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REVIEW 3 major objections 5 minor 59 references

Cepstrum-based interferometric microscopy (CIM) for quantitative phase imaging

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Four holograms with one-pixel shifts give three quantitative phase images.

desk verdict CIM is a genuinely new way to do QPI without a clean reference and triples the FOV, but the written derivation misuses the cepstrum and the universal/no-restrictions claim overreaches. read the letter →

arxiv 2501.10022 v1 pith:2D6PYZ2P submitted 2025-01-17 physics.optics

Ricardo Rubio-Oliver , Javier Garcia , Z. Zalevsky , J. Picazo-Bueno , V. Mico This is my paper · ORCID
classification physics.optics
keywords digitalholographicmicroscopyquantitativephaseimagingretrievalcomplexcepstrumSpatial-Shiftingfieldofviewtriplingoff-axisholographyMichelsoninterferometer
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

Conventional off-axis digital holographic microscopy assumes one of the two interfering beams is a known clean reference. This paper claims that assumption is unnecessary: two arbitrary unknown complex fields can be separated from their cross-correlation. The proposed Cepstrum-based Interferometric Microscopy (CIM) records four off-axis holograms, applying a one-pixel shift to one beam in horizontal and vertical directions, and then uses the Spatial-Shifting Cepstrum (SSC) algorithm to recover the static field. The two shifted fields are obtained by subtraction, yielding three quantitative phase images from four recordings and tripling the usable field of view. Validation on calibrated phase targets and fixed biological cells shows agreement with conventional digital holographic microscopy, with slightly more noise.

What carries the argument

The central object is the Spatial-Shifting Cepstrum (SSC) algorithm, built on the complex cepstrum, defined as the inverse Fourier transform of the logarithm of a Fourier-transformed field. The algorithm takes the filtered cross-correlation terms from two off-axis holograms in the same direction, one containing an exact one-pixel shift, computes their complex cepstra, and subtracts them. The shift enters as the transfer function $1 - \exp(-i 2\pi u x_0)$ in Eq. (5); division by this factor recovers the static field's spectrum. The companion field is then obtained by subtracting the static spectrum from the original cross-correlation and exponentiating. Complementary bow-tie masks in the horizontal and vertical Fourier domains combine the two partial spectra so that only the DC term remains ambiguous, and a high-pass filter removes the resulting background inhomogeneity.

What would settle it

Record a CIM sequence on a phase target while a small opaque absorber obscures part of only one of the three fields, then compare the recovered static field with a conventional off-axis hologram of the same region: at pixels where the shifted beam has near-zero amplitude, the complex logarithm becomes undefined and the reconstruction should show localized artifacts that mark the exact failure of the nonzero-field assumption.

Watch

Extended reading notes

Core claim

The central discovery asserted is that the cross-correlation of two unknown fields, $\tilde U(u,v) = \tilde O_1(u,v) \otimes \tilde O_2^*(u,v)$, can be inverted without knowing either field, provided a second hologram in the same direction includes an exact one-pixel shift of one of the fields. In the complex-cepstrum domain the product becomes a sum, and subtracting the shifted hologram cancels the unknown companion. Equation (5) then yields the static object spectrum divided by $1 - \exp(-i 2\pi u x_0)$, leaving a null line in the Fourier domain. Repeating in an orthogonal direction and combining with complementary bow-tie masks collapses the null lines to the DC term, and the two shifted fields are recovered by complex subtraction. The result is a full quantitative phase image of each of the three fields involved in the two orthogonal interferometric recordings.

Load-bearing premise

For the math to work, the one-pixel shift must be an exact rigid translation of one complex field while the other stays fixed, both fields must be nonzero wherever the algorithm uses them, and the four recordings must share the same coherent noise with no sample motion between frames.

Editorial extensions

If this is right

  • A compact Michelson module placed after a standard microscope tube lens can provide quantitative phase imaging without pinholes, sparse-sample constraints, or spatially reserved reference regions.
  • Four time-sequential holograms supply three complex images, making the temporal footprint comparable to phase-shifting holography while tripling the imaged area.
  • The one-pixel shift direction need not be horizontal and vertical; any two non-parallel directions work, making the geometry adaptable to different mirror stages and optical layouts.
  • The DC-only ambiguity left after bow-tie masking can be removed by high-pass filtering without erasing low-frequency sample content, as confirmed by comparison with conventional off-axis holography on a calibrated phase target.
  • The three recovered fields need not be adjacent in the current implementation, but adjusting the off-axis angle and mirror distance could make the extended field of view contiguous.

