Abstract
This review highlights the various electromagnetic methods, geometrical and physical optics approximations developed so far in the literature to predict the light scattering properties of large bubbles in an optically dilute regime. The underlying problematic is essentially linked to the characterization of bubbly flows or, more generally, multiphase flows, where most optical diagnostics are based on the analysis of the scattering diagrams, caustics and singularities with interferometric or diffractometric techniques.
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References
Abramowitz M, Stegun IA (1965) Handbook of mathematical functions. Dover Inc, New York
Adam JA (2002) The mathematical physics of rainbows and glories. Phys Rep 356(4–5):229–365
Aiello A, Woerdman J (2008) Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts. Opt Lett 33(13):1437–1439
Arnott WP, Marston PL (1988) Optical glory of small freely rising gas bubbles in water: observed and computed cross-polarized backscattering patterns. J Opt Soc Am A 5(4):496–506
Artmann K (1948) Berechnung der Seitenversetzung des totalreflektierten Strahles. Ann Phys 437(1–2):87–102
Asano S, Yamamoto G (1975) Light scattering by a spheroidal particle. Appl Opt 14(1):29–49
Barber SC, Hill PW (1990) Light scattering by particles: computational methods. World Scientific, Singapore
Barton JP (1997) Electromagnetic-field calculations for a sphere illuminated by a higher-order Gaussian beam. I. Internal and near-field effects. Appl Opt 36(6):1303–1311
Berman P (2012) Goos-Hänchen effect. Scholarpedia 7(3):11584
Bhandari R (1985) Scattering coefficients for a multilayered sphere: analytic expressions and algorithms. Appl Opt 24(13):1960–1967
Bohren CF, Clothiaux EE (2008) Fundamentals of atmospheric radiation: an introduction with 400 problems. Wiley VCH, Weinheim
Bohren CF, Huffman DR (1998) Absorption and scattering of light by small particles. Wiley, New York
Borghese F, Denti P, Saija R (1994) Optical properties of spheres containing several spherical inclusions. Appl Opt 33(3):484–493
Bosbach J, Kühn M, Wagner C (2009) Large scale particle image velocimetry with helium filled soap bubbles. Exp Fluids 46(3):539–547
Brennen CE (1995) Cavitation and bubble dynamics. Oxford University Press, Oxford
Bunkin NF, Suyazov NV, Shkirin AV, Ignatiev PS, Indukaev KV (2009) Nanoscale structure of dissolved air bubbles in water as studied by measuring the elements of the scattering matrix. J Chem Phys 130(13):134308
Bunner B, Tryggvason G (1999) Direct numerical simulations of three-dimensional bubbly flows. Phys Fluids 11:1967–1969
Celata GP, D’Annibale F, Di Marco P, Memoli G, Tomiyama A (2007) Measurements of rising velocity of a small bubble in a stagnant fluid in one- and two-component systems. Exp Thermal Fluid Sci 31(6):609–623
Chang SC, Jin JM, Jin J, Zhang S (1996) Computations of special functions. Wiley, New York
Clift R, Grace JR, Weber ME (1978) Bubbles drops and particles. Academic Press, New York
Cooke DD, Kerker M (1969) Light scattering from long thin glass cylinders at oblique incidence. J Opt Soc Am A 59(1):43–48
Cooray MFR, Ciric IR (1993) Wave scattering by a chiral spheroid. J Opt Soc Am A 10(6):1197–1203
Dave JV (1969) Scattering of visible light by large water spheres. Appl Opt 8(1):155–164
Davis GE (1955) Scattering of light by an air bubble in water. J Opt Soc Am A 45(7):572–581
Debye P (1909) Der lichtdruck auf kugeln von beliebigem material. Ann Phys 30:57–136
Dehaeck S, van Beeck JPAJ, Riethmuller ML (2005) Extended glare point velocimetry and sizing for bubbly flows. Exp Fluids 39(2):407–419
