Abstract

In a schlieren setup, a lens system forms an image of the refractive index fluctuations of a transparent sample onto a matrix detector while an intensity mask is positioned in the Fourier plane of a collecting lens to perform the required spatial filtering. In the absence of the mask, the resulting technique is that of a shadowgraph. The two methods provide different information about the refractive index of transparent fluids and can be used both for visualization purposes and scattering measurements. Here, we describe the effect of the intensity mask on the technique transfer function, i.e., its ability to detect different spatial frequencies and show how the special cases of shadowgraph, schlieren, and the transition between the two can be derived. We also present experimental data that agree well with our predictions.

© 2011 Optical Society of America

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References

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    [CrossRef]
  5. J. W. Tang, T. J. Liebner, B. A. Craven, and G. S. Settles, “A schlieren optical study of the human cough with and without wearing masks for aerosol infection control,” J. R. Soc. Interface 6, S727–S736 (2009).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  26. R. Kumar, D. P. Chhachhia, and A. K. Aggarwal, “Folding mirror schlieren diffraction interferometer,” Appl. Opt. 45, 6708–6711 (2006).
    [CrossRef] [PubMed]
  27. R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, “Knife-edge diffraction pattern as an interference phenomenon: an experimental reality,” Opt. Laser Technol. 39, 256–261 (2007).
    [CrossRef]
  28. R. Kumar, S. K. Kaura, D. P. Chhachhia, D. Mohan, and A. K. Aggarwal, “Comparative study of different schlieren diffracting elements,” Pramana 70, 121–129 (2008).
    [CrossRef]
  29. D. Brogioli, A. Vailati, and M. Giglio, “Universal behavior of nonequilibrium fluctuations in free diffusion processes,” Phys. Rev. E 61, R1–R4 (2000).
    [CrossRef]
  30. A. Vailati and M. Giglio, “Giant fluctuations in a free diffusion process,” Nature 390, 262–265 (1997).
    [CrossRef]
  31. A. Oprisan, S. Oprisan, and A. Teklu, “Experimental study of nonequilibrium fluctuations during free diffusion in nanocolloids using microscopy techniques,” Appl. Opt. 49, 86–98 (2010).
    [CrossRef] [PubMed]

2010 (1)

2009 (5)

D. Brogioli, V. Cassina, D. Salerno, F. Croccolo, and F. Mantegazza, “Characterization of anisotropic nano-particles by using depolarized dynamic light scattering in the near field,” Opt. Express 17, 1222–1233 (2009).
[CrossRef] [PubMed]

D. Brogioli, D. Salerno, V. Cassina, and F. Mantegazza, “Nanoparticle characterization by using tilted laser microscopy: back scattering measurement in near field,” Opt. Express 17, 15431–15448 (2009).
[CrossRef] [PubMed]

J. W. Tang, T. J. Liebner, B. A. Craven, and G. S. Settles, “A schlieren optical study of the human cough with and without wearing masks for aerosol infection control,” J. R. Soc. Interface 6, S727–S736 (2009).
[CrossRef] [PubMed]

R. Cerbino and A. Vailati, “Near-field scattering techniques: novel instrumentation and results from time and spatially resolved investigations of soft matter systems,” Curr. Opin. Colloid Interface Sci. 14, 416–425 (2009).
[CrossRef]

A. Duri, D. A. Sessoms, V. Trappe, and L. Cipelletti, “Resolving long-range spatial correlations in jammed colloidal systems using photon correlation imaging,” Phys. Rev. Lett. 102, 085702 (2009).
[CrossRef] [PubMed]

2008 (3)

F. Croccolo, R. Cerbino, A. Vailati, and M. Giglio, “Non-equilibrium fluctuations in diffusion experiments,” in Anomalous Fluctuation Phenomena in Complex Systems: Plasmas, Fluids, and Financial Markets, C.Riccardi and H.E.Roman, eds. (Research Signpost, 2008).