Reading between the lines

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

  • Editorial inference: the same cepstrum-subtraction logic should work with shifts larger than one pixel, but at the cost of additional null lines in the Fourier domain; the paper chooses one pixel to minimize these singularities.
  • Editorial inference: the coherent-noise mismatch that the Discussion concedes should appear as a systematic high-frequency error in the recovered static field; averaging multiple interferograms per shift could test whether the mismatch is random speckle or slow drift between frames.
  • Editorial extension: because the method records four frames from a static sample, applying CIM to live or flowing cells would require rapid motorized switching between shift directions; the paper mentions video-rate implementation as future work but does not demonstrate it.
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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 / 5 minor

Summary. The manuscript proposes Cepstrum-based Interferometric Microscopy (CIM), a quantitative phase imaging (QPI) method based on four off-axis holograms in which one interferometric beam is shifted by one pixel in two orthogonal directions. The authors introduce a Spatial-Shifting Cepstrum (SSC) algorithm intended to recover the complex amplitude distributions of three fields without requiring a clean reference beam, thereby tripling the field of view. The method is validated on a phase resolution test target and on fixed biological samples (LnCaP and PC3 prostate cancer cells, cheek cells), with thickness measurements compared to AFM and conventional and common-path digital holographic microscopy (DHM).

Significance. If the claims are upheld, CIM would be a practically attractive QPI approach that removes the sparse-sample or clean-reference constraints of many common-path interferometers and extends the usable field of view. The experimental validation is substantial: measured thicknesses agree with AFM values within uncertainty (316±26 nm vs 329.5 nm for the static FOV; 400±24 nm vs 388 nm and 287±24 nm vs 278 nm for the shifted FOVs), and the phase comparison with common-path DHM shows a mean difference of -0.02±0.24 rad. The authors also honestly discuss limitations, including the zero-ambiguity at DC and the instability of coherent noise between recordings. However, the central mathematical derivation in Sec. 2.3 is flawed, and the claimed universality (no assumptions on either beam) is not supported as written. The paper is a promising proof-of-concept but requires a corrected derivation and appropriately qualified claims before publication.

major comments (3)
  1. [Sec. 2.3, Eq. (3)] Equation (3) is not a valid consequence of applying the complex cepstrum to Eq. (1). From Eq. (1), U~(u,v) = O1~(u,v) ⊗ O2~*(u,v), so the cepstrum gives F^{-1} log[O1~ ⊗ O2~*], and the logarithm of a convolution is not the sum of logarithms. The standard cepstrum property applies to convolutions in the spatial domain, not to the Fourier-domain convolution of two spectra. The working formulas (6)-(7) are indeed based on a different, pointwise logarithmic operation on U(x,y)=O1(x,y)O2*(x,y). The derivation should be rewritten to state the pointwise-product/log-domain assumptions and to remove the incorrect statement that applying Eq. (2) to Eq. (1) yields Eq. (3).
  2. [Sec. 2.3, Eqs. (6)-(7)] The amplitude and phase formulas require that, for each direction, the second recording contains exactly the same O2(x,y) (and O1 shifted by x0), with no change in coherent noise or illumination between the two frames. This condition is not a mere practical detail: it is essential to the subtraction step, and it is also a restriction on the beams that contradicts the abstract's claim that no assumptions are required for the two interferometric beams. The Discussion (Sec. 4) itself concedes that coherent noise is not constant between interferograms, causing high-frequency mismatches. These restrictions, together with the nonzero-field and phase-unwrapping requirements of the pointwise complex logarithm, should be stated explicitly in the derivation and in the statements of generality.
  3. [Sec. 2.3, Eq. (5) and Sec. 4] The reconstruction divides by 1-exp(-i2πu x0), which is singular at u=0 for x0=1, and the resulting zero-ambiguity is removed by bow-tie masking followed by Gaussian high-pass filtering with a manually chosen FWHM of 9 pixels. This operation discards the DC and low-frequency content of the retrieved field, so the method yields relative phase/thickness variations rather than an absolute phase offset. The paper should state this limitation clearly; in particular, the choice of the Gaussian FWHM is a free parameter that affects the low-frequency content of the final QPI image, and the claim of a parameter-free or fully assumption-free reconstruction should be tempered accordingly.
minor comments (5)
  1. [Sec. 4 (Discussion)] The in-text citations [48-49] for Kramers-Kronig approaches do not match the reference list, where Ref. [48] is a transport-of-intensity tutorial and Ref. [49] is the Oppenheim and Schafer cepstrum paper. Please correct the citation numbering.
  2. [Sec. 2.3, Eqs. (5)-(7)] The notation for the retrieved quantities is inconsistent: Õ0̃1, Õ1, and Re{Õ1} are used without clear definitions. In particular, Eqs. (6)-(7) should explicitly define the logarithm of the spectrum (or the cepstrum) that is being inverse-Fourier-transformed, rather than writing Re{Õ1(u,v)} where Õ1 is the ordinary Fourier transform of O1.
  3. [Sec. 2.2 (Calibration Procedure)] The sentence "forty frames integrate a displacement of a single pixel" is ambiguous: it is not explained how the forty frames are used to determine or ensure the exact one-pixel shift, nor how the 25-thousandths-of-a-pixel confidence was obtained from the cross-correlation registration. Please elaborate.
  4. [Fig. 2] The workflow figure is dense, and the numbered step labels are small relative to the panels. Consider enlarging the step numbers or splitting the figure into two panels for readability.
  5. [Table 2] The noise comparison for the biosample background reports only the mean and SD of the phase; the authors could also provide a phase-noise map or an RMS value to separate low-frequency background variations from high-frequency phase noise, which would better support the comparison between CIM and the two DHM alternatives.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: SSC is a self-contained algebraic inversion validated against independent AFM and conventional DHM references.