Deschamps GA (1972) Ray techniques in electromagnetics. Proc IEEE 60:1022–1035
Draine BT, Flatau PJ (1994) Discrete-dipole approximation for scattering calculations. J Opt Soc Am A 11(4):1491–1499
Eremina E, Wriedt T, Eremin Y (2006) Discrete sources method for analysis of a light scattering by an air bubble on resist for immersion lithography. J Quant Spectrosc Radiat Transf 100:131–136
Farafonov VG, Voshchinnikov NV, Somsikov VV (1996) Light scattering by a core–mantle spheroidal particle. Appl Opt 35(27):5412–5426
Felsen LB (1984) Geometrical theory of diffraction, evanescent waves, complex rays and Gaussian beams. Geophys J Int 79(1):77–88
Fiedler-Ferrari N (1983) Espalhamento de Mie na Vizinhanca do angulo critico. PhD thesis, University of SĂŁo Paulo
Fiedler-Ferrari N, Nussenzveig HM, Wiscombe WJ (1991) Theory of near-critical-angle scattering from a curved interface. Phys Rev A 43(2):1005–1038
Fowles GR (1987) Introduction to modern optics. Dover books on physics. Dover Publications, New York
Goodman JW (1960) Introduction to fourier optic. McGraw-Hill, New York
Goos F, Hänchen H (1947) Ein neuer und fundamentaler Versuch zur Totalreflexion. Ann Phys 436(7–8):333–346
Gordon HR, Boynton GC (1998) Radiance–irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: vertically stratified water bodies. Appl Opt 37(18):3886–3896
Gouesbet G, Gréhan G (2011) Generalized Lorenz-Mie theories. Springer, Berlin
Gouesbet G, Lock JA (1994) Rigourous justification of the localized approximation to the beam shape coefficients in the generalized Lorenz-Mie theory. Part 1: Off-axis beams. J Opt Soc Am A 11(9):2503–2515
Gouesbet G, Maheu B, Gréhan G (1988) Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation. J Opt Soc Am A 5(9):1427–1443
Grace JR (1973) Shapes and velocities of bubbles rising in infinite liquids. T I Chem Eng Lond 51:116–120
Gréhan G, Onofri F, Girasole T, Gouesbet G, Durst G, Tropea C (1996) Measurement of bubbles by phase doppler technique and trajectory ambiguity. In: Adrian RJ, Durão DFG, Durst F, Heitor MV, Maeda M, Whitelaw JH (eds) Developments in laser techniques and applications to fluid mechanics: Proceedings of the 7th international symposium Lisbon, Portugal, 11–14 July 1994, pp 290–302. Springer
He H, Li W, Zhang X, Xia M, Yang K (2012) Light scattering by a spheroidal bubble with geometrical optics approximation. J Quant Spectrosc Radiat Transf 113(12):1467–1475
Hergert W, Wriedt T (2012) The Mie theory: basics and applications. Springer series in optical sciences. Springer-Verlag
Hovenac EA (1991) Calculation of far-field scattering from nonspherical particles using a geometrical optics approach. Appl Opt 30(33):4739–4746
Hovenac EA, Lock JA (1992) Assessing the contribution of surface waves and complex rays to far-field scattering by use of the Debye series. J Opt Soc Am A 9(5):781–795
Jiang K, Han X, Ren KF (2013) Scattering of a Gaussian beam by an elliptical cylinder using the vectorial complex ray model. J Opt Soc Am A 30(8):1548–1556
Johnson BD, Cooke RC (1981) Generation of stabilized microbubbles in seawater. Science 213(4504):209–211
Jonasz M, Fournier G (2007a) Light scattering by particles in water: theoretical and experimental foundations. Academic Press, New York
Jonasz M, Fournier GR (2007b) Chapter 2—Optical properties of pure water, seawater, and natural waters. In: Light Scattering by Particles in Water. Academic Press, Amsterdam, pp 33–85
