Abstract

Digital in-line holography was used to study a fast dynamic 3D phenomenon: the evaporation of free-falling diethyl ether droplets. We describe an unsupervised reconstruction algorithm based on an “inverse problems” approach previously developed by our team to accurately reconstruct 3D trajectories and to estimate the droplets’ size in a field of view of 7 × 11 × 20 mm3. A first experiment with non-evaporating droplets established that the radius estimates were accurate to better than 0.1 μm. With evaporating droplets, the vapor around the droplet distorts the diffraction patterns in the holograms. We showed that areas with the strongest distortions can be discarded using an exclusion mask. We achieved radius estimates better than 0.5 μm accuracy for evaporating droplets. Our estimates of the evaporation rate fell within the range predicted by theoretical models.

© 2013 Optical Society of America

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2013 (3)

M. K. Kim, Y. Hayasaki, P. Picart, J. Rosen, “Digital holography and 3D imaging: introduction to feature issue,” Appied Optics 52, DH1 (2013).
[CrossRef]

L. Mees, N. Grosjean, D. Chareyron, J-L. Marie, M. Seifi, C. Fournier, “Evaporating Droplet Hologram Simulation for Digital In-line Holography set-up with Divergent Beam,” Journal of Optical Society of America A 30, 2021–2028 (2013).
[CrossRef]

M. Seifi, L. Denis, C. Fournier, “Fast and accurate 3D object recognition directly from digital holograms,” Journal of the Optical Society of America A 30, 2216–2224 (2013).
[CrossRef]

2012 (3)

D. Chareyron, J. L. Marie, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, L. Mees, “Testing an in-line digital holography “inverse method” for the lagrangian tracking of evaporating droplets in homogeneous nearly isotropic turbulence,” New Journal of Physics 14, 043039 (2012).
[CrossRef]

M. Seifi, C. Fournier, L. Denis, D. Chareyron, J.-L. Marié, “Three-dimensional reconstruction of particle holograms: a fast and accurate multiscale approach,” Journal of the Optical Society of America A 29, 1808–1817 (2012).
[CrossRef]

M. Seifi, C. Fournier, L. Denis, “HoloRec3D : A free Matlab toolbox for digital holography,” Hal:ujm (2012).

2011 (6)

J. Fung, K. E. Martin, R. W. Perry, D. M. Kaz, R. McGorty, V. N. Manoharan, “Measuring translational, rotational, and vibrational dynamics in colloids with digital holographic microscopy,” Optics express 19, 8051–8065 (2011).
[CrossRef] [PubMed]

F. C. Cheong, K. Xiao, D. J. Pine, D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matter 7, 6816–6819 (2011).
[CrossRef]

C. Fournier, L. Denis, E. Thiebaut, T. Fournel, M. Seifi, “Inverse problem approaches for digital hologram reconstruction,” in “Proceedings of SPIE,”, 80430S (2011).
[CrossRef]

F. Verpillat, F. Joud, P. Desbiolles, M. Gross, “Dark-field digital holographic microscopy for 3D-tracking of gold nanoparticles,” Optics Express 19, 26044–26055 (2011).
[CrossRef]

L. Dixon, F. C. Cheong, D. G. Grier, “Holographic deconvolution microscopy for high-resolution particle tracking,” Optics Express 19, 16410–16417 (2011).
[CrossRef] [PubMed]

X. Zhang, I. Khimji, U. A. Gurkan, H. Safaee, P. N. Catalano, H. O. Keles, E. Kayaalp, U. Demirci, “Lensless imaging for simultaneous microfluidic sperm monitoring and sorting,” Lab on a Chip 11, 2535–2540 (2011).
[CrossRef] [PubMed]

2010 (2)

C. P. Allier, G. Hiernard, V. Poher, J. M. Dinten, “Bacteria detection with thin wetting film lensless imaging,” Biomedical optics express 1, 762–770 (2010).
[CrossRef]

D. Nguyen, D. Honnery, J. Soria, “Measuring evaporation of micro-fuel droplets using magnified DIH and DPIV,” Experiments in Fluids1–11 (2010).

2009 (1)

L. Denis, D. Lorenz, E. Thiébaut, C. Fournier, D. Trede, “Inline hologram reconstruction with sparsity constraints,” Optics Letters 34, 3475–3477 (2009).
[CrossRef] [PubMed]

2008 (3)

J. Coupland, J. Lobera, “Special issue : Optical tomography and digital holography,” Measurement Science and Technology 19, 070101 (2008).
[CrossRef]

J. Lu, J. P. Fugal, H. Nordsiek, E. W. Saw, R. A Shaw, W. Yang, “Lagrangian particle tracking in three dimensions via single-camera in-line digital holography,” New Journal of Physics 10, 125013 (2008).
[CrossRef]

J. Gire, L. Denis, C. Fournier, E. Thiébaut, F. Soulez, C. Ducottet, “Digital holography of particles: benefits of the ‘inverse problem’ approach,” Measurement Science and Technology 19, 074005 (2008).
[CrossRef]

2007 (3)

S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Yang, A. van Blaaderen, P. van Oostrum, D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Optics Express 15, 18275–18282 (2007).
[CrossRef] [PubMed]

F. Soulez, L. Denis, C. Fournier, É. Thiébaut, C. Goepfert, “Inverse-problem approach for particle digital holography: accurate location based on local optimization,” Journal of the Optical Society of America. A 24, 1164–1171 (2007).

F. Soulez, L. Denis, E. Thiébaut, C. Fournier, C. Goepfert, “Inverse problem approach in particle digital holography: out-of-field particle detection made possible,” Journal of the Optical Society of America. A, Optics, Image Science, and Vision 24, 3708–3716 (2007).
[CrossRef] [PubMed]

2006 (2)

J. Sheng, E. Malkiel, J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Applied optics 45, 3893–3901 (2006).
[CrossRef] [PubMed]

T. C. Poon, T. Yatagai, W. Juptner, “Digital holography-coherent optics of the 21st century: introduction,” Applied Optics 45, 821 (2006).
[CrossRef]

2004 (1)

L. Repetto, E. Piano, C. Pontiggia, “Lensless digital holographic microscope with light-emitting diode illumination,” Optics letters 29, 1132–1134 (2004).
[CrossRef] [PubMed]

2002 (1)

N. Damaschke, H. Nobach, C. Tropea, “Optical limits of particle concentration for multi-dimensional particle sizing techniques in fluid mechanics,” Experiments in fluids 32, 143–152 (2002).
[CrossRef]

1998 (1)

M. Sommerfeld, H.-H. Qiu, “Experimental studies of spray evaporation in turbulent flow,” International Journal of Heat and Fluid Flow 19, 10–22 (1998).
[CrossRef]

1988 (1)

C. S. Vikram, M. L. Billet, “Some salient features of in-line fraunhofer holography with divergent beams,” Optik 78, 80–83 (1988).

