Closure phase ($\Phi ={\varphi }_{12}+{\varphi }_{23}+{\varphi }_{31}$)

For three collectors whose measured pair phases are ${\varphi }_{ij}={\varphi }_{ij}^{\mathrm{source}}+{ϵ}_i-{ϵ}_j$, the oriented sum around the triangle cancels the collector-based errors. closure phase retains source phase information, including asymmetry, but does not cancel arbitrary baseline-dependent errors or fill missing spatial-frequency coverage.