full rationale

The central SSC reconstruction (Eqs. 5-7) is an algebraic inversion of the recording model U(x,y) = O1(x,y)O2*(x,y), using the 1-pixel-shifted product Ux(x,y) = O1(x-x0,y)O2*(x,y) to solve for O1, then obtaining O2 and O3 by division/subtraction. The output fields are not used to set any parameter used in the reconstruction; the lateral shift x0 is set by an independent calibration with an amplitude USAF target, and the quantitative phase-target validation is compared against manufacturer AFM values and conventional DHM, not against CIM's own fitted constants. The only manually chosen processing value is the 9-pixel FWHM high-pass filter, which affects background rendering but does not by itself force the measured bar thicknesses (316 +/- 26 nm vs 329.5 nm AFM). There are self-citations, but they are contextual (prior spatially multiplexed and Hilbert-Huang DHM work) and not load-bearing for the SSC derivation. Two caveats belong to correctness, not circularity: Eq. (3) states log of a convolution as a sum, which is not valid generally, whereas the implemented Eqs. (6)-(7) use pointwise logarithms of the spatial cross-correlation, which require nonzero fields, unwrapped phase, and identical coherent noise between shifted exposures; the Discussion explicitly concedes the last condition is violated ('coherent noise is not constant between the set of interferograms'). These are limitations of the derivation, not reductions of the prediction to its inputs.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim is algorithmic; it introduces no new physical entities and no fitted constants. The only hand-set parameters are the 1-pixel shift and the Gaussian FWHM used to mask the DC ambiguity; neither is fitted to make quantitative thickness values match the known target. The mathematical derivation assumes log-separability of the cross-correlation and exact global translation, conditions that are only partially satisfied experimentally.

free parameters (2)
  • Spatial shift x0 = 1 pixel (calibrated to ±0.025 px)
    Chosen by hand to minimize zero-ambiguity lines; sets the transfer function 1-exp(-i2πu x0) in Eq. (5); subpixel errors amplify noise near u=0.
  • Gaussian high-pass filter FWHM = 9 pixels
    Chosen to remove the DC ambiguity and homogenize the background; discards low spatial-frequency phase information, as acknowledged in the Discussion.
assumptions (4)
  • domain assumption Complex logarithm factorizes the filtered cross-correlation: log(O1·O2*) = log O1 + log O2*
    Needed for Eqs (5)-(7); fails when the complex field has zeros or the phase branch jumps.
  • standard math Fourier shift theorem applies to log-magnitude and phase fields: F{f(x-x0)} = exp(-i2πu x0)F{f(x)}
    Basis for the denominator 1-exp(-i2πu x0) in Eq. (5).
  • domain assumption Off-axis filtering isolates the +1 order containing O1·O2* without crosstalk from the zero order
    Requires sufficient spectral separation; the paper notes the filter mask doubles the width used in classical off-axis DHM.
  • domain assumption Sample and optical fields are static across the four sequential recordings
    The experimental validation uses fixed samples; the Discussion mentions coherent noise is not constant between interferograms, a partial violation.

