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REVIEW 3 major objections 4 minor 32 references

Successive optimization of optics and post-processing with differentiable coherent PSF operator and field information

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper introduces a differentiable coherent point-spread-function model that simulates wavefront aberrations and diffraction in complex refractive lenses, matches commercial software's Huygens PSF accuracy, and jointly optimizes lens…

desk verdict Strong forward coherent PSF model and a clever memory-saving backprop, but the phase-gradient derivation in Eq. (6) is identically zero and the per-ray gradient is never given, so the joint-optimization claim is unsupported as printed. read the letter →

arxiv 2412.14603 v2 pith:FL2CKZY5 submitted 2024-12-19 cs.CV physics.optics

Zheng Ren , Jingwen Zhou , Wenguan Zhang , Jiapu Yan , Bingkun Chen , Huajun Feng , Shiqi Chen This is my paper · ORCID
classification cs.CVphysics.optics
keywords differentiableopticalsimulationcoherentpointspreadfunctionjointlensdesignimagereconstructionraytracingfieldinformationmemory-efficientbackpropagationasphericoptimization
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 claims that a fully differentiable optical simulation can be built on coherent point spread functions (PSFs) — summing rays as plane waves with accumulated optical path — so that wavefront aberrations and aperture diffraction enter the optimization directly, not just geometric spot sizes. The authors argue this makes joint design of complex refractive lenses and image-restoration networks practical: the coherent PSF matches the accuracy of commercial optical-design software while cutting training memory about 18-fold, and their successive-optimization pipeline improves both raw and reconstructed image quality across three professional-level lenses. If true, camera designers could co-optimize optics and post-processing for compact mobile modules where pixel sizes below 2 µm make diffraction and wave effects dominant. The paper also introduces an initial-value strategy for Newton's method to keep ray-surface intersections inside the aperture on highly aspherical surfaces.

What carries the argument

The load-bearing object is the differential coherent PSF operator: each ray is treated as a plane wave from field point to image plane, accumulated optical path $OPL = \int n(\lambda)\,ds$ gives the phase $k\cdot OPL$, and the complex amplitude at grid point $(x,y)$ is the coherent sum of ray contributions; the PSF is $|A|^2$. Around this, three mechanisms do the work: (1) a reference-point initial-guess strategy that starts Newton's ray-surface intersection near the true in-aperture point on high aspherics; (2) a custom differential operator that backpropagates analytically through the PSF computation without materializing the $N\times M$ broadcast tensor, decoupling ray and grid dimensions; and (3) a joint optimization loop in which the MIMO-UNet reconstruction loss serves as a field-aware PSF merit function, with normalized pixel coordinates concatenated as extra input channels, alongside optical constraints (total track length, EFFL, surface gap, spot RMS, distortion).

What would settle it

Compute the gradient of $PSF = |A|^2$ with respect to the phase variable $\varphi$ in Eq. (6) by finite differences on a single ray's optical path: because the intensity is invariant to a common phase shift, the printed expression evaluates to zero, and a nonzero per-ray phase gradient does not follow from it; a symbolic or numeric check would settle whether the optimization has any path to update lens shapes.

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Extended reading notes

Core claim

The central discovery is that a ray-traced coherent PSF — obtained by accumulating each ray's optical path length and coherently summing the complex amplitudes at image-plane grid points — is accurate enough to serve as a differentiable surrogate for rigorous wave-optics PSFs across diverse lens designs, and that using a restoration network as a PSF merit function, with field coordinates fed to the network, lets gradient descent successively improve lenses that were already professionally optimized. The paper reports MTF errors near zero relative to the commercial Huygens PSF, an 18.4-fold memory reduction from a manually backpropagated differential operator, and quantitative gains in PSNR, SSIM, and LPIPS on degraded and reconstructed images for Double-Gauss, Enna, and aspheric lenses, with MTF pushed closer to the diffraction limit.

Load-bearing premise

The whole lens-update loop relies on the analytical gradient of PSF intensity with respect to the ray-phase $\varphi$ in Eq. (6) being correct and nonzero; if that gradient vanishes or is mis-derived, no optical update signal reaches the lens surfaces.

