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Perturbative Fourier Ptychographic Microscopy for Fast Quantitative Phase Imaging

T0 review · 1 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Five illuminations match FPM resolution at DPC speed.

desk verdict A clean, well-documented extension of DPC to iterative dark-field Gauss-Newton with a real speed-resolution win; the main risk is the unproven basin-of-attraction assumption, but the empirical case is strong enough to referee. read the letter →

arxiv 2501.07308 v2 pith:CAYDZ7GG submitted 2025-01-13 physics.optics

Martin Zach , Kuan-Chen Shen , Ruiming Cao , Michael Unser , Laura Waller , Jonathan Dong This is my paper · ORCID
classification physics.optics
keywords FourierptychographicmicroscopydifferentialphasecontrastquantitativeimagingproximalGauss-Newtondark-fieldilluminationLEDarraymicroscoperetrievalcomputational
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

Perturbative Fourier ptychographic microscopy (pFPM) claims that differential phase contrast (DPC) is only the first step of a more general iterative scheme: interpret DPC as the initial iteration of a proximal Gauss-Newton algorithm, add dark-field illumination, and the same fast few-measurement setup recovers the high-frequency phase that DPC misses. The paper argues that with five illumination patterns — the classic DPC antisymmetric bright-field pair, one full bright-field measurement, and two dark-field annuli — the method reaches resolutions comparable to conventional Fourier ptychographic microscopy while cutting acquisition time from 126 s to 550 ms. If correct, this turns a two-measurement low-resolution technique into a five-measurement high-resolution one without any learned components or hardware changes beyond the already-programmable LED array.

What carries the argument

The proximal Gauss-Newton algorithm with quadratic or total-variation regularization, in which each iteration solves a regularized linear least-squares problem around the current estimate rather than around a fixed weak-object assumption; the paper proves that the first such iteration starting from $o=1$ reproduces DPC exactly. The tailored illumination strategy is the second half: two annular dark-field patterns spanning $[1,1.5]\nu_{\text{obj}}$ and $[1.5,2]\nu_{\text{obj}}$ are chosen to 'push' recovered Fourier frequencies outward, and the paper recommends two annuli because more give diminishing returns.

What would settle it

Image a strong phase object with phase excursions well beyond 0.5 rad, or with significant absorption, under the same five illumination patterns; if DF-pFPM fails to resolve the high-frequency elements it resolves for weak objects, or produces streak artifacts that do not diminish with more iterations, the assumed basin of attraction is too optimistic.

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Extended reading notes

Core claim

The paper establishes that DPC is exactly the first iteration of a proximal Gauss-Newton algorithm starting from the uniform-transmission guess $o=1$ with quadratic regularization, and then removes the weak-object restriction by running more iterations. Because later iterations do not rely on the weak-object approximation, the same linearized-update structure can be applied to dark-field measurements, whose scattered light carries the high spatial frequencies that DPC's bright-field-only model discards. Adding two annular dark-field illumination patterns, spanning $[1,1.5]\nu_{\text{obj}}$ and $[1.5,2]\nu_{\text{obj}}$, allows the recovered Fourier support to be 'pushed' outward, yielding simulated SNR 17.35 dB and experimentally resolving USAF Group 9 Element 5 with hints of Element 6, in roughly 5 total measurements and 550 ms acquisition time.

Load-bearing premise

The initial DPC estimate, obtained by linearizing around a uniform transparent object, must lie in the region where the nonlinear Gauss-Newton iterations converge to the true high-frequency content rather than to a local minimum, with only five multiplexed measurements and no proof for the outer nonconvex iterations.

Editorial extensions

If this is right

  • DPC users can upgrade to near-FPM resolution with only three additional exposures and no change of hardware, provided their microscope has a programmable LED array.
  • The identification of DPC as the first Gauss-Newton iteration gives a principled way to design illumination patterns: each dark-field annulus extends the recovered Fourier support by a controlled amount, replacing ad-hoc or learned pattern choices.
  • Total-variation regularization inside the proximal Gauss-Newton framework suppresses the high-frequency noise and ringing that appear in L2-regularized DPC reconstructions, as demonstrated on the USAF phantom.
  • A five-pattern acquisition is fast enough for time-lapse phase imaging of moving or live samples, where the 126 s needed for conventional FPM at 1 s exposure per LED is impractical.

