Resolution enhancement in quantitative phase microscopy: a review

Javier Garcia; Juanjuan Zheng; Peng Gao; Vicente Mico; Zeev Zalevsky

REVIEW 2 major objections 4 minor 300 references

Resolution enhancement in quantitative phase microscopy: a review

T0 review · 2 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A review of quantitative phase microscopy argues that every resolution-enhancement technique reduces to one principle: synthesizing a larger effective numerical aperture, $NA_{\text{eff}} = NA_{\text{illum}} + NA_{\text{system}}$.

desk verdict A useful, comprehensive review of SR in QPM, with an overstated concluding generalization; worth refereeing but needs a qualification. read the letter →

arxiv 2501.09548 v1 pith:5RUWXAQT submitted 2025-01-16 physics.optics

Vicente Mico , Juanjuan Zheng , Javier Garcia , Zeev Zalevsky , Peng Gao This is my paper · ORCID

classification physics.optics

keywords quantitativephasemicroscopysuperresolutionsyntheticaperturenumericalstructuredilluminationFourierptychographicevanescentwavesspace-bandwidthproduct

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

Quantitative phase microscopy (QPM) images transparent samples by measuring the phase they imprint on transmitted light, and its resolution is bounded by the trade-off between numerical aperture and field of view. This review argues that the many apparently distinct resolution-boosting approaches in QPM—oblique illumination, structured illumination, speckle illumination, Fourier ptychography, and lensless synthetic-aperture methods—all reduce to the same mechanism: synthesizing a larger effective aperture with $NA_{\text{eff}} = NA_{\text{illum}} + NA_{\text{system}}$. The paper also clarifies that for propagating waves this synthesis cannot beat the Abbe diffraction limit of $\lambda/2$, and that going further requires evanescent-wave coupling or nonlinear frequency conversion. A reader cares because the review offers a single organizing formula for a crowded literature and a sharp standard for what counts as 'superresolution' in coherent microscopy.

What carries the argument

The synthetic aperture (SA) formed by angular diversity: off-axis illumination downshifts spatial frequencies that normally fall outside the objective's passband, the hologram records them inside the limited aperture, and numerical processing shifts them back to their true positions in Fourier space; the collected elementary apertures are coherently added into a single expanded pupil. The supporting theoretical framework is the invariance of the number of degrees of freedom of an imaging system—resolution can be improved only by sacrificing another degree of freedom such as time—formalized through the space-bandwidth product (SBP) and its adaptation.

What would settle it

A setup that records quantitative phase images using only propagating, linearly scattered light yet resolves features smaller than $\lambda/2$, or an experiment reporting an effective aperture larger than $NA_{\text{illum}} + NA_{\text{system}}$, would falsify the paper's central bound; conversely, a sharp measurement of the synthesized cutoff frequency under maximum oblique illumination should show it saturating at $(NA_{\text{illum}} + NA_{\text{system}})/\lambda$.

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Extended reading notes

Core claim

The central claim, stated in the Conclusions, is that 'the key of resolution enhancement approaches is to synthesize a larger aperture yielding in an effective NA value of $NA_{\text{eff}} = NA_{\text{illum}} + NA_{\text{system}}$.' All the multiplexing schemes in the review—oblique, structured, and speckle illumination in reference-based QPM; aperture synthesis and pixel superresolution in lensless setups; Fourier ptychography and modulated-illumination phase retrieval in reference-less QPM—are read as instances of this single principle. The paper further maintains that the resolution ceiling for propagating waves is the Abbe limit $\lambda/2$, which can be exceeded only by evanescent-field methods (solid-immersion nanoscopy, total internal reflection holography, surface-plasmon holography) or nonlinear methods such as second-harmonic generation. It also draws a terminological boundary: in this literature 'superresolution' conventionally means surpassing the diffraction limit set by $\lambda/NA$, not the physics limit $\lambda/(2n_{\text{med}})$.

Load-bearing premise

The review's organizing claims rest on the accuracy of the published experimental results it surveys; it does not independently re-verify any of those reports.

