Abstract

A novel approach to reduce the multiple light scattering contribution in planar laser images of atomizing sprays is reported. This new technique, named Structured Laser Illumination Planar Imaging (SLIPI), has been demonstrated in the dense region of a hollow-cone water spray generated in ambient air at 50 bars injection pressure. The idea is based on using an incident laser sheet which is spatially modulated along the vertical direction. By properly shifting the spatial phase of the modulation and using post-processing of the successive recorded images, the blurring effects from multiple light scattering can be mitigated. Since hollow-cone sprays have a known inner structure in the central region, the efficiency of the method could be evaluated. We demonstrate, for the case of averaged images, that an unwanted contribution of 44% of the detected light intensity can be removed. The suppression of this diffuse light enables an increase from 55% to 80% in image contrast. Such an improvement allows a more accurate description of the near-field region and of the spray interior. The possibility of extracting instantaneous flow motion is also shown, here, for a dilute flow of water droplets. These results indicate promising applications of the technique to denser two-phase flows such as air-blast atomizer and diesel sprays.

© 2008 Optical Society of America

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References

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  1. R. J. Adrian, "Twenty years of particle image Velocimetry," Exp. Fluids 39, 159-69 (2005).
    [CrossRef]
  2. H.-G. Maas, A. Grün, and D. Papantoniou, "Particle Tracking in three dimensional turbulent flows - Part I: Photogrammetric determination of particle coordinates," Exp. Fluids. 15, 133-146 (1993).
  3. L. A. Melton and J. F. Verdieck, "Vapor/liquid visualization for fuel sprays," in Proceedings of the 20th International Symposium on Combustion (The Combustion Institute, Pittsburgh, Pa., 1984), pp. 1283-1290.
  4. A. Serpenguzel, S. Kucuksenel, and R. K. Chang, "Microdroplet identification and size measurement in sprays with lasing images," Opt. Express 10, 1118-1132 (2002).
    [PubMed]
  5. R. Domann and Y. Hardalupas, "Quantitative measurement of planar droplet Sauter mean diameter in sprays using planar droplet sizing," Part. Part. Syst. Charact. 20, 209-218 (2003).
    [CrossRef]
  6. P. LeGal, N. Farrugia, and D. A. Greenhalgh, "Laser sheet dropsizing of dense sprays," Opt. Laser Technol. 31, 75-83 (1999).
    [CrossRef]
  7. E. Berrocal, Multiple scattering of light in optical diagnostics of dense sprays and other complex turbid media (PhD Thesis, Cranfield University, 2006).
  8. E. Berrocal, I. Meglinski, and M. Jermy, "New model for light propagation in highly inhomogeneous polydisperse turbid media with applications in spray diagnostics," Opt. Express 13, 9181-9195 (2005).
    [CrossRef] [PubMed]
  9. D. Stepowski, O. Werquin, C. Roze, and T. Girasole, "Account for extinction and multiple scattering in planar droplet sizing of dense sprays," in 13th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Lisbon, 2006), paper 1061.
  10. C. T. Brown, V. G. McDonell, and D. G. Talley, "Accounting for laser extinction, signal attenuation, and secondary emission while performing optical patternation in a single plane," ILASS Americas 15th Ann. Conf. on Liquid Atomization and Spray Systems (Madison, WI: ILASS-Americas 2002).
  11. H. M. Hertz and M. Aldén, "Calibration of imaging laser-induced fluorescence measurements in highly absorbing flames," Appl. Phys. B 42, 97-102 (1987).
    [CrossRef]
  12. R. Abu-Gharbieh, J. L. Persson, M. Forsth, A. Rosen, A. Karlstrom, and T. Gustavsson, "Compensation method for attenuated planar laser images of optically dense sprays," Appl. Opt. 39, 1260-1267 (2000).
    [CrossRef]
  13. D. G. Talley, J. F. Verdieck, S. W. Lee, V. G. McDonnell, and G. S. Samuelsen, "Accounting for laser sheet extinction in applying PLLIF to sprays," paper AIAA-96-0469, presented at the Thirty-Fourth Aerospace Sciences Meeting, Reno, Nev., 15-18 Jan. 1996 (American Institute of Aeronautics and Astronautics, New York, 1996).
  14. V. Sick and B. Stojkovic, "Attenuation effects on imaging diagnostics in hollow-cone sprays," Appl. Opt. 40, 2435-2442 (2001).
    [CrossRef]
  15. H. Koh, J. Jeon, D. Kim, Y. Yoon, and J-Y Koo, "Analysis of signal attenuation for quantification of planar imaging technique," Meas. Sci. Technol. 14, 1829-39 (2003).
    [CrossRef]
  16. M. A. A. Neil, R. Juskaitis, and T. Wilson, "Method of obtaining optical sectioning by using structured light in a conventional microscope," Opt. Lett. 22, 1905-1907 (1997).
    [CrossRef]
  17. T. Breuninger, K. Greger, and E. H. K. Stelzer, "Lateral modulation boosts image quality in single plane illumination fluorescence microscopy," Opt. Lett. 32, 1938-1940 (2007).
    [CrossRef] [PubMed]
  18. S. E. D. Webb, Y. Gu, S. Lévêque-Fort, J. Siegel, M. J. Cole, K. Dowling, R. Jones, P. M. W. French, M. A. A. Neil, R. Juskaitis, L. O. D. Sucharov, T. Wilson, and M. J. Lever, "A wide-field time-domain fluorescence lifetime imaging microscope with optical sectioning," Rev. Sci. Instrum. 73, 1898-1907 (2002).
    [CrossRef]
  19. B. P. Husted, Experimental measurements of water mist systems and implications for modelling in CFD (PhD Thesis, Lund University, 2007).
  20. E. Kristensson, E. Berrocal, M. Richter, S-G. Pettersson, and M. Aldén, "High-speed structured planar laser illumination for contrast improvement of two phase flow images," Accepted for publication in Opt. Lett.

