Toshimitsu Asakura

Statistical properties of the sum of partially developed speckle patterns

The probability density function and average contrast of the sum of n uncorrelated, partially developed speckle patterns have been theoretically investigated. A new form of the probability density function is given for the sum of n uncorrelated, partially developed speckle patterns under the assumption that the individual speckle fields to be added follow the circular statistics.

Correlation properties of speckles produced by diffractal-illuminated diffusers

Correlation properties are investigated theoretically for the field scattered by a rough surface which is illuminated by a diffractal produced in the Fraunhofer diffraction region of a random fractal object. In this configuration, the diffractal illuminating the rough surface has a power-law average intensity distribution with a saturated finite value at the center. The second scattering by the rough surface produces another speckle pattern in its Fraunhofer diffraction region. It is shown that the resultant speckled speckles are described by an intensity correlation function expressed by the modified Bessel function. This correlation function approaches a power function for small values of the argument, provided that the fractal dimension of the fractal object is between 1 and 2. Hence, the resultant speckle intensity distribution is considered to be fractal.

Enhanced backscattering of partially coherent light.

The backscattering enhancement of light from random media is analyzed for situations in which the scatterers are illuminated with spatially partially coherent light. The effect of coherence is incorporated into the existing theories by use of the angular correlation description for the illuminating light field. When the area of illumination is infinite, an analogy to the van Cittert-Zernike theorem leads to the expression for the intensity distribution that is given by the sum of backscattered intensities, each of which would arise from each incident plane-wave component of the angular spectrum. It is shown that the backscattering cone is partially suppressed and deformed owing to breaking of the time-reversal symmetry of mutiple-scattering paths.

Fraunhofer Diffraction from Apertures Bounded by Regular Fractals

Abstract Some properties of fields diffracted in the Fraunhofer region by apertures bounded by regular fractals are investigated. A recursion relation describing such apertures is introduced and the associated relation in the Fourier transform domain is described. For a triadic Koch aperture whose edge has the fractal dimension of Ds = 1·262, the recursion relation is numerically evaluated. Self-similar structures of intensity distributions in the Fraunhofer region are verified for the present objects. The relationship of the fractal dimension D s of the fractal edge with the power-law decay of the Fraunhofer diffraction intensities is also verified.

Ballistic propagation of light through fractal gels

Abstract The scattering mean free path of light propagating through a fractal gel consisting of particles comparable in size with the wavelength of light is shown to have a non-trivial dependence on the size of clusters. It is verified experimentally that, when D>2, the attenuation coefficient scales with the volume fraction Φ of monomers as Φ1/(3−D). On the basis of this dependence, a simple alternative for the characterization of a fractal gel is suggested.

Evaluation of planar fractal images by optical autocorrelation

Optical autocorrelation of two-dimensional fractal images is discussed. Coherent and incoherent optical autocorrelations, depending upon the illumination mode, are analysed in the specific context of the evaluation of fractal dimensions. The newly proposed methods are alternatives to the classical diffraction-based approaches and their complementary character is emphasized. The results of the experiments with two-dimensional maps of regular and statistical self-similar fractals are also presented and the abilities of the two methods are comparatively discussed.

Contrast of speckle patterns produced by white light near the image plane

The contrast of speckle patterns produced by white light near the image plane has been experimentally investigated. The varying feature of the speckle contrast as a function of the receiving plane is found to depend strongly on the mean wavelength and temporal coherence length of the illuminating white light and on the surface roughness of a diffuse object under illumination.

Cross-correlation properties of multiply-scattered dichromatic light from flowing colloidal particles

The cross-correlation properties of dichromatic light multiply-scattered by colloidal particles in a uniform flow are studied experimentally. It is shown that the correlation peak value of intensity fluctuations depends on the optical thickness of the sample and the number density of particles, whereas the decay time of cross-correlation functions is almost independent of the characteristics of particle suspensions. This result indicates that the number fluctuations as well as the speckle fluctuations contribute to the temporal variations in the intensity, and that the velocity of the uniform flow is measurable without being affected by the diffusive motion of the scatterers. The effect of wavelength difference is also examined.

SCALING PROPERTIES OF THE SCATTERING COEFFICIENTS FOR MUTUALLY SELF-SIMILAR GELS

The observable quantities in an optical experiment are influenced by the fractal dimension and the average cluster size of mutually self-similar gels. We study the scaling properties of the scattering and the transport mean free path in order to use them for the microscopical characterization of fractal gels.