Editorial extensions

If this is right

Oblique, structured, speckle, wavelength-multiplexed, and ptychographic illumination are interchangeable implementations of the same synthetic-aperture principle, so results from one transfer directly to the others.
Any far-field, linear, propagating-wave QPM system is bound by $\lambda/2$; reported resolutions below that must be scrutinized for evanescent or nonlinear mechanisms.
The resolution gain of a technique is capped by the ratio $(NA_{\text{illum}} + NA_{\text{system}})/NA_{\text{system}}$, so engineering illumination angle is as important as the objective lens itself.
Lensless and lens-based QPM obey the same formula, with the camera aperture or pixel size playing the role of the system aperture.
Because gains are paid in time or other degrees of freedom, speed and resolution can be traded against each other unless multiplexing is used.

Reading between the lines

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

If the $NA_{\text{eff}}$ formula holds, it gives a quantitative benchmark for anyone assessing a QPM superresolution paper: the report should state both $NA_{\text{illum}}$ and $NA_{\text{system}}$, and any gain claimed beyond their sum should be examined.
The $\lambda/2$ ceiling for propagating waves implies that purely computational methods (deconvolution, deep-learning upsampling) cannot, by themselves, add real information beyond Abbe's limit; they can only recover it if the information was already encoded in the recorded field.
A testable extension: pool the reported experimental resolutions from the reviewed literature and check whether they lie at or below the $NA_{\text{eff}}$ envelope; the review predicts a tight bound.
The same aperture-synthesis framing should apply to other coherent imaging modalities, such as optical diffraction tomography, where illumination-angle diversity already acts as $NA_{\text{illum}}$.

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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

Colleague,

What you should know: this is a solid, up-to-date review of resolution-enhancement techniques in quantitative phase microscopy. It organizes a fragmented literature into a clear taxonomy (reference-based vs reference-less, lensless vs lens-based, far-field vs near-field) and provides a genuinely useful theoretical background on space-bandwidth product adaptation and degrees of freedom. If one of your students asks where to start on this topic, this is a good first stop.

The paper does not present new data or derivations; its value is synthesis. The authors are leaders in the area, and that shows in the coverage: oblique illumination, structured illumination, speckle, FPM, lensless holography, microsphere-assisted methods, evanescent-wave techniques, and SHG are all treated with concise but technical descriptions and good figures. The explicit definition of 'superresolution' — surpassing the λ/NA limit rather than the λ/2n physics limit — is a useful clarification, and the distinction between sampling-limited and diffraction-limited gains is made in Section 4.1.2. The mathematics (Fellgett–Linfoot capacity, Lukosz invariance, SBP adaptation) is correct and consistently applied.

Soft spots, in proportion. The main one is the conclusion's central claim. Section 6 states that 'the key of resolution enhancement approaches is to synthesize a larger aperture yielding in an effective NA value of NA_eff = NA_illum + NA_system,' applied to Sections 3 and 4. But the review itself notes that pixel-SR (Section 4.1.2) improves sampling without generating a synthetic aperture, and microsphere-assisted methods (Section 5.2) work by evanescent-to-propagating conversion with a λ/(2 n_SIL NA) limit, not by NA addition. So the 'key' is really the key for aperture-synthesis and multiplexing methods, not for every approach covered. This is more an overstatement than a fatal flaw — the individual sections are honest about the mechanisms — but for a paper whose stated aim is to resolve confusion about resolution definitions, the conclusion should say explicitly that pixel-SR and near-field methods are separate categories.

Two more minor issues. The citation pattern is heavily self-referential; many illustrative examples and conceptual foundations trace back to the authors' own prior work. That doesn't invalidate anything, but a more balanced footprint would help a newcomer weigh the field. And, as with any review, the reported numbers (e.g., 0.6 µm resolution over 24.4 mm², 250 nm lines under 700 nm illumination) are taken on faith from the primary literature; no independent verification is attempted. That is inherent to the genre, not a defect.

