}-10^{-11}$) at short angular separations. To achieve such high performance on a real instrument, many limitations must be overcome: complex component defects (coronagraph, deformable mirror), optical aberrations and scattering, mechanical vibrations and drifts, polarization effects, etc. To study the overall impact on a complete system representative of high contrast instruments, we have developed a test bench at Paris Observatory, called THD2. In this paper, we focus on the polarization effects that are present on the bench which creates differential aberrations between the two linear polarization states. We compare the recorded beam positions of the two polarization states with the predicted from the Goos-H\"anchen and Imbert-Fedorov effects, both of which cause spatial shifts and angular deviations of the beam, longitudinal and transverse respectively. Although these effects have already been studied in the literature from the optical and quantum mechanical points of view, their measurement and impact on a complete optical bench are rather rare, although they are crucial for high-contrast instruments. After describing the Goos-H\"anchen and Imbert-Fedorov effects and estimating their amplitude on the THD2 bench, we present the protocol we used to measure these effects of polarization on the light beam. We compare predictions and measurements and we conclude on the most limiting elements on our bench polarization-wise.

Figures

Figures reproduced from arXiv: 2411.13746 by the authors.

**Figure 2.** Image contrast recorded on THD2 as a function of analyzer angles (placed in front of the camera). The dark [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Bottom left: DH images for 50◦ and 140◦ analyzer angles (like in Fig.2). Top left: DH image for 50◦ analyzer angle using the 140◦ -optimized LOWFS calibration and simulated image with 800 nm tip-tilt shift (9 · 10−3λ/D). Right: Radial profiles of the normalized intensity of the 4 images. • The DH recorded with analyzer=140◦ using 50◦ -optimized DM shapes and 50◦ -optimized LOWFS. This image corresponds to the second… view at source ↗

Figures from the paper (8 more)

**Figure 4.** Figure 4: Scheme of the Goos-H¨anchen and Imbert-Fedorov effects. The normal of the reflection plane surface is in the [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: Scheme of the beam reflection at the plane interface (x-axis) in the incident plane ( [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 6.** Figure 6: The GH and IF spatial shift (left) and angular (right) deviation s − p on the THD2 bench as a function of the incident angle i on a silver coating mirror. The red vertical line at ∼ 15◦ represent the incident angle on the FM2, which has the greatest incident angle on t…

**Figure 7.** Figure 7: Images recorded around cross-polarization for the case of a simple mirror measurement (2 bottom rows) and [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

**Figure 8.** Figure 8: Example of center of gravities (CoG) for all measured angles as a function of pixel position on the detector. [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

**Figure 9.** Figure 9: CoG in X and Y as a function of angle ω around crossed polarization angle ω⊥ for the case of a single mirror tested outside of the THD2 bench (corresponding to the 2 bottom rows in [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]

**Figure 10.** Figure 10: CoG in X and Y as a function of angle ω around crossed polarization angle ω⊥ measured between FM2 and DM2. The data used is the same as the one shown on the 2D plot in [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]

**Figure 11.** Figure 11: A 0.6 mm x 0.6 mm image of DM2 mirror measured using a dedicated imaging interferometer [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]

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Reference graph

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