D. Brogioli, F. Croccolo, V. Cassina, D. Salerno, and F. Mantegazza, “Nano-particle characterization by using exposure time-dependent spectrum and scattering in the near field methods: how to get fast dynamics with low-speed CCD camera,” Opt. Express 16, 20272–20282 (2008).
[CrossRef] [PubMed]

R. Kumar, S. K. Kaura, D. P. Chhachhia, D. Mohan, and A. K. Aggarwal, “Comparative study of different schlieren diffracting elements,” Pramana 70, 121–129 (2008).
[CrossRef]

2007 (4)

R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, “Knife-edge diffraction pattern as an interference phenomenon: an experimental reality,” Opt. Laser Technol. 39, 256–261 (2007).
[CrossRef]

R. Kumar, D. Mohan, S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, “Phase knife-edge laser schlieren diffraction interferometry with boundary diffraction wave theory,” Pramana 68, 581–589 (2007).
[CrossRef]

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Non-diffusive decay of gradient driven fluctuations in a free-diffusion process,” Phys. Rev. E 76, 41112 (2007).
[CrossRef]

F. Scheffold and R. Cerbino, “New trends in light scattering,” Curr. Opin. Colloid Interface Sci. 12, 50–57 (2007).
[CrossRef]

2006 (5)

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Effect of gravity on the dynamics of nonequilibrium fluctuations in a free diffusion experiment,” Ann. N.Y. Acad. Sci. 1077, 365–379 (2006).
[CrossRef] [PubMed]

D. R. Jonassen, G. S. Settles, and M. D. Tronosky, “Schlieren “PIV” for turbulent flows,” Opt. Lasers Eng. 44, 190–207(2006).
[CrossRef]

H. Kleine, H. Grönig, and K. Takayama, “Simultaneous shadow, schlieren and interferometric visualization of compressible flows,” Opt. Lasers Eng. 44, 170–189(2006).
[CrossRef]

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Use of dynamic schlieren to study fluctuations during free diffusion,” Appl. Opt. 45, 2166–2173 (2006).
[CrossRef] [PubMed]

R. Kumar, D. P. Chhachhia, and A. K. Aggarwal, “Folding mirror schlieren diffraction interferometer,” Appl. Opt. 45, 6708–6711 (2006).
[CrossRef] [PubMed]

2004 (2)

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 41405 (2004).
[CrossRef]

B. Zakharin and J. Stricker, “Schlieren systems with coherent illumination for quantitative measurements,” Appl. Opt. 43, 4786–4795 (2004).
[CrossRef] [PubMed]

2003 (1)

D. Brogioli, A. Vailati, and M. Giglio, “A schlieren method for ultra-low angle light scattering measurements,” Europhys. Lett. 63, 220–225 (2003).
[CrossRef]

2002 (2)

D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near-field scattering,” Appl. Phys. Lett. 81, 4109–4111 (2002).
[CrossRef]

S. P. Trainoff and D. S. Cannell, “Physical optics treatment of the shadowgraph,” Phys. Fluids 14, 1340–1363 (2002).
[CrossRef]

2001 (1)

G. S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media (Springer, 2001).

2000 (2)

M. Giglio, M. Carpineti, and A. Vailati, “Space intensity correlations in the near field of the scattered light: a direct measurement of the density correlation function g(r),” Phys. Rev. Lett. 85, 1416–1419 (2000).
[CrossRef] [PubMed]

D. Brogioli, A. Vailati, and M. Giglio, “Universal behavior of nonequilibrium fluctuations in free diffusion processes,” Phys. Rev. E 61, R1–R4 (2000).
[CrossRef]

1999 (1)

1997 (1)

A. Vailati and M. Giglio, “Giant fluctuations in a free diffusion process,” Nature 390, 262–265 (1997).
[CrossRef]

1996 (1)

M. M. J. Treacy and J. M. Gibson, “Variable coherence microscopy: a rich source of structural information from disordered materials,” Acta Crystallogr. Sect. A 52, 212–220 (1996).
[CrossRef]

1981 (2)

R. B. Owen and M. H. Johnston, “Laser shadowgraph and schlieren studies of gravity-related flow during solidification,” Opt. Lasers Eng. 2, 129–146 (1981).
[CrossRef]

G. Jellison and C. R. Parsons, “Resonant shadowgraph and schlieren studies of magnetized laser-produced plasmas,” Phys. Fluids 24, 1787–1790 (1981).
[CrossRef]

Aggarwal, A. K.

R. Kumar, S. K. Kaura, D. P. Chhachhia, D. Mohan, and A. K. Aggarwal, “Comparative study of different schlieren diffracting elements,” Pramana 70, 121–129 (2008).
[CrossRef]

R. Kumar, D. Mohan, S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, “Phase knife-edge laser schlieren diffraction interferometry with boundary diffraction wave theory,” Pramana 68, 581–589 (2007).
[CrossRef]

R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, “Knife-edge diffraction pattern as an interference phenomenon: an experimental reality,” Opt. Laser Technol. 39, 256–261 (2007).
[CrossRef]

R. Kumar, D. P. Chhachhia, and A. K. Aggarwal, “Folding mirror schlieren diffraction interferometer,” Appl. Opt. 45, 6708–6711 (2006).
[CrossRef] [PubMed]

Brogioli, D.