Bottom line: this paper deserves a serious referee. It is a competent, comprehensive review that will be useful to many readers. I would ask the referee to request a revised conclusion that separates aperture-synthesis from sampling and near-field methods, and perhaps a note about the self-citation pattern. With those changes, it is a solid contribution to the review literature.

Referee Report

2 major / 4 minor

Summary. The paper is a review of resolution enhancement approaches in quantitative phase microscopy (QPM), covering both reference-based and reference-less techniques, lensless holography, and near-field/nonlinear methods. It introduces a theoretical framework based on the space-bandwidth product (SBP), degrees of freedom, and SBP adaptation, and it presents a central claim in the Conclusions that the key of resolution enhancement is synthetic-aperture generation with an effective NA of NA_eff = NA_illum + NA_system, ultimately bounded by the Abbe limit lambda/2 for propagating waves, with Section 5 methods (SHG, microlenses, evanescent waves, surface plasmons) enabling resolution beyond that limit. The review surveys a large body of literature, including oblique illumination, structured illumination, speckle illumination, Fourier ptychographic microscopy, and on-chip microscopy, and aims to clarify the confusion about resolution definitions in QPM.

Significance. If properly qualified, the review is a valuable survey that organizes a diverse literature under a coherent SBP/degrees-of-freedom framework. It explicitly distinguishes the coherent resolution limit (0.82 lambda/NA) from the incoherent limit (0.61 lambda/NA), and maintains the distinction between the lambda/NA and lambda/2 limits throughout. The paper also clearly separates propagating-wave synthetic-aperture methods from evanescent and nonlinear approaches in Section 5, and it flags important practical limitations such as FOV restrictions in microsphere-assisted DHM and acquisition time in FPM. The extensive reference list and the consistent use of NA_eff = NA_illum + NA_system across Sections 3 and 4 make the review a useful entry point for researchers in the field. However, the central unifying claim in Section 6 overgeneralizes, because at least one method in Section 4 (geometrical pixel super-resolution in on-chip microscopy) does not follow the aperture-synthesis formula, and Section 5 methods rely on distinct physical mechanisms. This internal inconsistency is load-bearing given the paper's stated goal of resolving definitional confusion.

major comments (2)

[Section 6, Conclusions; Section 4.1.2] The central claim in Section 6 that "the key of resolution enhancement approaches is to synthesize a larger aperture yielding in an effective NA value of NA_eff = NA_illum + NA_system" is presented as the unifying principle for Sections 3 and 4. However, Section 4.1.2 explicitly states that sub-pixel shifting "will not generate a SA but it improves the sampling when the pixel size of CCD pixels is fixed." Geometrical (pixel) super-resolution is a sampling-limited mechanism that reduces the effective pixel size without extending the optical cutoff frequency, so it does not fit the NA_eff formula. Because the paper's goal is to resolve "the confusion on resolution definition claims," the conclusion should qualify the claim: aperture synthesis (oblique illumination, SI, speckle, FPM, DIHM-SA) obeys NA_eff = NA_illum + NA_system, while pixel-SR and related sampling techniques are a separate category. Without this qualification, the unifying "key" is overbroad and internally inconsistent with the body of the review.
[Section 5.2, Section 6] The microlens-assisted DHM approach reviewed in Section 5.2 is described as achieving resolution enhancement through a solid-immersion-lens effect, with a resolution limit proportional to lambda/(2 n_SIL NA) rather than NA_illum + NA_system. Even though Section 6 excludes Section 5 from the "key" statement, the phrase "the key of resolution enhancement approaches" remains too general when read against Section 5. Suggest explicitly stating that the NA_eff = NA_illum + NA_system relation applies to aperture-synthesis techniques for propagating waves, and that Section 5 methods (SHG, microlenses, evanescent/surface-plasmon) rely on different physical mechanisms (wavelength conversion, near-field coupling, evanescent-to-propagating conversion). This would strengthen the definitional clarity the review aims to provide.

minor comments (4)

