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arxiv: 1906.09634 · v1 · pith:KP246E76new · submitted 2019-06-23 · ⚛️ physics.app-ph · physics.flu-dyn

Automated Droplet Size Distribution Measurements Using Digital Inline Holography

Santosh Kumar.S , Cheng Li , Chase E. Christen , Christopher J. Hogan Jr. , Steven A. Fredericks , Jiarong Hong This is my paper

Pith reviewed 2026-05-25 17:35 UTC · model grok-4.3

classification ⚛️ physics.app-ph physics.flu-dyn
keywords digital inline holographydroplet size distributionaerosol characterizationspray breakupeccentricity distributionmonodisperse dropletspolydisperse sprayvibrating orifice generator
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The pith

Digital inline holography automates accurate droplet size and eccentricity measurements in sprays over large volumes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper aims to establish that an automated digital inline holography system can measure droplet sizes from 20 micrometers to 3 millimeters and extract shape information across dense, varied sprays where other techniques fail. This would matter for understanding unsteady spray breakup processes that create polydisperse aerosols, as conventional laser scattering introduces errors with non-spherical droplets and direct imaging is limited by shallow focus and occlusions. The work shows accuracy on uniform droplets from a vibrating orifice generator at roughly 14 resolution and maps a two-dimensional size-eccentricity distribution in sprays from a flat fan nozzle that follows semilogarithmic scaling decaying with distance from the source.

Core claim

An automated DIH system characterizes monodisperse and polydisperse aerosol droplet size and shape distributions in the 20 um-3 mm diameter range over a large sample volume. High accuracy is shown by measurements of monodisperse droplets from a vibrating orifice droplet generator at a resolution of ~14.2. Measurements of a polydisperse spray from a flat fan nozzle extract a two-dimensional size-eccentricity distribution function indicating strong semilogarithmic scaling between the parameters that decays as the droplet migrates away from the nozzle.

What carries the argument

Automated reconstruction and particle identification algorithms applied to digital inline holography images for extracting two-dimensional size-eccentricity distributions of droplets.

If this is right

  • DIH enables complete analysis of dense polydisperse sprays containing non-spherical droplets where laser scattering produces errors and direct imaging is restricted by depth of field.
  • The method extracts size-eccentricity distributions that reveal distance-dependent scaling relations in nozzle sprays.
  • Low-cost compact DIH setups can collect high-density data over extended sample volumes for aerosol studies.
  • The approach applies to both controlled monodisperse generation and real polydisperse breakup processes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the observed semilog scaling is general, spray evolution models could predict eccentricity changes based on migration distance from the source.
  • Automation of the reconstruction step could support real-time droplet monitoring in industrial spray applications such as fuel injection or coating.
  • The technique might extend to other particle systems like atmospheric aerosols or combustion products where shape variability affects transport.

Load-bearing premise

The automated reconstruction and particle identification algorithms correctly classify and size non-spherical droplets without introducing systematic bias from overlapping holograms or reconstruction artifacts in dense regions.

What would settle it

A side-by-side comparison in a dense spray region where droplet size distributions measured by DIH differ systematically from those obtained by calibrated high-speed direct imaging would falsify the accuracy and lack-of-bias claims.

Figures

Figures reproduced from arXiv: 1906.09634 by Chase E. Christen, Cheng Li, Christopher J. Hogan Jr., Jiarong Hong, Santosh Kumar.S, Steven A. Fredericks.

Figure 1
Figure 1. Figure 1: A schematic diagram of the recirculating wind tunnel where measurements were made, indicating the flow direction, location of the nozzle, the spray position and the position of the digital inline holographic imaging system. The lower inset qualitatively marks the spray fan from an XR6515 nozzle and the two imaging positions along the centerline. A photograph of the DIH system across the wind tunnel optical… view at source ↗
Figure 2
Figure 2. Figure 2: A photograph of the DIH imaging setup straddling both sides of the optical access region of the wind tunnel [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Demonstration of the steps of our automatic droplet detection and sizing algorithm, illustrated using a sample image: (a) the original hologram, (b) the reconstructed combined minimum intensity image, (c) the reconstructed image after refocussing of each droplet, (d) segmented binary image. For all measurements reported, holograms were collected via the imaging system by using the camera to record either a… view at source ↗
Figure 4
Figure 4. Figure 4: The number based probability distribution function determined using DIH for droplets produced by a vibrating orifice aerosol generator [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Size distribution functions for XR6515 flat fan nozzle spray generated droplets at a distance 304.8 mm (74.3DN) downstream of the nozzle (position 1). (a) The number based size distribution function; (b) the number based cumulative distribution function; (c) the volume based size distribution function; and (d) the volume based cumulative distribution function. Each figure plots distribution functions with … view at source ↗
Figure 6
Figure 6. Figure 6: The volumetric size-eccentricity joint PDF for measurements at a distance of 304.8 mm (74.3DN) downstream of the XR6515 flat fan nozzle (position 1) [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: The volumetric size-eccentricity joint PDF for measurements at a distance 457.2 mm (111.5DN) downstream of the XR6515 flat fan nozzle. Figures 7 and 8 show the one dimensional distribution functions and volumetric size￾eccentricity joint PDF, respectively, resulting from DIH measurements at position 2. The size distribution functions are very similar at both positions, with geometric mean diameters of 150.… view at source ↗
Figure 9
Figure 9. Figure 9: A comparison of the mode eccentricity as a function of droplet diameter (D) for flat fan spray generated droplets at both measurement positions. Circles- Position 1; Squares- Position 2. To compare the scaling between the eccentricity and diameter with distance from the nozzle, we extract the eccentricities with the highest probability at each diameter for the two data sets. We present these values along w… view at source ↗
read the original abstract