D. Brogioli, D. Salerno, V. Cassina, and F. Mantegazza, “Nanoparticle characterization by using tilted laser microscopy: back scattering measurement in near field,” Opt. Express 17, 15431–15448 (2009).
[CrossRef] [PubMed]

D. Brogioli, V. Cassina, D. Salerno, F. Croccolo, and F. Mantegazza, “Characterization of anisotropic nano-particles by using depolarized dynamic light scattering in the near field,” Opt. Express 17, 1222–1233 (2009).
[CrossRef] [PubMed]

D. Brogioli, F. Croccolo, V. Cassina, D. Salerno, and F. Mantegazza, “Nano-particle characterization by using exposure time-dependent spectrum and scattering in the near field methods: how to get fast dynamics with low-speed CCD camera,” Opt. Express 16, 20272–20282 (2008).
[CrossRef] [PubMed]

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Non-diffusive decay of gradient driven fluctuations in a free-diffusion process,” Phys. Rev. E 76, 41112 (2007).
[CrossRef]

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Use of dynamic schlieren to study fluctuations during free diffusion,” Appl. Opt. 45, 2166–2173 (2006).
[CrossRef] [PubMed]

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Effect of gravity on the dynamics of nonequilibrium fluctuations in a free diffusion experiment,” Ann. N.Y. Acad. Sci. 1077, 365–379 (2006).
[CrossRef] [PubMed]

D. Brogioli, A. Vailati, and M. Giglio, “A schlieren method for ultra-low angle light scattering measurements,” Europhys. Lett. 63, 220–225 (2003).
[CrossRef]

D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near-field scattering,” Appl. Phys. Lett. 81, 4109–4111 (2002).
[CrossRef]

D. Brogioli, A. Vailati, and M. Giglio, “Universal behavior of nonequilibrium fluctuations in free diffusion processes,” Phys. Rev. E 61, R1–R4 (2000).
[CrossRef]

Cannell, D. S.

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Non-diffusive decay of gradient driven fluctuations in a free-diffusion process,” Phys. Rev. E 76, 41112 (2007).
[CrossRef]

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Use of dynamic schlieren to study fluctuations during free diffusion,” Appl. Opt. 45, 2166–2173 (2006).
[CrossRef] [PubMed]

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Effect of gravity on the dynamics of nonequilibrium fluctuations in a free diffusion experiment,” Ann. N.Y. Acad. Sci. 1077, 365–379 (2006).
[CrossRef] [PubMed]

S. P. Trainoff and D. S. Cannell, “Physical optics treatment of the shadowgraph,” Phys. Fluids 14, 1340–1363 (2002).
[CrossRef]

Carpineti, M.

M. Giglio, M. Carpineti, and A. Vailati, “Space intensity correlations in the near field of the scattered light: a direct measurement of the density correlation function g(r),” Phys. Rev. Lett. 85, 1416–1419 (2000).
[CrossRef] [PubMed]

Cassina, V.

Cerbino, R.

R. Cerbino and A. Vailati, “Near-field scattering techniques: novel instrumentation and results from time and spatially resolved investigations of soft matter systems,” Curr. Opin. Colloid Interface Sci. 14, 416–425 (2009).
[CrossRef]

F. Croccolo, R. Cerbino, A. Vailati, and M. Giglio, “Non-equilibrium fluctuations in diffusion experiments,” in Anomalous Fluctuation Phenomena in Complex Systems: Plasmas, Fluids, and Financial Markets, C.Riccardi and H.E.Roman, eds. (Research Signpost, 2008).

F. Scheffold and R. Cerbino, “New trends in light scattering,” Curr. Opin. Colloid Interface Sci. 12, 50–57 (2007).
[CrossRef]

Chhachhia, D. P.

R. Kumar, S. K. Kaura, D. P. Chhachhia, D. Mohan, and A. K. Aggarwal, “Comparative study of different schlieren diffracting elements,” Pramana 70, 121–129 (2008).
[CrossRef]

R. Kumar, D. Mohan, S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, “Phase knife-edge laser schlieren diffraction interferometry with boundary diffraction wave theory,” Pramana 68, 581–589 (2007).
[CrossRef]

R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, “Knife-edge diffraction pattern as an interference phenomenon: an experimental reality,” Opt. Laser Technol. 39, 256–261 (2007).
[CrossRef]

R. Kumar, D. P. Chhachhia, and A. K. Aggarwal, “Folding mirror schlieren diffraction interferometer,” Appl. Opt. 45, 6708–6711 (2006).
[CrossRef] [PubMed]

Cipelletti, L.

