Studies On The Properties Of Speckle Fields Based On The Experimental Detection Of Complex Amplitudes

Speckle pattern is the random intensity distribution produced by the coherent light scattering from a random surface. Moreover, great attention has been paid to the study of the statistical properties of speckle. There is abundant information of complex amplitude and phase in the phase vortices, forming around the zero-point of speckle intensity, so more and more papers pay attention to the investigation of phase vortices, and it is of great importance in many science and technology fields such as the nonlinear optics, the laser physics and the optical information processing, etc. After the experimental extraction of amplitude and phase distribution is realized, which is based on the interference technique of speckle fields with reference beam and the digital Fourier transform, most of the papers in the literature are focused on the experimental investigation of phase vortices. There is more abundant random surface information in the speckle pattern in the extremely deep Fresnel diffraction region than in the normal far field, so the statistical properties of speckle in the extremely deep Fresnel diffraction region would be interest in the study of the measurements of random surface.Combining the interference technique of speckle fields and reference beam with the digital Fourier transform arithmetic, we have finished the experimental extraction of the amplitude, phase, intensity and phase vortices of speckle and studied their properties of statistical and the propagation etc. In the theoretical studies, based on the Frankenthal's multiscale phase screens model, we have proposed a new empirical analytic expression of the intensity correlation function of the regional fractal speckle. We also have explained the intensity probability density and the contrast of the speckle in the extremely deep Fresnel diffraction region by the theory of the sum of zero-order diffraction and circular Gauss speckle. In experimental studies, we have designed an interference system of speckle and reference beam to extract the complex amplitude and the phase of random light field in far field. Moreover, we have realized the experimental measure and extraction of the speckle in the extremely deep Fresnel diffraction region with a microscope system. In the numerical simulations, we have tackled a series of problems in the extraction of random light fields, and we have calculated the speckle in the extremely deep Fresnel diffraction region based on the Kirchhoff approximation and Green's function. The whole paper is divided into six chapters.Chapter 1: Introduction. In this part, we give a summary and an overall review of the background and the current situation of the research on speckles as well as some conceptions about speckles. First, we introduce the characterization, the measurement, the primary statistical parameters and high statistical functions of random surfaces. Then we recite the fundamental theories of light scattering, the formation and the application of speckles; the definition and the character of the phase vortices; the Fourier-transform method of fringe-pattern and the experimental extraction of amplitude and phase of speckles.Chapter 2: The experimental studies on phase vortices of speckles and their propagation properties. By recording the interference patterns of the speckle fields and the reference beam with the charge-coupled device (CCD), and using the digital Fourier transform technique, we realize the experimental extraction of the amplitude and the phase distribution of the speckle fields. We find that at the tangential points of the zero curves of the real and the imaginary parts, a new kind of speckle phase singularities may appear. Differing from the conventional singularities at the zero crossings of the real and imaginary parts with the monotonically spiral change of phase, this new kind of singularities has the property that the phase undergoing an increase and then a decrease around singular point and assuming nearly a symmetric distribution. Otherwise, the range of the phase around the singular point less than2π, that is to say, there always lose some phase around the tangential point. We introduce the concept of quasi twin phase vortices to explain the formation of the new kind of phase vortices. We also experimentally observe the propagation of the phase vortices of speckles based on a theoretical study of the longitudinal autocorrelation function of the speckle intensities. It is found that in planes at the different propagation distances but within a longitudinal correlation length, the real and the imaginary parts of the complex speckle fields vary considerably, but the position of the phase vortices and the angles of the zero crossings of the real and imaginary parts remain almost unchanged.Chapter 3: The experimental studies on the statistical functions of speckle fields produced in different angle scattering based on the extraction of the complex amplitudes by use of interference beam. Using the interference patterns of speckle fields and the reference beam, we extract digitally the complex amplitudes, phases and intensities of speckles fields and then study experimentally their properties. The influences of the noises on the measurement of statistical functions, especially on that of the probability density function, appearing in the conventional method is satisfactorily eliminated. The experimental studies of the statistical properties of the complex amplitude and the phases of the speckle fields are also fulfilled. By the practical measurement of speckle fields produced in different angle scattering, we find that the speckles are laterally broadened gradually with the increase of the scattering angle and the average size of speckles become anisotropic. Such anisotropy brings no change in the probability density function of the speckle fields. The speckle fields produced in large angle scattering remain the circularly Gaussian distribution as that produced in the traditional small angle scattering. Based on the investigation of the amplitude and the phase extracted digitally, we find that there are some special properties of phase singularity when the scattering angle is large enough. With the increase of the scattering angle the spatial distribution of the amplitude and the phase have taken place great changes, and the probability of the angle between the zero-contour lines of real part and that of imaginary part tends to small value, and the average eccentricity of the intensity contours around the phase singularity is gradually increasing. Moreover, the most interesting thing is that the eccentricity is probably greater than 1 in large anger scattering, and the convergence of the correlation curve of phase vortices becomes slower with the spatial distance increasing. All of the properties originate from the appearance of the phase singularity line in larger angle scattering.In chapter 4, we use the higher-power laser produced by semiconductor pump laser Verdi V-5 (the maximum power is 5W) to enhance the weak intensity in large angle scattering and record them with a charge-coupled device (CCD) camera. The complex amplitudes of the speckle are extracted experimentally according to the technique of the interference of the speckle and the spherical reference wave. By studying the intensity correlation function of the speckle, we find that the fractal property of the speckle is related to the spatial separate distanceρ. In the area of smallρ, the fractal exponentα= 1, but the fractal exponentαbecomes less than 1 whenρincrease to a certain number. Such speckle is named regional fractal speckle by us. We deduce an empirical analytic expression of the intensity correlation function of regional fractal speckle, and calculate the fractal exponentαby fitting the experimental curves with the empirical intensity correlation analytic expression. From the probability distribution properties of the intensities and the complex amplitudes, we demonstrate that the regional fractal speckle still obeys Gaussian distribution.In chapter 5, we first make a theoretical analysis of the speckles in the region infinitely close to the random surface (also called the extremely deep Fresnel diffraction region) based on the Kirchhoff approximation and Green's function theory, and then produce the 2D speckle field by numerical simulation. By comparing the 2D speckle field with the corresponding random surfaces, we find that both the intensity space distribution and the fractal property of the speckles depend on the random height distribution of the surfaces, and the intensity probability density of the speckles don't obey negative exponential law. We explain the intensity probability density and the contrast of the speckle in the extremely deep Fresnel diffraction region by the theory of the sum of zero-order diffraction and circular Gauss speckle. We design a microscope system to detect the speckles in the extremely deep Fresnel diffraction region and find experimental evidence of the conclusions we reached in the numerical simulation. Based on the interference technique of speckle fields with reference beam and the digital Fourier transform, we realize the experimental extraction of the amplitude and phase of the speckles in the extremely deep Fresnel diffraction region.In chapter 6, we sum up the main conclusions and the innovations of the dissertation, and briefly introduce the in-depth researches we will conduct.