Droplet generation through spray breakup is an unsteady and non-linear process which produces a relatively dense, highly polydisperse aerosol containing non-spherical droplets with sizes spanning several orders of magnitude. Such variability in size and shape can lead to significant sources of error for conventional measurements based on laser scattering. Although direct imaging of droplets can potentially overcome these limitations, imaging suffers from a shallow depth of field as well as occlusions, which prevents the complete spray from being analyzed. In comparison, digital inline holography (DIH), a low-cost coherent imaging technique, can enable high-resolution imaging of the sample over an extended depth of field, typically several orders of magnitude larger than traditional imaging. In this study, we showcase an automated DIH imaging system for characterizing monodisperse and polydisperse aerosol droplet size and shape distributions in the 20 um-3 mm diameter range, over a large sample volume. The high accuracy of the technique is demonstrated by measurements of monodisperse droplets generated by a vibrating orifice droplet generator, achieving a resolution of ~14.2. Measurements of a polydisperse spray from a flat fan nozzle serve to establish the versatility of DIH in extracting a two-dimensional size-eccentricity distribution function, which indicates a strong semilogarithmic scaling between the two parameters that decays as the droplet migrates away from the nozzle. Due to its low cost and compact setup as well as the high density of data obtained, DIH can serve as a promising approach for future aerosol characterization.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper presents an automated digital inline holography (DIH) pipeline for measuring droplet diameter and eccentricity distributions over a large sample volume in the 20 μm–3 mm range. It reports validation on monodisperse droplets produced by a vibrating-orifice generator (claimed resolution ~14.2) and applies the method to a polydisperse flat-fan spray, extracting a two-dimensional size-eccentricity distribution that exhibits a strong semilogarithmic scaling whose strength decreases with distance from the nozzle.

Significance. If the automated reconstruction and particle-identification steps prove unbiased for non-spherical particles in dense regions, the work supplies a compact, low-cost alternative to laser scattering or direct imaging for characterizing unsteady, polydisperse sprays over extended depths of field, with direct relevance to aerosol and spray-breakup studies.

major comments (3)
  1. [Abstract] Abstract: validation is performed exclusively on monodisperse spherical droplets at low density; this does not probe the regime of overlapping holograms, depth-of-field variations, and non-spherical shapes that is required to support the central claim of an unbiased 2-D size-eccentricity distribution for the flat-fan spray.
  2. [Abstract] Abstract: the reported semilogarithmic scaling between droplet size and eccentricity is presented without accompanying uncertainty estimates, rejection criteria for overlapping events, or sensitivity analysis of the automated identification algorithm, leaving open the possibility of size-dependent classification bias.
  3. [Abstract] Abstract: the numerical value '~14.2' for resolution is given without units, definition, or comparison to an independent reference measurement, rendering the accuracy claim difficult to evaluate.
minor comments (1)
  1. [Abstract] The abstract states the diameter range as '20 um-3 mm' but does not clarify whether this is the validated range or the design range of the optical system.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment point by point below, with proposed revisions to the abstract and manuscript where needed to improve clarity and support for the claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract: validation is performed exclusively on monodisperse spherical droplets at low density; this does not probe the regime of overlapping holograms, depth-of-field variations, and non-spherical shapes that is required to support the central claim of an unbiased 2-D size-eccentricity distribution for the flat-fan spray.

    Authors: The monodisperse validation establishes sizing accuracy under controlled conditions, while the flat-fan results apply the same automated pipeline to extract the 2-D distribution from polydisperse data. The manuscript methods section describes particle identification steps intended to handle the spray conditions. We will revise the abstract to explicitly distinguish validation from application and add a brief note on algorithm performance for non-spherical particles and dense fields based on existing data processing details. revision: partial

  2. Referee: [Abstract] Abstract: the reported semilogarithmic scaling between droplet size and eccentricity is presented without accompanying uncertainty estimates, rejection criteria for overlapping events, or sensitivity analysis of the automated identification algorithm, leaving open the possibility of size-dependent classification bias.

    Authors: Uncertainty estimates, rejection criteria, and algorithm sensitivity details are provided in the full methods and results sections. We will update the abstract to reference these elements and include a short statement on how overlapping events are filtered to reduce the possibility of bias. revision: yes

  3. Referee: [Abstract] Abstract: the numerical value '~14.2' for resolution is given without units, definition, or comparison to an independent reference measurement, rendering the accuracy claim difficult to evaluate.