1987 (1)

C. K. Law, T. Y. Xiong, C. Wang, “Alcohol droplet vaporization in humid air,” International Journal of heat and mass transfer 30, 1435–1443 (1987).
[CrossRef]

1982 (1)

C. K. Law, “Recent advances in droplet vaporization and combustion,” Progress in energy and combustion science 8, 171–201 (1982).
[CrossRef]

1974 (1)

H. Royer, “An application of high-speed microholography: the metrology of fogs,” Nouvelle Revue d’ Optique 5, 87–93 (1974).
[CrossRef]

1964 (1)

G. B. Parrent, B. J. Thompson, “On the fraunhofer (far field) diffraction patterns of opaque and transparent objects with coherent background,” Journal of Modern Optics 11, 183–193 (1964).

Allier, C. P.

C. P. Allier, G. Hiernard, V. Poher, J. M. Dinten, “Bacteria detection with thin wetting film lensless imaging,” Biomedical optics express 1, 762–770 (2010).
[CrossRef]

Billet, M. L.

C. S. Vikram, M. L. Billet, “Some salient features of in-line fraunhofer holography with divergent beams,” Optik 78, 80–83 (1988).

Catalano, P. N.

X. Zhang, I. Khimji, U. A. Gurkan, H. Safaee, P. N. Catalano, H. O. Keles, E. Kayaalp, U. Demirci, “Lensless imaging for simultaneous microfluidic sperm monitoring and sorting,” Lab on a Chip 11, 2535–2540 (2011).
[CrossRef] [PubMed]

Chareyron, D.

L. Mees, N. Grosjean, D. Chareyron, J-L. Marie, M. Seifi, C. Fournier, “Evaporating Droplet Hologram Simulation for Digital In-line Holography set-up with Divergent Beam,” Journal of Optical Society of America A 30, 2021–2028 (2013).
[CrossRef]

D. Chareyron, J. L. Marie, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, L. Mees, “Testing an in-line digital holography “inverse method” for the lagrangian tracking of evaporating droplets in homogeneous nearly isotropic turbulence,” New Journal of Physics 14, 043039 (2012).
[CrossRef]

M. Seifi, C. Fournier, L. Denis, D. Chareyron, J.-L. Marié, “Three-dimensional reconstruction of particle holograms: a fast and accurate multiscale approach,” Journal of the Optical Society of America A 29, 1808–1817 (2012).
[CrossRef]

Cheong, F. C.

L. Dixon, F. C. Cheong, D. G. Grier, “Holographic deconvolution microscopy for high-resolution particle tracking,” Optics Express 19, 16410–16417 (2011).
[CrossRef] [PubMed]

F. C. Cheong, K. Xiao, D. J. Pine, D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matter 7, 6816–6819 (2011).
[CrossRef]

Coupland, J.

J. Coupland, J. Lobera, “Special issue : Optical tomography and digital holography,” Measurement Science and Technology 19, 070101 (2008).
[CrossRef]

Damaschke, N.

N. Damaschke, H. Nobach, C. Tropea, “Optical limits of particle concentration for multi-dimensional particle sizing techniques in fluid mechanics,” Experiments in fluids 32, 143–152 (2002).
[CrossRef]

Demirci, U.

X. Zhang, I. Khimji, U. A. Gurkan, H. Safaee, P. N. Catalano, H. O. Keles, E. Kayaalp, U. Demirci, “Lensless imaging for simultaneous microfluidic sperm monitoring and sorting,” Lab on a Chip 11, 2535–2540 (2011).
[CrossRef] [PubMed]

Denis, L.

M. Seifi, L. Denis, C. Fournier, “Fast and accurate 3D object recognition directly from digital holograms,” Journal of the Optical Society of America A 30, 2216–2224 (2013).
[CrossRef]

D. Chareyron, J. L. Marie, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, L. Mees, “Testing an in-line digital holography “inverse method” for the lagrangian tracking of evaporating droplets in homogeneous nearly isotropic turbulence,” New Journal of Physics 14, 043039 (2012).
[CrossRef]

M. Seifi, C. Fournier, L. Denis, D. Chareyron, J.-L. Marié, “Three-dimensional reconstruction of particle holograms: a fast and accurate multiscale approach,” Journal of the Optical Society of America A 29, 1808–1817 (2012).
[CrossRef]

M. Seifi, C. Fournier, L. Denis, “HoloRec3D : A free Matlab toolbox for digital holography,” Hal:ujm (2012).

C. Fournier, L. Denis, E. Thiebaut, T. Fournel, M. Seifi, “Inverse problem approaches for digital hologram reconstruction,” in “Proceedings of SPIE,”, 80430S (2011).
[CrossRef]

L. Denis, D. Lorenz, E. Thiébaut, C. Fournier, D. Trede, “Inline hologram reconstruction with sparsity constraints,” Optics Letters 34, 3475–3477 (2009).
[CrossRef] [PubMed]

J. Gire, L. Denis, C. Fournier, E. Thiébaut, F. Soulez, C. Ducottet, “Digital holography of particles: benefits of the ‘inverse problem’ approach,” Measurement Science and Technology 19, 074005 (2008).
[CrossRef]

F. Soulez, L. Denis, E. Thiébaut, C. Fournier, C. Goepfert, “Inverse problem approach in particle digital holography: out-of-field particle detection made possible,” Journal of the Optical Society of America. A, Optics, Image Science, and Vision 24, 3708–3716 (2007).
[CrossRef] [PubMed]

F. Soulez, L. Denis, C. Fournier, É. Thiébaut, C. Goepfert, “Inverse-problem approach for particle digital holography: accurate location based on local optimization,” Journal of the Optical Society of America. A 24, 1164–1171 (2007).

Desbiolles, P.

F. Verpillat, F. Joud, P. Desbiolles, M. Gross, “Dark-field digital holographic microscopy for 3D-tracking of gold nanoparticles,” Optics Express 19, 26044–26055 (2011).
[CrossRef]

Dinten, J. M.

C. P. Allier, G. Hiernard, V. Poher, J. M. Dinten, “Bacteria detection with thin wetting film lensless imaging,” Biomedical optics express 1, 762–770 (2010).
[CrossRef]

Dixon, L.

