A Robust COTS Objective for Diffraction-Limited, High-NA, Long Front Working Distance Imaging

Christopher M. Seck; Gilles Buchs; Jiafeng Cui

REVIEW 3 major objections 4 minor 21 references

A Robust COTS Objective for Diffraction-Limited, High-NA, Long Front Working Distance Imaging

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Five off-the-shelf singlet lenses deliver diffraction-limited 0.87 µm imaging from 61 mm away.

desk verdict A genuinely useful engineering demonstration: an all-COTS five-singlet objective that directly projects diffraction-limited images with long working distance and high NA, verified at three wavelengths, but the 'robust' claim outruns the evidence because there is no tolerance analysis. read the letter →

arxiv 2507.15786 v1 pith:NDNDE6YC submitted 2025-07-21 physics.atom-ph physics.opticsquant-ph

Jiafeng Cui , Gilles Buchs , Christopher M. Seck This is my paper · ORCID

classification physics.atom-phphysics.opticsquant-ph

keywords COTSobjectivelensdiffraction-limitedimaginghighnumericalaperturelongworkingdistancesingletdesigntrapped-ionfluorescenceStrehlratiofieldofviewmeasurement

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 argues that a compound objective made entirely from commercial off-the-shelf (COTS) singlet lenses can achieve diffraction-limited performance at high numerical aperture and long front working distance, without the usual separate collimation and refocusing stages. The authors build a five-lens example for 397 nm light from trapped calcium ions, with a 61 mm front working distance, an aperture-clipped NA of 0.30 (0.37 unclipped), a measured resolution of 0.87 µm, and a 540 µm field of view. They verify experimentally that the same lens stack stays diffraction limited from 375 nm to 866 nm and tolerates a 46 mm variation in total length by adjusting mainly the back working distance. They also introduce a quantitative method to measure field of view by scanning a calibrated pinhole and mapping Strehl ratio. If correct, this makes high-resolution, long-working-distance imaging substantially easier to build and align for quantum and atomic physics experiments.

What carries the argument

The design is carried by an iterative optimization process that starts from a three-lens meniscus/plano-convex/plano-concave group, adds singlets until the RMS spot size falls below the Airy-disk radius, and then replaces each element with a closely matching COTS singlet while re-optimizing. The first meniscus lens maintains the required NA while limiting spherical aberration, the positive lenses converge the image, and a final plano-concave element compensates for residual aberration. Precision-machined brass spacer rings set the inter-lens distances and align the stack. The key simplification is direct projection of the image onto the back focal plane, which removes the separate refocusing stage and its associated bulk and effective-NA restriction.

What would settle it

Assemble a second copy of the objective from the same part numbers with the same 10 µm spacer-ring machining tolerance and measure Strehl ratio or USAF resolution at 375, 397, and 866 nm and at both ends of the 46 mm length range; if any configuration fails the diffraction-limited criterion (for example, cannot resolve the 0.87 µm target at 397 nm), the claimed robustness would be contradicted.

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Extended reading notes

Core claim

The central claim is that spherical aberration from thick vacuum and cryostat windows at high NA can be corrected entirely with five off-the-shelf singlets arranged in a single lens group that converges light directly onto the back focal plane, eliminating the refocusing optics required by earlier COTS designs. The authors validate this with a concrete implementation: under 397 nm illumination, the objective resolves Group 9 Element 2 of a 1951 USAF target corresponding to 0.87 µm line widths, matching the diffraction-limited Airy radius, while the measured Strehl-based field of view and magnification agree with simulation. They further show that only a small adjustment of the gap between the first lens and the window keeps the system diffraction limited across 375–866 nm and across a −14 mm to +32 mm change in total length, with all lenses and inter-lens spacings fixed.

Load-bearing premise

The robustness claims rest on the assumption that the as-built COTS singlets and machined brass spacer rings reproduce the Zemax prescription within tolerances that keep the system diffraction limited, but the paper reports only 10 µm machining tolerances for the spacer rings and gives no Monte Carlo tolerance or sensitivity analysis, while experimental checks cover only a few wavelengths and total-length points.

Editorial extensions

If this is right

Researchers can reproduce the reported 61 mm working distance, 0.30 NA objective by ordering the listed COTS singlets and machining spacer rings to the published table.
The same lens stack, with only a small change in the front gap, is simulated to remain diffraction limited at wavelengths for other atomic species (Yb⁺, Sr⁺, Ba⁺, Rb, Cs) at NA 0.35–0.37.
A 46 mm tolerance on total length means the camera and objective do not require precise placement, easing integration into vacuum and cryostat systems.
The pinhole-scan Strehl method provides a quantitative, repeatable field-of-view measurement that can be applied to other imaging systems.