Reading between the lines

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

  • The same interpretative move — linearize, iterate, then add dark-field patterns — could be applied to other linearized phase-retrieval techniques, turning any single-shot linear inversion into a multi-iteration nonlinear refinement with few extra measurements.
  • Because each annulus corresponds to a controlled Fourier-support extension, the design suggests a direct tradeoff curve between measurement count and resolution that could be probed systematically for X-ray or electron imaging, where LED-array-style illumination geometries differ but the Fourier-support logic persists.
  • The paper's own comparison shows diminishing returns beyond two annuli, implying that the practical limit of this scheme may be set by model mismatch and noise rather than by information content, so better forward models (including pupil aberrations) could push resolution further at the same measurement count.
  • A natural testable extension is to replace the hand-set regularization with a data-driven prior inside the same proximal Gauss-Newton loop; if that prior keeps the high-frequency content while reducing artifacts, the method could tolerate stronger or more absorbing objects than the currently demonstrated weak-phase regime.
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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

1 major / 4 minor

Summary. The paper proposes perturbative Fourier ptychographic microscopy (pFPM), an iterative extension of differential phase contrast (DPC) that combines a proximal Gauss-Newton reconstruction with tailored annular dark-field illumination patterns. The authors show that the first proximal Gauss-Newton iteration with quadratic regularization is equivalent to DPC, and then generalize this to multiple iterations and TV regularization. They report that adding two dark-field annuli to the two DPC bright-field patterns enables recovery of higher spatial frequencies, and they demonstrate the method on a simulated cameraman phase object and on an experimental USAF-1951 phantom, with acquisition times around 550 ms versus 126 s for conventional FPM. The appendices contain derivations of the transfer functions, the DPC-equivalence proof, discretization details, the inner solver algorithm, and comparisons with alternative illumination patterns.

Significance. If the reported results hold, pFPM provides a practical speed-resolution tradeoff for LED-array microscopes: it retains the speed and simplicity of DPC while extending resolution into the dark-field region with only five measurements and no learned components. The paper's derivation of the transfer functions and the identification of DPC as the first Gauss-Newton step are clean and self-contained, and the authors ship code and data for reproducibility. The main caveat is that the outer nonconvex Gauss-Newton loop lacks a convergence or basin-of-attraction analysis, so the central claim that the method 'does not rely on the weak-object approximation' is currently only empirically supported for the tested objects. Overall, this is a solid, clearly presented contribution to fast quantitative phase imaging, with a limitation that should be addressed in revision.

