| Speckles are the granular and random intensity distributions produced by the light scatteringfrom random surfaces. Based on the distances from the random surfaces, speckles are dividedinto the far-field speckles including the speckles in the Fraunhofer diffraction region and in theFresnel diffraction region and the near-field speckles within the region one wavelength awayfrom the random surfaces. Theories and experiments show that the far-field speckles do notcontain the information of the random surfaces. However the near-field speckles contain richinformation in the order of magnitude of the submicron. The speckles studied in this paper are inthe extremely deep Fresnel diffraction region that is between the near field and the far field, andthey contain abundant information of the random surface producing them and attract moreattention recently. Besides, according to the coherence of the incident light, speckles are alsodivided into the coherent speckles generated when the laser light impinges on a random surfaceand the partially coherent speckles when the incident light doesn’t have good temporal coherenceor spatial coherence. In the chapter6of this paper we have studied the evolutions of thedistribution characteristics and the statistical properties of the speckle intensities produced whenthe parallel white light impinges on scattering screens with different roughness in the extremelydeep Fresnel diffraction region.Phase vortex appears at the position where both the real and the imaginary parts of the lightfield equal zero simultaneously and the phase is undefined at the location of the phase vortex.The equal phase lines radiate from the location of the phase vortex and the phase increases ordecreases in a helical path with the location of phase vortex as the center. The phenomenon ofphase vortices is common in many physical fields and has been widely used in the fields ofoptical microcontroller, quantum entanglement, information transmission and so on. The phasevortices in speckle fields are the most complicated and typical and have leading role.In recent years, many papers have studied the speckle fields produced by the strongscattering screens in the extremely deep Fresnel diffraction region. As far as we know, no papershave studied the problems relative to the speckle fields produced by weak scattering screens in the extremely deep Fresnel diffraction region, such as the evolutions of phase vortices, phase andspeckle intensities with the roughness of scattering screens and the distances from the scatteringscreens, the relations between the distribution characteristics of speckle intensities or the phaseand the morphology of corresponding scattering screen. Besides, the relations between thedistribution characteristics of the white light speckle intensities and the morphology ofcorresponding scattering screen and the evolutions of statistical properties of white light speckleswith the roughness of scattering screens and the distances from the scattering screens have notbeen investigated. All the problems mentioned above have been studied in this paper based onexperiments and numerical simulations. The results show that the speckle intensity, specklephase, speckle phase vortices and their statistical properties are all closely related with thecorresponding scattering screens. This paper is significant for us to realize the speckle fieldsproduced by the weak scattering screens in the extremely deep Fresnel diffraction region and itwould be helpful for us to obtain the information of the scattering screens from the speckle fieldsin the extremely deep Fresnel diffraction region.In this paper, we have obtained different scattering screens with different roughness bygrinding, designed an experimental system, recorded by CCD the interference intensities of thereference beam and the speckle fields produced by different scattering screens with differentroughness at different scattering distances in the extremely deep Fresnel diffraction region.Basing on the digital Fourier transform arithmetic, we have successfully extracted the specklefields produced by the weak scattering screens at different scattering distances in the extremelydeep Fresnel diffraction region, and discussed the evolutions of the speckle intensity, specklephase, phase vortices and their statistical properties with the sample roughness and the scatteringdistances from the sample. Based on the Kirchhoff approximation theory and Green function, theformula to numerically calculate the speckle fields in the extremely deep Fresnel diffractionregion has been inferred and the speckle fields produced by weak scattering screens in theextremely deep Fresnel diffraction region are obtained by numerical simulations, and therelations between the speckle intensity distributions, the phase distributions and the samplesurface morphology are discussed, and the comparisons are made between the statisticalproperties of speckle intensity, speckle phase and phase vortices and that from experiment. Wehave obtained by numerical simulations the speckle fields produced by one weak scatteringscreen at different scattering distances in the extremely deep Fresnel diffraction region with thered, the green and the blue incident light impinging on the weak scattering screen respectively,and studied the influences of the wavelength of incident light on the speckle intensity, specklephase and phase vortices and their statistical properties. The formula to numerically calculate the speckle fields with the white light as the incident light is given and the white light speckles atdifferent scattering distances in the extremely deep Fresnel diffraction region are alsonumerically simulated, and the relations between the white light speckle intensity distributionsand the corresponding random surface morphology are analyzed, and the evolutions of the whitelight speckle and their statistical