利用部分相干光理论对多色光源照明下光栅的菲涅耳衍射进行了理论分析,得到了任意谱相干度照明下光栅衍射光强分布的一般公式,并对脉冲激光光源和连续的多色光源照明下光栅的菲涅耳衍射进行了相应的数值计算,进而讨论了光源的频谱分布对光栅泰伯效应的影响。理论结果表明超短脉冲的有限弛豫时间对光栅自成像的影响与多色连续光源的谱分布对光栅自成像的影响完全等价。这一等价性为借助于连续多色光照明下光栅的菲涅耳衍射来研究超短脉冲激光照明下光栅的菲涅耳衍射提供了理论依据。实验中选用发光二极管(LED)作为照明光源,对连续多色光照明下光栅的自成像分布进行了测量,实验结果和理论分析相符合。

Using of the cross mutual spectral density of the partially coherent theory, the self-imaging of grating under illumination with arbitrary degree of partial coherence is developed. Both the temporal and the averaged distributions of diffracted intensities at the self-imaging distances are formulated, which can be applied to either continuous or pulsed illuminations with any kind of spectra. The theoretical result shows that the ultra-short laser pulse and the continuous polychromatic illuminations, whose spectrum distributions are the same, have the similar averaged self-image distribution. So, the Talbot effect may help to study the temporal and spectral characteristics of ultra-short laser pulses. An experiment using a light-emitting diode (LED) as the source of illumination is performed, and the experimental results confirm with the theoretical ones.