 Equal-brightness binary-star visibility

Let identical spatially incoherent stellar brightness profiles of equal integrated flux be displaced by projected angles $\pm \beta /2$ along an interferometer baseline. The Fourier shift property makes their normalized signed coherence $g(Y)=g_{\star }(Y)\cos (\pi \beta Y/\lambda )$. The observed visibility is its absolute value. The slow single-star envelope depends on each star's brightness profile, while the oscillatory factor records projected separation. Unequal flux prevents complete cancellation at the binary minima.