L. Dixon, F. C. Cheong, D. G. Grier, “Holographic deconvolution microscopy for high-resolution particle tracking,” Optics Express 19, 16410–16417 (2011).
[CrossRef] [PubMed]

Ducottet, C.

J. Gire, L. Denis, C. Fournier, E. Thiébaut, F. Soulez, C. Ducottet, “Digital holography of particles: benefits of the ‘inverse problem’ approach,” Measurement Science and Technology 19, 074005 (2008).
[CrossRef]

Fienup, J. R.

J. R. Fienup, “Coherent lensless imaging,” in “Imaging Systems,” (2010).
[CrossRef]

Flannery, B. P.

W. H. Press, T. A. Saul, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, The Art of Scientific Computing (Cambridge University Press, 1992), cambridge university press ed.

Fournel, T.

C. Fournier, L. Denis, E. Thiebaut, T. Fournel, M. Seifi, “Inverse problem approaches for digital hologram reconstruction,” in “Proceedings of SPIE,”, 80430S (2011).
[CrossRef]

Fournier, C.

M. Seifi, L. Denis, C. Fournier, “Fast and accurate 3D object recognition directly from digital holograms,” Journal of the Optical Society of America A 30, 2216–2224 (2013).
[CrossRef]

L. Mees, N. Grosjean, D. Chareyron, J-L. Marie, M. Seifi, C. Fournier, “Evaporating Droplet Hologram Simulation for Digital In-line Holography set-up with Divergent Beam,” Journal of Optical Society of America A 30, 2021–2028 (2013).
[CrossRef]

M. Seifi, C. Fournier, L. Denis, D. Chareyron, J.-L. Marié, “Three-dimensional reconstruction of particle holograms: a fast and accurate multiscale approach,” Journal of the Optical Society of America A 29, 1808–1817 (2012).
[CrossRef]

D. Chareyron, J. L. Marie, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, L. Mees, “Testing an in-line digital holography “inverse method” for the lagrangian tracking of evaporating droplets in homogeneous nearly isotropic turbulence,” New Journal of Physics 14, 043039 (2012).
[CrossRef]

M. Seifi, C. Fournier, L. Denis, “HoloRec3D : A free Matlab toolbox for digital holography,” Hal:ujm (2012).

C. Fournier, L. Denis, E. Thiebaut, T. Fournel, M. Seifi, “Inverse problem approaches for digital hologram reconstruction,” in “Proceedings of SPIE,”, 80430S (2011).
[CrossRef]

L. Denis, D. Lorenz, E. Thiébaut, C. Fournier, D. Trede, “Inline hologram reconstruction with sparsity constraints,” Optics Letters 34, 3475–3477 (2009).
[CrossRef] [PubMed]

J. Gire, L. Denis, C. Fournier, E. Thiébaut, F. Soulez, C. Ducottet, “Digital holography of particles: benefits of the ‘inverse problem’ approach,” Measurement Science and Technology 19, 074005 (2008).
[CrossRef]

F. Soulez, L. Denis, E. Thiébaut, C. Fournier, C. Goepfert, “Inverse problem approach in particle digital holography: out-of-field particle detection made possible,” Journal of the Optical Society of America. A, Optics, Image Science, and Vision 24, 3708–3716 (2007).
[CrossRef] [PubMed]

F. Soulez, L. Denis, C. Fournier, É. Thiébaut, C. Goepfert, “Inverse-problem approach for particle digital holography: accurate location based on local optimization,” Journal of the Optical Society of America. A 24, 1164–1171 (2007).

Fugal, J. P.

J. Lu, J. P. Fugal, H. Nordsiek, E. W. Saw, R. A Shaw, W. Yang, “Lagrangian particle tracking in three dimensions via single-camera in-line digital holography,” New Journal of Physics 10, 125013 (2008).
[CrossRef]

Fung, J.

J. Fung, K. E. Martin, R. W. Perry, D. M. Kaz, R. McGorty, V. N. Manoharan, “Measuring translational, rotational, and vibrational dynamics in colloids with digital holographic microscopy,” Optics express 19, 8051–8065 (2011).
[CrossRef] [PubMed]

Gire, J.

D. Chareyron, J. L. Marie, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, L. Mees, “Testing an in-line digital holography “inverse method” for the lagrangian tracking of evaporating droplets in homogeneous nearly isotropic turbulence,” New Journal of Physics 14, 043039 (2012).
[CrossRef]

J. Gire, L. Denis, C. Fournier, E. Thiébaut, F. Soulez, C. Ducottet, “Digital holography of particles: benefits of the ‘inverse problem’ approach,” Measurement Science and Technology 19, 074005 (2008).
[CrossRef]

Goepfert, C.

F. Soulez, L. Denis, E. Thiébaut, C. Fournier, C. Goepfert, “Inverse problem approach in particle digital holography: out-of-field particle detection made possible,” Journal of the Optical Society of America. A, Optics, Image Science, and Vision 24, 3708–3716 (2007).
[CrossRef] [PubMed]

F. Soulez, L. Denis, C. Fournier, É. Thiébaut, C. Goepfert, “Inverse-problem approach for particle digital holography: accurate location based on local optimization,” Journal of the Optical Society of America. A 24, 1164–1171 (2007).

Grier, D. G.

F. C. Cheong, K. Xiao, D. J. Pine, D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matter 7, 6816–6819 (2011).
[CrossRef]

L. Dixon, F. C. Cheong, D. G. Grier, “Holographic deconvolution microscopy for high-resolution particle tracking,” Optics Express 19, 16410–16417 (2011).
[CrossRef] [PubMed]

S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Yang, A. van Blaaderen, P. van Oostrum, D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Optics Express 15, 18275–18282 (2007).
[CrossRef] [PubMed]

Grosjean, N.

L. Mees, N. Grosjean, D. Chareyron, J-L. Marie, M. Seifi, C. Fournier, “Evaporating Droplet Hologram Simulation for Digital In-line Holography set-up with Divergent Beam,” Journal of Optical Society of America A 30, 2021–2028 (2013).
[CrossRef]

D. Chareyron, J. L. Marie, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, L. Mees, “Testing an in-line digital holography “inverse method” for the lagrangian tracking of evaporating droplets in homogeneous nearly isotropic turbulence,” New Journal of Physics 14, 043039 (2012).
[CrossRef]

Gross, M.

F. Verpillat, F. Joud, P. Desbiolles, M. Gross, “Dark-field digital holographic microscopy for 3D-tracking of gold nanoparticles,” Optics Express 19, 26044–26055 (2011).
[CrossRef]

Gurkan, U. A.

