Abstract

We report experimental investigations on the influence of various optical effects on the far-field scattering pattern produced by a cloud of optical bubbles near the critical scattering angle. Among the effects considered, there is the change of the relative refractive index of the bubbles (gas bubbles or some liquid–liquid droplets), the influence of intensity gradients induced by the laser beam intensity profile and by the spatial filtering of the collection optics, the coherent and multiple scattering effects occurring for densely packed bubbles, and the tilt angle of spheroidal optical bubbles. The results obtained herein are thought to be fundamental for the development of future works to model these effects and for the extension of the range of applicability of an inverse technique (referenced herein as the critical angle refractometry and sizing technique), which is used to determine the size distribution and composition of bubbly flows.

© 2011 Optical Society of America

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    [CrossRef] [PubMed]
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  31. T. Kawaguchi, Y. Akasaka, and M. Maeda, “Size measurements of droplets and bubbles by advanced interferometric laser imaging technique,” Meas. Sci. Technol. 13, 308–316(2002).
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    [CrossRef]
  37. C. Pilz and G. Brenn, “On the critical bubble volume at the rise velocity jump discontinuity in viscoelastic liquids,” J. Non-Newton. Fluid Mech. 145, 124–138 (2007).
    [CrossRef]
  38. A. Aresu, A. Martelluccia, and A. Paraboni, “Experimental assessment of rain anisotropy and canting angle in a horizontal path at 30 GHz,” IEEE Trans. Antennas Propag. Mag. 41, 1331–1335 (1993).
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2011 (2)

F. R. A. Onofri, M. Wozniak, and S. Barbosa, “On the optical characterisation of nanoparticles and their aggregates in plasma systems,” Contrib. Plasma Phys. 51, 228–236(2011).
[CrossRef]

K.-F. Ren, F. R. A. Onofri, C. Rozé, and T. Girasole, “Vectorial complex ray model and application to two-dimensional scattering of plane wave by a spheroidal particle,” Opt. Lett. 36, 370–372 (2011).
[CrossRef] [PubMed]

2010 (1)

2009 (1)

F. R. A. Onofri, M. Krzysiek, J. Mroczka, K.-F. Ren, S. Radev, and J.-P. Bonnet, “Optical characterization of bubbly flows with a near-critical-angle scattering technique,” Exp. Fluids 47, 721–732 (2009).
[CrossRef]

2007 (3)

G. P. Celata, F. D’Annibalea, P. Di Marcob, G. Memolib, and A. Tomiyama, “Measurements of rising velocity of a small bubble in a stagnant fluid in one- and two-component systems,” Exp. Therm. Fluid Sci. 31, 609–623 (2007).
[CrossRef]

C. Pilz and G. Brenn, “On the critical bubble volume at the rise velocity jump discontinuity in viscoelastic liquids,” J. Non-Newton. Fluid Mech. 145, 124–138 (2007).
[CrossRef]

F. Onofri, M. Krzysiek, and J. Mroczka, “Critical angle refractometry and sizing for bubbly flow characterization,” Opt. Lett. 32, 2070–2072 (2007).
[CrossRef] [PubMed]

2004 (2)

M. R. Vetrano, J. P. A. J. van Beeck, and M. L. Riethmuller, “Global rainbow thermometry: improvements in the data inversion algorithm and validation technique in liquid–liquid suspension,” Appl. Opt. 43, 3600–3607 (2004).
[CrossRef] [PubMed]

F. Onofri, A. Lenoble, B. Bultynck, and P. H. Guéring, “High-resolution laser diffractometry for the online sizing of small transparent fibres,” Opt. Commun. 234, 183–191 (2004).
[CrossRef]

2003 (1)

2002 (1)

T. Kawaguchi, Y. Akasaka, and M. Maeda, “Size measurements of droplets and bubbles by advanced interferometric laser imaging technique,” Meas. Sci. Technol. 13, 308–316(2002).
[CrossRef]

1999 (2)

F. Onofri, “Critical angle refractometry: for simultaneous measurement of particles in flow size and relative refractive index,” Part. Part. Syst. Charact. 16, 119–127 (1999).
[CrossRef]