A. Duri, D. A. Sessoms, V. Trappe, and L. Cipelletti, “Resolving long-range spatial correlations in jammed colloidal systems using photon correlation imaging,” Phys. Rev. Lett. 102, 085702 (2009).
[CrossRef] [PubMed]

Craven, B. A.

J. W. Tang, T. J. Liebner, B. A. Craven, and G. S. Settles, “A schlieren optical study of the human cough with and without wearing masks for aerosol infection control,” J. R. Soc. Interface 6, S727–S736 (2009).
[CrossRef] [PubMed]

Croccolo, F.

D. Brogioli, V. Cassina, D. Salerno, F. Croccolo, and F. Mantegazza, “Characterization of anisotropic nano-particles by using depolarized dynamic light scattering in the near field,” Opt. Express 17, 1222–1233 (2009).
[CrossRef] [PubMed]

D. Brogioli, F. Croccolo, V. Cassina, D. Salerno, and F. Mantegazza, “Nano-particle characterization by using exposure time-dependent spectrum and scattering in the near field methods: how to get fast dynamics with low-speed CCD camera,” Opt. Express 16, 20272–20282 (2008).
[CrossRef] [PubMed]

F. Croccolo, R. Cerbino, A. Vailati, and M. Giglio, “Non-equilibrium fluctuations in diffusion experiments,” in Anomalous Fluctuation Phenomena in Complex Systems: Plasmas, Fluids, and Financial Markets, C.Riccardi and H.E.Roman, eds. (Research Signpost, 2008).

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Non-diffusive decay of gradient driven fluctuations in a free-diffusion process,” Phys. Rev. E 76, 41112 (2007).
[CrossRef]

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Use of dynamic schlieren to study fluctuations during free diffusion,” Appl. Opt. 45, 2166–2173 (2006).
[CrossRef] [PubMed]

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Effect of gravity on the dynamics of nonequilibrium fluctuations in a free diffusion experiment,” Ann. N.Y. Acad. Sci. 1077, 365–379 (2006).
[CrossRef] [PubMed]

Duri, A.

A. Duri, D. A. Sessoms, V. Trappe, and L. Cipelletti, “Resolving long-range spatial correlations in jammed colloidal systems using photon correlation imaging,” Phys. Rev. Lett. 102, 085702 (2009).
[CrossRef] [PubMed]

Ferri, F.

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 41405 (2004).
[CrossRef]

Gibson, J. M.

M. M. J. Treacy and J. M. Gibson, “Variable coherence microscopy: a rich source of structural information from disordered materials,” Acta Crystallogr. Sect. A 52, 212–220 (1996).
[CrossRef]

Giglio, M.

F. Croccolo, R. Cerbino, A. Vailati, and M. Giglio, “Non-equilibrium fluctuations in diffusion experiments,” in Anomalous Fluctuation Phenomena in Complex Systems: Plasmas, Fluids, and Financial Markets, C.Riccardi and H.E.Roman, eds. (Research Signpost, 2008).

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Non-diffusive decay of gradient driven fluctuations in a free-diffusion process,” Phys. Rev. E 76, 41112 (2007).
[CrossRef]

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Use of dynamic schlieren to study fluctuations during free diffusion,” Appl. Opt. 45, 2166–2173 (2006).
[CrossRef] [PubMed]

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Effect of gravity on the dynamics of nonequilibrium fluctuations in a free diffusion experiment,” Ann. N.Y. Acad. Sci. 1077, 365–379 (2006).
[CrossRef] [PubMed]

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 41405 (2004).
[CrossRef]

D. Brogioli, A. Vailati, and M. Giglio, “A schlieren method for ultra-low angle light scattering measurements,” Europhys. Lett. 63, 220–225 (2003).
[CrossRef]

D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near-field scattering,” Appl. Phys. Lett. 81, 4109–4111 (2002).
[CrossRef]

M. Giglio, M. Carpineti, and A. Vailati, “Space intensity correlations in the near field of the scattered light: a direct measurement of the density correlation function g(r),” Phys. Rev. Lett. 85, 1416–1419 (2000).
[CrossRef] [PubMed]

D. Brogioli, A. Vailati, and M. Giglio, “Universal behavior of nonequilibrium fluctuations in free diffusion processes,” Phys. Rev. E 61, R1–R4 (2000).
[CrossRef]

A. Vailati and M. Giglio, “Giant fluctuations in a free diffusion process,” Nature 390, 262–265 (1997).
[CrossRef]

Grönig, H.

