Pollux: decisions affecting the optical architecture of a high-resolution spectrograph and polarimeter for the Habitable Worlds Observatory

Adrien Girardot; Coralie Neiner; David Le Mignant; Eduard Muslimov; Jean-Claude Bouret; Jean-Michel Reess; Kjetil Dohlen; Luca Fossati

REVIEW 3 major objections 4 minor 15 references

For HWO's POLLUX instrument, each UV channel can use a single 9k×8k detector, but only at the price of long collimators, shallow echelle blaze angles, and up to 2× oversampling at long wavelengths.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-01 04:31 UTC pith:DBZ27YZ6

load-bearing objection Useful UV instrument trade study with a real internal inconsistency in Table 2 that undermines the quantitative conclusions until fixed. the 3 major comments →

arxiv 2607.22500 v1 pith:DBZ27YZ6 submitted 2026-07-24 astro-ph.IM

Pollux: decisions affecting the optical architecture of a high-resolution spectrograph and polarimeter for the Habitable Worlds Observatory

Eduard Muslimov , Luca Fossati , Coralie Neiner , Jean-Claude Bouret , David Le Mignant , Kjetil Dohlen , Jean-Michel Reess , Adrien Girardot This is my paper

classification astro-ph.IM

keywords Habitable Worlds ObservatoryPOLLUXultraviolet spectrographechelle spectrographspectropolarimetryoptical designdetector samplingtelescope jitter

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper establishes that the three ultraviolet channels of the POLLUX spectrograph can each be built around a single 9k×8k, 10-micron-pixel CMOS detector, but that this choice, combined with a diffraction-limited telescope PSF and residual pointing jitter, imposes specific architectural constraints: strong de-magnification, collimator focal lengths up to about 5.5 meters in the NUV channel, echelle blaze angles smaller than typical commercial gratings, and unavoidable spectral oversampling of up to roughly 2× at the long-wavelength end of each channel. It also shows two ways to avoid refocus mechanisms: bypassing the FUV polarimeter with a single lithium-fluoride-coated mirror yields up to about 5.9× higher transmission for pure spectroscopy, and a nearly-achromatic LiF compensator lens allows MUV and NUV polarimeters to be retracted without moving the detector. These results matter because they determine whether POLLUX can meet its resolving-power goal of roughly 100,000 across a 100 nm to 1.75 micron range using available detector formats and without complex mechanisms.

Core claim

The paper's central claim is that, for the HWO telescope with a Gaussian PSF convolved with Gaussian jitter of 0.3 to 4 milliarcseconds, fitting each UV echelle spectrogram on one 9k×8k detector forces a large de-magnification and therefore long collimators—up to 5.5 meters in the NUV—along with echelle blaze angles near 15 degrees and an oversampling factor that grows to about 2× at the long-wavelength end because the PSF width scales with wavelength. It further claims that the FUV polarimeter can be bypassed by a fixed mirror arrangement rather than a retractable mechanism, giving up to 5.9× transmission gain for spectroscopy, and that a LiF compensator lens placed in place of the Wollasto

What carries the argument

The argument rests on a Gaussian model of the telescope PSF: the aberrated diffraction ring is approximated as a Gaussian with R1ring = 3σ = 4.46 λ f_tel / D_tel, and the jitter is a second Gaussian convolved with it. The single-detector constraint is enforced through the Nyquist sampling condition FWHM ≥ 2 pixels at the short-wavelength end of each spectrogram, which, along with the echelle resolving-power formula R_FWHM = λ / (FWHM · f_cam/f_col · ∂λ/∂y′), drives the collimator focal length and de-magnification. The polarimeter bypass and compensator lens are geometric solutions that keep the optical path length constant so no refocus mechanism is needed.

Load-bearing premise

The quantitative design relies on representing the telescope PSF and pointing jitter as two Gaussians with >99% of energy in the first diffraction ring and jitter between 0.3 and 4 milliarcseconds; if the actual wavefront error is non-Gaussian or the jitter power spectrum differs, the computed pinhole sizes, oversampling values, and collimator lengths would change.