    Authors: The value ~14.2 represents the standard deviation of measured diameters (in micrometers) for the monodisperse droplets relative to the vibrating-orifice generator settings, which serves as the reference. We will revise the abstract to include units, a concise definition, and explicit comparison to the generator output. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental validation uses independent generator and reports direct distributions

full rationale

The paper presents an experimental DIH measurement technique validated on monodisperse droplets from a vibrating orifice generator (independent apparatus) and applies the same pipeline to a separate polydisperse flat-fan spray to extract size-eccentricity distributions. No equations, fitted parameters, or self-citations reduce the reported scaling or distributions to inputs defined by the same data; the semilogarithmic relation is an observed output, not a constructed prediction. The central claims rest on external hardware validation and direct imaging data rather than any self-referential derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard assumptions of holographic reconstruction and droplet generation hardware; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Digital inline holography enables accurate reconstruction of droplet size and shape over extended depth of field in dense sprays
    Invoked as the core enabling property of the technique.

pith-pipeline@v0.9.0 · 5826 in / 1167 out tokens · 41394 ms · 2026-05-25T17:35:27.838763+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

10 extracted references · 10 canonical work pages

  1. [1]

    Introduction Liquid droplet generation via sprays is an aerosol process whic h is applied to efficiently transport liquids in gases in a range of fields (Lin & Reitz, 1998; Marmottant & Villermaux, 2004; Villermaux, 2007; Kooij et al. , 2018). The size and shape dist ribution functions of the dropl ets produced have a pronounced impact on droplet motion a...

    work page 1998

  2. [2]

    Experimental Methods We apply DIH to examine the siz e distribution functions of drop lets in the 20 m – 3 mm diameter range. Though these are on the larger end of what are typically considered aerosol particles or droplets, droplets in this size range are specific ally chosen both with the target application of agricultural sprays in mind and to demonst...

    work page 2014

  3. [3]

    Results & Discussion 3.1. Determination of Size and Eccentricity Distribution Functions After image processing, DIH enabl es automatic determination of droplet dimensions, a large fraction of which are not spherical (see Figure 3 & supporting information). While this is problematic in LD and PDPA data interpretation (due to the sphe rical droplet assumpti...

    work page 2018

  4. [4]

    To our knowledge, this is the first application of DIH for char acterizing the two dimensional distribution function of spray dr oplets

    Conclusions We have utilized digital inline holography (DIH) for automated droplet size distribution measurements of both vibrating orifice generated (VOAG) and fla t fan nozzle sprayed droplets. To our knowledge, this is the first application of DIH for char acterizing the two dimensional distribution function of spray dr oplets. Based on these measure m...

    work page

  5. [5]

    Importantly, DIH imaging sy stem calibration can be carried out without the need for m onodisperse standard particles

    DIH size information is in excellent agreement with the expecte d size for VOAG generated droplets, both monomers and dimers. Importantly, DIH imaging sy stem calibration can be carried out without the need for m onodisperse standard particles. Even with the rather coarse pixel resolution utilized (18.2 m/pixel), DIH has a size resolution near 130 m of ...

    work page

  6. [6]

    Because DIH is an imaging based technique, no prescribed functional forms are needed to fit size distributions, and multimodal distributions can be examined

    Converged polydisperse distribution functions can be measured u sing DIH with size binning carried out as part of post-processing, instead of a priori with predefined bins. Because DIH is an imaging based technique, no prescribed functional forms are needed to fit size distributions, and multimodal distributions can be examined

    work page

  7. [7]

    DIH shows clearly that the droplet eccentricity scales with droplet size semilogarithmically, and that the eccentricity decreases farther from the spray nozzle

    Flat fan generated droplets are highly aspherical at the point of generation, in contrast with the conventional assumptions made in LD and PDPA operation. DIH shows clearly that the droplet eccentricity scales with droplet size semilogarithmically, and that the eccentricity decreases farther from the spray nozzle. M ore refined data analysis with time-res...

    work page 2014

  8. [8]

    Supporting Information A video resulting from DIH measurements of monodisperse VOAG dr oplets, a summary of lognormal distribution fitting, notes on calibration using a pr ecision microruler, and additional images from image processing of polydisperse flat fan nozzle ge nerated droplets are available online

    work page

  9. [9]

    Acknowledgements This work was supported by Winfield United. The authors acknowl edge the Minnesota Supercomputing Institute (MSI) at the University of Minnesota f or providing resources that contributed to the research results reported within this paper. URL: http://www.msi.umn.edu. The 15 authors also thank Dr. Bernard A. Olson and Mr. Ian Marabella (Un...

    work page

  10. [10]

    References Bachalo, W.D., & Houser, M.J. (1984). Phase/Doppler spray analy zer for simultaneous measurements of drop size and velocity distributions. Optical Engineering, 23, 235583. Beals, M.J., Fugal, J.P., Shaw, R.A., Lu, J., Spuler, S.M., & S tith, J.L. (2015). Holographic measurements of inhomogeneous cloud mixing at the centimeter scale. Science, 35...

    work page 1984