H. Kleine, H. Grönig, and K. Takayama, “Simultaneous shadow, schlieren and interferometric visualization of compressible flows,” Opt. Lasers Eng. 44, 170–189(2006).
[CrossRef]

Jellison, G.

G. Jellison and C. R. Parsons, “Resonant shadowgraph and schlieren studies of magnetized laser-produced plasmas,” Phys. Fluids 24, 1787–1790 (1981).
[CrossRef]

Johnston, M. H.

R. B. Owen and M. H. Johnston, “Laser shadowgraph and schlieren studies of gravity-related flow during solidification,” Opt. Lasers Eng. 2, 129–146 (1981).
[CrossRef]

Jonassen, D. R.

D. R. Jonassen, G. S. Settles, and M. D. Tronosky, “Schlieren “PIV” for turbulent flows,” Opt. Lasers Eng. 44, 190–207(2006).
[CrossRef]

Kaplan, P. D.

Kaura, S. K.

R. Kumar, S. K. Kaura, D. P. Chhachhia, D. Mohan, and A. K. Aggarwal, “Comparative study of different schlieren diffracting elements,” Pramana 70, 121–129 (2008).
[CrossRef]

R. Kumar, D. Mohan, S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, “Phase knife-edge laser schlieren diffraction interferometry with boundary diffraction wave theory,” Pramana 68, 581–589 (2007).
[CrossRef]

R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, “Knife-edge diffraction pattern as an interference phenomenon: an experimental reality,” Opt. Laser Technol. 39, 256–261 (2007).
[CrossRef]

Kleine, H.

H. Kleine, H. Grönig, and K. Takayama, “Simultaneous shadow, schlieren and interferometric visualization of compressible flows,” Opt. Lasers Eng. 44, 170–189(2006).
[CrossRef]

Kumar, R.

R. Kumar, S. K. Kaura, D. P. Chhachhia, D. Mohan, and A. K. Aggarwal, “Comparative study of different schlieren diffracting elements,” Pramana 70, 121–129 (2008).
[CrossRef]

R. Kumar, D. Mohan, S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, “Phase knife-edge laser schlieren diffraction interferometry with boundary diffraction wave theory,” Pramana 68, 581–589 (2007).
[CrossRef]

R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, “Knife-edge diffraction pattern as an interference phenomenon: an experimental reality,” Opt. Laser Technol. 39, 256–261 (2007).
[CrossRef]

R. Kumar, D. P. Chhachhia, and A. K. Aggarwal, “Folding mirror schlieren diffraction interferometer,” Appl. Opt. 45, 6708–6711 (2006).
[CrossRef] [PubMed]

Liebner, T. J.

J. W. Tang, T. J. Liebner, B. A. Craven, and G. S. Settles, “A schlieren optical study of the human cough with and without wearing masks for aerosol infection control,” J. R. Soc. Interface 6, S727–S736 (2009).
[CrossRef] [PubMed]

Magatti, D.

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 41405 (2004).
[CrossRef]

Mantegazza, F.

Mohan, D.

R. Kumar, S. K. Kaura, D. P. Chhachhia, D. Mohan, and A. K. Aggarwal, “Comparative study of different schlieren diffracting elements,” Pramana 70, 121–129 (2008).
[CrossRef]

R. Kumar, D. Mohan, S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, “Phase knife-edge laser schlieren diffraction interferometry with boundary diffraction wave theory,” Pramana 68, 581–589 (2007).
[CrossRef]

Oprisan, A.

Oprisan, S.

Owen, R. B.

R. B. Owen and M. H. Johnston, “Laser shadowgraph and schlieren studies of gravity-related flow during solidification,” Opt. Lasers Eng. 2, 129–146 (1981).
[CrossRef]

Parsons, C. R.

G. Jellison and C. R. Parsons, “Resonant shadowgraph and schlieren studies of magnetized laser-produced plasmas,” Phys. Fluids 24, 1787–1790 (1981).
[CrossRef]

Pescini, D.

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 41405 (2004).
[CrossRef]

Potenza, M. A. C.

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 41405 (2004).
[CrossRef]

Salerno, D.

Scheffold, F.

F. Scheffold and R. Cerbino, “New trends in light scattering,” Curr. Opin. Colloid Interface Sci. 12, 50–57 (2007).
[CrossRef]

Sessoms, D. A.

