针对叠栅层析研究中采用基于相位重建方法处理叠栅条纹图像的问题, 用标量衍射理论对叠栅偏折仪的叠栅条纹形成原理进行分析。通过小孔滤波分别提取光场的零级和一级频谱, 分析结果与传统的通过几何叠加原理的结果一致, 在形式上更加精确。结论表明, 叠栅条纹是多波面剪切干涉的结果, 且一级频谱滤波下的叠栅条纹图像满足严格的余弦强度分布。采用基于多重网格相位展开的傅里叶变换方法和叠栅层析滤波反投影算法对丙烷燃烧场进行了层析重建。

According to the problem that processing moiré fringes based on phase reconstruction methods in moiré deflection tomography, the formation of moiré fringes is analyzed from the scalar diffraction theory. The zero-and first-order frequency spectrum is extracted respectively by pinhole filtering. Compared with results from the traditional geometric superposition principle of moiré effect, Result in this paper fits well and has a more accurate form. Results show that the moiré fringes are generated by shearing interference of multiple wave fronts and moiré patterns with first-order filtering are the strict cosinusoidal intensity distribution. Finally, the combustion of propane in the air is reconstructed by using the Fourier transform method which based on multi-grid phase unwrapping algorithm and the filtered back-projection algorithm of moiré tomography.