= Transverse coherence estimate
Convert the distances to SI units: $r=1.5\times10^{11}\,\mathrm m$ and $D=1.4\times10^9\,\mathrm m$. The angular solar diameter is
$$
\Theta\simeq\frac Dr=9.33\times10^{-3}\,\mathrm{rad}.
$$
Two receivers separated by a transverse baseline $b$ see a spread of relative <wave phases> of order $2\pi b\Theta/\lambda$. Averaging over incoherent source directions therefore reduces <interferometric visibility> when $b$ reaches the <transverse optical coherence length> scale $\lambda/\Theta$. At $\lambda=500\,\mathrm{nm}$,
$$
\boxed{\ell_\perp\sim\frac{\lambda r}{D}
=\frac{(5.00\times10^{-7})(1.5\times10^{11})}{1.4\times10^9}\,\mathrm m
=5.36\times10^{-5}\,\mathrm m\simeq54\,\mu\mathrm m.}
$$
If “coherence length” specifically means the first zero of <uniform-disk stellar visibility>, a uniformly bright circular solar disk gives $g^{(1)}(b)=2J_1(x)/x$, with $x=\pi b\Theta/\lambda$. The first zero then lies at $\boxed{b_0=1.21967\lambda/\Theta\simeq65\,\mu\mathrm m}$. This more specific number assumes a uniform disk and a first-zero criterion; the characteristic estimate is approximately $50$–$60\,\mu\mathrm m$. Solar brightness variation across the disk changes the exact contrast curve.
Back to article page