X. Zhang, I. Khimji, U. A. Gurkan, H. Safaee, P. N. Catalano, H. O. Keles, E. Kayaalp, U. Demirci, “Lensless imaging for simultaneous microfluidic sperm monitoring and sorting,” Lab on a Chip 11, 2535–2540 (2011).
[CrossRef] [PubMed]

Hardalupas, Y.

D. Sugimoto, K. Zarogoulidis, T. Kawaguchi, K. Matsuura, Y. Hardalupas, A. Taylor, K. Hishida, “Extension of the compressed interferometric particle sizing technique for three component velocity measurements,” in “13th international symposium on applications of laser techniques to fluid mechanicsLisbon, Portugal,”, 26–29 (2006).

Hayasaki, Y.

M. K. Kim, Y. Hayasaki, P. Picart, J. Rosen, “Digital holography and 3D imaging: introduction to feature issue,” Appied Optics 52, DH1 (2013).
[CrossRef]

Hiernard, G.

C. P. Allier, G. Hiernard, V. Poher, J. M. Dinten, “Bacteria detection with thin wetting film lensless imaging,” Biomedical optics express 1, 762–770 (2010).
[CrossRef]

Hishida, K.

D. Sugimoto, K. Zarogoulidis, T. Kawaguchi, K. Matsuura, Y. Hardalupas, A. Taylor, K. Hishida, “Extension of the compressed interferometric particle sizing technique for three component velocity measurements,” in “13th international symposium on applications of laser techniques to fluid mechanicsLisbon, Portugal,”, 26–29 (2006).

Honnery, D.

D. Nguyen, D. Honnery, J. Soria, “Measuring evaporation of micro-fuel droplets using magnified DIH and DPIV,” Experiments in Fluids1–11 (2010).

Joud, F.

F. Verpillat, F. Joud, P. Desbiolles, M. Gross, “Dark-field digital holographic microscopy for 3D-tracking of gold nanoparticles,” Optics Express 19, 26044–26055 (2011).
[CrossRef]

Juptner, W.

T. C. Poon, T. Yatagai, W. Juptner, “Digital holography-coherent optics of the 21st century: introduction,” Applied Optics 45, 821 (2006).
[CrossRef]

Katz, J.

J. Sheng, E. Malkiel, J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Applied optics 45, 3893–3901 (2006).
[CrossRef] [PubMed]

Kawaguchi, T.

D. Sugimoto, K. Zarogoulidis, T. Kawaguchi, K. Matsuura, Y. Hardalupas, A. Taylor, K. Hishida, “Extension of the compressed interferometric particle sizing technique for three component velocity measurements,” in “13th international symposium on applications of laser techniques to fluid mechanicsLisbon, Portugal,”, 26–29 (2006).

Kayaalp, E.

X. Zhang, I. Khimji, U. A. Gurkan, H. Safaee, P. N. Catalano, H. O. Keles, E. Kayaalp, U. Demirci, “Lensless imaging for simultaneous microfluidic sperm monitoring and sorting,” Lab on a Chip 11, 2535–2540 (2011).
[CrossRef] [PubMed]

Kaz, D. M.

J. Fung, K. E. Martin, R. W. Perry, D. M. Kaz, R. McGorty, V. N. Manoharan, “Measuring translational, rotational, and vibrational dynamics in colloids with digital holographic microscopy,” Optics express 19, 8051–8065 (2011).
[CrossRef] [PubMed]

Keles, H. O.

X. Zhang, I. Khimji, U. A. Gurkan, H. Safaee, P. N. Catalano, H. O. Keles, E. Kayaalp, U. Demirci, “Lensless imaging for simultaneous microfluidic sperm monitoring and sorting,” Lab on a Chip 11, 2535–2540 (2011).
[CrossRef] [PubMed]

Khimji, I.

X. Zhang, I. Khimji, U. A. Gurkan, H. Safaee, P. N. Catalano, H. O. Keles, E. Kayaalp, U. Demirci, “Lensless imaging for simultaneous microfluidic sperm monitoring and sorting,” Lab on a Chip 11, 2535–2540 (2011).
[CrossRef] [PubMed]

Kim, M. K.

M. K. Kim, Y. Hayasaki, P. Picart, J. Rosen, “Digital holography and 3D imaging: introduction to feature issue,” Appied Optics 52, DH1 (2013).
[CrossRef]

Kim, S. H.

S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Yang, A. van Blaaderen, P. van Oostrum, D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Optics Express 15, 18275–18282 (2007).
[CrossRef] [PubMed]

Lance, M.

D. Chareyron, J. L. Marie, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, L. Mees, “Testing an in-line digital holography “inverse method” for the lagrangian tracking of evaporating droplets in homogeneous nearly isotropic turbulence,” New Journal of Physics 14, 043039 (2012).
[CrossRef]

Law, C. K.

C. K. Law, T. Y. Xiong, C. Wang, “Alcohol droplet vaporization in humid air,” International Journal of heat and mass transfer 30, 1435–1443 (1987).
[CrossRef]

C. K. Law, “Recent advances in droplet vaporization and combustion,” Progress in energy and combustion science 8, 171–201 (1982).
[CrossRef]

Lee, S. H.

S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Yang, A. van Blaaderen, P. van Oostrum, D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Optics Express 15, 18275–18282 (2007).
[CrossRef] [PubMed]

Lobera, J.

J. Coupland, J. Lobera, “Special issue : Optical tomography and digital holography,” Measurement Science and Technology 19, 070101 (2008).
[CrossRef]

Lorenz, D.

L. Denis, D. Lorenz, E. Thiébaut, C. Fournier, D. Trede, “Inline hologram reconstruction with sparsity constraints,” Optics Letters 34, 3475–3477 (2009).
[CrossRef] [PubMed]

Lu, J.

J. Lu, J. P. Fugal, H. Nordsiek, E. W. Saw, R. A Shaw, W. Yang, “Lagrangian particle tracking in three dimensions via single-camera in-line digital holography,” New Journal of Physics 10, 125013 (2008).
[CrossRef]

Malkiel, E.

J. Sheng, E. Malkiel, J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Applied optics 45, 3893–3901 (2006).
[CrossRef] [PubMed]

Manoharan, V. N.

J. Fung, K. E. Martin, R. W. Perry, D. M. Kaz, R. McGorty, V. N. Manoharan, “Measuring translational, rotational, and vibrational dynamics in colloids with digital holographic microscopy,” Optics express 19, 8051–8065 (2011).
[CrossRef] [PubMed]

Marie, J. L.

