X-Ray Source Control Depth Scans

Projected Spot Address Family Scan

The reciprocal-map spot is a projected source address, not a free label. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The displayed spot is only the projected address

The reflection ledger records all three Miller indices, while the training map displays the projected pair.

(h,k,l)↦(h,k)(h,k,l)\mapsto(h,k)
X-ray reflection ledgerThe Miller spacing, Bragg path, and projected reciprocal spot share one source.spacingspacingplane familyhkl=2,1,2spot=2,1d=5 mlambda=6 mpath=6 maccepted=1planeplanepath: 6 m

Three families keep the projection source-bound

Changing the hidden third index can change the spacing without changing the two-dimensional rule.

(h,k,l)(h,k)d(1,0,0)(1,0)15 m(2,1,2)(2,1)5 m(3,0,4)(3,0)3 m\begin{array}{c|c|c}(h,k,l)&(h,k)&d\\(1,0,0)&(1,0)&15\ \text{m}\\(2,1,2)&(2,1)&5\ \text{m}\\(3,0,4)&(3,0)&3\ \text{m}\\\end{array}

The middle row projects to two comma one

Family 2,1,2 projects to spot 2,1 while spacing stays 5 m.

(2,1,2)↦(2,1)d=5 m(2,1,2)\mapsto(2,1)\quad d=5\ \text{m}
X-ray reflection ledgerThe Miller spacing, Bragg path, and projected reciprocal spot share one source.spacingspacingplane familyhkl=2,1,2spot=2,1d=5 mlambda=6 mpath=6 maccepted=1planeplanepath: 6 m