= Existing-opening constraint in Fresnel aperture optimization
If a screen already has an interval hole, additional removal cannot reduce that hole. A connected final aperture must contain it, imposing lower/upper endpoint constraints on its <Cornu spiral> chord. The unrestricted longest chord need not be feasible. For an existing interval $0\le w\le1.76777$, constrained chord maximization gives approximately $w_-=-1.21578$, $w_+=2.34054$, with point-power ratio1.60257. The two aperture endpoints, rather than just a nominal Fresnel-zone width, determine the received field.
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