Jonasz M, Fournier GR (2007c) Chapter 4—Measurements of light scattering by particles in water. In: Light scattering by particles in water. Academic Press, New York, pp 145–265
Jörg BG, Susumu S, Martina H (2013) Are Fresnel filtering and the angular Goos-Hänchen shift the same? J Opt 15(1):014009
Keller JB (1962) Geometrical theory of diffraction. J Opt Soc Am A 52(2):116–130
Kerker M (1969) The scattering of light and other electromagnetic radiation. Academic Press, New York
Kingsbury DL, Marston PL (1981) Mie scattering near the critical angle of bubbles in water. J Opt Soc Am A 71(3):358–361
Kita-Tokarczyk K, Grumelard J, Haefele T, Meier W (2005) Block copolymer vesicles—using concepts from polymer chemistry to mimic biomembranes. Polymer 46(11):3540–3563
Kokhanovsky A (2006) Cloud optics. Kokhanovsky, Alexander Springer
Krzysiek M (2009) Particle systems characterization by inversion of critical light scattering patterns. PhD thesis, Aix-Marseille University
Lamadie F, Bruel L, Himbert M (2012) Digital holographic measurement of liquid–liquid two-phase flows. Opt Lasers Eng 50(12):1716–1725
Langley DS, Marston PL (1984) Critical-angle scattering of laser light from bubbles in water: measurements, models, and application to sizing of bubbles. Appl Opt 23(7):1044–1054
Latham L (2017) Where to find bubbles in nature. Available online at url-http://frogmom.com/bubbles-in-nature/
Lin CH, Wang LA (2005) Simulation of air bubble scattering effects in 193 nm immersion interferometric lithography. J Vac Sci Technol B 23(6):2684–2693
Liping S, Deming R, Yanchen Q, Weijiang Z, Xiaoyong H (2006) Study on dirty bubbles of volumetric scattering function in ship wakes. In: Conference on lasers and electro-optics/quantum electronics and laser science conference and photonic applications systems technologies, Long Beach, California, 2006/05/21 2006. Technical Digest (CD), p CFD6. Optical Society of America
Lock JA (1996a) Ray scattering by an arbitrarily oriented spheroid. I. Diffraction and specular reflection. Appl Opt 35(3):500–514
Lock JA (1996b) Ray scattering by an arbitrarily oriented spheroid. II. Transmission and cross-polarization effects. Appl Opt 35(3):515–531
Lock JA (2003) Role of the tunneling ray in near-critical-angle scattering by a dielectric sphere. J Opt Soc Am A 20:499–507
Lock JA (2008) Scattering of an electromagnetic plane wave by a Luneburg lens. III. Finely stratified sphere model. J Opt Soc Am A 25(12):2991–3000
Lock JA, Adler CL (1997) Debye-series analysis of the first-order rainbow produced in scattering of a diagonally incident plane wave by a circular cylinder. J Opt Soc Am A 14(6):1316–1328
Lotsch HKV (1968) Reflection and refraction of a beam of light at a plane interface. J Opt Soc Am A 58(4):551–561
Lotsch HKV (1971) Beam displacement at total reflection: the Goos-Hänchen effect. Optick 32:553–569
Macke A, Mishchenko MI (1996) Applicability of regular particle shapes in light scattering calculations for atmospheric ice particles. Appl Opt 35(21):4291–4296
Marston PL (1979) Critical angle scattering by a bubble: physical-optics approximation and observations. J Opt Soc Am A 69(9):1205–1211
Marston PL (1992) 1 - Geometrical and catastrophe optics methods in scattering. In: Pierce AD, Thurston RN (eds) Physical acoustics, vol 21. Academic Press, Boston, pp 1–234
Marston PL (1999) light scattering by bubbles in liquids and applications to physical acoustics. In: Crum LA, Mason TJ, Reisse JL, Suslick KS (eds) Sonochemistry and Sonoluminescence. Springer, pp. 73–86
Marston PL (2015) Surprises and anomalies in acoustical and optical scattering and radiation forces. J Quant Spectrosc Radiat Transf 162:8–17
