Pith. sign in

REVIEW 1 major objections 4 minor 12 references

Diffraction and partial coherence make HARMONI spectral lines narrower than the geometric slit, undersampling the detector unless grisms supply anamorphic stretch.

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 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-12 08:17 UTC pith:MNJD73TZ

load-bearing objection Solid instrumentation note that correctly flags HARMONI undersampling from partial coherence and offers a constrained grism fix; physics is old, residual-error budget is the only soft spot. the 1 major comments →

arxiv 2607.02223 v2 pith:MNJD73TZ submitted 2026-07-02 astro-ph.IM

HARMONI at ELT: line spread functions in a diffraction limited spectrometer

Stephen P. Todd (1) , \'Eamonn J. Harvey (1) , Anna MacIver (1) , William Taylor (1) , Eduard Muslimov (2) , Kjetil Dohlen (3) , Matthias Tecza (2) , Magali Loupias (4)
show 8 more authors
Paula Ba\~nares-Palacios (5) Mark Swinbank (6) Ryan Griffiths (2) ((1) UK Astronomy Technology Centre (2) Oxford University (3) Laboratoire d'Astrophysique de Marseille (4) Centre de Recherche Astrophysique de Lyon (5) Instituto de Astrof\'isica de Canarias (6) Durham University)
This is my paper
classification astro-ph.IM
keywords SpectroscopyDiffractionSpatial filteringLine spread functionLSFHARMONIELTintegral field spectrograph
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.

When a spectrograph slit is comparable to the diffraction-limited PSF of an adaptive-optics telescope, the finite pupil imposes partial spatial coherence. That coherence, together with clipping of the diffracted beam at the grating aperture, acts as a spatial filter and can shrink the line-spread function well below the geometric image of the slit. The authors show that this effect places HARMONI below the two-pixel sampling target at every wavelength and both spatial scales, most severely at long wavelengths in the 6 mas mode. Because the integral-field unit is already in manufacture, they cannot simply enlarge the slit; instead they introduce modest, band-dependent anamorphic magnification through the grism geometry so that the measured FWHM returns close to two detector pixels. The same dimensionless parameters that diagnose the problem also give designers of future diffraction-limited spectrographs a rapid way to size grating apertures and slits before detailed optical design begins.

Core claim

Including diffraction and partial spatial coherence shows that HARMONI’s spectral line-spread function has FWHM less than two detector pixels at all wavelengths in both the 6 mas and 25 mas scales; geometric slit imaging alone therefore produces undersampling that must be corrected by small, band-specific anamorphic factors introduced through the grism sandwich.

What carries the argument

The dimensionless parameters φ = w_s w_G / (λ f_C) and grating oversizing Ω_G, which map any spectrograph onto the family of partially coherent line profiles whose FWHM is read directly from a single curve.

Load-bearing premise

That adding optical aberrations, grating errors, vibration and detector effects in an RSS spreadsheet still yields a reliable as-built FWHM, even though a full Fourier-optics model that folds free-form aberrations together with partial coherence has not yet been finished.

What would settle it

Measure the monochromatic line profiles of the finished HARMONI spectrograph (or a laboratory breadboard with the same slit, grism and free-form optics) across 0.8–2.45 µm and check whether the FWHM values match the post-mitigation curves of Figure 9 rather than the purely geometric two-pixel target.

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

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 4 minor

Summary. The paper shows that diffraction and partial spatial coherence at the slit/grating make the HARMONI line-spread function narrower than the geometric slit image. Using Casini and Mielenz expressions re-parameterized by φ = w_s w_G / (λ f_C) and grating oversizing Ω_G, the authors compute FWHM versus wavelength for the 6 mas and 25 mas scales (Figs. 6–8). With geometric imaging sized for two detector pixels, the ideal optical LSF (convolved with the pixel) falls below 2 pixels at all wavelengths, most severely at long λ in the 6 mas scale. They therefore propose grism anamorphic factors (1 ≤ f_j ≤ 1.15) to restore near-Nyquist sampling (Fig. 9) and outline a Fourier-optics path for combining free-form aberrations with partial coherence.