Reading between the lines

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

Because the design uses standard parts, the same iterative optimization could be adapted quickly to other working distances and window configurations by substituting different COTS catalogs.
A natural stress test would be to add a Monte Carlo tolerance analysis on lens curvatures, thicknesses, and spacer lengths, since the paper's robustness claim currently rests on simulation plus a limited set of experimental points.
The single-group direct-focusing scheme may also reduce the number of optical surfaces and stray-light paths compared to two-stage designs, though the paper does not quantify stray light.
The field-of-view method's dependence on an experimentally calibrated pinhole diameter could be extended to infer wavefront quality across the full aperture, not just on-axis.

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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

The paper delivers a solid experimental result: a five-singlet, all-COTS objective that images directly onto the back focal plane, with 61 mm front working distance and NA 0.30, resolving U.S. Air Force group 9 element 2 at 397 nm and 375 nm and group 8 at 866 nm. The direct-projection layout without a separate refocusing stage is new at the experimental level; the earlier work in Refs. 18–19 was design/simulation only. That alone makes this worth reading for anyone building ion-trap or cold-atom fluorescence imaging behind vacuum windows.

What the paper does well: the design is simple, the assembly uses standard parts and brass spacers, and the wavelength flexibility (375–866 nm by adjusting one air gap) is practical. The FOV measurement via pinhole scanning and Strehl mapping is a useful addition, even if the method is not revolutionary. The figures and tables are clear enough for someone to reproduce the setup in their own lab.

The soft spots are real but not fatal. The biggest one is the robustness claim. The paper states that the system tolerates 46 mm of total-length variation and works across the wavelength range, but the experiments cover a few discrete wavelengths and two length extremes on one prototype. There is no Monte Carlo tolerance analysis over the vendor tolerances of the five COTS singlets, whose surface radii and center thicknesses are not controlled by the paper. At NA 0.30 with 13.4 mm of fused silica windows, the design deliberately balances spherical aberration; a typical singlet's radius tolerance can shift that balance. The experimental images are credible evidence that this one copy works, but they do not establish that the design is robust across lens lots. This is a gap between title and evidence, not a contradiction.

The FOV method has a mild circularity: the POP reference is generated from the same Zemax design whose FOV is being measured, and the pinhole size is calibrated using the objective's own PSF. In practice the pinhole size agrees with the manufacturer's specification and the measured FOV matches simulation, so the method is not empty, but it would be stronger with an independently measured reference or at least a cross-check at a second wavelength. Also, the design file is only available on request; a public Zemax or open-lens prescription would increase confidence.

Bottom line: this is an engineering contribution, not a fundamental one, and it is an honest one. The central result—that one can build a usable high-NA long-working-distance objective from catalog singlets—holds for the demonstrated prototype. The robustness claim needs either a tolerance study or a softened wording. I would send this to peer review; a competent referee can push for the sensitivity analysis.

Recommendation: engage with it, ask for the tolerance analysis or a revised claim, and publish after revision.

Referee Report

3 major / 4 minor

Summary. The manuscript presents a compound imaging objective built from five commercial fused-silica singlet lenses in a single lens group that images directly onto the back focal plane, without separate collimation/refocusing optics. The example system has a 61 mm front working distance, a clipped NA of 0.30, and a simulated/measured resolution of 0.87 µm at 397 nm. The authors report USAF target images at 375, 397, and 866 nm, images at two extremes of a 46 mm total-length variation, and a pinhole-scan method for measuring the field of view. The stated central claims are: diffraction-limited performance across 375–866 nm, robustness to a 46 mm total-length change, a 540 µm FOV at 397 nm, and an experimentally validated FOV-measurement technique.