Marston PL, Kingsbury DL (1981) Scattering by a bubble in water near the critical angle: interference effects. J Opt Soc Am A 71(2):192–196
Marston PL, Langley DS, Kingsbury DL (1982) Light scattering by bubbles in liquids: Mie theory, physical-optics approximations, and experiments. Appl Sci Res 38(1):373–383
Mees L, Gréhan G, Gouesbet G (2001) Time-resolved scattering diagrams for a sphere illuminated by plane wave and focused short pulses. Opt Commun 194(1–3):59–65
Merano M, Aiello A, t’Hooft G, Van Exter M, Eliel E, Woerdman J (2007) Observation of Goos-Hänchen shifts in metallic reflection. Opt Express 15(24):15928–15934
Mie G (1908) Beiträge zur Optik Trüber Medien Speziell Kolloidaler Metallösungen. Ann Phys 330(3):377–445
Minnaert M (1980) The nature of light & colour in the open air. Dover Publications, New York
Mishchenko MI, Travis LD (1998) Capabilities and limitations of a current FORTRAN implementation of the T-matrix method for randomly oriented, rotationally symmetric scatterers. J Quant Spectrosc Radiat Transf 60(3):309
Mishchenko MI, Travis LD, Lacis AA (2006) Multiple scattering of light by particles: radiative transfer and coherent backscattering. Cambridge University Press, Cambridge
Mitri FG (2011) Arbitrary scattering of an electromagnetic zero-order Bessel beam by a dielectric sphere. Opt Lett 36(5):766–768
Muinonen K, Nousiainen T, Fast P, Lumme K, Peltoniemi JI (1996) Light scattering by Gaussian random particles: ray optics approximation. J Quant Spectrosc Radiat Transf 55(5):577–601
Nussenzveig HM (1992) Diffraction effects in semiclassical scattering. Cambridge University Press, Cambridge
Nye JF (1999) Natural focusing and fine structure of light: caustics and wave dislocations. IOP Publishing Ltd, Bristol
Onofri F (1999) Critical angle refractometry for simultaneous measurement of particles in flow: size and relative refractive index. Part Part Syst Char 16(3):119–127
Onofri F, Gréhan G, Gouesbet G (1995) Electromagnetic scattering from a multilayered sphere located in an arbitrary beam. Appl Opt 34(30):7113–7124
Onofri F, Blondel D, Gréhan G, Gouesbet G (1996) On the optical diagnosis and sizing of spherical coated and multilayered particles with phase-doppler anemometry. Part Part Syst Char 13(2):104–111
Onofri F, Lenoble A, Bultynck H, Guéring P-H (2004) High-resolution laser diffractometry for the on-line sizing of small transparent fibres. Opt Commun 234(1–6):183–191
Onofri F, Krysiek M, Mroczka J (2007a) Critical angle refractometry and sizing of bubble clouds. Opt Lett 32(14):2070–2072
Onofri F, Lenoble A, Radev S, Guering P-H (2007b) High resolution monitoring of an unsteady glass fibre drawing process. Exp Fluids 42(4):601–610
Onofri FA, Krzysiek M, Mroczka J, Ren K-F, Radev S, Bonnet J-P (2009) Optical characterization of bubbly flows with a near-critical-angle scattering technique. Exp Fluids 47(4–5):721–732
Onofri FRA, Krzysiek MA, Barbosa S, Messager V, Ren K-F, Mroczka J (2011) Near-critical-angle scattering for the characterization of clouds of bubbles: particular effects. Appl Opt 50(30):5759–5769
Onofri FRA, Radev S, Sentis M, Barbosa S (2012) Physical-optics approximation of near-critical-angle scattering by spheroidal bubbles. Opt Lett 37(22):4780–4782
Onofri FRA, Ren KF, Sentis M, Gaubert Q, Pelcé C (2015) Experimental validation of the vectorial complex ray model on the inter-caustics scattering of oblate droplets. Opt Express 23(12):15768–15773
Prosperetti A, Tryggvason G (2007) Computational methods for multiphase flow. Cambridge University Press, Cambridge
