Vector analysis on the characteristics of continuous phase plate speckle under the strong focusing
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摘要: 连续位相板(CPP)经过透镜聚焦后，在焦平面上形成一个散斑场，散斑场的统计性质决定了CPP的束匀滑特性。当使用大数值孔径透镜聚焦后，傍轴近似不再成立，因此分析CPP焦斑特性时标量衍射理论不再适用。采用Richard-Wolf矢量衍射理论对强聚焦条件下的CPP焦斑进行了计算，在此基础上分析了矢量焦斑场的统计特性，讨论了焦斑的轮廓。结果表明，由于非近轴的原因，矢量分析得到的焦斑尺寸略大，且通过矢量分析后能够得到z轴方向的光场分量。散斑场的振幅分布满足瑞利分布特性，强度分布满足负指数分布特性，且矢量合成方向的光强分布会略微偏离负指数分布特性。Abstract: Continuous phase plate (CPP) is a typical phase optical element. It will form a speckle field focused by a lens. The statistical characteristics of the speckle field affect the beam smoothing result. When a lens with large number aperture is used, scalar diffraction theory is unsuitable to analyze the distribution character of the focal spot because the paraxial approximation is no longer valid. In this paper, the Richar-Wolf vector diffraction theory is employed to calculate the focal spot of CPP under the strong focusing condition. Then both the profile of the focal spot and its statistical characteristics are discussed in detail. The results show that the spot size that calculated by the vector method is larger than which calculated by scalar method due to the non-paraxial effect. According to the feature of the vector method, the z-component of the light field can be obtained. The amplitude distribution of the speckle meets the Rayleigh distribution character, and its intensity distribution meets the negative exponential distribution character. Influenced by the z-component, the intensity distribution in the vectorial resultant direction will slightly deviate from the negative exponential distribution character .
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Key words:
- continuous phase plate /
- speckle /
- strong focusing condition /
- vector diffraction
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图 2 焦平面上矢量散斑光场的相对振幅
Figure 2. Electric field relative amplitude of vector speckles on the focus plate
图 3 散斑振幅的统计分布，接近瑞利分布
Figure 3. Statistical distribution of speckles amplitude, it’s Rayleigh distribution
图 4 CPP矢量散斑场的光强分布特性
Figure 4. Statistical distribution of vector speckles intensity of CPP
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