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Cite this review

Pith. "Pith review of Cepstrum-based interferometric microscopy (CIM) for quantitative phase imaging." pith.science (2026). https://pith.science/paper/2D6PYZ2P

@misc{pith2026250110022,
  author       = {Pith},
  title        = {Pith review of: Cepstrum-based interferometric microscopy (CIM) for quantitative phase imaging},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2D6PYZ2P}},
  note         = {Machine review of arXiv:2501.10022}
}
read the original abstract

A universal methodology for coding-decoding the complex amplitude field of an imaged sample in coherent microscopy is presented, where no restrictions on any of the two interferometric beams are required. Thus, the imaging beam can be overlapped with, in general, any other complex amplitude distribution and, in particular, with a coherent and shifted version of itself considering two orthogonal directions. The complex field values are retrieved by a novel Cepstrum-based algorithm, named as Spatial-Shifting Cepstrum (SSC), based on a weighted subtraction of the Cepstrum transform in the cross-correlation term of the object field spectrum in addition with the generation of a complex pupil from the combination of the information retrieved from different holographic recordings (one in horizontal and one in vertical direction) where one of the interferometric beams is shifted 1 pixel. As a result, the field of view is tripled since the complex amplitudes of the three interferometric fields involved in the process are retrieved. Proof-of-concept validation of this methodology, named as Cepstrum-based Interferometric Microscopy (CIM), is provided considering an off-axis holographic configuration for retrieving the cross-correlation of the two interferometric complex amplitude fields in a compact quasi-common path Michelson interferometric configuration. Experimental results for different types of phase samples (resolution test targets for step-by-step calibration and demonstration as well as fixed biosamples) are included.

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Works this paper leans on

59 extracted references · 51 canonical work pages

  1. [1]

    Popescu, Quantitative Phase Imaging of Cells and Tissues, 1st Edition, McGraw -Hill Education, New York, 2011

    G. Popescu, Quantitative Phase Imaging of Cells and Tissues, 1st Edition, McGraw -Hill Education, New York, 2011

    work page 2011

  2. [2]

    Shaked, Z

    N.T. Shaked, Z. Zalevsky, L.L. Satterwhite, Biomedical Optical Phase Microscopy and Nanoscopy, Elsevier, 2013

    work page 2013

  3. [3]

    Zhou, L.L

    R. Zhou, L.L. Goddard, B. Bhaduri, H. Pham, T.H. Nguyen, C. Edwards, G. Popescu, Diffraction phase microscopy: principles and applications in materials and life sciences, Advances in Optics and Photonics, Vol. 6, Issue 1, Pp. 57-119. 6 (2014) 57–119. https://doi.org/10.1364/AOP.6.000057

    doi:10.1364/aop.6.000057 2014

  4. [4]

    Y. Park, C. Depeursinge, G. Popescu, Quantitative phase imaging in biomedicine, Nat Photonics. 12 (2018) 578–589. https://doi.org/10.1038/s41566-018-0253-x

    doi:10.1038/s41566-018-0253-x 2018

  5. [5]

    Y. Shu, J. Sun, J. Lyu, Y. Fan, N. Zhou, R. Ye, G. Zheng, Q. Chen, C. Zuo, Adaptive optical quantitative phase imaging based on annular illumination Fourier ptychographic microscopy, PhotoniX. 3 (2022) 1–15. https://doi.org/10.1186/S43074-022-00071-3/FIGURES/5

    work page doi:10.1186/s43074-022-00071-3/figures/5 2022

  6. [6]

    Rappaz, C

    B. Rappaz, C. Depeursinge, P. Marquet, Y. Emery, E. Cuche, T. Colomb, P.J. Magistretti, Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy, Optics Letters, Vol. 30, Issue 5, Pp. 468-470. 30 (2005) 468–470. https://doi.org/10.1364/OL.30.000468

    work page doi:10.1364/ol.30.000468 2005

  7. [7]

