https://www.ipgp.fr/~jacquemoud/publications/ustin2009.pdf

Retrieval of foliar information about plant pigment systems from high resolution spectroscopy

The solution of electromagnetic scattering by a homogeneous prolate (or oblate) spheroidal particle with an arbitrary size and refractive index is obtained for any angle of incidence by solving Maxwell's equations under given boundary conditions. The method used is that of separating the vector wave equations in the spheroidal coordinates and expanding them in terms of the spheroidal wavefunctions. The unknown coefficients for the expansion are determined by a system of equations derived from the boundary conditions regarding the continuity of tangential components of the electric and magnetic vectors across the surface of the spheroid. The solutions both in the prolate and oblate spheroidal coordinate systems result in a same form, and the equations for the oblate spheroidal system can be obtained from those for the prolate one by replacing the prolate spheroidal wavefunctions with the oblate ones and vice versa. For an oblique incidence, the polarized incident wave is resolved into two components, the TM mode for which the magnetic vector vibrates perpendicularly to the incident plane and the TE mode for which the electric vector vibrates perpendicularly to this plane. For the incidence along the rotation axis the resultant equations are given in the form similar to the one for a sphere given by the Mie theory. The physical parameters involved are the following five quantities: the size parameter defined by the product of the semifocal distance of the spheroid and the propagation constant of the incident wave, the eccentricity, the refractive index of the spheroid relative to the surrounding medium, the incident angle between the direction of the incident wave and the rotation axis, and the angles that specify the direction of the scattered wave.

Light Scattering by a Spheroidal Particle

The spectral variation of the optical properties of soot particles is determined by combining classical and dynamic light scattering measurements with the Kramers-Kronig relations. Particle size and number densities are determined from scattering/extinction and autocorrelation measurements at the wavelength of 0.488 μm. This information is then combined with the spectral extinction measurements in the wavelength range 0.2 to 6.4 μm to determine the spectral variation of the refractive indices of flame soot. Results are presented for a premixed propane-oxygen flame with a fuel equivalence ratio ϕ = 1.8. The sensitivity of the technique and its advantage over the previous methods are discussed.

Determination of the Wavelength Dependence of Refractive Indices of Flame Soot

Leaves of six species selected to represent a broad range in internal structure were collected in the field and studied in the laboratory to determine primary and secondary effects of water content on leaf spectral reflectance. Primary effects were those that resulted solely from the radiative properties of water. Secondary effects were those that could not be explained solely by these properties. Decreased leaf water content generally increased reflectance throughout the 400-2,500-nm wavelength range. For the aquatics Eichhornia crassippes and Nuphar luteum, the broadleaved trees Liquidambar styraciflua and Magnolia grandiflora, the cane-grass Arundinaria tecta, and the needle-leaved Pinus taeda, the sensitivity of reflectance to water content was greatest in the water absorption bands near 1,450, 1,940, and 2,500 nm. Sensitivity maxima occurred also between 400 and 720 nm, indicating secondary effects that resulted from decreased absorption by pigments. Secondary effects of water content on reflectance that were largely wavelength-independent, together with any wavelength-independenteffects of leafinternal structure, were far less significant than primary and secondary effects resulting from decreased absorption by water and pigments, respectively.

Primary and secondary effects of water content on the spectral reflectance of leaves

The use of “equivalent” spheres to represent the scattering and absorption properties of nonspherical particles has been unsatisfactory in the past because the sphere of equal volume has too little surface area and thus too little scattering, whereas the sphere of equal area has too much volume giving too much absorption. Their asymmetry factors are also too large. These problems can largely be avoided if the real cloud of nonspherical particles is represented by a model cloud of spheres where the model cloud contains the same total surface area as well as the same total volume. Each nonspherical particle is then represented not by just one sphere but rather by a collection of independent spheres that has the same volume-to-surface-area (V/A) ratio as the nonspherical particle. To demonstrate the broad utility of this approach, we show results for ice, whose absorption coefficient varies with wavelength by 8 orders of magnitude. Randomly oriented infinitely long circular cylinders are used as a test case because an exact solution is available for all size parameters. The extinction efficiency and single-scattering coalbedo are closely approximated by the values for equal-V/A spheres across the ultraviolet, visible, and infrared from 0.2 to 50 μm wavelength; the asymmetry factor is matched somewhat less well. Errors in hemispheric reflectance, absorptance, and transmittance are calculated for horizontally homogeneous clouds which cover the range of crystal sizes and optical depths from polar stratospheric clouds through cirrus clouds to surface snow. The errors are less than 0.05 at all wavelengths over most of this space.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/1999JD900496

Representation of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation

Pattern generation in Talbot planes has generally been interpreted in terms of image formation, the repetitive slits are said to make repetitive images of themselves. In this context, Fourier optics developments have correctly predicted the positions of some but not all of the Talbot planes. Now, wave-optics methods are used to obtain general expressions for the positions of all known Talbot planes and the lateral positions of the diffraction fringes within them. These equations predict the key features of the Talbot effect, and they better relate multiple-slit diffraction in the Fresnel and Fraunhofer domains.

Talbot effect reinterpreted

The “anomalous diffraction” approximation of van de Hulst is extended to new particles and orientations thereof. It predicts the extinction and absorption efficiencies, Kext and Kabs, of particles larger than the wavelength and of refractive index not too different from that of the medium. Existing expressions for the normally oriented thin disc and long thin cylinder are found to be equally applicable to the same particles when arbitrarily oriented if the particle parameters are redefined. Geometrical relations are used to prove that van de Hulst's expressions for the homogeneous sphere also describe the ellipsoid of revolution of arbitrary axial ratio and orientation if the particle size parameter is suitably redefined. Numerical solutions of the basic relations for Kext are outlined and illustrated. They are applicable to particles of almost any shape, gross internal structure, and orientation. To support the extension of this “large particle” approximation, its domain is re-examined in terms of the conditions needed for ray propagation within the particle. These conditions can define how sophisticated an optical model of the particle should be. If the particle used is not too large, they can also justify the representation of a nonspherical particle by a spherical model. New expressions and methods are used to determine the effects of random particle orientation on effective K values of various particles. Random orientation is found to cause many nonspherical particles to behave optically almost like spherical particles of equal volumes.

Paul Latimer

Papers

Talbot effect reinterpreted

Optical efficiencies of large particles of arbitrary shape and orientation

Absolute optical cross sections of cells and chloroplasts.

Changes in total light scattering and absorption caused by changes in particle conformation

Light scattering by ellipsoids