Puri A, Birman JL (1986) Goos-Hänchen beam shift at total internal reflection with application to spatially dispersive media. J Opt Soc Am A 3(4):543–549
Reinhard L, Martin B, Rumiana D, Thomas F, Jan K, Xinzhao Z (2005) Droplets, bubbles, and vesicles at chemically structured surfaces. J Phys Condens Mat 17(9):S537
Ren KF, Gréhan G, Gouesbet G (1997) Scattering of a Gaussian beam by an infinite cylinder in the framework of generalized Lorenz-Mie theory: formulation and numerical results. J Opt Soc Am A 14(11):3014–3025
Ren KF, Onofri F, Rozé C, Girasole T (2011) Vectorial complex ray model and application to two-dimensional scattering of plane wave by a spheroidal particle. Opt Lett 36(3):370–372
Renard RH (1964) Total reflection: a new evaluation of the Goos-Hänchen shift. J Opt Soc Am A 54(10):1190–1196
Salkin L, Schmit A, Panizza P, Courbin L (2016) Generating soap bubbles by blowing on soap films. Phys Rev Lett 116(7):077801
Sentis M, Onofri FRA, Dhez O, Laurent J-Y, Chauchard F (2015) Organic photo sensors for multi-angle light scattering characterization of particle systems. Opt Express 23(21):27536–27541
Sentis MPL, Onofri FRA, Méès L, Radev S (2016) Scattering of light by large bubbles: coupling of geometrical and physical optics approximations. J Quant Spectrosc Radiat Transf 170:8–18
Sentis MPL, Bruel L, Charton S, Onofri FRA, Lamadie F (2017) Digital in-line holography for the characterization of flowing particles in astigmatic optical systems. Opt Lasers Eng 88:184–196
Sharma SK, Somerford DJ (2006) Light scattering by optically soft particles: theory and applications. Praxis Publishing Ltd, Chichester
Shelby JE (2005) Introduction to glass science and technology. Royal Society of Chemistry, Cambridge
Silvestre CIC, Santos JLM, Lima JLFC, Zagatto EAG (2009) Liquid–liquid extraction in flow analysis: a critical review. Anal Chim Acta 652(1–2):54–65
Stavroudis ON (2006) The mathematics of geometrical and physical optics. Wiler-VCH Verlag & Co. KGaA, weinheim
Stockschläder P, Kreismann J, Hentschel M (2014) Curvature dependence of semiclassical corrections to ray optics: how Goos-Hänchen shift and Fresnel filtering deviate from the planar case result. Europhys Lett 107(6):64001
Stratton JA (1941) Electromagnetic theory. McGraw-Hill, New York
Tadros TF (2013) Emulsion formation, stability, and rheology. In: Emulsion formation and stability. Wiley-VCH Verlag GmbH & Co. KGaA, pp 1–75
Tatsuya K, Yukihiro A, Masanobu M (2002) Size measurements of droplets and bubbles by advanced interferometric laser imaging technique. Meas Sci Technol 13(3):308
Tian L, Loomis N, DomĂnguez-Caballero JA, Barbastathis G (2010) Quantitative measurement of size and three-dimensional position of fast-moving bubbles in air-water mixture flows using digital holography. Appl Opt 49(9):1549–1554
Tran NH, Dutriaux L, Balcou P, Le Floch A, Bretenaker F (1995) Angular Goos-Hänchen effect in curved dielectric microstructures. Opt Lett 20(11):1233–1235
Trefil JS (1984) A scientist at the seashore. Scribner, New York
Ushikubo FY, Furukawa T, Nakagawa R, Enari M, Makino Y, Kawagoe Y, Shiina T, Oshita S (2010) Evidence of the existence and the stability of nano-bubbles in water. ‎Colloids Surf A 361(1–3):31–37
van de Hulst HC (1957) Light scattering by small particles. Dover Publications, New York
van Sint Annaland M, Deen NG, Kuipers JAM (2005) Numerical simulation of gas bubbles behaviour using a three-dimensional volume of fluid method. Chem Eng Sci 60(11):2999–3011
Vera MU, Saint-Jalmes A, Durian DJ (2001) Scattering optics of foam. Appl Opt 40(24):4210–4214