2007

2005

2003

R. Domann and Y. Hardalupas, "Quantitative measurement of planar droplet Sauter mean diameter in sprays using planar droplet sizing," Part. Part. Syst. Charact. 20, 209-218 (2003).
[CrossRef]

H. Koh, J. Jeon, D. Kim, Y. Yoon, and J-Y Koo, "Analysis of signal attenuation for quantification of planar imaging technique," Meas. Sci. Technol. 14, 1829-39 (2003).
[CrossRef]

2002

S. E. D. Webb, Y. Gu, S. Lévêque-Fort, J. Siegel, M. J. Cole, K. Dowling, R. Jones, P. M. W. French, M. A. A. Neil, R. Juskaitis, L. O. D. Sucharov, T. Wilson, and M. J. Lever, "A wide-field time-domain fluorescence lifetime imaging microscope with optical sectioning," Rev. Sci. Instrum. 73, 1898-1907 (2002).
[CrossRef]

A. Serpenguzel, S. Kucuksenel, and R. K. Chang, "Microdroplet identification and size measurement in sprays with lasing images," Opt. Express 10, 1118-1132 (2002).
[PubMed]

2001

2000

1999

P. LeGal, N. Farrugia, and D. A. Greenhalgh, "Laser sheet dropsizing of dense sprays," Opt. Laser Technol. 31, 75-83 (1999).
[CrossRef]

1997

1993

H.-G. Maas, A. Grün, and D. Papantoniou, "Particle Tracking in three dimensional turbulent flows - Part I: Photogrammetric determination of particle coordinates," Exp. Fluids. 15, 133-146 (1993).

1987

H. M. Hertz and M. Aldén, "Calibration of imaging laser-induced fluorescence measurements in highly absorbing flames," Appl. Phys. B 42, 97-102 (1987).
[CrossRef]

Abu-Gharbieh, R.

Adrian, R. J.

R. J. Adrian, "Twenty years of particle image Velocimetry," Exp. Fluids 39, 159-69 (2005).
[CrossRef]

Aldén, M.

H. M. Hertz and M. Aldén, "Calibration of imaging laser-induced fluorescence measurements in highly absorbing flames," Appl. Phys. B 42, 97-102 (1987).
[CrossRef]

E. Kristensson, E. Berrocal, M. Richter, S-G. Pettersson, and M. Aldén, "High-speed structured planar laser illumination for contrast improvement of two phase flow images," Accepted for publication in Opt. Lett.

Berrocal, E.

E. Berrocal, I. Meglinski, and M. Jermy, "New model for light propagation in highly inhomogeneous polydisperse turbid media with applications in spray diagnostics," Opt. Express 13, 9181-9195 (2005).
[CrossRef] [PubMed]

E. Kristensson, E. Berrocal, M. Richter, S-G. Pettersson, and M. Aldén, "High-speed structured planar laser illumination for contrast improvement of two phase flow images," Accepted for publication in Opt. Lett.