[Section 6] The phrase "SPB adaptation process" should read "SBP adaptation process" (space-bandwidth product).
[Section 6] The acronym "SGH DHM" should be "SHG DHM" (second harmonic generation); the same typo appears in the concluding section.
[Section 2.1, Eq. (2)] The typeset formula for the eventual resolution appears garbled in the manuscript; please ensure the max operator and the terms (kappa lambda / NA_eff and M delta) are rendered unambiguously.
[Abstract and general] The abstract promises a discussion of pros and cons of each technique, but the body mentions pros and cons only sporadically (e.g., FOV restriction for SMIM, acquisition time for FPM, FOV restriction for microsphere-assisted DHM). A summary table comparing resolution gain, FOV, speed, complexity, and whether the method is aperture-synthesis or sampling-based would make the review more useful and directly support the stated aim of resolving definitional confusion.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular derivation; the review's claims rest on standard Fourier optics and external experimental reports, not on self-referential fitting.

full rationale

This is a review paper, not a derivation chain, and I find no step in which a prediction reduces by construction to an input. Section 2.1's NA_eff = NA_illum + NA_system is an elementary Fourier-space aperture-synthesis statement: off-axis illumination downshifts spectral content so that the cutoff becomes (NA_illum + NA_obj)/lambda, and the lambda/2 propagating-wave limit is traced to the free-space transfer function in Section 5.3, not to a fitted parameter. Equations (1) and (2) define a resolution estimate rather than fitting a hidden parameter and renaming it a prediction. The heavy use of the authors' earlier work, including the SBP adaptation framework from Refs. [92,148-150] and illustrative figures from Refs. [119,171,211,230,401], is ordinary self-citation in a review, but that material is not invoked as a uniqueness theorem or as the sole justification for the central claim; the review also relies on independent information-theoretic results such as Lukosz's invariance theorem and Cox-Sheppard's extension, as well as external experimental reports. The only substantive concern is that Section 6's universal formulation, 'the key of resolution enhancement approaches is to synthesize a larger aperture yielding in an effective NA value of NA_eff = NA_illum + NA_system,' is overbroad relative to the paper's own Section 4.1.2, which correctly states that sub-pixel shifting 'will not generate a SA but it improves the sampling.' That is an internal consistency or scope issue, not circularity, because the geometrical-sampling pathway is explicitly admitted and is not used to derive NA_eff. Hence the circularity score is low.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

The review introduces no new entities or fitted parameters. It relies on standard Fourier-optics background and on the correctness of the cited experimental reports.

assumptions (3)

domain assumption Lukosz invariance theorem: the total number of degrees of freedom of an optical system is fixed, so spatial resolution can be increased by proportionally reducing another degree of freedom such as time, polarization, or field of view.
Invoked in Section 2.2 as the theoretical basis for all superresolution approaches reviewed in the paper; the paper does not prove this theorem.
standard math Fellgett and Linfoot's information capacity formulas for 2D optical systems (Eqs. 3 and 4).
Used in Section 2.2 to relate space-bandwidth product and SNR to the number of degrees of freedom.
standard math Angular-spectrum transfer function limits propagating wave components to (lambda*u)^2 + (lambda*v)^2 < 1 and exponentially attenuates evanescent components.
Used in Section 5.3 (Eqs. 10-12) to define the physical cutoff and to justify evanescent-wave approaches.

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Cite this review

Pith. "Pith review of Resolution enhancement in quantitative phase microscopy: a review." pith.science (2026). https://pith.science/paper/5RUWXAQT

@misc{pith2026250109548,
  author       = {Pith},
  title        = {Pith review of: Resolution enhancement in quantitative phase microscopy: a review},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5RUWXAQT}},
  note         = {Machine review of arXiv:2501.09548}
}

read the original abstract

Quantitative phase microscopy (QPM), a technique combining phase imaging and microscopy, enables visualization of the 3D topography in reflective samples, as well as the inner structure or refractive index distribution of transparent and translucent samples. Similar to other imaging modalities, QPM is constrained by the conflict between numerical aperture (NA) and field of view (FOV): an imaging system with a low NA has to be employed to maintain a large FOV. This fact severely limits the resolution in QPM up to being the illumination wavelength. Consequently, finer structures of samples cannot be resolved by using modest NA objectives in QPM. Aimed to that, many approaches, such as oblique illumination, structured illumination, and speckle illumination (just to cite a few), have been proposed to improve the spatial resolution (or the space bandwidth product) in phase microscopy by restricting other degrees of freedom (mostly time). This paper aims to provide an up to date review on the resolution enhancement approaches in QPM, discussing the pros and cons of each technique as well as the confusion on resolution definition claims on QPM and other coherent microscopy methods. Through this survey, we will review the most appealing and useful techniques for superresolution in coherent microscopy, working with and without lenses and with special attention to QPM.

