Spatial coherence of bending magnet radiation and application limit of the van Cittert-Zernike theorem

In this paper we discuss how the first-order spatial coherence of bending magnet radiation is determined. We present an analytical representation of the coherence and compare it with the numerical calculations based on the first principles. It is shown that if the electron-beam size is so large that some conditions are satisfied, the van Cittert-Zernike theorem can be used without any modification in the vertical and horizontal directions. The formalism presented will be useful in judging whether or not the electron-beam size in the storage ring can be estimated directly from the van Cittert-Zernike theorem using the synchrotron radiation interferometer.