Breuninger, T.

Chang, R. K.

Cole, M. J.

S. E. D. Webb, Y. Gu, S. Lévêque-Fort, J. Siegel, M. J. Cole, K. Dowling, R. Jones, P. M. W. French, M. A. A. Neil, R. Juskaitis, L. O. D. Sucharov, T. Wilson, and M. J. Lever, "A wide-field time-domain fluorescence lifetime imaging microscope with optical sectioning," Rev. Sci. Instrum. 73, 1898-1907 (2002).
[CrossRef]

Domann, R.

R. Domann and Y. Hardalupas, "Quantitative measurement of planar droplet Sauter mean diameter in sprays using planar droplet sizing," Part. Part. Syst. Charact. 20, 209-218 (2003).
[CrossRef]

Dowling, K.

S. E. D. Webb, Y. Gu, S. Lévêque-Fort, J. Siegel, M. J. Cole, K. Dowling, R. Jones, P. M. W. French, M. A. A. Neil, R. Juskaitis, L. O. D. Sucharov, T. Wilson, and M. J. Lever, "A wide-field time-domain fluorescence lifetime imaging microscope with optical sectioning," Rev. Sci. Instrum. 73, 1898-1907 (2002).
[CrossRef]

Farrugia, N.

P. LeGal, N. Farrugia, and D. A. Greenhalgh, "Laser sheet dropsizing of dense sprays," Opt. Laser Technol. 31, 75-83 (1999).
[CrossRef]

Forsth, M.

French, P. M. W.

S. E. D. Webb, Y. Gu, S. Lévêque-Fort, J. Siegel, M. J. Cole, K. Dowling, R. Jones, P. M. W. French, M. A. A. Neil, R. Juskaitis, L. O. D. Sucharov, T. Wilson, and M. J. Lever, "A wide-field time-domain fluorescence lifetime imaging microscope with optical sectioning," Rev. Sci. Instrum. 73, 1898-1907 (2002).
[CrossRef]

Greenhalgh, D. A.

P. LeGal, N. Farrugia, and D. A. Greenhalgh, "Laser sheet dropsizing of dense sprays," Opt. Laser Technol. 31, 75-83 (1999).
[CrossRef]

Greger, K.

Grün, A.

H.-G. Maas, A. Grün, and D. Papantoniou, "Particle Tracking in three dimensional turbulent flows - Part I: Photogrammetric determination of particle coordinates," Exp. Fluids. 15, 133-146 (1993).

Gu, Y.

S. E. D. Webb, Y. Gu, S. Lévêque-Fort, J. Siegel, M. J. Cole, K. Dowling, R. Jones, P. M. W. French, M. A. A. Neil, R. Juskaitis, L. O. D. Sucharov, T. Wilson, and M. J. Lever, "A wide-field time-domain fluorescence lifetime imaging microscope with optical sectioning," Rev. Sci. Instrum. 73, 1898-1907 (2002).
[CrossRef]

Gustavsson, T.

Hardalupas, Y.

R. Domann and Y. Hardalupas, "Quantitative measurement of planar droplet Sauter mean diameter in sprays using planar droplet sizing," Part. Part. Syst. Charact. 20, 209-218 (2003).
[CrossRef]

Hertz, H. M.

H. M. Hertz and M. Aldén, "Calibration of imaging laser-induced fluorescence measurements in highly absorbing flames," Appl. Phys. B 42, 97-102 (1987).
[CrossRef]

Jeon, J.

H. Koh, J. Jeon, D. Kim, Y. Yoon, and J-Y Koo, "Analysis of signal attenuation for quantification of planar imaging technique," Meas. Sci. Technol. 14, 1829-39 (2003).
[CrossRef]

Jermy, M.

Jones, R.

S. E. D. Webb, Y. Gu, S. Lévêque-Fort, J. Siegel, M. J. Cole, K. Dowling, R. Jones, P. M. W. French, M. A. A. Neil, R. Juskaitis, L. O. D. Sucharov, T. Wilson, and M. J. Lever, "A wide-field time-domain fluorescence lifetime imaging microscope with optical sectioning," Rev. Sci. Instrum. 73, 1898-1907 (2002).
[CrossRef]

Juskaitis, R.