major comments (1)
  1. [Section 3.1 / Appendix D] The statement that 'subsequent iterations of the proximal Gauss-Newton algorithm do not rely on the weak-object approximation' in Section 3.1 is not supported by the provided analysis. The proximal Gauss-Newton update (13) remains a local method: its accuracy depends on how well G(ok)+G'(ok)(o-ok) approximates G(o) near the current iterate. Appendix D proves only that the inner Conduit-Vu stepsizes (42)-(44) satisfy the convex-convergence condition, and Proposition 6 of [15] merely identifies the proximal update with the linearized subproblem (36). No result is given on whether the DPC initialization lies in the basin of attraction of the outer nonconvex iteration or whether the iterates avoid local minima. Because the resolution advantage over DPC is explicitly attributed to this nonlinear refinement, this missing convergence argument is load-bearing. I recommend either adding a local convergence analysis (e.g., regularity conditions on G and a neighborhood estimate around the DPC solution) or reformulating the claim to state that the method does not rely on the weak-object approximation only where the linearized model remains accurate, with convergence validated empirically.
minor comments (4)
  1. [Section 4.1 / Figure 3 caption] The caption in Figure 3 states 'SNR and RMSE in Fourier space', but the definitions in (15) and (16) are image-domain metrics applied to the phase of the reconstruction. Please correct the caption or the equations to avoid confusion.
  2. [Section 3.1 / Appendix B] The identification of DPC as the first proximal Gauss-Newton iteration requires the phase-only and zero-mean assumptions stated at the end of Appendix B. This assumption should be stated explicitly in Section 3.1 where the claim is made, so that readers do not infer the equivalence for general complex objects with absorption.
  3. [Section 4.2 / Figure 6] The comparison with conventional FPM is informal: the FPM reconstruction in Figure 6 is obtained by 50 iterations of a simple gradient descent and shows visible artifacts. Please report the number of FPM measurements, the reconstruction settings, and ideally a quantitative comparison metric (e.g., line-profile error or correlation with the DF-pFPM result) to support the 126 s versus 550 ms comparison.
  4. [Appendix D / Algorithm 1] The inner solver is run for a fixed K=100 iterations with warm start, which makes the method inexact. Please state explicitly whether the reported reconstructions use this inexact setting and whether the outer iteration count (8, or 4 for BF-pFPM*) was chosen by performance on validation data.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: pFPM's DPC equivalence is derived in Appendix B, and the dark-field annuli are validated against alternative patterns rather than fitted; self-citations are motivational only.

full rationale

The paper's derivation chain is self-contained. The central identification of DPC as the first proximal Gauss-Newton iteration is proved in Appendix B, where the linearized model matches the conventional DPC transfer functions and both minimize the same L2 loss; it is not an input renamed as a prediction. The annular dark-field patterns are motivated by perturbation theory and by Kellmann et al.'s learned-pattern observation, but their advantage is established by direct comparison against sector and random patterns in Appendix F, not by construction. No parameter is fitted to produce the claimed high-frequency recovery: the simulation uses a standard cameraman phase object with phase in [-0.5,0.5] rad, and the USAF-1951 experimental phantom is independent; DPC starts at SNR 3.24 dB and DF-pFPM reaches 17.35 dB. The load-bearing convergence assumption for the outer Gauss-Newton loop is not proven beyond Appendix D's inner-subproblem stepsize conditions, but that is an unproven empirical convergence claim, not circularity, since the success is demonstrated on data and not assumed in the derivation. Self-citations to Waller-group DPC and mFPM work appear as background motivation and are not the basis for the equivalence or the pattern design; the cited numerical-analysis results (Salzo-Villa, Chambolle-Pock) are external. Therefore no step reduces by construction to its own input, and the paper receives a low score reflecting only minor motivational self-citation.

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

The central claim rests on standard optical modeling assumptions (weak object, aberration-free pupil, incoherent LED superposition) and on hand-chosen algorithm hyperparameters. The most fragile item is the empirical convergence assumption for nonconvex proximal Gauss-Newton, which is not proven. No new physical entities are introduced.

free parameters (4)
  • regularization weight alpha = 0.1 (simulation), 9e4 (L2 experiment), 1.5e4 (TV experiment)
    Hand-selected per setup in Appendix D; controls the balance between data fidelity and regularizer, and directly affects reconstruction quality.
  • number of outer Gauss-Newton iterations = 8 for DF-pFPM, 4 for BF-pFPM* and BF-pFPM
    Fixed practical choices with no convergence criterion; chosen in Appendix D and does not adapt to the data.
  • dark-field annulus radii = [1, 1.5] nu_obj and [1.5, 2] nu_obj
    Design parameters recommended by the authors based on simulations and experiments; the number and spacing of annuli are tunable and directly set the acquisition pattern.
  • inner solver iterations and step sizes = K=100; tau and sigma from power iteration estimates
    Algorithmic hyperparameters chosen for speed and stability in Appendix D; not derived from the physics.
assumptions (5)
  • domain assumption Weak-object parametrization o = 1 + j phi - mu with small phi and mu.
    Used in Eq. (5) and Appendix A to derive transfer functions and to identify DPC as the first Gauss-Newton step. Real samples can violate the weak-scattering condition.
  • domain assumption Aberration-free pupil function p equal to 1 inside the aperture and 0 outside.
    Assumed in Eq. (1) and throughout Section 2; the authors list pupil aberrations as future work in Section 5, but the experimental system may contain unmodeled aberrations.
  • domain assumption Phase-only sample with mu = 0.
    Section 2.4 simplifies the model to phase-only reconstruction; both the simulated phantom and the USAF-1951 phantom are phase-only, so absorption robustness is untested.
  • ad hoc to paper The DPC estimate lies in the basin of attraction of the proximal Gauss-Newton scheme for nonconvex phase retrieval.
    Appendix D proves stepsize conditions for the inner convex subproblems but provides no convergence or local-minimum guarantee for the outer nonconvex iterations. The central experimental success depends on this empirical convergence.
  • domain assumption Incoherent superposition of intensities from multiplexed LEDs.
    Standard in LED-array microscopy and used in Eq. (2); assumes no source coherence or crosstalk between LEDs.