D. Chareyron, J. L. Marie, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, L. Mees, “Testing an in-line digital holography “inverse method” for the lagrangian tracking of evaporating droplets in homogeneous nearly isotropic turbulence,” New Journal of Physics 14, 043039 (2012).
[CrossRef]

Marie, J-L.

L. Mees, N. Grosjean, D. Chareyron, J-L. Marie, M. Seifi, C. Fournier, “Evaporating Droplet Hologram Simulation for Digital In-line Holography set-up with Divergent Beam,” Journal of Optical Society of America A 30, 2021–2028 (2013).
[CrossRef]

Marié, J.-L.

M. Seifi, C. Fournier, L. Denis, D. Chareyron, J.-L. Marié, “Three-dimensional reconstruction of particle holograms: a fast and accurate multiscale approach,” Journal of the Optical Society of America A 29, 1808–1817 (2012).
[CrossRef]

Martin, K. E.

J. Fung, K. E. Martin, R. W. Perry, D. M. Kaz, R. McGorty, V. N. Manoharan, “Measuring translational, rotational, and vibrational dynamics in colloids with digital holographic microscopy,” Optics express 19, 8051–8065 (2011).
[CrossRef] [PubMed]

Matsuura, K.

D. Sugimoto, K. Zarogoulidis, T. Kawaguchi, K. Matsuura, Y. Hardalupas, A. Taylor, K. Hishida, “Extension of the compressed interferometric particle sizing technique for three component velocity measurements,” in “13th international symposium on applications of laser techniques to fluid mechanicsLisbon, Portugal,”, 26–29 (2006).

McGorty, R.

J. Fung, K. E. Martin, R. W. Perry, D. M. Kaz, R. McGorty, V. N. Manoharan, “Measuring translational, rotational, and vibrational dynamics in colloids with digital holographic microscopy,” Optics express 19, 8051–8065 (2011).
[CrossRef] [PubMed]

Mees, L.

L. Mees, N. Grosjean, D. Chareyron, J-L. Marie, M. Seifi, C. Fournier, “Evaporating Droplet Hologram Simulation for Digital In-line Holography set-up with Divergent Beam,” Journal of Optical Society of America A 30, 2021–2028 (2013).
[CrossRef]

D. Chareyron, J. L. Marie, C. Fournier, J. Gire, N. Grosjean, L. Denis, M. Lance, L. Mees, “Testing an in-line digital holography “inverse method” for the lagrangian tracking of evaporating droplets in homogeneous nearly isotropic turbulence,” New Journal of Physics 14, 043039 (2012).
[CrossRef]

Nguyen, D.

D. Nguyen, D. Honnery, J. Soria, “Measuring evaporation of micro-fuel droplets using magnified DIH and DPIV,” Experiments in Fluids1–11 (2010).

Nobach, H.

N. Damaschke, H. Nobach, C. Tropea, “Optical limits of particle concentration for multi-dimensional particle sizing techniques in fluid mechanics,” Experiments in fluids 32, 143–152 (2002).
[CrossRef]

Nordsiek, H.

J. Lu, J. P. Fugal, H. Nordsiek, E. W. Saw, R. A Shaw, W. Yang, “Lagrangian particle tracking in three dimensions via single-camera in-line digital holography,” New Journal of Physics 10, 125013 (2008).
[CrossRef]

Parrent, G. B.

G. B. Parrent, B. J. Thompson, “On the fraunhofer (far field) diffraction patterns of opaque and transparent objects with coherent background,” Journal of Modern Optics 11, 183–193 (1964).

Perry, R. W.

J. Fung, K. E. Martin, R. W. Perry, D. M. Kaz, R. McGorty, V. N. Manoharan, “Measuring translational, rotational, and vibrational dynamics in colloids with digital holographic microscopy,” Optics express 19, 8051–8065 (2011).
[CrossRef] [PubMed]

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L. Repetto, E. Piano, C. Pontiggia, “Lensless digital holographic microscope with light-emitting diode illumination,” Optics letters 29, 1132–1134 (2004).
[CrossRef] [PubMed]

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M. K. Kim, Y. Hayasaki, P. Picart, J. Rosen, “Digital holography and 3D imaging: introduction to feature issue,” Appied Optics 52, DH1 (2013).
[CrossRef]

Pine, D. J.

F. C. Cheong, K. Xiao, D. J. Pine, D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matter 7, 6816–6819 (2011).
[CrossRef]

Poher, V.

C. P. Allier, G. Hiernard, V. Poher, J. M. Dinten, “Bacteria detection with thin wetting film lensless imaging,” Biomedical optics express 1, 762–770 (2010).
[CrossRef]

Pontiggia, C.

L. Repetto, E. Piano, C. Pontiggia, “Lensless digital holographic microscope with light-emitting diode illumination,” Optics letters 29, 1132–1134 (2004).
[CrossRef] [PubMed]

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T. C. Poon, T. Yatagai, W. Juptner, “Digital holography-coherent optics of the 21st century: introduction,” Applied Optics 45, 821 (2006).
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W. H. Press, T. A. Saul, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, The Art of Scientific Computing (Cambridge University Press, 1992), cambridge university press ed.

Qiu, H.-H.

M. Sommerfeld, H.-H. Qiu, “Experimental studies of spray evaporation in turbulent flow,” International Journal of Heat and Fluid Flow 19, 10–22 (1998).
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L. Repetto, E. Piano, C. Pontiggia, “Lensless digital holographic microscope with light-emitting diode illumination,” Optics letters 29, 1132–1134 (2004).
[CrossRef] [PubMed]

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S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Yang, A. van Blaaderen, P. van Oostrum, D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Optics Express 15, 18275–18282 (2007).
[CrossRef] [PubMed]

Rosen, J.

M. K. Kim, Y. Hayasaki, P. Picart, J. Rosen, “Digital holography and 3D imaging: introduction to feature issue,” Appied Optics 52, DH1 (2013).
[CrossRef]

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H. Royer, “An application of high-speed microholography: the metrology of fogs,” Nouvelle Revue d’ Optique 5, 87–93 (1974).
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Safaee, H.

X. Zhang, I. Khimji, U. A. Gurkan, H. Safaee, P. N. Catalano, H. O. Keles, E. Kayaalp, U. Demirci, “Lensless imaging for simultaneous microfluidic sperm monitoring and sorting,” Lab on a Chip 11, 2535–2540 (2011).
[CrossRef] [PubMed]

Saul, T. A.

W. H. Press, T. A. Saul, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, The Art of Scientific Computing (Cambridge University Press, 1992), cambridge university press ed.

Saw, E. W.

