= Optical path delay in crossed-beam interference
{title2=$\Delta y=\Delta\ell/\sqrt2$}
For the right-angle geometry of <temporal coherence from crossed beams>, a physical arm-path delay $\Delta\ell$ gives $I(y)=I_0+\operatorname{Re}\Gamma(\sqrt2y/c+\Delta\ell/c)$, with the sign set by the delayed arm. A quarter-cycle optical phase delay requires $\Delta\ell=\lambda/4$; it shifts the fringe pattern by a quarter of its period, $\lambda/(4\sqrt2)$. A path delay equal to that latter length is a different operation. Replacing the shifted correlation by a phase multiplier additionally requires the delay to be small compared with the envelope <optical coherence time>.
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