J. P. A. J. van Beeck, D. Giannoulis, L. Zimmer, and M. L. Riethmuller, “Global rainbow thermometry for droplet-temperature measurement,” Opt. Lett. 24, 1696–1698 (1999).
[CrossRef]

1998 (1)

P. H. Kaye, “Spatial light scattering as a means of characterising and classifying non-spherical particles,” Meas. Sci. Technol. 9, 141–149 (1998).
[CrossRef]

1996 (1)

1995 (1)

1994 (1)

P. C. Hansen, “Regularization tools, a Matlab package for analysis and solution of discrete ill-posed problems,” Numer. Algorithms 6, 1–35 (1994).
[CrossRef]

1993 (1)

A. Aresu, A. Martelluccia, and A. Paraboni, “Experimental assessment of rain anisotropy and canting angle in a horizontal path at 30 GHz,” IEEE Trans. Antennas Propag. Mag. 41, 1331–1335 (1993).
[CrossRef]

1991 (3)

1988 (2)

1984 (1)

1981 (2)

D. L. Kingsbury and P. L. Marston, “Mie scattering near the critical angle of bubbles in water,” J. Opt. Soc. Am. A 71, 358–361 (1981).
[CrossRef]

P. L. Marston and D. L. Kingsbury, “Scattering by a bubble in water near the critical angle: interference effects,” J. Opt. Soc. Am. A 71, 358–361 (1981).
[CrossRef]

1979 (1)

P. L. Marston, “Critical scattering angle by a bubble: physical optics approximation and observations,” J. Opt. Soc. Am. A 69, 1205–1211 (1979).
[CrossRef]

1976 (1)

J. R. Grace, T. Wairegi, and Т. Н. Nguyen, “Shapes and velocities of single drops and bubbles moving freely through immiscible liquids,” Trans. Inst. Chem. Eng. 54, 167–173(1976).

1971 (1)

H. K. V. Lötsch, “Beam displacement at total reflection: the Goos-Hänchen effect,” Optik 32, 553–569 (1971).

1955 (1)

G. E. Davis, “Scattering of light by an air bubble in water,” J. Opt. Soc. Am. A 45, 572–581 (1955).
[CrossRef]

Akasaka, Y.

T. Kawaguchi, Y. Akasaka, and M. Maeda, “Size measurements of droplets and bubbles by advanced interferometric laser imaging technique,” Meas. Sci. Technol. 13, 308–316(2002).
[CrossRef]

Aresu, A.

A. Aresu, A. Martelluccia, and A. Paraboni, “Experimental assessment of rain anisotropy and canting angle in a horizontal path at 30 GHz,” IEEE Trans. Antennas Propag. Mag. 41, 1331–1335 (1993).
[CrossRef]

Arnott, W. P.

Barbastathis, G.

Barber, S. C.

S. C. Barber, and P. W. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990).
[CrossRef]

Barbosa, S.

F. R. A. Onofri, M. Wozniak, and S. Barbosa, “On the optical characterisation of nanoparticles and their aggregates in plasma systems,” Contrib. Plasma Phys. 51, 228–236(2011).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1988).

Bonnet, J.-P.

F. R. A. Onofri, M. Krzysiek, J. Mroczka, K.-F. Ren, S. Radev, and J.-P. Bonnet, “Optical characterization of bubbly flows with a near-critical-angle scattering technique,” Exp. Fluids 47, 721–732 (2009).
[CrossRef]

Brenn, G.

C. Pilz and G. Brenn, “On the critical bubble volume at the rise velocity jump discontinuity in viscoelastic liquids,” J. Non-Newton. Fluid Mech. 145, 124–138 (2007).
[CrossRef]

Bultynck, B.

F. Onofri, A. Lenoble, B. Bultynck, and P. H. Guéring, “High-resolution laser diffractometry for the online sizing of small transparent fibres,” Opt. Commun. 234, 183–191 (2004).
[CrossRef]

Celata, G. P.