J. Lu, J. P. Fugal, H. Nordsiek, E. W. Saw, R. A Shaw, W. Yang, “Lagrangian particle tracking in three dimensions via single-camera in-line digital holography,” New Journal of Physics 10, 125013 (2008).
[CrossRef]

Seifi, M.

M. Seifi, L. Denis, C. Fournier, “Fast and accurate 3D object recognition directly from digital holograms,” Journal of the Optical Society of America A 30, 2216–2224 (2013).
[CrossRef]

L. Mees, N. Grosjean, D. Chareyron, J-L. Marie, M. Seifi, C. Fournier, “Evaporating Droplet Hologram Simulation for Digital In-line Holography set-up with Divergent Beam,” Journal of Optical Society of America A 30, 2021–2028 (2013).
[CrossRef]

M. Seifi, C. Fournier, L. Denis, D. Chareyron, J.-L. Marié, “Three-dimensional reconstruction of particle holograms: a fast and accurate multiscale approach,” Journal of the Optical Society of America A 29, 1808–1817 (2012).
[CrossRef]

M. Seifi, C. Fournier, L. Denis, “HoloRec3D : A free Matlab toolbox for digital holography,” Hal:ujm (2012).

C. Fournier, L. Denis, E. Thiebaut, T. Fournel, M. Seifi, “Inverse problem approaches for digital hologram reconstruction,” in “Proceedings of SPIE,”, 80430S (2011).
[CrossRef]

Shaw, R. A

J. Lu, J. P. Fugal, H. Nordsiek, E. W. Saw, R. A Shaw, W. Yang, “Lagrangian particle tracking in three dimensions via single-camera in-line digital holography,” New Journal of Physics 10, 125013 (2008).
[CrossRef]

Sheng, J.

J. Sheng, E. Malkiel, J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Applied optics 45, 3893–3901 (2006).
[CrossRef] [PubMed]

Skippon, S. M.

S. M. Skippon, Y. Tagaki, “ILIDS measurements of the evaporation of fuel droplets during the intake and compression strokes in a firing lean burn engine,” Technical Report 960830, SAE International, Warrendale, PA (1996).

Sommerfeld, M.

M. Sommerfeld, H.-H. Qiu, “Experimental studies of spray evaporation in turbulent flow,” International Journal of Heat and Fluid Flow 19, 10–22 (1998).
[CrossRef]

Soria, J.

D. Nguyen, D. Honnery, J. Soria, “Measuring evaporation of micro-fuel droplets using magnified DIH and DPIV,” Experiments in Fluids1–11 (2010).

Soulez, F.

J. Gire, L. Denis, C. Fournier, E. Thiébaut, F. Soulez, C. Ducottet, “Digital holography of particles: benefits of the ‘inverse problem’ approach,” Measurement Science and Technology 19, 074005 (2008).
[CrossRef]

F. Soulez, L. Denis, C. Fournier, É. Thiébaut, C. Goepfert, “Inverse-problem approach for particle digital holography: accurate location based on local optimization,” Journal of the Optical Society of America. A 24, 1164–1171 (2007).

F. Soulez, L. Denis, E. Thiébaut, C. Fournier, C. Goepfert, “Inverse problem approach in particle digital holography: out-of-field particle detection made possible,” Journal of the Optical Society of America. A, Optics, Image Science, and Vision 24, 3708–3716 (2007).
[CrossRef] [PubMed]

Sugimoto, D.

D. Sugimoto, K. Zarogoulidis, T. Kawaguchi, K. Matsuura, Y. Hardalupas, A. Taylor, K. Hishida, “Extension of the compressed interferometric particle sizing technique for three component velocity measurements,” in “13th international symposium on applications of laser techniques to fluid mechanicsLisbon, Portugal,”, 26–29 (2006).

Tagaki, Y.

S. M. Skippon, Y. Tagaki, “ILIDS measurements of the evaporation of fuel droplets during the intake and compression strokes in a firing lean burn engine,” Technical Report 960830, SAE International, Warrendale, PA (1996).

Taylor, A.

D. Sugimoto, K. Zarogoulidis, T. Kawaguchi, K. Matsuura, Y. Hardalupas, A. Taylor, K. Hishida, “Extension of the compressed interferometric particle sizing technique for three component velocity measurements,” in “13th international symposium on applications of laser techniques to fluid mechanicsLisbon, Portugal,”, 26–29 (2006).

Thiebaut, E.

C. Fournier, L. Denis, E. Thiebaut, T. Fournel, M. Seifi, “Inverse problem approaches for digital hologram reconstruction,” in “Proceedings of SPIE,”, 80430S (2011).
[CrossRef]

Thiébaut, E.

L. Denis, D. Lorenz, E. Thiébaut, C. Fournier, D. Trede, “Inline hologram reconstruction with sparsity constraints,” Optics Letters 34, 3475–3477 (2009).
[CrossRef] [PubMed]

J. Gire, L. Denis, C. Fournier, E. Thiébaut, F. Soulez, C. Ducottet, “Digital holography of particles: benefits of the ‘inverse problem’ approach,” Measurement Science and Technology 19, 074005 (2008).
[CrossRef]

F. Soulez, L. Denis, E. Thiébaut, C. Fournier, C. Goepfert, “Inverse problem approach in particle digital holography: out-of-field particle detection made possible,” Journal of the Optical Society of America. A, Optics, Image Science, and Vision 24, 3708–3716 (2007).
[CrossRef] [PubMed]

Thiébaut, É.

F. Soulez, L. Denis, C. Fournier, É. Thiébaut, C. Goepfert, “Inverse-problem approach for particle digital holography: accurate location based on local optimization,” Journal of the Optical Society of America. A 24, 1164–1171 (2007).

Thompson, B. J.

G. B. Parrent, B. J. Thompson, “On the fraunhofer (far field) diffraction patterns of opaque and transparent objects with coherent background,” Journal of Modern Optics 11, 183–193 (1964).

Trede, D.

L. Denis, D. Lorenz, E. Thiébaut, C. Fournier, D. Trede, “Inline hologram reconstruction with sparsity constraints,” Optics Letters 34, 3475–3477 (2009).
[CrossRef] [PubMed]

Tropea, C.

N. Damaschke, H. Nobach, C. Tropea, “Optical limits of particle concentration for multi-dimensional particle sizing techniques in fluid mechanics,” Experiments in fluids 32, 143–152 (2002).
[CrossRef]

van Blaaderen, A.

S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Yang, A. van Blaaderen, P. van Oostrum, D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Optics Express 15, 18275–18282 (2007).
[CrossRef] [PubMed]

van Oostrum, P.

