Spatial and temporal coherence via polarization mutual coherence function

Abstract

We address polarization coherence in terms of correlations of Stokes variables. We develop an scalar polarization mutual coherence function that allows us to define a polarization coherence time. We find a suitable spectral polarization density allowing a polarization version of the Wiener-Khintchine theorem. With these tools we also address the polarization version of the van Cittert-Zernike theorem.

Identification of Wind Load Exerted on the Jacket Wind Turbines from Optimally Placed Strain Gauges Using C-Optimal Design and Mathematical Model Reduction

“…The stress data parallel to the axial direction of the tower are denoted as y 1 (t), y 2 (t), • • • , y 384 (t), the data at a −45 • angle to the axial direction are represented as y 385 (t), y 386 (t), • • • , y 768 (t), and the data at a 45 • angle to the axial direction are denoted as y 769 (t), y 770 (t), • • • , y 1152 (t). Autocorrelation and cross-correlation functions were computed for these datasets, followed by a Fourier transformation based on the Wiener-Sinchin theorem [41] on the resultant outcomes to derive the spectral matrix of the response of the structure. For example, the autocorrelation and cross-correlation functions were calculated for y 1 (t) and y 2 (t), and a Fourier transform was applied to obtain S y 1 , S y 2 , S y 1 y 2 , and S y 2 y 1 .…”

“…The stress data parallel to the axial dire tion of the tower are denoted as 𝑦 (𝑡), 𝑦 (𝑡), ⋯ , 𝑦 (𝑡), the data at a −45° angle to the ax direction are represented as 𝑦 (𝑡), 𝑦 (𝑡), ⋯ , 𝑦 (𝑡), and the data at a 45° angle to t axial direction are denoted as 𝑦 (𝑡), 𝑦 (𝑡), ⋯ , 𝑦 (𝑡). Autocorrelation and cross-co relation functions were computed for these datasets, followed by a Fourier transformati based on the Wiener-Sinchin theorem [41] on the resultant outcomes to derive the spectr TRM + L-curve was used to solve Equation (22), and the load identification results are presented in Figure 8.…”