Significance. If fully substantiated, the design would be a practical, low-cost, all-singlet alternative to custom aspheric or multi-group objectives for AMO and QIS experiments that require imaging through thick vacuum/cryostat windows at long working distance. The paper's concrete strengths are the clear step-by-step design methodology, the detailed optical prescription in Table 1, the experimental demonstrations at three wavelengths and two total-length extremes, and the quantitative FOV-mapping procedure. The main gaps are the absence of a tolerance analysis for the COTS lenses and the visual, non-quantitative basis for the 'diffraction-limited' claim. Both are fixable within the manuscript's scope, so the work is suitable for major revision rather than rejection.

major comments (3)

[Section 3, Table 1] The central 'robust' claim is not supported by a tolerance analysis. The only tolerance mentioned is the 10 µm machining tolerance for the brass spacer rings; there is no Monte Carlo or sensitivity study over the five COTS lenses' manufacturing tolerances (surface radius, center thickness, wedge, refractive index, surface irregularity) or over assembly errors. At NA=0.30 with 13.4 mm of fused-silica windows, the design balances spherical aberration among five catalog surfaces, so small perturbations can plausibly shift the aberration balance. The experimental validation covers one assembled copy at a few wavelengths and total lengths and cannot bound the distribution over lens lots. Please add a Zemax tolerance analysis (e.g., Monte Carlo with vendor tolerances) and report the predicted Strehl distribution; if that is not feasible, explicitly limit the robustness claim to the demonstrated prototype.
[Section 4, Figs. 3-5] The claim 'experimentally verify diffraction-limited resolution' is inferred solely from visual inspection of USAF target images ('clearly resolved' Group 9 Element 2). Resolving line pairs at 0.87 µm is strong evidence of good image quality, but it is not a quantitative measurement of diffraction-limited performance; contrast at the resolution limit, MTF/CTF, or a measured PSF/Strehl ratio are needed to support the stronger claim. The images in Fig. 3b show visible diffraction fringes and possible degradation, and no error bars are provided for the resolution. Please add a contrast transfer function measurement or an equivalent quantitative metric, or qualify the claim accordingly.
[Section 5, Fig. 6] The FOV measurement is partly self-referential. The ideal reference image is generated with the POP module from the same Zemax model whose field behavior is under test, and the pinhole diameter is calibrated from the objective's own Airy pattern. Consequently, agreement between the measured Strehl contour and the simulated FOV (red circle in Fig. 6c) does not provide an independent validation of the model. In particular, if the POP reference includes the model's field-dependent aberrations, the measured ratio would be approximately flat even for a system that exactly follows the model, making it insensitive to the very aberrations that define the FOV. Please state clearly whether the POP reference is on-axis only, and consider an independent reference (e.g., an ideal Airy disk at the measured NA, or a pinhole diameter verified by SEM) to break the circularity.

minor comments (4)

[Throughout] Several typos and grammatical errors should be corrected: 'a a' in the Conclusion, 'Elemenet' in the Fig. 4 caption, 'Veiwport' in the Table 2 caption, and missing closing parentheses after 'Figure 6b' and 'dashed grey lines' in Section 5.
[Ref. [21]] The statement 'Documents are available upon request' is not sufficient for reproducibility; please archive the Zemax file or provide it as supplementary material.
[Abstract and Introduction] The phrase 'all-COTS' could be misread as applying to the entire assembly; only the optical lenses are COTS, while the brass spacer rings and aperture mask are custom-machined. Please clarify this in the abstract or introduction.
[Abstract and Conclusion] The experimental wavelength coverage is 375, 397, and 866 nm; intermediate wavelengths between these points are demonstrated only in simulation. Please word the abstract and conclusion to distinguish measured wavelengths from simulated ones.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: central resolution and robustness claims are externally benchmarked, and the FOV method uses a diffraction-limited POP reference, not a circular reduction.

full rationale

The paper's central claims are supported by external benchmarks: the 0.87 um resolution is verified with a 1951 USAF target (Group 9 Element 2), and wavelength/total-length robustness is verified at discrete experimental points (375 nm, 866 nm, and total lengths of approximately 714 mm and 760 mm). The design methodology is a forward Zemax optimization loop that minimizes RMS wavefront error; no parameter fitted to a subset of data is renamed as a prediction. The FOV measurement in Section 5 uses a POP ideal reference generated from the same optical design, which is a legitimate point to scrutinize, but the reference is the diffraction-limited Airy disk at 397 nm for NA=0.30, convolved with the pinhole; it is not the design's predicted off-axis FOV. The pinhole diameter (0.88(3) um) is calibrated using the objective's PSF but is cross-checked against manufacturing tolerances, and the resulting Strehl map is an independent experimental dataset compared with, not derived from, the simulated FOV contour. The robustness claim lacks a Monte Carlo tolerance analysis over COTS lens manufacturing variations, but this is a missing-support concern, not circularity: it does not reduce a predicted quantity to an input by construction.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The design is an explicit optimization problem in Zemax: curvatures, thicknesses, and air gaps are free parameters; the only physical postulates are that catalog lenses, windows, and ray tracing are accurate. No new entities are introduced.

