{"id":"543e166c-04e9-46cd-9fcb-2c08286bca3f","arxiv_id":"2412.14603","paper_version":2,"verdict":"REJECT","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"A differentiable coherent-PSF ray tracer with a memory-efficient manual backward pass enables joint optimization of lens surfaces and a restoration network, improving simulated image quality and pushing lenses toward the diffraction limit.","lead":"This paper presents a differentiable optical simulator that computes coherent point spread functions with wavefront aberration and diffraction effects, then uses it to jointly optimize camera lens parameters and a neural-network image restorer. It reports sharper simulated images and improved MTF for three professional-grade lens designs, but the code is only promised and no hardware validation is provided.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Equation (6) derives the derivative of PSF with respect to a global phase of the total field, which is identically zero; the per-ray phase gradient required for lens optimization is never derived, so the central differentiability claim is unsupported as printed.","rationale":"The paper's central contribution is joint optimization of optics and post-processing, which requires gradients of the PSF with respect to lens parameters. The forward coherent PSF model is validated against Zemax, and the memory-efficiency claim is plausible from decoupling ray and grid dimensions. However, the backward pass is the essential enabling step, and Eq. (6) is the only place where the phase derivative is derived. As written, it cancels to zero because it differentiates with respect to a global phase of the total field. The correct per-ray derivative is straightforward but absent. This is not a cosmetic issue in an auxiliary equation: the manual backward operator described in Fig. 4(b) must propagate through φ_i = k(OPL_i + Δr_i), and OPL_i is a function of intersection points, Snell's law, and surface parameters. Without the per-ray gradient, there is no path from the reconstruction loss L_net to the lens parameters. The ablation labeled 'Lnet detached from ϕlens' in Table V confirms that lens updates are supposed to flow through the network loss via the PSF, making the missing gradient load-bearing. The absence of code prevents verifying whether the implementation silently uses a corrected formula. The other issues, such as the ZEBASE citation error and missing error statistics, are secondary and do not affect this core concern. Therefore the reader's rejection is justified; the paper needs a corrected derivation and reproducible code before the differentiability claim can be accepted.","tokens_in":14399,"tokens_out":4343,"duration_ms":32706,"concrete_test":"Perform a numerical gradient check on the claimed operator: for the Double-Gauss lens, take one field point and one image-plane grid point, compute the PSF intensity with Eq. (4)-(5), perturb a single ray's accumulated phase φ_i by 10^{-6}, and compare ∂PSF/∂φ_i from the printed Eq. (6) (zero) with the finite-difference value. Then perturb one surface curvature by 10^{-6} mm and compare the full manual-BP gradient of the PSF intensity against central finite differences. If the printed Eq. (6) is used, the gradient is zero and the joint optimization cannot proceed; if a corrected per-ray formula is used, it must be stated explicitly and must match finite differences to within ~1%.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the manual backward pass through the coherent PSF operator in Section II-B. Equation (6) states ∂PSF/∂φ = 2Re(A)(−Im(A)) + 2Im(A)Re(A) = 0. This expression treats φ as a single global phase multiplying the total complex amplitude A = Σ_i a_i e^{iφ_i}; changing such a global phase indeed leaves |A|^2 invariant. But the quantity the optimizer needs is ∂PSF/∂φ_i for each ray phase φ_i, where φ_i = k(OPL_i + Δr_i(x,y)). By the chain rule, ∂PSF/∂φ_i = 2 Re(conj(A) · i a_i e^{iφ_i}) = 2 Im(conj(A) a_i e^{iφ_i}), which is generally nonzero and depends on i. The paper never derives or writes this per-ray gradient; it only gives the identically zero global-phase expression in Eq. (6). Consequently, the claimed differentiable coupling from lens parameters (surface curvatures, aspheric coefficients, thicknesses) through OPL and phase to PSF and reconstruction loss has no written derivation. The forward PSF accuracy comparison with Zemax in Section IV-A is credible evidence for the forward model, but it says nothing about the gradient. Since no code is provided, the central claim that every operation in the pipeline is differentiable and that joint optimization updates lens parameters is not supported by the manuscript. A corrected per-ray gradient derivation, or code whose gradient passes a finite-difference check, is required.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":14764,"tokens_out":7109,"duration_ms":52032,"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":[{"comment":"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.","section":"Section II-B, Eq. (6)"},{"comment":"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.","section":"Section III-B, Eq. (8)"},{"comment":"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.","section":"Section IV-A and II-B"}],"minor_comments":[{"comment":"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.","section":"Throughout"},{"comment":"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.","section":"Section IV-B, Table IV"},{"comment":"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.","section":"Section I and Fig. 5"},{"comment":"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.","section":"Section II-A, Eq. (1)"}],"recommendation":"major_revision","confidential_remarks":"The two errors in core equations (Eq. (6) and Eq. (8)) are serious, but they appear to be fixable in revision: the per-ray phase gradient can be derived, and the loss target can be corrected. However, the authors should be required to provide a gradient verification (e.g., finite-difference check) and, ideally, release the code so that reviewers can reproduce the claimed joint optimization results. Without such evidence, the manuscript's central contribution remains unsubstantiated."