Stellar angular diameter from a visibility envelope ($\alpha =1.21967\lambda /Y_0$)

For a uniform circular stellar disc, the first zero of $J_1$ at $x=3.831706\dots$ gives $Y_0=1.21967\lambda /\alpha$ when $\alpha$ is full angular diameter. In contrast a one-dimensional top-hat angular profile of full width $\alpha$ has a sinc envelope with $Y_0=\lambda /\alpha$. Diameter estimates therefore require a brightness-profile convention. A binary additionally multiplies the envelope by its separation-dependent interference factor.