    Kemper, G

    B. Kemper, G. Von Bally, Digital holographic microscopy for live cell applications and technical inspection, Applied Optics, Vol. 47, Issue 4, Pp. A52-A61. 47 (2008) A52–A61. https://doi.org/10.1364/AO.47.000A52

    work page doi:10.1364/ao.47.000a52 2008

  8. [8]

    Kim, Principles and techniques of digital holographic microscopy, J Photonics Energy

    M.K. Kim, Principles and techniques of digital holographic microscopy, J Photonics Energy. 1 (2010) 018005. https://doi.org/10.1117/6.0000006

    work page doi:10.1117/6.0000006 2010

Show all 59 references
  1. [9]

    K. Toda, M. Tamamitsu, T. Ideguchi, Adaptive dynamic range shift (ADRIFT) quantitative phase imaging, Light: Science & Applications 2021 10:1. 10 (2021) 1–10. https://doi.org/10.1038/s41377- 020-00435-z

    2021 doi

  2. [10]

    Micó, N.T

    V. Micó, N.T. Shaked, A. Kuś, S.K. Mirsky, M. Trusiak, Off-axis digital holographic multiplexing for rapid wavefront acquisition and processing, Advances in Optics and Photonics, Vol. 12, Issue 3, Pp. 556-611. 12 (2020) 556–611. https://doi.org/10.1364/AOP.384612

    2020 doi

  3. [11]

    Chhaniwal, A.S.G

    V. Chhaniwal, A.S.G. Singh, R.A. Leitgeb, B. Javidi, A. Anand, Quantitative phase -contrast imaging with compact digital holographic microscope employing Lloyd’s mirror, Opt Lett. 37 (2012) 5127. https://doi.org/10.1364/OL.37.005127

    2012 doi

  4. [12]

    T. Sun, Z. Zhuo, W. Zhang, J. Lu, P. Lu, Single-shot interference microscopy using a wedged glass plate for quantitative phase imaging of biological cells, Laser Phys. 28 (2018) 125601. https://doi.org/10.1088/1555-6611/AAE036

    2018 doi

  5. [13]

    Ebrahimi, M

    S. Ebrahimi, M. Dashtdar, E. Sánchez-Ortiga, M. Martínez-Corral, B. Javidi, Stable and simple quantitative phase-contrast imaging by Fresnel biprism, Appl Phys Lett. 112 (2018) 113701. https://doi.org/10.1063/1.5021008/34657

    2018 doi

  6. [14]

    Picazo-Bueno, Z

    J.Á. Picazo-Bueno, Z. Zalevsky, J. García, C. Ferreira, V. Micó, Spatially multiplexed interferometric microscopy with partially coherent illumination, J Biomed Opt. 21 (2016) 1. https://doi.org/10.1117/1.JBO.21.10.106007

    2016 doi

  7. [15]

    Picazo-Bueno, M

    J.Á. Picazo-Bueno, M. Trusiak, J. García, K. Patorski, V. Micó, Hilbert–Huang single-shot spatially multiplexed interferometric microscopy, Opt Lett. 43 (2018) 1007. https://doi.org/10.1364/OL.43.001007

    2018 doi

  8. [16]

    Trusiak, V

    M. Trusiak, V. Micó, J.A. Picazo-Bueno, Single-shot slightly off-axis digital holographic microscopy with add-on module based on beamsplitter cube, Optics Express, Vol. 27, Issue 4, Pp. 5655- 5669. 27 (2019) 5655–5669. https://doi.org/10.1364/OE.27.005655

    2019 doi

  9. [17]

    Trusiak, J.-A

    M. Trusiak, J.-A. Picazo-Bueno, K. Patorski, P. Zdankowski, V. Mico, Single-shot two-frame π- shifted spatially multiplexed interference phase microscopy, J Biomed Opt. 24 (2019) 1. https://doi.org/10.1117/1.JBO.24.9.096004

    2019 doi

  10. [18]

    Ebrahimi, M

    S. Ebrahimi, M. Dashtdar, Quantitative phase imaging based on Fresnel diffraction from a phase plate, Appl Phys Lett. 115 (2019) 203702. https://doi.org/10.1063/1.5123353/37427