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Cite this review

Pith. "Pith review of Perturbative Fourier Ptychographic Microscopy for Fast Quantitative Phase Imaging." pith.science (2026). https://pith.science/paper/CAYDZ7GG

@misc{pith2026250107308,
  author       = {Pith},
  title        = {Pith review of: Perturbative Fourier Ptychographic Microscopy for Fast Quantitative Phase Imaging},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CAYDZ7GG}},
  note         = {Machine review of arXiv:2501.07308}
}
read the original abstract

In computational phase imaging with a microscope equipped with an array of light emitting diodes as illumination unit, conventional Fourier ptychographic microscopy achieves high resolution and wide-field reconstructions but is constrained by a lengthy acquisition time. Conversely, differential phase contrast (DPC) offers fast imaging but is limited in resolution. Here, we introduce perturbative Fourier ptychographic microscopy (pFPM). pFPM is an extension of DPC that incorporates dark-field illumination to enable fast, high-resolution, wide-field quantitative phase imaging with few measurements. We interpret DPC as the initial iteration of a Gauss-Newton algorithm with quadratic regularization and generalize it to multiple iterations and more sophisticated regularizers. This broader framework is not restricted to bright-field measurements and allows us to overcome resolution limitations of DPC. We develop tailored annular dark-field illumination patterns that align with the perturbative interpretation and lead to an improvement in the quality of reconstruction with respect to other common illumination schemes. Consequently, our methodology combines an enhanced phase reconstruction algorithm with a specialized illumination strategy and offers significant advantages in both imaging speed and resolution.

Figures

Figures reproduced from arXiv: 2501.07308 by the authors.

Figure 1
Figure 1. LED microscope. A programmable LED array plays the role of the illumination unit. In [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Illumination patterns of different methods. The inner disk indicates the bright-field region [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Simulated measurements. Top to bottom: llumination patterns; phase reconstruction and [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Phase reconstruction from measurements of the USAF-1951 phantom. From top to bottom: [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: Influence of the regularizer on the phase reconstruction of the USAF-1951 phantom. From [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]
Figure 6
Figure 6. Figure 6: USAF-1951 phantom. From left to right: illumination by all bright-field LEDs; illumination [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]
Figure 7
Figure 7. Figure 7: Reconstructions from different designs of [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]
Figure 8
Figure 8. Figure 8: Reconstructions from different designs of [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]

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Reference graph

Works this paper leans on

27 extracted references · 23 canonical work pages

  1. [15]

    Convergence analysis of a proximal Gauss-Newton method

    Saverio Salzo and Silvia Villa. “Convergence analysis of a proximal Gauss-Newton method”. In: Computational Optimization and Applications 53.2 (Mar. 2012), pp. 557–589. issn: 1573-2894. doi: 10.1007/s10589-012-9476-9 . url: http://dx.doi.org/10.1007/s10589-012-9476-9

    work page doi:10.1007/s10589-012-9476-9 2012

  2. [1]