Significance. The work is of clear practical value for ELT/AO integral-field spectrographs and for any diffraction-limited spectrometer. It correctly re-expresses classical laboratory results (Casini, Mielenz) in the dimensionless parameters φ and Ω_G that instrument designers actually control, supplies explicit FWHM curves for HARMONI’s two scales, and documents a concrete, mechanism-free mitigation already compatible with the post-rescope free-form design. The analytic re-parameterization and numerical evaluation of the partial-coherence integral are reproducible from the given equations and HARMONI geometric inputs; the paper therefore supplies both a diagnostic tool and a design guideline that other projects can apply before detailed optical design freezes.

major comments (1)
  1. Section 4 bases the anamorphic factors f_j on an RSS spreadsheet that folds residual broadening (aberrations, grating errors, vibration, detector) into the ideal FWHM of Fig. 7. Section 5 states that a full end-to-end Fourier-optics model simultaneously including free-form aberrations and partial coherence has not yet been completed. Because the precise values of f_j (and the residual undersampling still visible at long λ in the 6 mas panel of Fig. 9) rest on that incomplete budget, the manuscript should either (a) quantify the uncertainty range on f_j that would still keep sampling within the stated 1–1.15 bounds, or (b) present at least one representative wavelength/scale case from the PROPER+Zemax pipeline to show that the RSS estimate does not reverse the need for, or the direction of, the anamorphic correction.
minor comments (4)
  1. Eq. (1) and the subsequent definitions of θ±_x, φ and α would benefit from an explicit statement that the grating is assumed rectangular and oversized in the cross-dispersion direction (already implicit in the 1-D treatment).
  2. Figure 5 caption and text: the shaded α ranges for the two HARMONI scales are useful; adding the corresponding φ or Ω_G values on a second axis would make the link to Fig. 6 immediate.
  3. Section 3.4: the numerical values w_s = 130 µm, w_G = 50 mm, f_C = 1319 mm are given without a reference to the post-rescope optical design; a short citation or table of the adopted geometric parameters would aid reproducibility.
  4. A few typographical slips remain (e.g., “ftel fC fL” in the Fig. 2 caption, missing units on some axis labels, and the incomplete sentence “fields of view on the sky of .” in Section 2).

Circularity Check

0 steps flagged

No circularity: LSF formulas are external literature results applied to fixed HARMONI design parameters; mitigation factors are derived from those predictions, not fitted to observed spectra.

full rationale

The paper's central claim (FWHM < 2 detector pixels from diffraction + partial coherence, Fig. 7) is obtained by numerically evaluating the established analytic line-profile expressions of Casini (coherent/incoherent limits) and Mielenz (partial coherence) after re-parameterizing them in terms of the dimensionless quantities φ = w_s w_G / (λ f_C) and Ω_G (grating oversizing). These formulas are independent of the present work; HARMONI values of slit width, collimator focal length, grating aperture and the two spatial scales are design inputs, not quantities fitted to any LSF data the paper claims to predict. The subsequent grism anamorphic factors (1 ≤ f_j ≤ 1.15) are chosen to restore ~2-pixel sampling given those predicted FWHMs and an RSS residual-error budget; they are not tuned to match already-observed spectra. Self-citations (prior HARMONI modeling papers, the rescope design papers) supply context or describe incomplete future end-to-end Fourier-optics work (Section 5) but do not close any logical loop that forces the undersampling result. The derivation is therefore self-contained against external benchmarks and exhibits no self-definitional, fitted-input-as-prediction, or load-bearing self-citation circularity.

Axiom & Free-Parameter Ledger

2 free parameters · 4 axioms · 0 invented entities

The central claim rests on standard Fourier optics and two classic laboratory papers; the only free choices are the practical bounds placed on grism anamorphic factors and the RSS combination rule for residual broadenings. No new physical entities are postulated.

free parameters (2)
  • anamorphic factor bounds 1 ≤ f_j ≤ 1.15 = 1–1.15
    Chosen by the team as the practical range achievable with VPH grism prism angles inside the existing spectrograph envelope; not derived from first principles.
  • RSS combination of residual FWHM contributions
    Aberrations, grating errors, vibration and detector effects are added in quadrature inside a spreadsheet; the individual term values and the quadrature assumption itself are design choices, not measured.
axioms (4)
  • domain assumption Line profiles for fully coherent and incoherent illumination are given by the sine-integral expressions of Casini (2014).
    Invoked in §3.1; the paper does not re-derive them.
  • domain assumption Average degree of coherence across a slit illuminated by a circular pupil is given by Mielenz’s μ_RMS formula.
    Used in §3.2 to justify the partial-coherence integral.
  • domain assumption A monochromatic extended source can be treated by integrating the coherent point-source response over the entrance pupil with a circular-apodization factor.
    Equation (8) in §3.3; standard but not re-proved.
  • domain assumption Geometric aberrations before the slit plane do not affect the monochromatic LSF of a spatially uniform extended source.
    Stated in §3.4; allows the simplified paraxial model.