S. E. D. Webb, Y. Gu, S. Lévêque-Fort, J. Siegel, M. J. Cole, K. Dowling, R. Jones, P. M. W. French, M. A. A. Neil, R. Juskaitis, L. O. D. Sucharov, T. Wilson, and M. J. Lever, "A wide-field time-domain fluorescence lifetime imaging microscope with optical sectioning," Rev. Sci. Instrum. 73, 1898-1907 (2002).
[CrossRef]

M. A. A. Neil, R. Juskaitis, and T. Wilson, "Method of obtaining optical sectioning by using structured light in a conventional microscope," Opt. Lett. 22, 1905-1907 (1997).
[CrossRef]

Karlstrom, A.

Kim, D.

H. Koh, J. Jeon, D. Kim, Y. Yoon, and J-Y Koo, "Analysis of signal attenuation for quantification of planar imaging technique," Meas. Sci. Technol. 14, 1829-39 (2003).
[CrossRef]

Koh, H.

H. Koh, J. Jeon, D. Kim, Y. Yoon, and J-Y Koo, "Analysis of signal attenuation for quantification of planar imaging technique," Meas. Sci. Technol. 14, 1829-39 (2003).
[CrossRef]

Koo, J-Y

H. Koh, J. Jeon, D. Kim, Y. Yoon, and J-Y Koo, "Analysis of signal attenuation for quantification of planar imaging technique," Meas. Sci. Technol. 14, 1829-39 (2003).
[CrossRef]

Kristensson, E.

E. Kristensson, E. Berrocal, M. Richter, S-G. Pettersson, and M. Aldén, "High-speed structured planar laser illumination for contrast improvement of two phase flow images," Accepted for publication in Opt. Lett.

Kucuksenel, S.

LeGal, P.

P. LeGal, N. Farrugia, and D. A. Greenhalgh, "Laser sheet dropsizing of dense sprays," Opt. Laser Technol. 31, 75-83 (1999).
[CrossRef]

Lévêque-Fort, S.

S. E. D. Webb, Y. Gu, S. Lévêque-Fort, J. Siegel, M. J. Cole, K. Dowling, R. Jones, P. M. W. French, M. A. A. Neil, R. Juskaitis, L. O. D. Sucharov, T. Wilson, and M. J. Lever, "A wide-field time-domain fluorescence lifetime imaging microscope with optical sectioning," Rev. Sci. Instrum. 73, 1898-1907 (2002).
[CrossRef]

Lever, M. J.

S. E. D. Webb, Y. Gu, S. Lévêque-Fort, J. Siegel, M. J. Cole, K. Dowling, R. Jones, P. M. W. French, M. A. A. Neil, R. Juskaitis, L. O. D. Sucharov, T. Wilson, and M. J. Lever, "A wide-field time-domain fluorescence lifetime imaging microscope with optical sectioning," Rev. Sci. Instrum. 73, 1898-1907 (2002).
[CrossRef]

Maas, H.-G.

H.-G. Maas, A. Grün, and D. Papantoniou, "Particle Tracking in three dimensional turbulent flows - Part I: Photogrammetric determination of particle coordinates," Exp. Fluids. 15, 133-146 (1993).

Meglinski, I.

Neil, M. A. A.

S. E. D. Webb, Y. Gu, S. Lévêque-Fort, J. Siegel, M. J. Cole, K. Dowling, R. Jones, P. M. W. French, M. A. A. Neil, R. Juskaitis, L. O. D. Sucharov, T. Wilson, and M. J. Lever, "A wide-field time-domain fluorescence lifetime imaging microscope with optical sectioning," Rev. Sci. Instrum. 73, 1898-1907 (2002).
[CrossRef]

M. A. A. Neil, R. Juskaitis, and T. Wilson, "Method of obtaining optical sectioning by using structured light in a conventional microscope," Opt. Lett. 22, 1905-1907 (1997).
[CrossRef]

Papantoniou, D.

H.-G. Maas, A. Grün, and D. Papantoniou, "Particle Tracking in three dimensional turbulent flows - Part I: Photogrammetric determination of particle coordinates," Exp. Fluids. 15, 133-146 (1993).

Persson, J. L.

Pettersson, S-G.

E. Kristensson, E. Berrocal, M. Richter, S-G. Pettersson, and M. Aldén, "High-speed structured planar laser illumination for contrast improvement of two phase flow images," Accepted for publication in Opt. Lett.

Richter, M.

