Laatikainen Jyrki, Luo Meilan, Halder Atri, Koivurova Matias, Setälä Tero, Turunen Jari, Friberg Ari T
J Opt Soc Am A Opt Image Sci Vis. 2023 Jun 1;40(6):1260-1267. doi: 10.1364/JOSAA.489647.
We examine cross-spectral purity of random, nonstationary (pulsed), scalar light fields with arbitrary spectral bandwidth. In particular, we derive a reduction formula in terms of time-integrated coherence functions, which ensures cross-spectral purity of interfering fields having identical normalized spectra. We further introduce fields that are cross-spectrally pure in either a global or local sense. Our analysis is based on an ideal field superposition realizable with all-reflective wavefront-shearing interferometers. Such devices avoid certain problems related to Young's interferometer, which is the framework customarily employed in assessing cross-spectral purity. We show that any partially coherent beam can be transformed into a locally cross-spectrally pure beam whose cross-spectral density is specular. On the other hand, lack of space-frequency (and space-time) coupling ensures cross-spectral purity in the global sense, i.e., across an entire transverse plane, regardless of the spectral bandwidth or the temporal shape of the pulses.
我们研究了具有任意光谱带宽的随机、非平稳（脉冲）标量光场的交叉谱纯度。特别地，我们根据时间积分相干函数推导了一个简化公式，该公式确保了具有相同归一化光谱的干涉场的交叉谱纯度。我们进一步引入了在全局或局部意义上交叉谱纯的场。我们的分析基于全反射波前剪切干涉仪可实现的理想场叠加。此类装置避免了与杨氏干涉仪相关的某些问题，杨氏干涉仪是评估交叉谱纯度时通常采用的框架。我们表明，任何部分相干光束都可以转换为局部交叉谱纯光束，其交叉谱密度是镜面反射的。另一方面，缺乏空间频率（和时空）耦合确保了全局意义上的交叉谱纯度，即在整个横向平面上，无论光谱带宽或脉冲的时间形状如何。