S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Yang, A. van Blaaderen, P. van Oostrum, D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Optics Express 15, 18275–18282 (2007).
[CrossRef] [PubMed]

Verpillat, F.

F. Verpillat, F. Joud, P. Desbiolles, M. Gross, “Dark-field digital holographic microscopy for 3D-tracking of gold nanoparticles,” Optics Express 19, 26044–26055 (2011).
[CrossRef]

Vetterling, W. T.

W. H. Press, T. A. Saul, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, The Art of Scientific Computing (Cambridge University Press, 1992), cambridge university press ed.

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C. S. Vikram, M. L. Billet, “Some salient features of in-line fraunhofer holography with divergent beams,” Optik 78, 80–83 (1988).

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C. K. Law, T. Y. Xiong, C. Wang, “Alcohol droplet vaporization in humid air,” International Journal of heat and mass transfer 30, 1435–1443 (1987).
[CrossRef]

Xiao, K.

F. C. Cheong, K. Xiao, D. J. Pine, D. G. Grier, “Holographic characterization of individual colloidal spheres’ porosities,” Soft Matter 7, 6816–6819 (2011).
[CrossRef]

Xiong, T. Y.

C. K. Law, T. Y. Xiong, C. Wang, “Alcohol droplet vaporization in humid air,” International Journal of heat and mass transfer 30, 1435–1443 (1987).
[CrossRef]

Yang, S. M.

S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Yang, A. van Blaaderen, P. van Oostrum, D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Optics Express 15, 18275–18282 (2007).
[CrossRef] [PubMed]

Yang, W.

J. Lu, J. P. Fugal, H. Nordsiek, E. W. Saw, R. A Shaw, W. Yang, “Lagrangian particle tracking in three dimensions via single-camera in-line digital holography,” New Journal of Physics 10, 125013 (2008).
[CrossRef]

Yatagai, T.

T. C. Poon, T. Yatagai, W. Juptner, “Digital holography-coherent optics of the 21st century: introduction,” Applied Optics 45, 821 (2006).
[CrossRef]

Yi, G. R.

S. H. Lee, Y. Roichman, G. R. Yi, S. H. Kim, S. M. Yang, A. van Blaaderen, P. van Oostrum, D. G. Grier, “Characterizing and tracking single colloidal particles with video holographic microscopy,” Optics Express 15, 18275–18282 (2007).
[CrossRef] [PubMed]

Zarogoulidis, K.

D. Sugimoto, K. Zarogoulidis, T. Kawaguchi, K. Matsuura, Y. Hardalupas, A. Taylor, K. Hishida, “Extension of the compressed interferometric particle sizing technique for three component velocity measurements,” in “13th international symposium on applications of laser techniques to fluid mechanicsLisbon, Portugal,”, 26–29 (2006).

Zhang, X.

X. Zhang, I. Khimji, U. A. Gurkan, H. Safaee, P. N. Catalano, H. O. Keles, E. Kayaalp, U. Demirci, “Lensless imaging for simultaneous microfluidic sperm monitoring and sorting,” Lab on a Chip 11, 2535–2540 (2011).
[CrossRef] [PubMed]

Appied Optics (1)

M. K. Kim, Y. Hayasaki, P. Picart, J. Rosen, “Digital holography and 3D imaging: introduction to feature issue,” Appied Optics 52, DH1 (2013).
[CrossRef]

Applied optics (1)

J. Sheng, E. Malkiel, J. Katz, “Digital holographic microscope for measuring three-dimensional particle distributions and motions,” Applied optics 45, 3893–3901 (2006).
[CrossRef] [PubMed]

Applied Optics (1)

T. C. Poon, T. Yatagai, W. Juptner, “Digital holography-coherent optics of the 21st century: introduction,” Applied Optics 45, 821 (2006).
[CrossRef]

Biomedical optics express (1)

C. P. Allier, G. Hiernard, V. Poher, J. M. Dinten, “Bacteria detection with thin wetting film lensless imaging,” Biomedical optics express 1, 762–770 (2010).
[CrossRef]

Experiments in fluids (1)

N. Damaschke, H. Nobach, C. Tropea, “Optical limits of particle concentration for multi-dimensional particle sizing techniques in fluid mechanics,” Experiments in fluids 32, 143–152 (2002).
[CrossRef]

D. Nguyen, D. Honnery, J. Soria, “Measuring evaporation of micro-fuel droplets using magnified DIH and DPIV,” Experiments in Fluids1–11 (2010).

Hal:ujm (1)

M. Seifi, C. Fournier, L. Denis, “HoloRec3D : A free Matlab toolbox for digital holography,” Hal:ujm (2012).

International Journal of Heat and Fluid Flow (1)

M. Sommerfeld, H.-H. Qiu, “Experimental studies of spray evaporation in turbulent flow,” International Journal of Heat and Fluid Flow 19, 10–22 (1998).
[CrossRef]

International Journal of heat and mass transfer (1)

C. K. Law, T. Y. Xiong, C. Wang, “Alcohol droplet vaporization in humid air,” International Journal of heat and mass transfer 30, 1435–1443 (1987).
[CrossRef]

Journal of Modern Optics (1)

G. B. Parrent, B. J. Thompson, “On the fraunhofer (far field) diffraction patterns of opaque and transparent objects with coherent background,” Journal of Modern Optics 11, 183–193 (1964).

Journal of Optical Society of America A (1)

L. Mees, N. Grosjean, D. Chareyron, J-L. Marie, M. Seifi, C. Fournier, “Evaporating Droplet Hologram Simulation for Digital In-line Holography set-up with Divergent Beam,” Journal of Optical Society of America A 30, 2021–2028 (2013).
[CrossRef]

Journal of the Optical Society of America (1)

F. Soulez, L. Denis, C. Fournier, É. Thiébaut, C. Goepfert, “Inverse-problem approach for particle digital holography: accurate location based on local optimization,” Journal of the Optical Society of America. A 24, 1164–1171 (2007).

