Study Of The Longitudinal Correlation Function Of Speckles In The Deep Fresnel Zone

When a coherent laser beam was scattered by a random rough surface, a lot of light waveprimitives are produced because of the light scattering of the coarse particle on the rough surface,for the random interference of these light wave primitives, we can acquire some images on theobservation plane which is the so-called “speckles”. Due to the limitation of the light diffractionangle, the shorter the distance from the random rough surface to the observation plane is, the lessthe number of the light wave primitives is, otherwise, as the increase of this distance, there willbe more and more primitives join in the random interference. According to the difference of thespread space, the speckles can be divided into the image speckles (which were formed on thefocal plane of an optical system) and the speckles in diffraction region (which were formedthrough the free-space spreading of the coherent light). The diffraction speckles can also bedivided into the near-filed speckles (which can be observed within one wavelength behind thescattering screen) and the far-filed speckles (which were formed in the Fresnel zone or theFraunhofer zone).So, we can make a conclusion as follows: the near-filed speckles reflects the microcosmicproperties of the corresponding filed on the scattering screen, when all the light primitives canarrive at every point on the observation plane, the far-filed speckles has been formed, it reflectsthe macroscopic properties of the whole scattering screen. The deep Fresnel zone is just betweenthe near-filed and the far-filed, in our experiment, the position of the speckles we have collectedis about1cm behind the random scattering screen.According to the first paragraph, the near-field speckles contain the microscopic propertiesof scattering screen while the far-field speckles contain the macroscopic properties of the wholescattering screen. Because of it is very close to the near-field area, the deep Fresnel zone is alsocontains a large amount of information of the random surface, so the speckles in the deep Fresnelzone can be used to extract the statistical parameters of the random rough surface. In this paper,we mainly discuss the statistical properties of speckles in deep Fresnel zone and its relation with the random rough surface, and at the end of this paper the speckles longitudinal correlationcharacter in the deep Fresnel zone is discussed. The structure of this paper is organized asfollows:In the first chapter, we firstly introduce the concept of the speckles, the conditions toacquire speckles; secondly, we discuss the use of the speckles in many filed include themedicine, the astronomy, the architecture, the crystallography, climatology, etc; finally, wediscussed the description method and explored the statistical characteristics of speckles, weclassified the speckles according to the condition it forms and discusses distinction between thenear-field speckles and the far-field speckles.The second chapter firstly introduced the formation process of the speckles in the deepFresnel zone after the random scattering screen; secondly, we introduced the formation reasonand the leading factor of the speckles in the field of geometric optical effect, the transition filedfrom geometric optical effect to interference effect, the speckles field of a few scattered particles,the field of Gaussian speckles, the characteristics of the speckles in every region is also bediscussed later; lastly, we proposed several methods to extract the statistical parameters on thesurface by the speckles.In The third chapter, we start with the definition of the speckles intensity correlationfunction and deduced the autocorrelation function and longitudinal correlation function of thespeckles in the deep Fresnel zone theoretically, we get the expression of the correlation functionand the correlation interval. In experiment, we have designed an optical experiment system tocollect the speckles in the deep Fresnel zone and extracted the statistical parameters of the roughsurface that we use for scattering by fitting the autocorrelation function, then we compare thefitting results with what we have obtained by an atomic force microscopy, the results isconsistent; we finally analyze the characteristics of the speckles in the deep Fresnel zone anddiscussed the correlation between the longitudinal correlation function and the diffractiondistance and the fractal characteristics of speckles in the deep Fresnel zone.The fourth chapter is a summary of the full text, we predicted the prospect and trend of theresearch of the speckles in the deep Fresnel zone in the future.