G. P. Celata, F. D’Annibalea, P. Di Marcob, G. Memolib, and A. Tomiyama, “Measurements of rising velocity of a small bubble in a stagnant fluid in one- and two-component systems,” Exp. Therm. Fluid Sci. 31, 609–623 (2007).
[CrossRef]

D’Annibalea, F.

G. P. Celata, F. D’Annibalea, P. Di Marcob, G. Memolib, and A. Tomiyama, “Measurements of rising velocity of a small bubble in a stagnant fluid in one- and two-component systems,” Exp. Therm. Fluid Sci. 31, 609–623 (2007).
[CrossRef]

Davis, G. E.

G. E. Davis, “Scattering of light by an air bubble in water,” J. Opt. Soc. Am. A 45, 572–581 (1955).
[CrossRef]

Dean, C. E.

Di Marcob, P.

G. P. Celata, F. D’Annibalea, P. Di Marcob, G. Memolib, and A. Tomiyama, “Measurements of rising velocity of a small bubble in a stagnant fluid in one- and two-component systems,” Exp. Therm. Fluid Sci. 31, 609–623 (2007).
[CrossRef]

Domínguez-Caballero, J. A.

Fiedler-Ferrari, N.

N. Fiedler-Ferrari, H. M. Nussenzweig, and W. J. Wiscombe, “Theory of near-critical-angle scattering from a curved interface,” Phys. Rev. A 43, 1005–1038 (1991).
[CrossRef] [PubMed]

Giannoulis, D.

Girasole, T.

K.-F. Ren, F. R. A. Onofri, C. Rozé, and T. Girasole, “Vectorial complex ray model and application to two-dimensional scattering of plane wave by a spheroidal particle,” Opt. Lett. 36, 370–372 (2011).
[CrossRef] [PubMed]

G. Gréhan, F. Onofri, T. Girasole, and G. Gouesbet, “Measurement of bubbles by phase Doppler technique and trajectory ambiguity,” in Developments in Laser Techniques and Applications to Fluid Mechanics, R. J.Adrian, D.F. G.Durao, F.Durst, M.V.Heitor, M.Maeda, and J.Whitelaw, eds. (Springer, 1994), pp. 290–302.

Gouesbet, G.

F. Onofri, G. Gréhan, and G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
[CrossRef] [PubMed]

G. Gouesbet, B. Maheu, and G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443(1988).
[CrossRef]

G. Gréhan, F. Onofri, T. Girasole, and G. Gouesbet, “Measurement of bubbles by phase Doppler technique and trajectory ambiguity,” in Developments in Laser Techniques and Applications to Fluid Mechanics, R. J.Adrian, D.F. G.Durao, F.Durst, M.V.Heitor, M.Maeda, and J.Whitelaw, eds. (Springer, 1994), pp. 290–302.

Grace, J. R.

J. R. Grace, T. Wairegi, and Т. Н. Nguyen, “Shapes and velocities of single drops and bubbles moving freely through immiscible liquids,” Trans. Inst. Chem. Eng. 54, 167–173(1976).

Gréhan, G.

F. Onofri, G. Gréhan, and G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
[CrossRef] [PubMed]

G. Gouesbet, B. Maheu, and G. Gréhan, “Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation,” J. Opt. Soc. Am. A 5, 1427–1443(1988).
[CrossRef]

G. Gréhan, F. Onofri, T. Girasole, and G. Gouesbet, “Measurement of bubbles by phase Doppler technique and trajectory ambiguity,” in Developments in Laser Techniques and Applications to Fluid Mechanics, R. J.Adrian, D.F. G.Durao, F.Durst, M.V.Heitor, M.Maeda, and J.Whitelaw, eds. (Springer, 1994), pp. 290–302.

Guéring, P. H.

F. Onofri, A. Lenoble, B. Bultynck, and P. H. Guéring, “High-resolution laser diffractometry for the online sizing of small transparent fibres,” Opt. Commun. 234, 183–191 (2004).
[CrossRef]

Hansen, P. C.