A. Duri, D. A. Sessoms, V. Trappe, and L. Cipelletti, “Resolving long-range spatial correlations in jammed colloidal systems using photon correlation imaging,” Phys. Rev. Lett. 102, 085702 (2009).
[CrossRef] [PubMed]

Settles, G. S.

J. W. Tang, T. J. Liebner, B. A. Craven, and G. S. Settles, “A schlieren optical study of the human cough with and without wearing masks for aerosol infection control,” J. R. Soc. Interface 6, S727–S736 (2009).
[CrossRef] [PubMed]

D. R. Jonassen, G. S. Settles, and M. D. Tronosky, “Schlieren “PIV” for turbulent flows,” Opt. Lasers Eng. 44, 190–207(2006).
[CrossRef]

G. S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media (Springer, 2001).

Sharma, A. K.

R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, “Knife-edge diffraction pattern as an interference phenomenon: an experimental reality,” Opt. Laser Technol. 39, 256–261 (2007).
[CrossRef]

Stricker, J.

Takayama, K.

H. Kleine, H. Grönig, and K. Takayama, “Simultaneous shadow, schlieren and interferometric visualization of compressible flows,” Opt. Lasers Eng. 44, 170–189(2006).
[CrossRef]

Tang, J. W.

J. W. Tang, T. J. Liebner, B. A. Craven, and G. S. Settles, “A schlieren optical study of the human cough with and without wearing masks for aerosol infection control,” J. R. Soc. Interface 6, S727–S736 (2009).
[CrossRef] [PubMed]

Teklu, A.

Trainoff, S. P.

S. P. Trainoff and D. S. Cannell, “Physical optics treatment of the shadowgraph,” Phys. Fluids 14, 1340–1363 (2002).
[CrossRef]

Trappe, V.

A. Duri, D. A. Sessoms, V. Trappe, and L. Cipelletti, “Resolving long-range spatial correlations in jammed colloidal systems using photon correlation imaging,” Phys. Rev. Lett. 102, 085702 (2009).
[CrossRef] [PubMed]

P. D. Kaplan, V. Trappe, and D. A. Weitz, “Light-scattering microscope,” Appl. Opt. 38, 4151–4157 (1999).
[CrossRef]

Treacy, M. M. J.

M. M. J. Treacy and J. M. Gibson, “Variable coherence microscopy: a rich source of structural information from disordered materials,” Acta Crystallogr. Sect. A 52, 212–220 (1996).
[CrossRef]

Tronosky, M. D.

D. R. Jonassen, G. S. Settles, and M. D. Tronosky, “Schlieren “PIV” for turbulent flows,” Opt. Lasers Eng. 44, 190–207(2006).
[CrossRef]

Vailati, A.

R. Cerbino and A. Vailati, “Near-field scattering techniques: novel instrumentation and results from time and spatially resolved investigations of soft matter systems,” Curr. Opin. Colloid Interface Sci. 14, 416–425 (2009).
[CrossRef]

F. Croccolo, R. Cerbino, A. Vailati, and M. Giglio, “Non-equilibrium fluctuations in diffusion experiments,” in Anomalous Fluctuation Phenomena in Complex Systems: Plasmas, Fluids, and Financial Markets, C.Riccardi and H.E.Roman, eds. (Research Signpost, 2008).

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Non-diffusive decay of gradient driven fluctuations in a free-diffusion process,” Phys. Rev. E 76, 41112 (2007).
[CrossRef]

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Use of dynamic schlieren to study fluctuations during free diffusion,” Appl. Opt. 45, 2166–2173 (2006).
[CrossRef] [PubMed]

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Effect of gravity on the dynamics of nonequilibrium fluctuations in a free diffusion experiment,” Ann. N.Y. Acad. Sci. 1077, 365–379 (2006).
[CrossRef] [PubMed]

D. Brogioli, A. Vailati, and M. Giglio, “A schlieren method for ultra-low angle light scattering measurements,” Europhys. Lett. 63, 220–225 (2003).
[CrossRef]

D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near-field scattering,” Appl. Phys. Lett. 81, 4109–4111 (2002).
[CrossRef]

M. Giglio, M. Carpineti, and A. Vailati, “Space intensity correlations in the near field of the scattered light: a direct measurement of the density correlation function g(r),” Phys. Rev. Lett. 85, 1416–1419 (2000).
[CrossRef] [PubMed]

D. Brogioli, A. Vailati, and M. Giglio, “Universal behavior of nonequilibrium fluctuations in free diffusion processes,” Phys. Rev. E 61, R1–R4 (2000).
[CrossRef]

A. Vailati and M. Giglio, “Giant fluctuations in a free diffusion process,” Nature 390, 262–265 (1997).
[CrossRef]

Weitz, D. A.

