Source-Bound Boundary Scans

Path Difference Boundary Three-Row Scan

Model check. This lesson uses exact small training values (not measured constants) so every relationship is checkable to the digit. Real instruments report measured values with units, significant figures, and uncertainty; the idealized numbers here isolate the rule, not a measurement.

A one-metre path change can reject a bright row and accept a dark row. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Bright row closes at one whole wavelength

Path B is 12 m while path A stays ten metres. The path difference is 2 m. The bright target is 2 m, so the row is accepted.

Δ=12 m−10 m=2 mT=(1+0)2 m=2 mA=1\Delta=12\ \text{m}\mathbin{-}10\ \text{m}=2\ \text{m}\quad T=\left(1+0\right)2\ \text{m}=2\ \text{m}\quad A=1
Path boundary rowThe path vectors, wavelength, mode, half-wave bit, and acceptance bit are checked.path Apath BpathA=10 mpathB=12 mpathDifference=2 mwavelength=2 morder=1 counthalfWaveBit=0 bitmode=brightacceptedBit=1 bit

The same path misses the bright target

Path B is 13 m while path A stays ten metres. The path difference is 3 m. The bright target is 2 m, so the row is rejected.

Δ=13 m−10 m=3 mT=(1+0)2 m=2 mA=0\Delta=13\ \text{m}\mathbin{-}10\ \text{m}=3\ \text{m}\quad T=\left(1+0\right)2\ \text{m}=2\ \text{m}\quad A=0
Path boundary rowThe path vectors, wavelength, mode, half-wave bit, and acceptance bit are checked.path Apath BpathA=10 mpathB=13 mpathDifference=3 mwavelength=2 morder=1 counthalfWaveBit=0 bitmode=brightacceptedBit=0 bit

The missed bright row is a dark row

Path B is 13 m while path A stays ten metres. The path difference is 3 m. The dark target is 3 m, so the row is accepted.

Δ=13 m−10 m=3 mT=(1+12)2 m=3 mA=1\Delta=13\ \text{m}\mathbin{-}10\ \text{m}=3\ \text{m}\quad T=\left(1+\frac{1}{2}\right)2\ \text{m}=3\ \text{m}\quad A=1
Path boundary rowThe path vectors, wavelength, mode, half-wave bit, and acceptance bit are checked.path Apath BpathA=10 mpathB=13 mpathDifference=3 mwavelength=2 morder=1 counthalfWaveBit=1 bitmode=darkacceptedBit=1 bit