    2019 doi

  11. [19]

    Trindade, V

    K. Trindade, V. Micó, J.Á. Picazo-Bueno, Phase imaging microscopy under the Gabor regime in a minimally modified regular bright-field microscope, Optics Express, Vol. 29, Issue 26, Pp. 42738- 42750. 29 (2021) 42738–42750. https://doi.org/10.1364/OE.444884

    2021 doi

  12. [20]

    V. Micó, M. Rogalski, J.Á. Picazo-Bueno, M. Trusiak, Single-shot wavelength-multiplexed phase microscopy under Gabor regime in a regular microscope embodiment, Scientific Reports 2023 13:1. 13 (2023) 1–10. https://doi.org/10.1038/s41598-023-31300-9

    2023 doi

  13. [21]

    Wattellier, S

    B. Wattellier, S. Monneret, P. Bon, G. Maucort, Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells, Optics Express, Vol. 17, Issue 15, Pp. 13080 -13094. 17 (2009) 13080–13094. https://doi.org/10.1364/OE.17.013080

    2009 doi

  14. [22]

    J. Ren, X. Cui, G.J. Tearney, C. Yang, Wavefront image sensor chip, Optics Express, Vol. 18, Issue 16, Pp. 16685-16701. 18 (2010) 16685–16701. https://doi.org/10.1364/OE.18.016685

    2010 doi

  15. [23]

    C. Wang, Q. Fu, X. Dun, W. Heidrich, Quantitative Phase and Intensity Microscopy Using Snapshot White Light Wavefront Sensing, Scientific Reports 2019 9:1. 9 (2019) 1 –12. https://doi.org/10.1038/s41598-019-50264-3

    2019 doi

  16. [24]

    K. Lee, Y. Park, Quantitative phase imaging unit, Opt Lett. 39 (2014) 3630. https://doi.org/10.1364/OL.39.003630

    2014 doi

  17. [25]

    Y. Baek, K. Lee, J. Yoon, K. Kim, Y. Park, K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, Y. Park, C.A. Best, K. Badizadegan, R.R. Dasari, M.S. Feld, T. Kuriabova, M.L. Henle, A.J. Levine, G. Popescu, P. Jourdain, N. Pavillon, C. Moratal, D. Boss, B...

    2016 doi

  18. [26]

    Guo, S.K

    R. Guo, S.K. Mirsky, I. Barnea, M. Dudaie, N.T. Shaked, Quantitative phase imaging by wide -field interferometry with variable shearing distance uncoupled from the off-axis angle, Opt Express. 28 (2020) 5617. https://doi.org/10.1364/OE.385437

    2020 doi

  19. [27]

    T. Xi, J. Zhong, Y. Li, J. Di, C. Ma, J. Zhang, K. Wang, J. Zhao, Quantitative phase microscopy for cellular dynamics based on transport of intensity equation, Optics Express, Vol. 26, Issue 1, Pp. 586-

  20. [28]

    Micó, J.A

    V. Micó, J.A. Picazo-Bueno, Optical module for single-shot quantitative phase imaging based on the transport of intensity equation with field of view multiplexing, Optics Express, Vol. 29, Issue 24, Pp. 39904-39919. 29 (2021) 39904–39919. https://doi.org/10.1364/OE.439047

    2021 doi

  21. [29]

    Trusiak, M

    M. Trusiak, M. Cywinska, V. Mico, J.A. Picazo-Bueno, C. Zuo, P. Zdankowski, K. Patorski, Variational Hilbert Quantitative Phase Imaging, Scientific Reports 2020 10:1. 10 (2020) 1– 16. https://doi.org/10.1038/s41598-020-69717-1

    2020 doi

  22. [30]

    X. Fan, Z. Tang, K. O’dwyer, B.M. Hennelly, An Inexpensive Portable Self -Reference Module for Digital Holographic Microscopy, Photonics 2021, Vol. 8, Page 277. 8 (2021) 277. https://doi.org/10.3390/PHOTONICS8070277

    2021 doi

  23. [31]

    Mahajan, V

    S. Mahajan, V. Trivedi, P. Vora, V. Chhaniwal, B. Javidi, A. Anand, Highly stable digital holographic microscope using Sagnac interferometer, Opt Lett. 40 (2015) 3743. https://doi.org/10.1364/OL.40.003743