E. Kristensson, E. Berrocal, M. Richter, S-G. Pettersson, and M. Aldén, "High-speed structured planar laser illumination for contrast improvement of two phase flow images," Accepted for publication in Opt. Lett.

Rosen, A.

Serpenguzel, A.

Sick, V.

Siegel, J.

S. E. D. Webb, Y. Gu, S. Lévêque-Fort, J. Siegel, M. J. Cole, K. Dowling, R. Jones, P. M. W. French, M. A. A. Neil, R. Juskaitis, L. O. D. Sucharov, T. Wilson, and M. J. Lever, "A wide-field time-domain fluorescence lifetime imaging microscope with optical sectioning," Rev. Sci. Instrum. 73, 1898-1907 (2002).
[CrossRef]

Stelzer, E. H. K.

Stojkovic, B.

Sucharov, L. O. D.

S. E. D. Webb, Y. Gu, S. Lévêque-Fort, J. Siegel, M. J. Cole, K. Dowling, R. Jones, P. M. W. French, M. A. A. Neil, R. Juskaitis, L. O. D. Sucharov, T. Wilson, and M. J. Lever, "A wide-field time-domain fluorescence lifetime imaging microscope with optical sectioning," Rev. Sci. Instrum. 73, 1898-1907 (2002).
[CrossRef]

Webb, S. E. D.

S. E. D. Webb, Y. Gu, S. Lévêque-Fort, J. Siegel, M. J. Cole, K. Dowling, R. Jones, P. M. W. French, M. A. A. Neil, R. Juskaitis, L. O. D. Sucharov, T. Wilson, and M. J. Lever, "A wide-field time-domain fluorescence lifetime imaging microscope with optical sectioning," Rev. Sci. Instrum. 73, 1898-1907 (2002).
[CrossRef]

Wilson, T.

S. E. D. Webb, Y. Gu, S. Lévêque-Fort, J. Siegel, M. J. Cole, K. Dowling, R. Jones, P. M. W. French, M. A. A. Neil, R. Juskaitis, L. O. D. Sucharov, T. Wilson, and M. J. Lever, "A wide-field time-domain fluorescence lifetime imaging microscope with optical sectioning," Rev. Sci. Instrum. 73, 1898-1907 (2002).
[CrossRef]

M. A. A. Neil, R. Juskaitis, and T. Wilson, "Method of obtaining optical sectioning by using structured light in a conventional microscope," Opt. Lett. 22, 1905-1907 (1997).
[CrossRef]

Yoon, Y.

H. Koh, J. Jeon, D. Kim, Y. Yoon, and J-Y Koo, "Analysis of signal attenuation for quantification of planar imaging technique," Meas. Sci. Technol. 14, 1829-39 (2003).
[CrossRef]

Appl. Opt.

Appl. Phys. B

H. M. Hertz and M. Aldén, "Calibration of imaging laser-induced fluorescence measurements in highly absorbing flames," Appl. Phys. B 42, 97-102 (1987).
[CrossRef]

Exp. Fluids

R. J. Adrian, "Twenty years of particle image Velocimetry," Exp. Fluids 39, 159-69 (2005).
[CrossRef]

Exp. Fluids.

H.-G. Maas, A. Grün, and D. Papantoniou, "Particle Tracking in three dimensional turbulent flows - Part I: Photogrammetric determination of particle coordinates," Exp. Fluids. 15, 133-146 (1993).

Meas. Sci. Technol.

H. Koh, J. Jeon, D. Kim, Y. Yoon, and J-Y Koo, "Analysis of signal attenuation for quantification of planar imaging technique," Meas. Sci. Technol. 14, 1829-39 (2003).
[CrossRef]

Opt. Express

Opt. Laser Technol.

P. LeGal, N. Farrugia, and D. A. Greenhalgh, "Laser sheet dropsizing of dense sprays," Opt. Laser Technol. 31, 75-83 (1999).
[CrossRef]

Opt. Lett

E. Kristensson, E. Berrocal, M. Richter, S-G. Pettersson, and M. Aldén, "High-speed structured planar laser illumination for contrast improvement of two phase flow images," Accepted for publication in Opt. Lett.

Opt. Lett.

Part. Part. Syst. Charact.

R. Domann and Y. Hardalupas, "Quantitative measurement of planar droplet Sauter mean diameter in sprays using planar droplet sizing," Part. Part. Syst. Charact. 20, 209-218 (2003).
[CrossRef]

Rev. Sci. Instrum.