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things you should know. First, the forward model is genuinely good: the coherent PSF computed from ray tracing matches Zemax Huygens PSF across five lenses, and the manual backward pass that avoids materializing the M×N broadcast tensor is a real engineering win (18.4× memory reduction). Second, the paper's central differentiability claim is not actually derived. Eq. (6) computes ∂PSF/∂φ for a global phase multiplying the total complex amplitude; that derivative is identically zero, as the algebra shows. What the optimizer needs is ∂PSF/∂φ_i for each ray's phase φ_i = k(OPL_i + Δr_i(x,y)), which is generally nonzero and depends on i. That per-ray gradient is never written down. So the claimed coupling from lens parameters (curvatures, aspheric coefficients, thicknesses) through OPL and phase to the reconstruction loss has no written derivation. Since no implementation is included, the joint optimization results in Tables III–V and Figs. 10–11 rest on an unverified gradient.\n\nThe forward model validation, the initial-guess strategy for Newton's method on high aspherics, and the idea of using a restoration network with field coordinates as a global PSF merit function are all worth taking seriously. These are real contributions.\n\nThe soft spots beyond Eq. (6): the ZEBASE citation [15] points to a zebrafish database, not an optical lens database, which needs fixing. The metrics in Table III are reported without error bars or repeated runs, and there is no hardware prototype, so the practical impact is untested. The 'for the first time' field-level PSF control claim is a bit strong but not material.\n\nVerdict: I would not accept this in its current form. The gradient gap is load-bearing, not cosmetic. That said, the fix may be simple—the correct per-ray chain rule is a few lines—and the forward model is solid enough that the paper deserves refereeing rather than a desk reject. Ask for a corrected derivation, a public code release with a finite-difference gradient check, and a fix to the ZEBASE reference. If those land, it's a useful paper for computational optics.","headline":"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.","tokens_in":15303,"tokens_out":4153,"would_cite":false,"duration_ms":28982,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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…","keywords":["differentiable optical simulation","coherent point spread function","joint lens design","image reconstruction","ray tracing","field information","memory-efficient backpropagation","aspheric lens optimization"],"falsifier":"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.","tokens_in":14168,"feed_emoji":"📷","tokens_out":7256,"duration_ms":52321,"temperature":0.7,"pith_summary":"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.","feed_headline":"Wave-optics PSF model sharpens lenses via joint optimization","feed_subtitle":"Accurate coherent point-spread functions make end-to-end lens and software co-design practical for compact cameras.","key_machinery":"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).","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the end-to-end camera-design baseline that this pipeline extends to wave-optics PSFs.","marker":"[25]"},{"why":"Supplies the differentiable ray-tracing baseline for compound lens optimization.","marker":"[24]"},{"why":"Supplies the Gaussian-PSF baseline and a prior joint lens search method.","marker":"[9]"},{"why":"Supplies the geometric-PSF comparison baseline and a differentiable ray-tracing engine.","marker":"[26]"},{"why":"Supplies the geometric-PSF comparison and a prior joint design pipeline for refractive optics.","marker":"[27]"},{"why":"Provides the multi-scale deblurring network used as the field-aware PSF merit function.","marker":"[6]"},{"why":"Provides the high-resolution training images for the reconstruction network.","marker":"[2]"},{"why":"Provides the classical lens designs used as test cases.","marker":"[15]"}],"fun_headline_variants":["Differentiable wave-optics PSF boosts joint lens-software design","Coherent PSF model enables end-to-end lens and algorithm tuning","Joint optimization with field info sharpens compact camera lenses","Wave-optics PSF lens tuning cuts memory 18x","Successive lens refinement via differentiable PSF and field network"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Differentiable wave-optics PSF boosts joint lens-software design","Coherent PSF model enables end-to-end lens and algorithm tuning","Joint optimization with field info sharpens compact camera lenses","Wave-optics PSF lens tuning cuts memory 18x","Successive lens refinement via differentiable PSF and field network"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000581,"raw_usage":{"total_tokens":2709,"prompt_tokens":891,"completion_tokens":1818,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":507,"completion_tokens_details":{"reasoning_tokens":1731}},"tokens_in":507,"tokens_out":1818,"duration_ms":10520,"temperature":1.0,"reasoning_tokens":1731,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T12:04:53.199651+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Differen- tiable compound optics and processing pipeline optimization for end- to-end camera design,","cited_arxiv_id":null,"evidence_quote":"Supplies the end-to-end camera-design baseline that this pipeline extends to wave-optics PSFs."},{"cited_title":"End-to-end complex lens design with differentiable ray tracing,","cited_arxiv_id":null,"evidence_quote":"Supplies the differentiable ray-tracing baseline for compound lens optimization."},{"cited_title":"The dif- ferentiable lens: Compound lens search over glass surfaces and materials for object detection,","cited_arxiv_id":null,"evidence_quote":"Supplies the Gaussian-PSF baseline and a prior joint lens search method."},{"cited_title":"do: A differentiable engine for deep lens design of computational imaging systems,","cited_arxiv_id":null,"evidence_quote":"Supplies the geometric-PSF comparison baseline and a differentiable ray-tracing engine."},{"cited_title":"Curriculum learning for ab initio deep learned refractive optics,","cited_arxiv_id":null,"evidence_quote":"Supplies the geometric-PSF comparison and a prior joint design pipeline for refractive optics."},{"cited_title":"Zebase: an open-source relational database for zebrafish laboratories,","cited_arxiv_id":null,"evidence_quote":"Provides the classical lens designs used as test cases."}],"review_version":1}