    2015 doi

  24. [32]

    T. Xi, Y. Li, J. Di, C. Ma, J. Zhang, P. Li, J. Zhao, Lateral shearing common -path digital holographic microscopy based on a slightly trapezoid Sagnac interferometer, Optics Express, Vol. 25, Issue 12, Pp. 13659-13667. 25 (2017) 13659–13667. https://doi.org/10.1364/OE.25.013659

    2017 doi

  25. [33]

    Kemper, A

    B. Kemper, A. Vollmer, G. von Bally, C.E. Rommel, J. Schnekenburger, Simplified approach for quantitative digital holographic phase contrast imaging of living cells, J Biomed Opt. 16 (2011) 1. https://doi.org/10.1117/1.3540674

    2011 doi

  26. [34]

    Shaked, Quantitative phase microscopy of biological samples using a portable interferometer, Opt Lett

    N.T. Shaked, Quantitative phase microscopy of biological samples using a portable interferometer, Opt Lett. 37 (2012) 2016. https://doi.org/10.1364/OL.37.002016

    2012 doi

  27. [35]

    Girshovitz, N.T

    P. Girshovitz, N.T. Shaked, Compact and portable low-coherence interferometer with off-axis geometry for quantitative phase microscopy and nanoscopy, Opt Express. 21 (2013) 5701. https://doi.org/10.1364/OE.21.005701

    2013 doi

  28. [36]

    Nativ, N.T

    A. Nativ, N.T. Shaked, Compact interferometric module for full-field interferometric phase microscopy with low spatial coherence illumination, Opt Lett. 42 (2017) 1492. https://doi.org/10.1364/OL.42.001492

    2017 doi

  29. [37]

    Roitshtain, N.A

    D. Roitshtain, N.A. Turko, B. Javidi, N.T. Shaked, Flipping interferometry and its application for quantitative phase microscopy in a micro-channel, Opt Lett. 41 (2016) 2354. https://doi.org/10.1364/OL.41.002354

    2016 doi

  30. [38]

    Rotman-Nativ, N.A

    N. Rotman-Nativ, N.A. Turko, N.T. Shaked, Flipping interferometry with doubled imaging area, Opt Lett. 43 (2018) 5543. https://doi.org/10.1364/OL.43.005543

    2018 doi

  31. [39]

    Girshovitz, N.T

    P. Girshovitz, N.T. Shaked, Doubling the field of view in off-axis low-coherence interferometric imaging, Light Sci Appl. 3 (2014) e151–e151. https://doi.org/10.1038/lsa.2014.32

    2014 doi

  32. [40]

    Girshovitz, I

    P. Girshovitz, I. Frenklach, N.T. Shaked, Broadband quantitative phase microscopy with extended field of view using off-axis interferometric multiplexing, J Biomed Opt. 20 (2015) 1. https://doi.org/10.1117/1.JBO.20.11.111217

    2015 doi

  33. [41]

    Girshovitz, N.T

    P. Girshovitz, N.T. Shaked, I. Frenklach, Off-axis interferometric phase microscopy with tripled imaging area, Optics Letters, Vol. 39, Issue 6, Pp. 1525-1528. 39 (2014) 1525–1528. https://doi.org/10.1364/OL.39.001525

    2014 doi

  34. [42]

    Popescu, T

    G. Popescu, T. Ikeda, R.R. Dasari, M.S. Feld, Diffraction phase microscopy for quantifying cell structure and dynamics, Opt Lett. 31 (2006) 775. https://doi.org/10.1364/OL.31.000775

    2006 doi

  35. [43]

    V. Mico, Z. Zalevsky, P. García-Martínez, J. García, Synthetic aperture superresolution with multiple off-axis holograms, Journal of the Optical Society of America A. 23 (2006) 3162. https://doi.org/10.1364/JOSAA.23.003162

    2006 doi

  36. [44]

    V. Mico, Z. Zalevsky, J. García, Synthetic aperture microscopy using off -axis illumination and polarization coding, Opt Commun. 276 (2007) 209–217. https://doi.org/10.1016/j.optcom.2007.04.020

    2007 doi

  37. [45]

