杨氏双孔干涉光波通过准均匀介质散射的光谱恒定条件研究

Invariance for Spectral Density of Interfered Light from Young＇s Double Pinhole Scattering on Quasi-Homogeneous Medium

基于一阶玻恩近似和光波的傍轴传播条件，解析推演获得杨氏双孔干涉光波通过准均匀介质散射的光谱强度表示式。利用散射势强度的傅里叶变换项为空间快变函数这一重要性质，进一步将散射光谱强度近似展开为仅包含散射势相关系数的傅里叶变换项叠加的形式。此外，还得到一组使得散射光谱强度保持恒定的介质散射势标度定律。该定律表明，当散射势相关系数的傅里叶变换项可分解为频谱分量与空间函数乘积的形式，且分解的频谱量与频率二次方的倒数成正比时，散射光谱将保持恒定，并与入射杨氏双孔的平面波光谱分布完全相同。以上研究开拓了干涉光波经介质散射的理论模型，为鬼成像探测、光学相干层析等工作提供了重要的理论依据。

On the basis of the first-order Born approximation and paraxial assumption of light waves, we derive expressions for the spectral density of light which firstly interferes from Young′s pinholes and subsequently scatters on quasi-homogeneous （QH） medium. By utilizing the essential property that the Fourier transforms of the intensity of scattering potential can, in general, be a fast function with regard to spatial locations, the spectral density of scattered field can be approximately expanded into a sum of terms which only incorporate the Fourier transform of the correlation coefficient of scattering potential. Moreover, we also obtain a class of analytical conditions for the scattering potential which can ensure the invariance of the spectral density of scattered field. It shows that the spectral density of scattered field would be invariant and the same as that of plane waves which incidents upon Young′s pinholes, as long as the Fourier transform of correlation coefficient of scattering potential can be decomposed into the product of frequency term and spatial function, and also the decomposed frequency term should be proportional to the inverse of the square of frequency. The obtained results have developed the analytical model for interfered light waves scattering on medium and provided significant values for works such as the ghost imaging and optical coherence tomography.