= Interferometric visibility
{title2=$\mathcal V=(I_{\max}-I_{\min})/(I_{\max}+I_{\min})$}
{wiki}
= Interference visibility
{synonym}
<Interferometric visibility> measures the contrast of a scanned <interference fringe>. For the mutually coherent, equally polarized two-beam model in <wave interference>, with fixed individual <wave intensities> and $I_1+I_2>0$, the <constructive interference intensity> and <destructive interference intensity> give
$$
\mathcal V=\frac{I_{\max}-I_{\min}}{I_{\max}+I_{\min}}=\frac{2\sqrt{I_1I_2}}{I_1+I_2}.
$$
Equal nonzero <wave intensities> give $\mathcal V=1$; $I_1=1,I_2=0.25$ give $\mathcal V=0.8$. Unequal <wave intensities> can therefore reduce <interferometric visibility> even with perfect mutual <optical coherence>. Random <phase differences> or distinguishable <wave polarizations> can reduce it further; zero contrast alone does not identify the cause. Both intensities zero leave the ratio undefined.
For normalized paths with <complex amplitudes> $\alpha,\beta$ and identical internal states, the output <probability> is $1/2+\operatorname{Re}(\alpha^*\beta e^{i\theta})$, so $\mathcal V=2|\alpha\beta|$. A <photon polarization> fringe alone determines transverse <quantum coherence> but not the sign of the population difference.
// Target: optics.bigb
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