Zakharin, B.

Acta Crystallogr. Sect. A (1)

M. M. J. Treacy and J. M. Gibson, “Variable coherence microscopy: a rich source of structural information from disordered materials,” Acta Crystallogr. Sect. A 52, 212–220 (1996).
[CrossRef]

Ann. N.Y. Acad. Sci. (1)

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Effect of gravity on the dynamics of nonequilibrium fluctuations in a free diffusion experiment,” Ann. N.Y. Acad. Sci. 1077, 365–379 (2006).
[CrossRef] [PubMed]

Appl. Opt. (5)

Appl. Phys. Lett. (1)

D. Brogioli, A. Vailati, and M. Giglio, “Heterodyne near-field scattering,” Appl. Phys. Lett. 81, 4109–4111 (2002).
[CrossRef]

Curr. Opin. Colloid Interface Sci. (2)

R. Cerbino and A. Vailati, “Near-field scattering techniques: novel instrumentation and results from time and spatially resolved investigations of soft matter systems,” Curr. Opin. Colloid Interface Sci. 14, 416–425 (2009).
[CrossRef]

F. Scheffold and R. Cerbino, “New trends in light scattering,” Curr. Opin. Colloid Interface Sci. 12, 50–57 (2007).
[CrossRef]

Europhys. Lett. (1)

D. Brogioli, A. Vailati, and M. Giglio, “A schlieren method for ultra-low angle light scattering measurements,” Europhys. Lett. 63, 220–225 (2003).
[CrossRef]

J. R. Soc. Interface (1)

J. W. Tang, T. J. Liebner, B. A. Craven, and G. S. Settles, “A schlieren optical study of the human cough with and without wearing masks for aerosol infection control,” J. R. Soc. Interface 6, S727–S736 (2009).
[CrossRef] [PubMed]

Nature (1)

A. Vailati and M. Giglio, “Giant fluctuations in a free diffusion process,” Nature 390, 262–265 (1997).
[CrossRef]

Opt. Express (3)

Opt. Laser Technol. (1)

R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, “Knife-edge diffraction pattern as an interference phenomenon: an experimental reality,” Opt. Laser Technol. 39, 256–261 (2007).
[CrossRef]

Opt. Lasers Eng. (3)

D. R. Jonassen, G. S. Settles, and M. D. Tronosky, “Schlieren “PIV” for turbulent flows,” Opt. Lasers Eng. 44, 190–207(2006).
[CrossRef]

R. B. Owen and M. H. Johnston, “Laser shadowgraph and schlieren studies of gravity-related flow during solidification,” Opt. Lasers Eng. 2, 129–146 (1981).
[CrossRef]

H. Kleine, H. Grönig, and K. Takayama, “Simultaneous shadow, schlieren and interferometric visualization of compressible flows,” Opt. Lasers Eng. 44, 170–189(2006).
[CrossRef]

Phys. Fluids (2)

G. Jellison and C. R. Parsons, “Resonant shadowgraph and schlieren studies of magnetized laser-produced plasmas,” Phys. Fluids 24, 1787–1790 (1981).
[CrossRef]

S. P. Trainoff and D. S. Cannell, “Physical optics treatment of the shadowgraph,” Phys. Fluids 14, 1340–1363 (2002).
[CrossRef]

Phys. Rev. E (3)

F. Croccolo, D. Brogioli, A. Vailati, M. Giglio, and D. S. Cannell, “Non-diffusive decay of gradient driven fluctuations in a free-diffusion process,” Phys. Rev. E 76, 41112 (2007).
[CrossRef]

F. Ferri, D. Magatti, D. Pescini, M. A. C. Potenza, and M. Giglio, “Heterodyne near-field scattering: a technique for complex fluids,” Phys. Rev. E 70, 41405 (2004).
[CrossRef]

D. Brogioli, A. Vailati, and M. Giglio, “Universal behavior of nonequilibrium fluctuations in free diffusion processes,” Phys. Rev. E 61, R1–R4 (2000).
[CrossRef]

Phys. Rev. Lett. (2)

M. Giglio, M. Carpineti, and A. Vailati, “Space intensity correlations in the near field of the scattered light: a direct measurement of the density correlation function g(r),” Phys. Rev. Lett. 85, 1416–1419 (2000).
[CrossRef] [PubMed]

A. Duri, D. A. Sessoms, V. Trappe, and L. Cipelletti, “Resolving long-range spatial correlations in jammed colloidal systems using photon correlation imaging,” Phys. Rev. Lett. 102, 085702 (2009).
[CrossRef] [PubMed]

