The link between particle properties (size, composition, shape, internal structure) and IOP Emmanuel Boss

Two processes cause attenuation (loss of light): a- absorption. b- scattering (re-direction).  c = a + b

What is scattering: Scattering refers to the redirection of energy of an ‘infinite’ ‘plane- parallel’ electro-magnetic wave due to interaction with matter. By interaction we mean that the wave travels at different speed at different location within the medium due to inhomogeneities within the medium. Such inhomogeneities may be caused by particles of different optical properties within the medium or ‘fluctuations’, regions within the medium that have slightly different concentrations of molecules. The ‘relative’ index of refraction (n r ) of a particle relative to the medium in which it is embedded, is the ratio of the speeds of lights: n p =c medium /c p. For a given size and shape of particle, the more different the index of refraction is from 1 the more pronounced is the scattering.

What is scattering: Scattering is the sum of: 1.Reflection: at a boundary of a particle with different n than the medium in which it is embedded, a certain amount of radiation is reflected back. 2.Refraction: at a boundary of a particle with different n than the medium in which it is embedded, a certain amount of radiation penetrates into the particle, usually at a different angle than the angle of incidence (Snell). 3.Diffraction: the light propagating along the boundary of the particle responds to the boundary causing a change in direction. From:

refraction, reflection and diffraction: Large particles: scattering is dominated by diffraction, since light going through the particles is likely to be absorbed.  Geometric optics. Response is proportional to particle’s cross- sectional area (sensitive to shape). Small particles: scattering is dominated by refraction and reflection, Rayleigh scattering. Response is proportional to particle’s volume (insensitive to shape).

Marine particles are ‘soft’: Optical properties Index of refraction: Absorption index:

Optical properties Optical cross section: C ext =Geometric cross section x Light impinging on particle Light attenuated by particle Similar definition for other cross sections. Link to IOPs: Optical efficiency factors:

Size parameter: Phase shift parameter: Optical regimes Absorption parameter:

Recap: dependence of IOP on properties of particles: The output of scattering codes for a particles with a given D/ and n is: Cross sections (C, [m 2 ]) or efficiency factors (Q, [  ]) for absorption, scattering and attenuation as well as the phase function (multiply by C to get angular scattering cross- section). Example: the attenuation cross-section, C ext, is the attenuation due to a single particle in a m 3 of medium: c=C ext ·1=Q ext ·  r 2 ·1 Since the mass increase with size, it is instructive to study how the mass normalized optical properties vary as function of size and index of refraction. c/V=C ext ·1/{4  r 3 /3}  v

Dependence of IOP on properties of particles: c/V=C ext ·1/{4  r 3 /3}  v c  Volume C ext = 2·area  c/V  1/D Change of max with n (and ).

Dependence of IOP on properties of particles: a/V=C abs ·1/{4  r 3 /3} C abs = area  a/V  1/D n’=0.01 ‘Packaging’, Duysen, 1956 Little n influence Molecular absorption  volume.

Dependence of IOP on properties of particles: b b /V=C bb ·1/{4  r 3 /3} b Large n effect 0.1<D<10 contributes most Little n’ effect except at large D

Lab example: general angle scattering Response of the LSS/volume to size (Baker et al., 2001):

Dependence of IOP on properties of particles:  /V:  / V p Near forward scattering: Strong dependence on size, less on n. n=1.05  =4 Roesler and Boss, 2004

Index of refraction (n) from b bp /b p : Twardowski et al., 2001 n’=0 It turns out the b bp /b p is very sensitive to n and less so to the PSD:

n correlates with density (  )  sinking rates. n separates water-filled organic particles from inorganic particles. Zaneveld et al., 2002, OOXVI. Compiled from: Aas (1983) Carder et al. (1972) Carder et al. (1974) Babin et al., 2003 Why do we want to know n?

IOPs and scattering theory: Provides a calibration to our sensors (LISST, b b, flow-cytometers). For a given concentration of particles of a given size and n we expect a given signal. Provides a check on our measurements (relationship between concentration, size distribution and likely optical property). Examples: 1. what is the likely c(660) for a given concentration of phytoplankton ? r=20  m [Conc.]=10 5 /L= 10 8 m -3 c ext ~2·Area= 2·  ·(20) m 2  c=c ext ·[Conc]~0.25m Babin claims that b* 555 ~0.5m 2 /gr. Is it sensible? c scat ~1·Area. b* 555 =0.5=[conc.]*c scat / {[conc.]*volume*density}= 0.75/{r*density}. For sediments, density=2.5gr/cm 3 =2.5·10 6 gr/m 3  average r~0.6  m, a realistic size.

Effect of shape:

OMBAR, 2007

Example: VSF of natural particles

Effects of internal structure. Kitchen and Zaneveld, 1992.

Summary: Size (relative to wavelength) and index of refraction are the determinant of light interaction with particles. For particles small relative to the wavelength optical properties are proportional to particle volume and insensitive to shape. For particles large relative to wavelength optical properties are proportional to the average cross section of the particle and thus sensitive to shape. From all commonly used IOPs backscattering is the most sensitive to shape and internal structure (absorption the least). More work needs to be done to elucidate that dependency. Polarized scattering is the next frontier…