二维斜周期阵列的分数泰伯效应

对振幅型二维斜周期阵列分数泰伯效应的研究,可以为设计和制作新型阵列发生器提供必要的理论依据。通过坐标的旋转与倾斜描述二维振幅型斜周期阵列,根据菲涅耳变换公式在理论上研究这类斜周期阵列的自成像效应,并进一步讨论了分数泰伯距离处像场的振幅分布与相位分布,给出了具体的相位计算公式。以60°斜交周期菱形阵列为例,模拟计算了它们在各自分数泰伯距离处的像,模拟计算的结果与数学公式推导的结果一致。并简单讨论了利用这种周期结构,设计和制作新型阵列发生器的可行性。另外,还对二维斜周期菱形阵列与正交周期方形阵列在压缩比例和光斑模式等特性上进行了比较分析。

Fractional Talbot Effect of 2D Skewed Periodic Array

The study of fractional Talbot effect of the 2D amplitude skewed array is very important to the designation and manufacture of the new type array illumination. The fractional self-imaging effect of the 2D array with arbitrary shape and symmetry is studied theoretically, using scalar diffraction theory and the known periodic self-Fourier-Fresnel transform function comb(x,y). As a result, a general equation to calculate the phase of the fractional Talbot image of the 2D array is also got. As an example, the intensity distribution of the 60° skewed diamond periodic array in different fractional Talbot planes is numerically evaluated using Matlab. The result is a good agreement with the theory. Based on the theory, the reliability of the designation and manufacture of this skewed diamond array illumination is briefly discussed. Additionally, comparisons of the characteristics are made for the 2D amplitude skewed array and the 2D amplitude orthogonal array in the compression ratio and shape of the light spot.