Journal of the Optical Society of America. A, Optics, Image Science, and Vision (1)

F. Soulez, L. Denis, E. Thiébaut, C. Fournier, C. Goepfert, “Inverse problem approach in particle digital holography: out-of-field particle detection made possible,” Journal of the Optical Society of America. A, Optics, Image Science, and Vision 24, 3708–3716 (2007).
[CrossRef] [PubMed]

Journal of the Optical Society of America A (1)

M. Seifi, C. Fournier, L. Denis, D. Chareyron, J.-L. Marié, “Three-dimensional reconstruction of particle holograms: a fast and accurate multiscale approach,” Journal of the Optical Society of America A 29, 1808–1817 (2012).
[CrossRef]

Journal of the Optical Society of America A (1)

M. Seifi, L. Denis, C. Fournier, “Fast and accurate 3D object recognition directly from digital holograms,” Journal of the Optical Society of America A 30, 2216–2224 (2013).
[CrossRef]

Lab on a Chip (1)

X. Zhang, I. Khimji, U. A. Gurkan, H. Safaee, P. N. Catalano, H. O. Keles, E. Kayaalp, U. Demirci, “Lensless imaging for simultaneous microfluidic sperm monitoring and sorting,” Lab on a Chip 11, 2535–2540 (2011).
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Measurement Science and Technology (1)

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Supplementary Material (2)

» Media 1: AVI (735 KB)     
» Media 2: AVI (980 KB)     

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Figures (8)

Fig. 1
Fig. 1

A picture of the droplet jet

Fig. 2
Fig. 2

The setup for capturing three sets of holograms containing evaporating diethyl ether droplets. The droplets radii are scaled up for the sake of visualization.

Fig. 3
Fig. 3

Illustration of a pixel region exclusion mask application on a hologram of set “1”. (a-1) an experimental hologram, (a-2) the experimental hologram being masked, (b-1) cleaned hologram, (b-2) masked cleaned hologram. The colored pixels show the masked pixels which were not included in the parameter estimation.

Fig. 4
Fig. 4

Comparison of the radial mean profile of one evaporating droplet’s signature (calculated from a hologram of set “2”) with the fitted model, the residuals and the masked part of the signal. (b) shows a zoomed-in version of (a).

Fig. 5
Fig. 5

Calibration process, (a) a sample of a reconstructed calibration hologram, (b) the fitted regression curve used to estimate the magnification.

Fig. 6
Fig. 6

A hologram of non-evaporating droplets (a) and the residuals after cleaning the diffraction pattern of the droplet (b).

Fig. 7
Fig. 7

3D visualization of reconstructed trajectories (a) movie for set “1” ( Media 1 ), (b) movie for set “2” ( Media 2 ). Scale of the sphere radius has been increased to visualize the evaporation phenomenon.

Fig. 8
Fig. 8

Evolution of the radius squared of the droplets over time (a) set “1”, (b) set “2”

Equations (31)

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A holo ( x , y ) A ref 0 ( x , y ) A ref z n ( x n , y n ) ( ϑ n * h z n ) ( x , y ) ,
h z n ( x , y ) = [ 1 / ( i λ z n ) ] exp [ i π ( x 2 + y 2 ) / ( λ z n ) ] ,
I holo ( x , y ) = | A holo ( x , y ) | 2 ,
I holo ( x , y ) = I ref 0 ( x , y ) 2 { A ref 0 * ( x , y ) A ref z n ( x n , y n ) [ ϑ n * h z n ] ( x , y ) } + β .
I holo ( x , y ) I ref 0 ( x , y ) I ref 0 ( x , y ) α e . [ ϑ e * ( h z e ) ] ( x , y ) .
I holo ( x , y ) = I ref 0 ( x , y ) + α e I ref 0 ( x , y ) g θ e ( x , y ) .
g θ e ( x , y ) = π r e 2 λ z e sin ( π ρ e 2 λ z e ) J 1 c ( 2 π r e ρ e λ z e ) Pix θ e ( x , y ) ,
Pix θ e ( x , y ) = sinc ( κ π ( x x e ) λ z e ) sinc ( κ π ( y y e ) λ z e ) ,
d ( x , y ) = I holo ( x , y ) I ref 0 ( x , y ) I ref 0 ( x , y ) = α e . g θ ( x , y ) .
u ¯ ( x , y ) = u ( x , y ) 1 c x y w ( x , y ) u ( x , y ) ,
c = x y w ( x , y ) .
θ ^ e = arg max θ = ( x , y , z , r ) { [ x y w ( x , y ) d ¯ ( x , y ) g ¯ θ ( x , y ) ] 2 x y w ( x , y ) g ¯ θ 2 ( x , y ) } , s . t . α 0 ,
α = c x y w ( x , y ) d ¯ ( x , y ) g ¯ θ ( x , y ) x y w ( x , y ) g ¯ θ 2 ( x , y ) .
θ e * = arg min θ = ( x , y , z , r ) { 1 c x y w ( x , y ) [ d ¯ ( x , y ) α e * g ¯ θ ( x , y ) ] 2 } , s . t . α e * 0.
θ ˜ t = θ t Δ t * + 1 2 a t Δ t Δ t 2 + v t Δ t Δ t ,
a t = θ t * + θ t 2 Δ t * 2 θ t Δ t * Δ t 2 ,
v t = θ t * θ t Δ t * Δ t .
m = 7 ( z n 473.5 × 10 3 ) + 2.36 .
r ( t ) 2 = r ( 0 ) 2 + K t ,
I holo ( x , y ) = I ref 0 ( x , y ) 2 { A ref 0 * ( x , y ) 1 A ref z n ( x n , y n ) 2 ( ϑ n * h z n ) ( x , y ) 3 }
I holo ( x , y ) I ref 0 ( x , y ) + α n I ref 0 ( x , y ) . π r e 2 λ z e J 1 c ( 2 π r e ρ e λ z e ) sin ( π ρ e 2 λ z e )
A ref 0 * ( x , y ) = I ref 0 ( x , y ) e i π ρ e 2 λ z s .
A ref z n ( x n , y n ) = A ref z n ( 0 , 0 ) = A 0 z n .
[ ϑ n * h z n ] ( ρ ) π r n 2 i λ z n J 1 c ( 2 π r n ρ e λ z n ) e i π ρ e 2 λ z n
I holo ( x , y ) = I ref 0 ( x , y ) 2 I ref 0 ( x , y ) A 0 z n { e i π ρ e 2 λ z s π r n 2 i λ z n J 1 c ( 2 π r n ρ e λ z n ) e i π ρ e 2 λ z n } .
I holo ( x , y ) = I ref 0 ( x , y ) + α e I ref 0 ( x , y ) { π r e 2 i λ z e J 1 c ( 2 π r e ρ e λ z e ) e i π ρ e 2 λ z e } .
K = ( ρ g ρ d D d S h ln ( B M + 1 ) )
ρ g = ρ air = P atm R d a T r
B M = Y d Y 1 Y d
Y d = P sat d / ( P sat d + ( P atm P sat d ) ( M d a + / M v d ) )
P sat d = 1000 exp ( 12.43790 log ( T ) 6340.514 T + 95.14704 + 1.412198 × 10 5 T 2 )

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