P. C. Hansen, “Regularization tools, a Matlab package for analysis and solution of discrete ill-posed problems,” Numer. Algorithms 6, 1–35 (1994).
[CrossRef]

Hanson, R. J.

C. L. Lawson and R. J. Hanson, Solving Least Squares Problems (Prentice Hall, 1974).

Hill, P. W.

S. C. Barber, and P. W. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990).
[CrossRef]

Huffman, D. R.

C. F. Bohren, D. R. Huffman, and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1988).

C. F. Bohren, D. R. Huffman, and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1988).

Kawaguchi, T.

T. Kawaguchi, Y. Akasaka, and M. Maeda, “Size measurements of droplets and bubbles by advanced interferometric laser imaging technique,” Meas. Sci. Technol. 13, 308–316(2002).
[CrossRef]

Kaye, P. H.

P. H. Kaye, “Spatial light scattering as a means of characterising and classifying non-spherical particles,” Meas. Sci. Technol. 9, 141–149 (1998).
[CrossRef]

Kingsbury, D. L.

P. L. Marston and D. L. Kingsbury, “Scattering by a bubble in water near the critical angle: interference effects,” J. Opt. Soc. Am. A 71, 358–361 (1981).
[CrossRef]

D. L. Kingsbury and P. L. Marston, “Mie scattering near the critical angle of bubbles in water,” J. Opt. Soc. Am. A 71, 358–361 (1981).
[CrossRef]

Krzysiek, M.

F. R. A. Onofri, M. Krzysiek, J. Mroczka, K.-F. Ren, S. Radev, and J.-P. Bonnet, “Optical characterization of bubbly flows with a near-critical-angle scattering technique,” Exp. Fluids 47, 721–732 (2009).
[CrossRef]

F. Onofri, M. Krzysiek, and J. Mroczka, “Critical angle refractometry and sizing for bubbly flow characterization,” Opt. Lett. 32, 2070–2072 (2007).
[CrossRef] [PubMed]

M. Krzysiek, “Particle systems characterization by inversion of critical light scattering patterns,” Ph.D. dissertation (University of Provence, 2009).

Langley, D. S.

Lawson, C. L.

C. L. Lawson and R. J. Hanson, Solving Least Squares Problems (Prentice Hall, 1974).

Lenoble, A.

F. Onofri, A. Lenoble, B. Bultynck, and P. H. Guéring, “High-resolution laser diffractometry for the online sizing of small transparent fibres,” Opt. Commun. 234, 183–191 (2004).
[CrossRef]

Lock, J. A.

Loomis, N.

Lötsch, H. K. V.

H. K. V. Lötsch, “Beam displacement at total reflection: the Goos-Hänchen effect,” Optik 32, 553–569 (1971).

Maeda, M.

T. Kawaguchi, Y. Akasaka, and M. Maeda, “Size measurements of droplets and bubbles by advanced interferometric laser imaging technique,” Meas. Sci. Technol. 13, 308–316(2002).
[CrossRef]

Maheu, B.

Marston, P. L.

Martelluccia, A.

A. Aresu, A. Martelluccia, and A. Paraboni, “Experimental assessment of rain anisotropy and canting angle in a horizontal path at 30 GHz,” IEEE Trans. Antennas Propag. Mag. 41, 1331–1335 (1993).
[CrossRef]

Memolib, G.

G. P. Celata, F. D’Annibalea, P. Di Marcob, G. Memolib, and A. Tomiyama, “Measurements of rising velocity of a small bubble in a stagnant fluid in one- and two-component systems,” Exp. Therm. Fluid Sci. 31, 609–623 (2007).
[CrossRef]

Mroczka, J.

F. R. A. Onofri, M. Krzysiek, J. Mroczka, K.-F. Ren, S. Radev, and J.-P. Bonnet, “Optical characterization of bubbly flows with a near-critical-angle scattering technique,” Exp. Fluids 47, 721–732 (2009).
[CrossRef]

F. Onofri, M. Krzysiek, and J. Mroczka, “Critical angle refractometry and sizing for bubbly flow characterization,” Opt. Lett. 32, 2070–2072 (2007).
[CrossRef] [PubMed]

Nguyen, ?. ?.