free parameters (4)

d_gap (gap from last window to first lens) = -0.4 mm to +2.9 mm relative to design at 375-866 nm; 4.3-8.1 mm in Table 2
Optimized in simulation for each wavelength to restore diffraction-limited focus; experimental values matched to within 100 um.
Inter-lens air gaps and back focal length = Table 1; nominal BFL 613 mm, 46 mm adjustable range
Zemax optimization variables (curvatures, center thicknesses, air gaps) minimized RMS wavefront error; they define the design.
Aperture mask diameter for NA 0.30 = NA 0.30 (30 mm aperture at cryostat window)
Chosen to mimic the physical cryostat viewport aperture; unclipped NA 0.37 used in Table 2 simulations.
Reproduced pinhole diameter for FOV reference = 0.88(3) um
Deduced from first-dark-ring spacing of the objective's own pinhole image, then used in the POP ideal reference; checked against manufacturing tolerance.

assumptions (5)

domain assumption Zemax ray tracing correctly models diffraction and aberrations for the COTS design
Section 2, Steps 2-3 use RMS wavefront error minimization in Zemax; the claim that the design is diffraction-limited rests on the simulator's accuracy.
domain assumption Catalog lens prescriptions and fused silica material data match the delivered lenses
Section 3 and Table 1 assume the listed Thorlabs/EKSMA part numbers have catalog curvatures and thicknesses; no inbound metrology is reported.
domain assumption Optical flats used in the experiment replicate the simulated vacuum and cryostat viewports
Section 4, first paragraph: flats are 'matched to the thickness and materials' of the simulated windows; stress, birefringence, and coating effects are not characterized.
domain assumption The USAF target resolving a given group/element is sufficient evidence of diffraction-limited resolution
Section 4 and Figs. 3-5; no quantitative contrast or MTF criterion is used.
domain assumption Strehl ratio >= 0.8 defines the FOV boundary
Inherited from Kingslake Ref. [22], used in Sections 3 and 5.

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Cite this review

Pith. "Pith review of A Robust COTS Objective for Diffraction-Limited, High-NA, Long Front Working Distance Imaging." pith.science (2026). https://pith.science/paper/NDNDE6YC

@misc{pith2026250715786,
  author       = {Pith},
  title        = {Pith review of: A Robust COTS Objective for Diffraction-Limited, High-NA, Long Front Working Distance Imaging},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NDNDE6YC}},
  note         = {Machine review of arXiv:2507.15786}
}

abstract

We present a robust objective lens optimized for applications requiring both high numerical aperture (NA) and long front working distance imaging comprised of all commercial-off-the-shelf (COTS) singlet lenses. Unlike traditional designs that require separate collimation and refocusing stages, our approach directly converges imaged light to the back focal plane using a single lens group. Our configuration corrects spherical aberrations and efficiently collects light to achieve diffraction-limited performance across a wide range of wavelengths while simplifying alignment and assembly. Using this approach, we design and construct an example objective lens that features a long front working distance of 61 mm and a clipped NA of 0.30 (limited by an aperture in our experimental setup). We experimentally verify that it achieves monochromatic diffraction-limited resolution at wavelengths from 375 nm to 866 nm without requiring replacement of the lenses or changing the inter-lens spacings, and its performance remains robust across a 46 mm range variation in total length (by adjusting mainly the back working distances). Additionally, we develop a quantitative method to measure the field of view (FOV) using an experimentally-calibrated pinhole target. Under 397 nm illumination (i.e. from $^{40}$Ca$^+$ ion fluorescence), the objective achieves a resolution of 0.87 $\mu$m with a 540 $\mu$m FOV. This robust, all-COTS, and versatile design is well-suited for a broad range of experiments, supporting high-precision measurements and exploring quantum phenomena.

Figures

Figures reproduced from arXiv: 2507.15786 by the authors.

**Figure 2.** Simulation results for the example objective at 397 nm. (a) The calculated [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Image of a 1951 USAF resolution target under 397 nm diffused light illumination. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Images of a 1951 USAF resolution target under other wavelengths of interest for [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: Images of a 1951 USAF resolution target under total length extremes under [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: Experimental FOV results: (a) Image of Thorlabs P1K pinhole near the optical [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

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