    Dynamic Fourier ptychography with deep spatiotemporal priors

    Pakshal Bohra et al. “Dynamic Fourier ptychography with deep spatiotemporal priors”. In: Inverse Problems 39.6 (2023), p. 064005

    work page 2023

  3. [2]

    An Algorithm for Total Variation Minimization and Applications

    Antonin Chambolle. “An Algorithm for Total Variation Minimization and Applications”. In: Journal of Mathematical Imaging and Vision 20.1 (2004), pp. 89–97. doi: 10.1023/B:JMIV.0000 011325.36760.1e. url: https://doi.org/10.1023/B:JMIV.0000011325.36760.1e

    arXiv 2004

  4. [3]

    On the ergodic convergence rates of a first-order primal- dual algorithm

    Antonin Chambolle and Thomas Pock. “On the ergodic convergence rates of a first-order primal- dual algorithm”. In: Mathematical Programming 159.1–2 (Oct. 2015), pp. 253–287. issn: 1436-4646. doi: 10.1007/s10107-015-0957-3 . url: http://dx.doi.org/10.1007/s10107-015-0957-3

    doi:10.1007/s10107-015-0957-3 2015

  5. [4]

    Phase retrieval: From computational imaging to machine learning: A tutorial

    Jonathan Dong et al. “Phase retrieval: From computational imaging to machine learning: A tutorial”. In: IEEE Signal Processing Magazine 40.1 (2023), pp. 45–57

    2023

  6. [5]

    A new microscopic principle

    D Gabor. “A new microscopic principle”. In: Nature 161 (1948), p. 777

    work page 1948

  7. [6]

    Differential phase contrast in scanning optical microscopy

    DK Hamilton and CJR Sheppard. “Differential phase contrast in scanning optical microscopy”. In: Journal of Microscopy 133.1 (1984), pp. 27–39

    work page 1984

  8. [7]

    Data-driven design for Fourier ptychographic microscopy

    Michael Kellman et al. “Data-driven design for Fourier ptychographic microscopy”. In: 2019 IEEE International Conference on Computational Photography (ICCP) . Tokyo, Japan, 2019, pp. 1–8

    work page 2019

Show all 27 references
  1. [8]

    Physics-based learned design: Optimized coded-illumination for quantitative phase imaging

    Michael R Kellman et al. “Physics-based learned design: Optimized coded-illumination for quantitative phase imaging”. In: IEEE Transactions on Computational Imaging 5.3 (2019), pp. 344–353

    2019

  2. [9]

    High-resolution three-dimensional imaging of red blood cells parasitized by Plasmodium falciparum and in situ hemozoin crystals using optical diffraction tomography

    Kyoohyun Kim et al. “High-resolution three-dimensional imaging of red blood cells parasitized by Plasmodium falciparum and in situ hemozoin crystals using optical diffraction tomography”. In: Journal of Biomedical Optics 19.1 (2014), pp. 011005–011005

    2014

  3. [10]

    Quantitative phase-gradient imaging at high resolution with asymmetric illumination-based differential phase contrast

    Shalin B Mehta and Colin JR Sheppard. “Quantitative phase-gradient imaging at high resolution with asymmetric illumination-based differential phase contrast”. In: Optics Letters 34.13 (2009), pp. 1924–1926

    2009

  4. [11]

    Label-free characterization of emerging human neuronal networks

    Mustafa Mir et al. “Label-free characterization of emerging human neuronal networks”. In: Scientific Reports 4.1 (2014), p. 4434

    2014

  5. [12]

    Quantitative phase imaging in biomedicine

    YongKeun Park, Christian Depeursinge, and Gabriel Popescu. “Quantitative phase imaging in biomedicine”. In: Nature Photonics 12.10 (2018), pp. 578–589

    2018

  6. [13]

    Quasi-dome: A self-calibrated high-NA LED illuminator for Fourier ptychography

    Zachary F Phillips, Regina Eckert, and Laura Waller. “Quasi-dome: A self-calibrated high-NA LED illuminator for Fourier ptychography”. In: Imaging Systems and Applications . 2017, IW4E–5. 10