J. R. Grace, T. Wairegi, and Т. Н. Nguyen, “Shapes and velocities of single drops and bubbles moving freely through immiscible liquids,” Trans. Inst. Chem. Eng. 54, 167–173(1976).

Nussenzweig, H. M.

N. Fiedler-Ferrari, H. M. Nussenzweig, and W. J. Wiscombe, “Theory of near-critical-angle scattering from a curved interface,” Phys. Rev. A 43, 1005–1038 (1991).
[CrossRef] [PubMed]

H. M. Nussenzweig, Diffraction Effects in Semiclassical Scattering (Cambridge University, 1992).
[CrossRef]

Onofri, F.

F. Onofri, M. Krzysiek, and J. Mroczka, “Critical angle refractometry and sizing for bubbly flow characterization,” Opt. Lett. 32, 2070–2072 (2007).
[CrossRef] [PubMed]

F. Onofri, A. Lenoble, B. Bultynck, and P. H. Guéring, “High-resolution laser diffractometry for the online sizing of small transparent fibres,” Opt. Commun. 234, 183–191 (2004).
[CrossRef]

F. Onofri, “Critical angle refractometry: for simultaneous measurement of particles in flow size and relative refractive index,” Part. Part. Syst. Charact. 16, 119–127 (1999).
[CrossRef]

F. Onofri, G. Gréhan, and G. Gouesbet, “Electromagnetic scattering from a multilayered sphere located in an arbitrary beam,” Appl. Opt. 34, 7113–7124 (1995).
[CrossRef] [PubMed]

G. Gréhan, F. Onofri, T. Girasole, and G. Gouesbet, “Measurement of bubbles by phase Doppler technique and trajectory ambiguity,” in Developments in Laser Techniques and Applications to Fluid Mechanics, R. J.Adrian, D.F. G.Durao, F.Durst, M.V.Heitor, M.Maeda, and J.Whitelaw, eds. (Springer, 1994), pp. 290–302.

Onofri, F. R. A.

F. R. A. Onofri, M. Wozniak, and S. Barbosa, “On the optical characterisation of nanoparticles and their aggregates in plasma systems,” Contrib. Plasma Phys. 51, 228–236(2011).
[CrossRef]

K.-F. Ren, F. R. A. Onofri, C. Rozé, and T. Girasole, “Vectorial complex ray model and application to two-dimensional scattering of plane wave by a spheroidal particle,” Opt. Lett. 36, 370–372 (2011).
[CrossRef] [PubMed]

F. R. A. Onofri, M. Krzysiek, J. Mroczka, K.-F. Ren, S. Radev, and J.-P. Bonnet, “Optical characterization of bubbly flows with a near-critical-angle scattering technique,” Exp. Fluids 47, 721–732 (2009).
[CrossRef]

Paraboni, A.

A. Aresu, A. Martelluccia, and A. Paraboni, “Experimental assessment of rain anisotropy and canting angle in a horizontal path at 30 GHz,” IEEE Trans. Antennas Propag. Mag. 41, 1331–1335 (1993).
[CrossRef]

Pilz, C.

C. Pilz and G. Brenn, “On the critical bubble volume at the rise velocity jump discontinuity in viscoelastic liquids,” J. Non-Newton. Fluid Mech. 145, 124–138 (2007).
[CrossRef]

Radev, S.

F. R. A. Onofri, M. Krzysiek, J. Mroczka, K.-F. Ren, S. Radev, and J.-P. Bonnet, “Optical characterization of bubbly flows with a near-critical-angle scattering technique,” Exp. Fluids 47, 721–732 (2009).
[CrossRef]

Ren, K.-F.

K.-F. Ren, F. R. A. Onofri, C. Rozé, and T. Girasole, “Vectorial complex ray model and application to two-dimensional scattering of plane wave by a spheroidal particle,” Opt. Lett. 36, 370–372 (2011).
[CrossRef] [PubMed]

F. R. A. Onofri, M. Krzysiek, J. Mroczka, K.-F. Ren, S. Radev, and J.-P. Bonnet, “Optical characterization of bubbly flows with a near-critical-angle scattering technique,” Exp. Fluids 47, 721–732 (2009).
[CrossRef]

Riethmuller, M. L.