S. E. D. Webb, Y. Gu, S. Lévêque-Fort, J. Siegel, M. J. Cole, K. Dowling, R. Jones, P. M. W. French, M. A. A. Neil, R. Juskaitis, L. O. D. Sucharov, T. Wilson, and M. J. Lever, "A wide-field time-domain fluorescence lifetime imaging microscope with optical sectioning," Rev. Sci. Instrum. 73, 1898-1907 (2002).
[CrossRef]

Other

B. P. Husted, Experimental measurements of water mist systems and implications for modelling in CFD (PhD Thesis, Lund University, 2007).

E. Berrocal, Multiple scattering of light in optical diagnostics of dense sprays and other complex turbid media (PhD Thesis, Cranfield University, 2006).

D. Stepowski, O. Werquin, C. Roze, and T. Girasole, "Account for extinction and multiple scattering in planar droplet sizing of dense sprays," in 13th International Symposium on Applications of Laser Techniques to Fluid Mechanics (Lisbon, 2006), paper 1061.

C. T. Brown, V. G. McDonell, and D. G. Talley, "Accounting for laser extinction, signal attenuation, and secondary emission while performing optical patternation in a single plane," ILASS Americas 15th Ann. Conf. on Liquid Atomization and Spray Systems (Madison, WI: ILASS-Americas 2002).

L. A. Melton and J. F. Verdieck, "Vapor/liquid visualization for fuel sprays," in Proceedings of the 20th International Symposium on Combustion (The Combustion Institute, Pittsburgh, Pa., 1984), pp. 1283-1290.

D. G. Talley, J. F. Verdieck, S. W. Lee, V. G. McDonnell, and G. S. Samuelsen, "Accounting for laser sheet extinction in applying PLLIF to sprays," paper AIAA-96-0469, presented at the Thirty-Fourth Aerospace Sciences Meeting, Reno, Nev., 15-18 Jan. 1996 (American Institute of Aeronautics and Astronautics, New York, 1996).

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Figures (7)

Fig. 1.
Fig. 1.

Illustration of the conventional (a) and modulated components (b) with the resultant signal I(x’,y) in (c) for a given distance x=x’. Using three signals I(x’,y) each shifted one third of a period relative to each other, the SLIPI signal IS can be extracted as seen in (d).

Fig. 2.
Fig. 2.

Illustration of the SLIPI technique: 3 successive images are taken by illuminating different parts of the spray after shifting the spatial modulation one third of a period. When summing up the images, the conventional IC is obtained, whereas, when extracting the absolute value of the differences between the images, a new image IS is formed without most of the multiple light scattering. The modulated signal I(x’,y) is given for each image on the left side of the figure, at a given distance x=x’.

Fig. 3.
Fig. 3.

Illustration of the experimental set-up: The time separation Δt between each laser pulses (P1, P2 and P3) was 55 µs. By applying the appropriate rotation frequency, the rotating plate moved the modulated structure vertically one third of a period from pulse to pulse.

Fig. 4.
Fig. 4.

Comparison between the conventional planar Mie imaging and SLIPI for the central illumination. Each image corresponds to an average of 50 triple images. A magnified area indicated by the dashed lines in (a) is illustrated for the conventional and the SLIPI image in (c) and (d) respectively. The intensity profile along the horizontal direction is given at four vertical positions indicated by the arrows in (c).

Fig. 5.
Fig. 5.

Comparison between the conventional planar Mie imaging and SLIPI. The planar illumination is ~5mm off-axis (behind) from the nozzle centre. Each image corresponds to an average of 50 triple images. A magnified area indicated by the dashed lines in (a) is illustrated for the conventional and the SLIPI image in (c) and (d) respectively.

Fig. 7.
Fig. 7.

Comparison between conventional planar Mie imaging in (a) and (c) and SLIPI in (b) and (d) for a “single shot” triple image (see Kristensson et al. [20] for more details).

Tables (1)

Equations (5)

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

s ( x , y ) = 1 + m . cos ( 2 π ν y + Φ 0 )
I ( x , y ) = I c + I s . cos ( 2 π ν y + Φ 0 )
I S = 2 3 . [ ( I 1 I 2 ) 2 + ( I 1 I 3 ) 2 + ( I 2 I 3 ) 2 ] 1 2
and I C = I 1 + I 2 + I 3 3
C 1 = I max 1 I min I max 1 + I min and C 2 = I max 2 I min I max 2 + I min

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