What would settle it

Measure the actual on-orbit or pathfinder PSF and jitter power spectrum of the HWO telescope: if the jitter distribution has significant non-Gaussian tails or an amplitude exceeding 4 milliarcseconds, or if the residual aberrations place more than 1% of energy outside the first diffraction ring, then the specific pinhole diameters, R_FWHM values, and oversampling factors in Table 2 of the paper would need to be re-derived.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

If the Gaussian PSF and jitter model holds, the NUV channel will need collimator focal lengths around 5.5 meters, which can be folded with double-reflection collimators or compensated for with aspheric or variably-spaced cross-disperser gratings.
Up to 2× oversampling at long wavelengths is unavoidable unless jitter dominates the PSF, so the gratings and detector layouts must be designed to tolerate this extra dispersion.
The FUV spectroscopy mode can be enabled by re-pointing the telescope by about 14.9 arcseconds and using slightly larger SiC K-mirror mirrors, with no refocusing mechanism and a transmission gain of up to 5.9×.
The MUV and NUV polarimeters can be made retractable without refocus by inserting a LiF compensator lens, which is nearly achromatic and gives up to 2.2× higher transmission in the shortwave MUV compared to the MgF2 polarimeter elements.
Extending the NUV channel to a full octave (240–480 nm) would require four additional orders, a lower echelle frequency (85.3 mm−1), a shallower blaze angle (14.5°), and an even longer collimator (5.6 m), so the current band limits are preferable.

Where Pith is reading between the lines

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

The Gaussian PSF assumption may break down if the telescope has significant non-common-path aberrations or if the jitter has a non-Gaussian power spectrum; real wavefront measurements could change the optimal pinhole size and de-magnification.
The long collimators and shallow blaze angles suggest that a single-chip solution may not be the only driver; a mosaic of smaller detectors could relax the de-magnification and allow more conventional grating angles, at the cost of blind zones and alignment complexity.
The compensator lens approach could be adapted to other spectral channels or to correct for other sources of defocus, such as thermal drift, without adding moving parts.
If the HWO telescope's jitter turns out to be larger than 4 mas, the oversampling at long wavelengths would be moderated, but the resolving power would degrade; this trade-off could be tested with detailed end-to-end simulations incorporating a realistic jitter time series.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

Useful UV instrument trade study with a real internal inconsistency in Table 2 that undermines the quantitative conclusions until fixed.

read the letter

Short version: this is a useful engineering trade study with two or three genuinely interesting ideas, but Table 2 is internally inconsistent with the paper's own equations, so the quantitative conclusions should be treated as provisional.

The genuinely new material: a careful look at how telescope jitter and detector format constraints push Pollux's UV channels toward long collimators, small blaze angles, and over-sampling; a neat geometric bypass for the FUV polarimeter using a parking position and a single LiF-coated mirror (up to ~5.9x transmission gain); and a LiF compensator lens for the MUV/NUV polarimeter retraction that avoids refocus mechanisms. The writing is clear, the assumptions are stated (Gaussian PSF, Gaussian jitter, 8m f/20 telescope, CIS300-type detector), and the paper doesn't oversell what is known.

The soft spot is real: I could not reproduce Table 2 from Eq. (4) and the stated f_CAM=1500mm and Nyquist requirement. For NUV, the min-sampling of about 2.25 pixels with f_COL=5511mm implies an input PSF FWHM of ~83 microns, while the stated Gaussian+jitter model gives ~18 microns at 236nm. The same factor of four or so appears in the other channels. The R_FWHM values in Table 2 are also higher than what the equation allows with 20-micron sampling. This looks like an internal inconsistency, not a difference in assumptions; it affects the specific collimator lengths, de-magnification, and over-sampling numbers that are the paper's main quantitative output. The qualitative story — that PSF width scales with wavelength and jitter doesn't change the over-sampling much — probably survives, but the numbers need to be redone and checked against a self-consistent model.

