MRI Encoding Is a Signal Map

Phase Encoding Step

position becomes an index

A per-metre training scale turns position into a dimensionless phase index. 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 scale is per metre

The phase index scale is 2 per meter. Multiplying by position makes a dimensionless training index.

index scale=2 1/m\text{index scale}=2\ 1/\text{m}
Phase encodingA per-metre training index maps position to dimensionless phase.phasephasezero phase

Position maps to phase index

Positions 0 m, 1 m, and 2 m map to indices 0, 2, and 4. These are not physical radians or Bloch dynamics.

ϕindex=kz\phi_{\text{index}}=kz
Phase encodingA per-metre training index maps position to dimensionless phase.phasephasezero phase