pith-pipeline@v1.1.0-grok45 · 14644 in / 2728 out tokens · 30067 ms · 2026-07-12T08:17:50.167147+00:00 · methodology

0 comments
Cite this review

Pith. "Pith review of HARMONI at ELT: line spread functions in a diffraction limited spectrometer." pith.science (2026). https://pith.science/paper/MNJD73TZ

@misc{pith2026260702223,
  author       = {Pith},
  title        = {Pith review of: HARMONI at ELT: line spread functions in a diffraction limited spectrometer},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MNJD73TZ}},
  note         = {Machine review of arXiv:2607.02223}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

HARMONI is the first light, adaptive optics assisted, near-IR integral field spectrograph for the ELT. It covers a spectral range from 800~nm to 2450~nm with resolving powers from 3000 to 7000 and spatial sampling of 25~mas and 6~mas. It can operate in two adaptive optics modes - SCAO (including a high contrast capability) and MCAO. The project is resuming its final design phase after a rescope design phase in 2025. Diffraction of the pupil becomes significant in a spectrograph where the slit width is comparable to the diffraction limited PSF. When the spatial coherence due to the narrow slit is considered, the resulting line spread function can be narrower than the geometric width of the input slit, with a non-linear dependence on the size of the pupil aperture after the slit. We outline the impact of these diffraction and spatial filtering effects on the line spread function of HARMONI and identify parameters that should be considered when designing a diffraction limited spectrograph.

Figures

Figures reproduced from arXiv: 2607.02223 by (2) Oxford University, (3) Laboratoire d'Astrophysique de Marseille, (4) Centre de Recherche Astrophysique de Lyon, (5) Instituto de Astrof\'isica de Canarias, (6) Durham University), Anna MacIver (1), \'Eamonn J. Harvey (1), Eduard Muslimov (2), Kjetil Dohlen (3), Magali Loupias (4), Mark Swinbank (6), Matthias Tecza (2), Paula Ba\~nares-Palacios (5), Ryan Griffiths (2) ((1) UK Astronomy Technology Centre, Stephen P. Todd (1), William Taylor (1).

Figure 1
Figure 1. Figure 1: The layout of the HARMONI IFS Spectrograph (ISP) following the rescope process. The collimator and camera [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: A highly simplified model of a spectrograph, based on paraxial (ideal) lenses to represent the optics before the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Line profiles for the completely coherent and incoherent cases. All parameters of the spectrograph are the same [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FWHM as a function of ϕ for the coherent and incoherent cases discussed in the text. The transmission shows the proportion of light transmitted by the grating aperture [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: RMS coherence as a function of α. The two shaded regions indicate the range of α for the two spatial scales of HARMONI: 6 mas and 25 mas per spatial resolution element. diffraction limited spot at the slit, ftelλ/Dtel. This can be directly linked to ϕ if we define the factor ΩG as the oversizing of the rectangular grating aperture relative to the diameter of the geometric pupil image at the grating, so tha… view at source ↗
Figure 6
Figure 6. Figure 6: The FWHM of line profiles generated using the expressions for the partial coherence case described in the text. [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The FWHM of line profiles in an idealised model of the HARMONI spectrograph in the two spatial scales (6 [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: The current best estimate for the HARMONI spectral FWHM with the proposed mitigation using the grism [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗

Review history (2 revisions) →

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

12 extracted references

  1. [1]

    On the resolving power of telescopes and spectroscopes for lines of finite width,

    Wadsworth, F. L. O., “On the resolving power of telescopes and spectroscopes for lines of finite width,”The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science43(264), 317–343 (1897). https://doi.org/10.1080/14786449708621001

    doi:10.1080/14786449708621001

  2. [2]

