Coherence Boundary Depth Scans

readout-overlap-boundary-three-row-scan

Positive overlap has a boundary before endpoint touch fails. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Readout needs positive overlap with the window

The window is fixed, and the signal interval moves toward the edge.

m=Δtoverlap−Δtmin⁡m=\Delta t_{\text{overlap}}-\Delta t_{\min}
Positive overlapThe signal overlaps the window by more than the minimum.windowsignaloverlapsignal accepted

Three signal intervals show the positive-overlap boundary

A one-unit overlap is the boundary; endpoint touch has zero overlap and fails.

tstarttendΔtm583210111011130−1\begin{array}{c|c|c|c}t_{\text{start}}&t_{\text{end}}&\Delta t&m\\5&8&3&2\\10&11&1&0\\11&13&0&-1\\\end{array}
Overlap boundaryOne positive unit is still accepted.windowsignaloverlapsignal accepted

Endpoint touch fails because overlap is zero

The interval check treats endpoint touch as no positive overlap.

m=−1failm=-1\quad \text{fail}
Endpoint touch rejectedThe overlap duration is zero.windowsignalno overlapsignal rejected