Van Cittert-Zernike theorem (source code)

= Van Cittert-Zernike theorem
{c}
{title2=$g(\mathbf b)=\widetilde I(\mathbf b/\lambda)/\widetilde I(0)$}

For a distant spatially incoherent quasimonochromatic source in the small-angle regime, the equal-delay mutual coherence across projected baseline $\mathbf b$ is the <Fourier transform> of its angular <intensity>. With matched collector response, the normalized degree is $g(\mathbf b)=\int I(\boldsymbol\theta)e^{-i2\pi\mathbf b\cdot\boldsymbol\theta/\lambda}d^2\theta/\int I(\boldsymbol\theta)d^2\theta$. Equal collector <intensities> and matched polarizations make fringe visibility $|g|$. Finite bandwidth and unmatched optical paths introduce additional temporal-coherence averaging.