Rozé, C.

Tian, L.

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Figures (18)

Fig. 1
Fig. 1

Intensity of the electromagnetic field inside and around an air bubble in water ( D = 100 μm ) , m b = 1.0 , m s = 1.333 illuminated by a parallel polarized plane wave ( λ 0 = 0.532 μm ) .

Fig. 2
Fig. 2

Experimental setup : tank (1), probe volume (2), laser (3), polarization maintaining single-mode fiber (4), beam expander (5), λ / 2 plate (6), mirror (7), collection optics (8), spatial filter (9), achromatic doublets (10), interference filter (11), digital CCD camera (12), goniometer (13), interferometric laser imaging system (14), flash lamp (15), shadowgraphy's collection system and camera (16), optical triggering system (17), and drop-on-demand injector (18).

Fig. 3
Fig. 3

Coordinate systems used.

Fig. 4
Fig. 4

Comparisons of the CARS results for water-glycerin bubbles of different mixing fractions: (a) mean diameter and (b) relative refractive index.

Fig. 5
Fig. 5

CARS response (without recalibration) to a change of the surrounding fluid composition: (a) diameter and (b) refractive index.

Fig. 6
Fig. 6

Raw critical scattering patterns and the corresponding intensity profiles for 25 positions of the bubbles within the x z plane and three values of the spatial filter aperture: (a)  23 mm , (b)  13 mm , and (c)  6 mm . Rows and columns correspond to x = 4 , 2 , , 4 mm and z = 4 , 2 , , 4 mm , respectively.

Fig. 7
Fig. 7

Effects of spatial filter aperture on critical scattering patterns and the CARS (log-norm) statistics.

Fig. 8
Fig. 8

Twins bubbles: critical scattering patterns and shadowgraphy images obtained when the bubbles are (a) parallel or (b) perpendicular to the collection optics axis; interbubble distance 1.1 D with D = 705 μm . The angular mean intensity profiles are averaged along the height of the extraction zone (i.e., 1.5 ° ).

Fig. 9
Fig. 9

Twins bubbles: experimental and reconstructed critical scattering patterns (log-norm) intensity profiles.

Fig. 10
Fig. 10

Critical scattering patterns produced by (a) dilute and (b) dense aggregates of water bubbles sinking in silicon oil.

Fig. 11
Fig. 11

Bubble aggregates: experimental and reconstructed intensity profiles corresponding to Fig. 10.

Fig. 12
Fig. 12

Bubble aggregates: comparison between shadowgraphy and CARS reconstructed bubble size distributions for Fig. 10b.

Fig. 13
Fig. 13

Bubble aggregates: CARS and shadowgraphy imaging technique estimation of the first two moments of the bubble size distribution.

Fig. 14
Fig. 14

Effects of the position of a bubble curtain onto critical scattering patterns and a shadowgraphy image.

Fig. 15
Fig. 15

Shadowgraphy image, measured and reconstructed critical scattering patterns of an elliptical air bubble in water with a large axis in the scattering plane.

Fig. 16
Fig. 16

Same results in Fig. 15 but for a bubble with a tilt angle, δ = 25 ° .

Fig. 17
Fig. 17

CARS estimation of the bubble size distribution of monodisperse tilted ellipsoidal bubbles.

Fig. 18
Fig. 18

Statistics obtained for ellipsoidal bubbles with various tilt angles.

Tables (2)

Tables Icon

Table 1 Statistics for Various Spatial Filter Apertures

Tables Icon

Table 2 Statistics for Various Positions of the Curtain of Bubbles

Equations (3)

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

I ¯ N 0 I ( θ , D , m , λ 0 ) f ( D ) d D ,
r F 2 = Min F > 0 S · F I ¯ 2 ,
m = { m n | M i n ( r F 2 ) } .

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