Vetrano MR, van Beeck JPAJ, Riethmuller ML (2004) Global rainbow thermometry: improvements in the data inversion algorithm and validation technique in liquid-liquid suspension. Appl Opt 43(18):3600–3607
Wiscombe WJ (1980) Improved Mie scattering algorithms. Appl Opt 19(9):1505–1509
Woolf DK (2001) Bubbles A2. In: Steele JH (ed) Encyclopedia of ocean sciences. Academic Press, London, pp 352–357
Woolf LD (2010) Multiple smatterings of insight: 10 years of interaction with Craig Bohren. NANOP 4(1), 041595–041597
Wriedt T (2007) Review of the null-field method with discrete sources. J Quant Spectrosc Radiat Transfer 106:535
Wriedt T (2017) Light Scattering programs (ScattPort). Available online at url-http://www.scattport.org/index.php/light-scattering-software
Wu ZS, Wang YP (1991) Electromagnetic scattering for multilayered sphere: recursive algorithms. Radio Sci 26(6):1393–1401
Wu L, Yang H, Li X, Yang B, Li G (2007) Scattering by large bubbles: comparisons between geometrical-optics theory and Debye series. J Quant Spectrosc Radiat Transf 108(1):54–64
Xu R (2001) Particle characterization: light scattering methods. Kluwer Academic Publishers, Dordrecht
Xu F, Ren KF, Cai X (2006a) Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. I. By a spherical particle. Appl Opt 45(20):4990–4999
Xu F, Ren KF, Cai X, Shen J (2006b) Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. II. By a spheroidal particle with end-on incidence. Appl Opt 45(20):5000–5009
Xu F, Lock JA, Tropea C (2010) Debye series for light scattering by a spheroid. J Opt Soc Am A 27(4):671–686
Yan B, Chen B, Stamnes K (2002) Role of oceanic air bubbles in atmospheric correction of ocean color imagery. Appl Opt 41(12):2202–2212
Yang P, Liou KN (2009) An “exact” geometric-optics approach for computing the optical properties of large absorbing particles. J Quant Spectrosc Radiat Transf 110(13):1162–1177
Yang M, Wu Y, Sheng X, Ren K-F (2015) Comparison of scattering diagrams of large non-spherical particles calculated by VCRM and MLFMA. J Quant Spectrosc Radiat Transf 163:143–153
Yu H, Shen J, Wei Y (2008) Geometrical optics approximation of light scattering by large air bubbles. Particuology 6(5):340–346
Yu H, Xu F, Tropea C (2013) Simulation of optical caustics associated with the secondary rainbow of oblate droplets. Opt Lett 38(21):4469–4472
Yuan Y, Ren K, Rozé C (2016) Fraunhofer diffraction of irregular apertures by Heisenberg uncertainty Monte Carlo model. Particuology 24:151–158
Yurkin MA, Kahnert M (2013) Light scattering by a cube: accuracy limits of the discrete dipole approximation and the T-matrix method. J Quant Spectrosc Radiat Transf 123:176–183
Zhang X, Lewis M, Johnson B (1998) Influence of bubbles on scattering of light in the ocean. Appl Opt 37(27):6525–6536
Zhang S, Wang KW, He F, Zhou B (2015) Simulation and analysis of light scattering by air bubble in optical glass. Adv Mat Res 1096:98–102
Acknowledgements
The authors want to acknowledge Prof. K-F. Ren for providing them calculations with VCRM. This work was partially funded by the French National Research Agency (ANR) under grants AMO-COPS (ANR-13-BS09-0008-02), Labex MEC (ANR-11-LABX-0092), and A*MIDEX (ANR-11-IDEX-0001-0).
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Onofri, F.R.A., Sentis, M.P.L. (2018). Light Scattering by Large Bubbles. In: Kokhanovsky, A. (eds) Springer Series in Light Scattering. Springer Series in Light Scattering. Springer, Cham. https://doi.org/10.1007/978-3-319-70808-9_3
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