Editorial extensions

If this is right

  • Coherent PSF simulation replaces geometric or Gaussian PSF approximations for joint design of compact cameras where pixel size is below 2 µm, making wavefront aberration and diffraction effects first-class citizens in the loss.
  • The 18.4-fold memory reduction from manual backpropagation through the coherent PSF operator allows sampling many more field points and PSFs per iteration, supporting field-level PSF control across the sensor.
  • Feeding normalized pixel coordinates to the restoration network makes the network act as a spatially varying PSF merit function, allowing the optimizer to trade MTF across fields rather than chasing a uniform PSF.
  • Adding optical constraints (TTL, EFFL, surface gap, spot RMS, distortion) to the joint loss keeps the optimized lenses manufacturable and within design specifications while image quality improves.
  • The observed trend of boosting lower MTF values suggests the optic and the deblurring network converge toward a PSF that is jointly optimal for the pair, not for the lens alone.

Reading between the lines

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

  • The phase-gradient issue in Eq. (6) is the pivot: as printed, the expression $\partial PSF/\partial \varphi = 2\Re(A)(-\Im(A)) + 2\Im(A)\Re(A)$ evaluates to zero for any complex amplitude $A$, so a corrected per-ray phase gradient would be needed to sustain the claimed lens-surface updates.
  • The field-information ablation suggests the network can compensate for field-varying blur without forcing the lens to a uniform MTF; an extension would optimize a lens for a specific downstream task, such as detection, where the merit function is task loss rather than image reconstruction.
  • The memory-efficiency result generalizes to any physics-based simulation that sums many emitter-receiver contributions; the same manual-backprop decoupling could be applied to other coherent imaging models such as holography or metasurface design.
  • The three-wavelength PSF model may not capture out-of-band chromatic effects, so a wavelength-sampled training scheme could further push MTF and is a natural testable extension.
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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

3 major / 4 minor

Summary. The paper proposes a differentiable ray-tracing-based coherent PSF simulation model for joint optimization of lens design and image post-processing. The model uses a Newton's method with a reference-point initial guess for ray-surface intersections, computes coherent PSFs by summing ray contributions, and implements a manually back-propagated differential operator to reduce memory. The authors validate the forward PSF accuracy against Zemax Huygens PSF, report an 18.4x memory reduction, and demonstrate joint optimization on three commercial-grade lenses, claiming improved MTF and reconstructed image quality.

Significance. If correct, the contribution would be valuable: a differentiable coherent PSF operator that handles aspherics and diffraction and is memory-efficient would enable end-to-end optimization of realistic compound lenses. The forward model validation is a genuine strength: the coherent PSF MTF errors are near zero across diverse lenses, and the proposed initial-value strategy improves Newton convergence on high aspherics. The memory-reduction idea, based on decoupling ray and grid dimensions in backpropagation, is also promising. However, the paper's central differentiability claim is not supported by the printed derivation: Eq. (6) gives a gradient that is identically zero for the phase variables that the optimizer must update, and Eq. (8) defines the reconstruction loss against the degraded image rather than the ground truth. These are load-bearing issues that undermine the joint optimization results as currently presented.