    2017

  7. [14]

    On the Inexact Proximal Gauss-Newton Methods for Regularized Nonlinear Least Squares Problems

    Federica Porta et al. “On the Inexact Proximal Gauss-Newton Methods for Regularized Nonlinear Least Squares Problems”. In: Advanced Techniques in Optimization for Machine Learning and Imaging. Ed. by Alessandro Benfenati et al. Singapore: Springer Nature Singapore, 2024, pp. 151–

    2024

  8. [16]

    Quantitative differential phase contrast imaging in an LED array microscope

    Lei Tian and Laura Waller. “Quantitative differential phase contrast imaging in an LED array microscope”. In: Optics Express 23.9 (2015), pp. 11394–11403

    2015

  9. [17]

    Computational illumination for high-speed in vitro Fourier ptychographic microscopy

    Lei Tian et al. “Computational illumination for high-speed in vitro Fourier ptychographic microscopy”. In: Optica 2.10 (Oct. 2015), pp. 904–911. doi: 10.1364/OPTICA.2.000904 . url: https://opg.optica.org/optica/abstract.cfm?URI=optica-2-10-904

    2015 doi

  10. [18]

    Multiplexed coded illumination for Fourier Ptychography with an LED array microscope

    Lei Tian et al. “Multiplexed coded illumination for Fourier Ptychography with an LED array microscope”. In: Biomedical Optics Express 5.7 (2014), pp. 2376–2389

    2014

  11. [19]

    NeuPh: Scalable and generalizable neural phase retrieval with local conditional neural fields

    Hao Wang et al. “NeuPh: Scalable and generalizable neural phase retrieval with local conditional neural fields”. In: Advanced Photonics Nexus 3.5 (2024), pp. 056005–056005

    2024

  12. [20]

    Reliable deep-learning-based phase imaging with uncertainty quantification

    Yujia Xue et al. “Reliable deep-learning-based phase imaging with uncertainty quantification”. In: Optica 6.5 (May 2019), pp. 618–629. doi: 10.1364/OPTICA.6.000618. url: https://opg.o ptica.org/optica/abstract.cfm?URI=optica-6-5-618

    2019 doi

  13. [21]

    Experimental robustness of Fourier ptychography phase retrieval algorithms

    Li-Hao Yeh et al. “Experimental robustness of Fourier ptychography phase retrieval algorithms”. In: Optics Express 23.26 (2015), pp. 33214–33240

    2015

  14. [22]

    Phase contrast, a new method for the microscopic observation of transparent objects

    Frits Zernike. “Phase contrast, a new method for the microscopic observation of transparent objects”. In: Physica 9.7 (1942), pp. 686–698

    1942

  15. [23]

    Fourier ptychographic microscopy reconstruction with multiscale deep residual network

    Jizhou Zhang et al. “Fourier ptychographic microscopy reconstruction with multiscale deep residual network”. In: Optics Express 27.6 (2019), pp. 8612–8625

    2019

  16. [24]

    Wide-field, high-resolution Fourier ptychographic microscopy

    Guoan Zheng, Roarke Horstmeyer, and Changhuei Yang. “Wide-field, high-resolution Fourier ptychographic microscopy”. In: Nature Photonics 7.9 (2013), pp. 739–745

    2013

  17. [25]

    Microscopy refocusing and dark-field imaging by using a simple LED array

    Guoan Zheng, Christopher Kolner, and Changhuei Yang. “Microscopy refocusing and dark-field imaging by using a simple LED array”. In: Optics Letters 36.20 (2011), pp. 3987–3989

    2011

  18. [26]

    Concept, implementations and applications of Fourier ptychography

    Guoan Zheng et al. “Concept, implementations and applications of Fourier ptychography”. In: Nature Reviews Physics 3.3 (2021), pp. 207–223. A Derivation of the Transfer Functions After parametrizing the transmission function o by 1 + jϕ − µ, the nonlinear measurement operator ...

    2021

  19. [165]

    isbn: 978-981-97-6769-4

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