    The enhanced resolution imager and spectrograph for the vlt,

    Davies, R., Absil, O., Agapito, G., et al., “The enhanced resolution imager and spectrograph for the vlt,” A&A674, A207 (2023). https://doi.org/10.1051/0004-6361/202346559

    doi:10.1051/0004-6361/202346559 2023

  3. [3]

    Spectral resolution modeling with partial coher- ence for the Atmospheric Infrared Sounder instrument,

    Dionne, C. E., Hatch, M., and Overoye, K. R., “Spectral resolution modeling with partial coher- ence for the Atmospheric Infrared Sounder instrument,”Optical Engineering47(2), 026402 (2008). https://doi.org/10.1117/1.2870198

    doi:10.1117/1.2870198 2008

  4. [4]

    On the instrument profile of slit spectrographs,

    Casini, R. and de Wijn, A. G., “On the instrument profile of slit spectrographs,”J. Opt. Soc. Am. A31, 2002–2010 (Sep 2014). https://doi.org/10.1364/JOSAA.31.002002

    doi:10.1364/josaa.31.002002 2002

  5. [5]

    Spectroscope slit images in partially coherent light,

    Mielenz, K. D., “Spectroscope slit images in partially coherent light,”J. Opt. Soc. Am.57, 66–74 (Jan 1967)

    1967

  6. [6]

    HARMONI at ELT: the revitalised high-resolution near-infrared IFU for the ESO ELT,

    Dunlop, J., Neichel, B., Chittick, S., et al., “HARMONI at ELT: the revitalised high-resolution near-infrared IFU for the ESO ELT,” in [Ground-based and Airborne Instrumentation for Astronomy XI],Proc. SPIE 14149, SPIE (2026)

    2026

  7. [7]

    HARMONI at ELT: a dynamic systems engineer- ing approach for rescoping the HARMONI integral field spectrograph,

    MacIver, A., Garc´ ıa, M. A. C., Ba˜ nares-Palacios, P., et al., “HARMONI at ELT: a dynamic systems engineer- ing approach for rescoping the HARMONI integral field spectrograph,” in [Modeling, Systems Engineering, and Project Management for Astronomy XII],Proc. SPIE14152, SPIE (2026)

    2026

  8. [8]

    HARMONI at ELT: optical design of the spectrograph sub-system,

    Muslimov, E. R., Tecza, M., Castillo-Dom´ ınguez, E., et al., “HARMONI at ELT: optical design of the spectrograph sub-system,” in [Ground-based and Airborne Instrumentation for Astronomy XI],Proc. SPIE 14149, SPIE (2026)

    2026

  9. [9]

    MORFEO at ELT: the adaptive optics module for ELT,

    Ciliegi, P., Agapito, G., Aliverti, M., et al., “MORFEO at ELT: the adaptive optics module for ELT,” in [Adaptive Optics Systems IX], Jackson, K. J., Schmidt, D., and Vernet, E., eds.,Proc. SPIE13097, 1309722, SPIE (2024). https://doi.org/10.1117/12.3019058

    doi:10.1117/12.3019058 2024

  10. [10]

    Detector sampling of optical/IR spectra: how many pixels per FWHM?,

    Robertson, J. G., “Detector sampling of optical/IR spectra: how many pixels per FWHM?,”Publications of the Astronomical Society of Australia34, e035 (2017)

    2017

  11. [11]

    HARMONI at ELT: modelling the optical performance of a diffraction limited integral field spectrograph,

    Todd, S. P., Bond, C. Z., Clarke, F., et al., “HARMONI at ELT: modelling the optical performance of a diffraction limited integral field spectrograph,” in [Modeling, Systems Engineering, and Project Management for Astronomy XI],Proc. SPIE13099, 1309906, SPIE (2024). https://doi.org/10.1117/12.3019747

    doi:10.1117/12.3019747 2024

  12. [12]

    Complex spectral line profiles resulting from cryogenic deforma- tion of the SINFONI/SPIFFI diffraction gratings,

    George, E. M., Gr¨ aff, D., Hartl, M., et al., “Complex spectral line profiles resulting from cryogenic deforma- tion of the SINFONI/SPIFFI diffraction gratings,”Journal of Astronomical Telescopes, Instruments, and Systems3(3), 035002 (2017). https://doi.org/10.1117/1.JATIS.3.3.035002

    doi:10.1117/1.jatis.3.3.035002 2017