major comments (3)
  1. [Section II-B, Eq. (6)] The derivative of the PSF with respect to the phase is derived incorrectly. In Eq. (6), φ is treated as a single scalar phase multiplying the total complex amplitude A, so the expression evaluates to zero: ∂PSF/∂φ = 2Re(A)(-Im(A)) + 2Im(A)Re(A) = 0. The quantity the optimizer needs is the gradient with respect to each ray phase φ_i = k(OPL_i + Δr_i(x,y)). That per-ray derivative is ∂PSF/∂φ_i = 2 Im(conj(A) · i a_i e^{iφ_i}), which is generally nonzero and index-dependent. The paper never writes or derives this per-ray gradient, so the claimed differentiability of the coherent PSF operator with respect to lens parameters through the phase term is not demonstrated. Every lens update via the reconstruction loss Lnet depends on this gradient, so the paper's central claim stands or falls on an unwritten corrected formula.
  2. [Section III-B, Eq. (8)] The imaging reconstruction loss compares the reconstructed image I_r,k to the degraded image I_d,k, not to the ground truth scene. Since I_d is defined in Eq. (7) as the blurred, noisy image, minimizing Lnet as printed would drive the network toward the identity mapping and would not produce the reported restoration gains (e.g., Table III recovery PSNR > 35 dB). The loss should compare I_r,k to the clean scene I_s (or an appropriate ground truth) at each scale, as in MIMO-UNet. As written, the training objective is inconsistent with the experimental results; this is a load-bearing error in the definition of the joint optimization goal.
  3. [Section IV-A and II-B] The paper does not provide any verification that the manually computed backward pass is correct. The memory-reduction claim of 18.4x is measured on a dummy PSF merit function, but without a finite-difference check of the analytical gradient against a numerical gradient, or a comparison between manual backward and automatic differentiation, the reported 18.4x memory saving does not establish a usable differentiable operator. Given that Eq. (6) is the only explicit gradient formula for the PSF and it is wrong, the experimental section provides no evidence that the joint optimization pipeline actually uses a correct gradient through the coherent PSF.
minor comments (4)
  1. [Throughout] There are several typos and grammatical issues: 'The initial Rays' should be 'The initial rays', 'The subsequent The ray tracing' should be 'The subsequent ray tracing', 'we have develop' should be 'we have developed', and 'PSFs' is sometimes used as a singular. These should be corrected in a revision.
  2. [Section IV-B, Table IV] Table IV's formatting is ambiguous. For the rows labeled 'w/o L_optic', the 'no self-intersection' column contains a '%' symbol, and the 'Mean spots RMS' and 'Max distortion' columns contain dashes. The text states that without L_optic the design deviates from specifications, but the table layout should be cleaned up to clearly indicate which constraints are violated.
  3. [Section I and Fig. 5] The abbreviation 'EMTF' is used in the contribution list but is never defined at first use; the full term 'effective modulation transfer function' appears in parentheses but the acronym is not expanded. In Fig. 5, the label 'nyu' for the Lagrange invariant is cryptic; the authors should use a standard symbol such as H or L and explain the relevance.
  4. [Section II-A, Eq. (1)] The argmin in Eq. (1) is not clearly a scalar metric. The expression (Ps - Pr) × Dr / ((Ps - Pr) · Dr) appears to be a vector, and it is unclear how the argmin is taken. The authors should define the distance measure precisely, for example by giving the scalar function being minimized.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the coherent PSF model is externally benchmarked against Zemax, no fitted constants enter the diffraction-limit claim, and the only author self-citation is motivational rather than load-bearing; the Eq. (6) phase-gradient defect is a mathematical correctness issue, not a circular reduction.

full rationale

The derivation chain is not circular. The coherent PSF forward model (Eqs. 3-5) is constructed from first principles of coherent wave summation, with ray-tracing OPL data and an explicit plane-wave superposition; its accuracy is validated against an external reference, Zemax's Huygens PSF, in Section IV-A (Figs. 6-7), reporting nearly zero MTF error. No parameters are fitted to the benchmark or to the diffraction-limit claim, so no prediction reduces to an input fit. The joint optimization objective (Eqs. 8-15) combines a network reconstruction loss with standard optical constraints, and the optimized lenses are evaluated not only by the differentiable simulator (Fig. 10) but also independently through Zemax MTF-vs-field analysis (Fig. 11), making the claimed improvement externally checkable rather than definitionally forced. The only author self-citation, reference [28], appears in the introduction as motivation for shifting imaging burden to post-processing; it is not load-bearing for the simulation, differentiability, or optimization claims. The paper does contain a serious mathematical defect: Eq. (6), as printed, differentiates the PSF with respect to a global phase and evaluates to zero, while the per-ray phase gradient actually required for lens parameter updates is not derived. This is a correctness/validity gap in the claimed differentiability, not a case of a result being equivalent to its inputs by construction, and therefore it does not raise the circularity score.

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

The central method rests on standard physical models plus a set of hand-chosen simulation parameters. The most important unstated inputs are the per-ray amplitude model and the reference-point sampling for the Newton initial guess. No new physical entities are introduced; circularity burden is low because of the external Zemax benchmark.