Figures

Figures reproduced from arXiv: 2501.09548 by the authors.

**Figure 2.** Applications of QPM. First image on the top taken from Ref. [25], and second/third images on the top taken from Ref. [69] (reprinted with permission from Lyncée Tec SA). The resolving power is of great importance since it determines the minimal distance that two infinitely small spatial features can be positioned near each other and yet be seen as two separable items. Similar to other coherent imaging approaches, Il… view at source ↗

**Figure 3.** Space-frequency cut-off during QPM imaging. (a) frequency cut-off in lensless QPM and (b) in lens-based systems; (c) Scheme of off-axis illumination for resolution enhancement; (d) Space-frequency domain representation of the SA based on off-axis illuminations; (e) resolution enhancement of off-axis illumination based QPM. Up in (e), the phase image of a swine sperm cell obtained with conventional QPM; down in (e), … view at source ↗

**Figure 4.** Space-frequency representation in Wigner space; (a) SBP distribution of a sample [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗

Figures from the paper (25 more)

**Figure 5.** Figure 5: SBP representation for different Fresnel-type holograms in Wigner space: (a) original SBP of the object, (b) SBP for in-line geometry, (c) SBP for off-axis geometry without [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]

**Figure 7.** Figure 7: The significance of phase matching of the recovered elementary apertures during [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]

**Figure 8.** Figure 8: Resolution-enhanced QPM imaging using oblique beam illumination for a human RBCs bio-sample. (a) the conventional (low resolution) image, (b) the superresolved image, [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]

**Figure 10.** Figure 10: DHM with SI. (a) Schematic setup; (b) four groups of SIs with different directions; (c) the synthesized spectrum. Images taken from Ref. [211]. Despite there are some similarities between SI-DHM and SI microscopy reconstruction, there are also some differences between…

**Figure 11.** Figure 11: Experimental results for resolution enhancement in DHM with SI. (a) and (b) reconstructed phase images by using plane wave illumination and SI; (d) the phase distributions along the two lines drawn in (a) and (b). Images taken from Ref. [211]. Recently, SI with unknow…

**Figure 12.** Figure 12: Schematics of DHM with sequential speckle illumination. (a) Experimental setup; (b)-(d) Phase maps of polystyrene beads (200nm diameter) under plane wave illumination (b-c) and speckle illumination(d-e). Scale bars in (d, e) are 500 nm. Images taken from Ref. [230]. I…

**Figure 13.** Figure 13: DH usly stated, sp illumination di of the object encies. This ex larger NA. Th ps: 1) initialize ucted object w ination comple wave ܣௌ ௜ ; 3) pe l to NA/λ), wit ng new high determine the r the retrieved object wave only the resolu nt speckle-base avoids mechan ces. e …

**Figure 15.** Figure 15: Superresolution QPM imaging via scattering media (a). The optical configuration used for the experiment. (b). The experimental results: the image reconstructed by using a single on-axis illumination (left) and wavelength-angular encoded illumination (right). Images ad…

**Figure 16.** Figure 16: Schematics of TLI. (a) Recording of the transmission matrix for a disordered [PITH_FULL_IMAGE:figures/full_fig_p024_16.png]

**Figure 17.** Figure 17: Experimental results for resolution enhancement of DIHM via (a) shifting the [PITH_FULL_IMAGE:figures/full_fig_p027_17.png]

**Figure 18.** Figure 18: Lens-free on-chip microscopy using pixel SR approach over a wide field-of-view: (a) scheme of the experimental layout, (b) experimental results when a phase grating is used as calibration object, and (c) results of a RBCs cluster (left column) and Caenorhabditis elega…