The paper would be useful at a reading group focused on HWO instrument concepts. The polarimeter bypass and compensator designs are worth thinking about even if the sampling analysis has to be redone. I'd send it to peer review, but the reviewers should be asked to verify the internal consistency of Table 2 before any of the numerical conclusions are used.

Would I cite it? Probably yes for the bypass and compensator concepts, with a note that the quantitative sampling analysis needs correction.

Referee Report

3 major / 4 minor

Summary. The paper reports architecture-level decisions for the three ultraviolet channels of POLLUX, the proposed European high-resolution spectropolarimeter for the Habitable Worlds Observatory. Using a Gaussian model for the telescope PSF and pointing jitter, a fixed 9k×8k 10 μm CMOS detector format, and a camera focal length f_CAM = 1500 mm, the authors derive spectral resolving power, sampling, pinhole sizes, collimator focal lengths, echelle blaze angles, and order structures for the FUV, MUV, and NUV channels. They then discuss a bypass option for the FUV polarimeter that replaces four SiC mirrors with one LiF-coated mirror, and a compensator lens that avoids refocusing when the MUV/NUV polarimeters are retracted. The main claims are that a single detector per channel forces large demagnification and long collimators (up to ~5.5 m in NUV), small echelle blaze angles, and unavoidable oversampling of up to ~2–3 pixels at long wavelengths, and that the FUV bypass and MUV/NUV compensators provide substantial transmission gains.

Significance. If the quantitative design conclusions are correct, the paper provides useful input to the HWO instrument trade space, particularly the detector-size constraint, the jitter sensitivity, and the polarimeter bypass/compensator concepts. The paper is explicit about its input assumptions and the analytic model is simple enough to be checked. The transmission comparisons in Sec. 5 are credible and likely to be useful. However, the central quantitative table cannot currently be reproduced from the paper's own equations, which undermines the design conclusions until the discrepancy is resolved.

major comments (3)

[§4, Eq. (4) and Table 2] Table 2 is internally inconsistent with Eq. (4) and the stated Nyquist requirement. For a Littrow echelle, the linear dispersion at the camera is dλ/dy' = λ/(2 f_CAM tanγ), so Eq. (4) reduces to R_FWHM = 2 f_CAM tanγ / D_pix, where D_pix is the PSF FWHM on the detector. With f_CAM = 1500 mm and D_pix ≥ 20 μm, the maximum possible R_FWHM is 75,450 for FUV (γ=26.7°), 39,600 for MUV (γ=14.8°), and 42,750 for NUV (γ=15.9°). Table 2 lists R_FWHM values of 123,360, 114,140, and 112,840, which exceed these limits by factors of 1.6–2.9. Equivalently, using the listed Min.samp and F_col, the implied input PSF FWHM is ~37.7 μm (FUV, 100 nm), ~44.7 μm (MUV, 120 nm), and ~82.7 μm (NUV, 236 nm), while Eqs. (1)–(2) with jitter in the 0.3–4 mas range give ~10 μm, ~11 μm, and ~17 μm respectively. The table cannot be reproduced from the stated model. This affects the central claims about collimator lengt
[§4, Table 2 and f_COL selection] The derivation of the collimator focal lengths and grating parameters is not given. The paper sets f_CAM = 1500 mm 'for simplicity' and then lists F_col values up to 5511 mm, with echelle groove densities and blaze angles, but no equation or optimisation is provided that connects these to the detector format, the wavelength range, and the required resolving power. For a reproducibility check, the reader needs at least the relation between L_sp, N_echelle, γ, k_min/k_max, and F_col. As it stands, the claim that 'large de-magnification' and 'long collimators' are forced by the single-detector constraint cannot be independently verified.
[§4, Eq. (1)] The numerical coefficient in Eq. (1), R1ring = 3σ = 4.46 λ f'/D, needs justification. For a standard Airy pattern, the first dark ring is at 1.22 λ f'/D and encircles ~84% of the energy, not >99%; the value 4.46 corresponds to a Gaussian with σ = 1.487 λ f'/D, much wider than the Airy core. If the intent is a Gaussian fit to an aberrated PSF, the coefficient and the relation to the 'first diffraction ring' should be stated explicitly, since it directly scales the input FWHM and pinhole sizes used in Table 2.

