Jun Uozumi

First-order probability density function of the laser speckle phase

An expression for the first-order probability density function of the laser speckle phase is analytically derived under the assumption that the speckle field obeys a non-circular, complex Gaussian, random process with a certain correlation between the real and imaginary parts of its complex amplitude. The probability density function of the speckle phase is actually evaluated for various cases and shown three-dimensionally as a function of the standard deviation of random object phase variations. The effect of random object phase variations on the probability density function is also investigated in detail.

Enhancement of the backscattered intensity from fractal aggregates

Abstract Comparative measurements were conducted for the backscattered intensities of light from uniform random and fractal aggregated media. Different features are found for the backscattered intensity peak shapes. A crossover between the θ1−D and θ−2 dependences of the backscattered intensity occurs in the case of fractal aggregated medium, where D indicates the fractal dimension.

First-order intensity and phase statistics of Gaussian speckle produced in the diffraction region

General expressions for first-order statistics of Gaussian speckle produced in the diffraction region are derived for an arbitrary profile of the illuminating beam with a plane wave front. The statistical properties of the complex amplitude, the intensity, and the phase of speckles are studied under illumination of a Gaussian beam. The joint probability density function of the speckle field characterized by an equiprobability density ellipse is investigated in some detail with an intimate relation to the correlation coefficient between the real and imaginary parts of the complex speckle amplitude. This correlation coefficient is found to affect appreciably the statistics of speckles produced especially in the near-field diffraction region when a standard deviation of the random phase variation produced by a diffuse object under illumination is relatively small and the number of independent scatterers contributing to the formation of speckles is small.

Speckle clustering in diffraction patterns of random objects under ring-slit illumination

Abstract Some optical conditions are discussed for producing speckle patterns having long intensity correlations in the diffraction geometry. A random rough surfaces under illumination of coherent light with a circular ring slit produces the speckles with a zero-order Bessel function for the intensity correlation when observed in the Fraunhofer diffraction region. This function has relatively long oscillating tails and, consequently, string or network structures appear in speckle patterns, which we may call speckle clustering . This clustering phenomenon can explain the similar appearance observed in diffraction patterns produced by random Koch fractals.

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.

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.

On simultaneous optical sensing of local curvature and roughness of metal surfaces

Abstract A novel sensor array for metal-surface curvature and roughness inspections is investigated. The sensor is based on the use of a computer-generated hologram as an analyser of surface curvature and roughness. The sensor can be exploited to estimate the optical surface roughness of irregularly curved surfaces. A contrast parameter to characterize the optical surface roughness is introduced.

The first-order statistics of partially developed non-Gaussian speckle patterns

The probability density function of the partially developed non-Gaussian speckle intensity is experimentally investigated and distinctive differences are confirmed to exist between the probability density functions of partially developed Gaussian and non-Gaussian speckle intensities. To characterise these differences, a new skewness parameter is introduced which describes the asymmetry of the probability density distribution of speckles, and some theoretical considerations are also presented. Finally it is shown that the skewness parameter expresses both the average contrast and the dependence of speckle statistics on both the random phase fluctuation of diffusers and the effective number of scatters contributing to the observation point.

Generation of fractal speckles by means of a spatial light modulator

It was shown in previous studies that, when a diffuser is illuminated by coherent light with an average spatial intensity distribution obeying a negative power function, the scattered field in the Fraunhofer diffraction region exhibits random fractal properties. The method employed so far for producing such fields has a disadvantage in that generated speckle intensities are low due to small transmittance of fractal apertures used in the illumination optics. To overcome this disadvantage, a generation of fractal speckles by means of a spatial light modulator is proposed. The principle is explained and experimental results are also shown.

Statistical properties of the Fraunhofer diffraction field produced by random fractals

First-order statistical properties of the speckle field and its intensity in the Fraunhofer diffraction region that is produced by random Koch fractals are investigated by means of computer simulations in comparison with the ordinary fully developed speckle.