free parameters (5)
  • Ray amplitude a_i in Eq. (4) = not specified
    No formula is given for per-ray amplitude; it may be equal weights or derived from vignetting and Fresnel factors, and the central PSF value depends on it.
  • Loss weights lambda_t, lambda_f, lambda_g, lambda_d in Eq. (14) = 0.5, 10, 3, 5
    Hand-selected weights balance optical constraints; no sensitivity analysis is reported.
  • lambda_lens in Eq. (15) = set individually per lens, values not reported
    The joint loss weight is chosen per lens but the values are not given, so the training protocol is incomplete.
  • Sensor noise sigma in Eq. (7) = 0.03
    White Gaussian noise level is a chosen simulation parameter affecting all degraded images and training.
  • Reference point set P_s on aspheric surfaces = not reported
    Number and placement of reference points for the Newton initial guess are not specified, yet they directly affect intersection accuracy on high aspherics.
assumptions (5)
  • domain assumption Snell's law and geometric ray tracing accurately describe propagation through the refractive lens system.
    The entire pipeline traces rays through surfaces and applies Snell's law; this is a physical model assumed valid, not derived in the paper.
  • domain assumption The coherent PSF can be computed as a coherent sum of plane waves with accumulated optical path length, as in Eq. (4).
    Huygens-style wave summation is invoked to include diffraction and wavefront aberration; validation against Zemax covers only the selected test lenses.
  • ad hoc to paper Newton's method with the proposed nearest-reference-point initial guess converges to the correct intersection on high aspherics.
    The initial value scheme is a new algorithmic heuristic; stability is demonstrated empirically in Table I, not proven.
  • ad hoc to paper The reconstruction loss Lnet is a valid overall PSF merit function for lens optimization.
    The network is used as the whole PSF merit function, an assumption the paper motivates but does not prove; see Section III.
  • domain assumption Simulation-based optimization transfers to real fabrication and measurement.
    No manufactured lens or physical measurement is presented; the paper's claims about improving professional lenses rely on this transfer.

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Cite this review

Pith. "Pith review of Successive optimization of optics and post-processing with differentiable coherent PSF operator and field information." pith.science (2026). https://pith.science/paper/FL2CKZY5

@misc{pith2026241214603,
  author       = {Pith},
  title        = {Pith review of: Successive optimization of optics and post-processing with differentiable coherent PSF operator and field information},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FL2CKZY5}},
  note         = {Machine review of arXiv:2412.14603}
}
read the original abstract

Recently, the joint design of optical systems and downstream algorithms is showing significant potential. However, existing rays-described methods are limited to optimizing geometric degradation, making it difficult to fully represent the optical characteristics of complex, miniaturized lenses constrained by wavefront aberration or diffraction effects. In this work, we introduce a precise optical simulation model, and every operation in pipeline is differentiable. This model employs a novel initial value strategy to enhance the reliability of intersection calculation on high aspherics. Moreover, it utilizes a differential operator to reduce memory consumption during coherent point spread function calculations. To efficiently address various degradation, we design a joint optimization procedure that leverages field information. Guided by a general restoration network, the proposed method not only enhances the image quality, but also successively improves the optical performance across multiple lenses that are already in professional level. This joint optimization pipeline offers innovative insights into the practical design of sophisticated optical systems and post-processing algorithms. The source code will be made publicly available at https://github.com/Zrr-ZJU/Successive-optimization

Figures

Figures reproduced from arXiv: 2412.14603 by the authors.

Figure 1
Figure 1. Schematic diagram of this work. In the left figure, we focus on successively optimizing the optical and image performance of advanced complex lens [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. (a) shows the differences between our proposed initial value estimation [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Comparison of the gradient computation flow. (a) demonstrates the [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: Overview of the lenses specifications and layouts in the experiments. The relative difficulty of each lens design is estimated based on the optical [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 7
Figure 7. Figure 7: Visualization of different PSF calculation results. The Airy disks are [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 6
Figure 6. Figure 6: MAE of MTF for different PSF calculation methods across various [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 8
Figure 8. Figure 8: The comparison of memory and time costs between traditional [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]
Figure 9
Figure 9. Figure 9: Visual comparison of the blurred and reconstructed images for Double-Gauss lens, with and without joint design. The magnified patches on the right [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]
Figure 10
Figure 10. Figure 10: (a) compares the PSF map of different lenses before (upper) and after (lower) joint design. Note that for visualization purposes, each PSF is normalized [PITH_FULL_IMAGE:figures/full_fig_p008_10.png]
Figure 11
Figure 11. Figure 11: Zemax MTF vs. field analysis comparison between original (left) and joint designed (right) Aspheric. Blue, green, red, and black lines represent [PITH_FULL_IMAGE:figures/full_fig_p008_11.png]

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    Available: https://opg.optica.org/optica/abstract.cfm? URI=optica-7-8-913

    [Online]. Available: https://opg.optica.org/optica/abstract.cfm? URI=optica-7-8-913

  24. [2021]

    Available: https://arxiv.org/abs/2104.03078

    [Online]. Available: https://arxiv.org/abs/2104.03078

    arXiv

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.