minor comments (4)

[Fig. 6 caption] The caption says 'Spectral resolving power changing across the working orders', but the plot shows sampling. The caption should be corrected.
[§5, first paragraph] Typo: 'polarimetes retractability' should be 'polarimeter retractability'; also 'it’s size' should be 'its size'.
[Conclusions, first bullet] The text says 'over-sampling of up to 2×', but Table 2 Max.samp values reach ~3.1 pixels (FUV) and ~4.5 pixels (MUV/NUV). Clarify whether '2×' means a factor-of-two margin (2 pixels) or a factor-of-two above Nyquist, and reconcile with the table.
[§4, text near Eq. (3)] Eq. (3) uses D_COL (collimated beam diameter) while Table 2 lists F_col (collimator focal length). The relationship between these quantities and the spectrograph layout should be defined to avoid ambiguity.

Circularity Check

0 steps flagged

No circular derivation found; Table 2 inconsistency is a consistency/correctness issue, not circularity.

full rationale

The paper's quantitative claims (R_FWHM, sampling, over-sampling, transmission gain) are derived from explicitly stated inputs: a Gaussian telescope PSF with 99% encircled energy in the first diffraction ring (Eq. 1), Gaussian jitter (Eq. 2), a 9k×8k 10 μm detector, a Nyquist requirement of ≥2 pixels, f_CAM = 1500 mm, and external coating/reflectivity data. No load-bearing step reduces to a self-citation: references [2], [3], and [5] provide science requirements and prior architecture context, but the Section 4 calculations use the paper's own formulas (Eqs. 3 and 4) and stated assumptions. The over-sampling conclusion follows transparently from fixing sampling at the short-wavelength end while the PSF FWHM scales with wavelength; this is an arithmetic consequence of the stated design rule, not a fitted parameter renamed as a prediction. The FUV by-pass transmission gain is computed from the number of replaced mirrors and external LiF/SiC data, not from the target gain. The only notable issue is an internal inconsistency in Table 2 relative to Eq. (4): for example, with f_CAM = 1500 mm, γ = 26.7°, and the listed minimum sampling of 2.39 pixels, the resolving power should be roughly 2·1500·tan(26.7°)/0.0239 ≈ 63,900, not the listed 123,360. But this is a consistency/correctness problem, not a circular reduction: the contradicting numbers are outputs, not inputs, and no circular step can be quoted. Therefore the circularity score is 0.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 0 invented entities

Core conclusions depend on the Gaussian PSF/jitter model, the single-chip CIS300 detector assumption, and hand-set parameters (f_CAM, jitter scenarios, sampling margins). The FUV bypass and compensator lens are design choices, not fitted results, and no new physical entities are introduced.

free parameters (4)

Camera focal length f_CAM = 1500 mm
Set by hand 'for the sake of simplicity' (Sec. 4); fixes allowable field of view and enters Eq. 4 for R_FWHM and de-magnification.
Residual jitter amplitude sigma_jitter = 4, 2, 1, 0.3 mas
Not measured; taken from early HWO estimates spanning more than an order of magnitude. All sampling and resolving-power values in Table 2 are scenario-dependent.
Minimum sampling margin = 2.5 pix (FUV), 2.2 pix (MUV/NUV)
Chosen safety margins above the strict Nyquist requirement; this sets the dispersion and magnification targets.
Telescope diameter and focal ratio = D_tel=8 m, f_tel/D_tel=20
Optimistic scenario, not fixed by the HWO design; affects pinhole sizes and resolving-power calculations.

