Deeper Calibration Gate Topology

Calibration Standard Line Scan

slope and offset identity

Standards determine slope and offset before any unknown is inverted. 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 first standard pair fixes slope and offset

Standards (0, 4) and (4, 12) give slope 2 and offset 4.

m=2,b=4m=2,\quad b=4
Calibration lineStandards fix slope, offset, inverse value, and range gate.low standardhigh standard

A shifted standard pair can give a smaller offset

Standards (1, 3) and (5, 11) still give slope 2, but offset 1.

m=2,b=1m=2,\quad b=1
Calibration lineStandards fix slope, offset, inverse value, and range gate.low standardhigh standard

A steeper standard pair changes the line identity

The third row uses standards (0, 3) and (3, 12), giving slope 3 and offset 3.

m=3,b=3m=3,\quad b=3
Calibration lineStandards fix slope, offset, inverse value, and range gate.low standardhigh standard