    Zhang, G

    Y. Zhang, G. Pedrini, W. Osten, H.J. Tiziani, Reconstruction of in- line digital holograms from two intensity measurements, Optics Letters, Vol. 29, Issue 15, Pp. 1787-1789. 29 (2004) 1787–1789. https://doi.org/10.1364/OL.29.001787

    2004 doi

  38. [46]

    Y. Pan, Y. Pan, K. Wang, G. Gu, Research and application of dual-camera dynamic in-line digital holography using a two-step phase-shifting cepstrum technique, Applied Optics, Vol. 59, Issue 10, Pp. 3187-3195. 59 (2020) 3187–3195. https://doi.org/10.1364/AO.384642

    2020 doi

  39. [47]

    Pavillon, C.S

    N. Pavillon, C.S. Seelamantula, J. Kühn, M. Unser, C. Depeursinge, Suppression of the zero- order term in off-axis digital holography through nonlinear filtering, Applied Optics, Vol. 48, Issue 34, Pp. H186-H195. 48 (2009) H186–H195. https://doi.org/10.1364/AO.48.00H186

    2009 doi

  40. [48]

    C. Zuo, J. Li, J. Sun, Y. Fan, J. Zhang, L. Lu, R. Zhang, B. Wang, L. Huang, Q. Chen, Transport of intensity equation: a tutorial, Opt Lasers Eng. 135 (2020) 106187. https://doi.org/10.1016/J.OPTLASENG.2020.106187

    2020

  41. [49]

    A. V. Oppenheim, R.W. Schafer, Homomorphic Analysis of Speech, IEEE Transactions on Audio and Electroacoustics. 16 (1968) 221–226. https://doi.org/10.1109/TAU.1968.1161965

    1968

  42. [50]

    https://www.benchmarktech.com/index.php?q=quantitativephasemicroscop

    Benchmark Technologies, Quantitative Phase Microscopy Target, (n.d.). https://www.benchmarktech.com/index.php?q=quantitativephasemicroscop

  43. [51]

    Merola, P

    F. Merola, P. Memmolo, L. Miccio, R. Savoia, M. Mugnano, A. Fontana, G. D’Ippolito, A. Sardo, A. Iolascon, A. Gambale, P. Ferraro, Tomographic flow cytometry by digital holography, Light: Science & Applications 2017 6:4. 6 (2016) e16241–e16241. https://doi.org/10.1038/lsa.2016.241

    2016 doi

  44. [52]

    Ulrych, Application of homomorphic deconvolution to seismology, Geophysics

    T.J. Ulrych, Application of homomorphic deconvolution to seismology, Geophysics. 36 (1971) 650 –

    1971

  45. [53]

    Hassab, R

    J.C. Hassab, R. Boucher, Analysis of signal extraction, echo detection and removal by complex cepstrum in presence of distortion and noise, J Sound Vib. 40 (1975) 321–335. https://doi.org/10.1016/S0022-460X(75)81304-6

    1975 doi

  46. [54]

    Childers, D.P

    D.G. Childers, D.P. Skinner, R.C. Kemerait, The Cepstrum: A Guide to Processing, Proceedings of the IEEE. 65 (1977) 1428–1443. https://doi.org/10.1109/PROC.1977.10747

    1977

  47. [55]

    Jeong, T.J

    J. Jeong, T.J. Moir, A real-time kepstrum approach to speech enhancement and noise cancellation, Neurocomputing. 71 (2008) 2635–2649. https://doi.org/10.1016/J.NEUCOM.2007.09.026

    2008 doi

  48. [56]

    Lee, T.F

    D.-J. Lee, T.F. Krile, S. Mitra, Power cepstrum and spectrum techniques applied to image registration, Appl Opt. 27 (1988) 1099. https://doi.org/10.1364/AO.27.001099

    1988 doi

  49. [57]

    J.K. Lee, M. Kabrisky, M.E. Oxley, S.K. Rogers, D.W. Ruck, The complex cepstrum applied to two- dimensional images, Pattern Recognit. 26 (1993) 1579–1592. https://doi.org/10.1016/0031- 3203(93)90162-P

    1993 doi

  50. [593]

    https://doi.org/10.1364/OE.26.000586

    26 (2018) 586–593. https://doi.org/10.1364/OE.26.000586

    2018 doi

  51. [660]

    https://doi.org/10.1190/1.1440202

    doi

Pith tools

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