properties with the roughness of samples and the scatteringdistances are discussed. There are seven chapters in this paper and the detailed contents are asfollows.In chapter1, we give some basic conceptions and methods involved in this paper. First, weintroduce how to describe a random surface, its primary parameters and height statisticalfunction. Then we describe the formation of speckles and their applications, light scatteringtheory, the definition of phase vortex and its history, the definition of phase vortex sign and theformula for its eccentricity, and the theory for the extractions of speckle fields from theinterference patterns of the speckle fields and the reference beams by using the Fourier transfermethod.In chapter2, different weak scattering screens with different roughness have been obtainedby grinding, an experimental system has been designed to obtain the speckle fields in theextremely deep Fresnel diffraction region, the interference intensity of the reference beam andthe speckle fields produced by different scattering screens with different roughness at differentscattering distances in the extremely deep Fresnel diffraction region have been recorded by CCD.The phase distributions of the speckle fields generated by weak scattering screens in theextremely deep Fresnel diffraction region have been extracted. We find that with the scatteringdistance certain and the roughness of weak scattering screens increasing, or with weak scatteringscreens certain and the scattering distances increasing, the random fluctuations of phase increaseand the phase distributions become more uniform; we have discussed the phase vortex evolutionswith the sample roughness and the scattering distances. It is found that the phase vortexphenomenon doesn’t appear until the surface of a weak scattering screen is rough enough; It isinteresting that there are phase vortices on the surfaces of scattering screens; For the weakscattering screens with larger roughness, the phase vortex average density increases with thescattering distance certain and the roughness of weak scattering screens increasing, or with weakscattering screen certain and the scattering distance increasing.In chapter3, Basing on the Kirchhoff approximation theory, we have obtained by numericalsimulations the speckle intensity distributions generated by different scattering samples withdifferent roughness at different scattering distances in the extremely deep Fresnel diffractionregion. It is interesting that for a sample with moderately large roughness, at some scattering distance, the speckle intensity distributions are extremely similar to the corresponding sample’smorphology. Besides, with the scattering distance certain, or for the same sample, the speckleintensity distribution characteristics, the speckle intensity probability densities and their contrastsvary with the roughness, or with the scattering distances. The numerical simulation results areroughly consistent with the experimental results. Qualitative analyses for the numericalsimulation results are also presented.In chapter4, we have obtained the phase distributions of speckle fields produced by threerandom screening screens at different scattering distances in the extremely deep Fresneldiffraction region by numerical simulations and discussed the relations between the specklephase distributions and the corresponding random surface morphology. It is found that for aweak scattering screen with its height fluctuations within one wavelength of the incident light, itsspeckle phase distributions immediately behind the screen could reflect its morphology well. Wehave also discussed respectively the evolutions of the phase and the phase vortices with theroughness of samples and the scattering distances and compared them with the experimentalresults and found that the results agree well with each other.In chapter5, we have numerically calculated the intensities and the phase distributions ofthe speckles at the scattering distance z2μmproduced by a weak scattering screen when thered, green, blue incident light impinge on it respectively, and then statistically analyzed theevolutions of the intensity probability density and the contrast of speckles and the phase vortexdensity with the incident light wavelength. The qualitative explanations are presented. Moreover,we have discussed the impacts of the changes of the incident light wavelengths on the relationsbetween the speckle phase distributions and the corresponding sample morphology.In chapter6, the formula to calculate the white light speckle fields is given. The white lightspeckles produced by three samples with different roughness at different scattering distances inthe extremely deep Fresnel diffraction region are numerically simulated. The evolutions of thedistribution characteristics of the white light speckles with the roughness and the scatteringdistances are discussed. It is found that, for a scattering screen with a moderately large roughness,there is a scattering distance at which the strip structures of the speckle intensity distributionsmatch the ridges of the height distributions of the scattering screen. The evolutions of thecontrast and the probability density of the white light speckle intensity with the roughness andthe scattering distances are also discussed. The results show that with the scattering distancecertain or for the same scattering screen, the distribution, the contrast and the probability of thewhite light speckle intensity vary with the roughness of the scattering samples or with thescattering distances. The mechanism of the evolutions and the comparisons with the experimental results are also given. It is indicated that the results of numerical simulations arecoincident well with that of experiments.In chapter7, the main conclusions of this paper are summarized and the in-depth researcheswe will conduct are briefly introduced. |