axioms (6)

domain assumption Telescope PSF can be represented as a Gaussian with 3σ=4.46 λ f/D (Eq. 1).
Used to compute pinhole radius and input FWHM; no wavefront-error simulation or derivation is given.
domain assumption Jitter is Gaussian and independent, so the input PSF is the convolution of two Gaussians (Eq. 2).
Assumed throughout Sec. 4; actual HWO pointing jitter statistics are not yet known.
standard math Echelle resolving power is governed by Eqs. 3 and 4.
Standard echelle spectrograph formulas; applicable for Littrow-mounted echelles.
domain assumption Residual telescope aberrations are small enough that >99% of energy lies in the first diffraction ring.
Stated in Sec. 4 to justify the Gaussian mapping; not tied to an HWO error budget.
domain assumption δ-doped CMOS CIS300 sensors with 9k×8k, 10 μm pixels are available for all channels.
Motivates the single-chip constraint and all detector-format numbers, citing ref [9] without a confirmed procurement path.
domain assumption The baseline Pollux architecture from prior papers [3,5] is accepted without re-derivation.
The present work optimizes within an existing subdivided echelle/channel architecture rather than validating it.

pith-pipeline@v1.3.0-alltime-deepseek · 8632 in / 12785 out tokens · 136894 ms · 2026-08-01T04:31:43.202040+00:00 · methodology

0 comments

read the original abstract

POLLUX is a candidate European instrumental contribution to the Habitable Worlds Observatory. It is a high-resolution spectrograph with polarimetric capabilities, covering from the far ultraviolet (FUV; 100nm) to the near infrared (NIR; 1.75mum). Such a broad spectral coverage is achieved by splitting the instrument into five channels, each comprising an echelle spectrograph: FUV, medium-UV (MUV), near-UV (NUV), optical (OPT), and NIR. A set of custom-made dichroics enables simultaneity across the MUV, NUV, OPT, and NIR channels.We present the latest developments in the optical design of the three UV channels. Specifically, we estimate the impact of telescope residual jitter on resolving power and sampling and discuss possible options to enable pure spectroscopy in the FUV channel without implementing a fully retractable polarimeter and to compensate the defocus when inserting MUV and NUV polarimeters. Finally, we estimate the impact of detector size limitation and potential advantages of shrinking or extending the wavelength coverage in the NUV channel.

Figures

Figures reproduced from arXiv: 2607.22500 by Adrien Girardot, Coralie Neiner, David Le Mignant, Eduard Muslimov, Jean-Claude Bouret, Jean-Michel Reess, Kjetil Dohlen, Luca Fossati.

**Figure 2.** Figure 2: Optical design of the FUV echelle spectropolarimeter and definition of the common axes notation. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Example of the 2D MUV spectrogram in pure spectroscopy mode. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: Simplified representation of the telescope PSF cross-section including jitter effects. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: Spectral resolving power changing across the working orders for the MUV channel. The colors correspond to [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 6.** Figure 6: Spectral resolving power changing across the working orders for the MUV channel. [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

**Figure 7.** Figure 7: Variance of the full order length and the free dispersion range for the MUV channel. [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗

**Figure 8.** Figure 8: Schematic of the FUV polarimeter by-pass. [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗

**Figure 9.** Figure 9: Change of the FUV polarimeter unit transmission resulting from by-passing the SiC mirrors comprising the [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗

**Figure 10.** Figure 10: Birefringent polarimeter unit for the MUV channel: top – optical design, middle – chromatic change of the [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗

**Figure 11.** Figure 11: Polarimeter retraction compensator for the MUV channel: top – optical design, middle – chromatic change [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗

**Figure 12.** Figure 12: Comparison of the spectral transmission between the MUV [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗

discussion (0)

Reference graph

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