Pramana (2)

R. Kumar, D. Mohan, S. K. Kaura, D. P. Chhachhia, and A. K. Aggarwal, “Phase knife-edge laser schlieren diffraction interferometry with boundary diffraction wave theory,” Pramana 68, 581–589 (2007).
[CrossRef]

R. Kumar, S. K. Kaura, D. P. Chhachhia, D. Mohan, and A. K. Aggarwal, “Comparative study of different schlieren diffracting elements,” Pramana 70, 121–129 (2008).
[CrossRef]

Other (2)

F. Croccolo, R. Cerbino, A. Vailati, and M. Giglio, “Non-equilibrium fluctuations in diffusion experiments,” in Anomalous Fluctuation Phenomena in Complex Systems: Plasmas, Fluids, and Financial Markets, C.Riccardi and H.E.Roman, eds. (Research Signpost, 2008).

G. S. Settles, Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media (Springer, 2001).

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Figures (6)

Fig. 1
Fig. 1

Schemes of the physical interference of the scattered (yellow) and unscattered (magenta) beams generating the (a) shadowgraph signal and (b) schlieren signal. In both schemes, the different planes are (from left to right): sample plane, near-field image (NFI) plane, and the reconstructed near-field intensity power spectrum (NFIPS), which mimics the Fourier plane of the collecting lens.

Fig. 2
Fig. 2

Scheme of different scattering regimes: while the sample is illuminated from the left by means of a plane parallel beam, light collected at different planes provides different conditions. Starting from the sample to the right, we can have focused imaging (optical microscopy and schlieren), SINF tech niques (shadowgraph, NFS, and TLM) and SIFF techniques (dynamic light scattering, diffusion wave spectroscopy, and static light scattering).

Fig. 3
Fig. 3

Optical setup: a plane parallel beam coming from below passes through the sample cell S C and is eventually collected together with the scattered light by a lens L, which images onto the sensor S a plane at a distance z from the interface plane in the middle of the S C . Spatial filtering is performed by a movable mask M at a focal distance f after L.

Fig. 4
Fig. 4

Measures static 2D power spectra S m ( q ) obtained with the blade edge at different distances from the optical axis: (a)  10 μm schlieren , (b)  50 μm , (c)  120 μm , (d)  170 μm , (e)  2 cm shadowgraph .

Fig. 5
Fig. 5

Transition wave vector q d as a function of the distance d. Continuous curve is the theoretical prediction of Eq. (16) without any adjustable parameter.

Fig. 6
Fig. 6

Measured static power spectra S m ( q ) as a function of the wave vector q as averaged inside (continuous curve) and outside (dashed curve) the shadowgraph band.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

z z SINF = k o q D 2 ,
z z shadow = k 0 q L * 2 ,
δ E ( x ) = i · δ E · k o · δ l ( x ) ,
δ E ( q , z ) = i · δ E · k o · δ l ( q ) · e i q 2 z 2 k o f ( q ) ,
I ( x ) = | E o + δ E ( x ) | 2 = I o + δ I ( x ) I o + 2 E o Re ( δ E ( x ) ) ,
δ I ( q ) = E o [ δ E ( x ) + δ E * ( x ) ] e i q · x d x = E o [ δ E ( q ) + δ E * ( q ) ] ,
δ I ( q ) = i · E o · δ E · k o · δ I ( q ) [ f ( q ) · e i q 2 z 2 k o f ( q ) · e i q 2 z 2 k o ] .
S 1 ( q ) = | δ I ( q ) | 2 = A · k o 2 | E o δ E | 2 T ( q ) · S δ l ( q ) ,
T ( q ) = | f ( q ) e i q 2 z 2 k o f ( q ) e i q 2 z 2 k o | 2 ,
T ( q ) = [ f 2 ( q ) + f 2 ( q ) 2 f ( q ) f ( q ) cos ( 2 q 2 z 2 k o ) ] .
f ( q ) = 1 ,     q .
T ( q ) = 4 sin 2 ( q 2 z 2 k o ) .
f ( q ) = χ q x [ 0 , ] ,
T ( q ) = 1 ,
f ( q ) = χ q x [ q d , ] ,
q d = d · k o f ,
T ( q ) = 1 + χ q x [ q d , q d ] · ( 4 sin 2 ( q 2 z 2 k o ) 1 ) .
S m ( q ) = | I ( i i ( x ) ) | 2 i = C · S ( q ) · T ( q ) + B ( q ) ,

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