**Figure 19.** Figure 19: Superresolved imaging of SMIM using oblique beam illumination. The configuration of SMIM using oblique beam illumination (a), the low-resolution image retrieved with on-axis illumination (b), the generated SA (c), and the finally retrieved superresolved image (d). Ima…

**Figure 20.** Figure 20: Iterative phase retrieval with oblique illumination. (a) Experimental setup and the schematic diffraction patterns recorded from different axial planes by moving the CCD camera for one illumination angle (b) reconstructed phase image with on-axis illumination and synt…

**Figure 21.** Figure 21: Quantitative phase contrast microscopy with oblique illumination. (a) Schematic configuration. (b) Representative phase image of micro-lenses fabricated on a glassplate. (c) Resolution test with a grating-like sample. The top and bottom are the images obtained with co…

**Figure 22.** Figure 22: Single-beam QPM using modulated illumination. (a) schematic setup; insets in (a) show the phase patterns displayed on SLM (left) and the diffraction patterns recorded by the CCD camera (right); (b) Representative phase image obtained by using single-beam QPM; (c) reso…

**Figure 23.** Figure 23: Principle of FPM. (a) Schematic configuration of FPM high NA, and (b) enlarged spectrum by using different illumination angles. Center red circle: Fourier support of the original microscope; white circle: Fourier support of one LED; green circle: synthesized Fourier s…

**Figure 24.** Figure 24: Label-free phase imaging of biological specimen (mouse tail dermis and epidermis) by second-harmonic DHM: (a) experimental layout working in off-axis configuration, (b) bright field image. (c) cross-polarization image showing phase retardation caused by the birefringe…

**Figure 25.** Figure 25: Microsphere-assisted super-resolved Mirau DHM: (a) scheme of the experimental layout, (b) hologram of a RBC considering the proposed technique, and (c) 3D phase map of a RBC. Images taken from Ref. [401]. However, one of the main drawbacks of microsphere-assisted supe…

**Figure 26.** Figure 26: Wetting film superresolved on-chip microscopy: (a) scheme of the experimental layout, (b) experimental results of a sperm cell sample: (b1-b2) phase reconstructions obtained from pixel SR algorithm in lens-free microscopy, (b3-b4) comparative images from a 60X 0.85NA …

**Figure 27.** Figure 27: (a) Illumination and collection configurations: A – objective normal to the substrate surface, B – objective with tilt away from the optic axis, C – objective on the side of the substrate with grating; (b) Manhattan test pattern used in the experiments, and (c)-(d) re…

**Figure 28.** Figure 28: SR imaging of TIRHM by evanescent-wave-induced frequency shift. As a [PITH_FULL_IMAGE:figures/full_fig_p045_28.png]

**Figure 29.** Figure 29: SR phase imaging via TIR DHM: (a) scheme of the experimental layout, (b) test sample, (c) conventional intensity image obtained at normal incidence in non-TIR mode, (d) one of the 6 retrieved elementary apertures in oblique beam evanescent wave illumination TR DHM, (e…

**Figure 30.** Figure 30: Surface plasmon holographic microscopy. (a) Experimental setup for SPHM, (b)-(c) AFM image and reconstructed 3D thickness distribution by SPHM, respectively, of the multilayer graphene film. Images taken from Ref. [449]. Similarly to TIRDHM, SPHM presents a high surfa…

**Figure 31.** Figure 31: shows the experimental setup for the surface wave illumination Fourier ptychographic microscopy (SWI-FPM) technique. A laser beam (λ = 640 nm) is used to sequentially illuminate the sample through an oil-immersion objective (1.49-NA, 100X) under different illumination…

**Figure 32.** Figure 32: Comparison of the image contrast on a 150 nm linewidth gratings achieved by the evanescent waves and the surface plasmon wave illuminations: (a1) and (b1) Raw images taken by counter-propagating evanescent wave illumination. (c1) Intensity image reconstructed with (a1…

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

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