Polarization Relation Cross-Scans

projection-axis-three-row-scan

Aligned, slanted, and crossed axes show the passed field component as a component ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Aligned axis passes the whole field component

With axis factor 1, the incoming 10 volts per metre remains 10 volts per metre along the polarizer axis.

E∥=10 V/m⋅1=10 V/mE_{\parallel}=10\ \text{V}/\text{m}\cdot1=10\ \text{V}/\text{m}
Projection scan rowThe aligned row keeps the full axis field.incidentField=10 V/maxisMode=alignedparallelFactor=1parallelField=10 V/mperpendicularField=0 V/macceptedBit=1 bit

A three-four-five axis passes six volts per metre

The middle row uses projection factor 3/5 and passes 6 volts per metre from the same incident field.

E∥=10 V/m⋅35=6 V/mE_{\parallel}=10\ \text{V}/\text{m}\cdot\frac{3}{5}=6\ \text{V}/\text{m}
Projection scan rowThe slanted row exposes the component split.incidentField=10 V/maxisMode=three-four-fiveparallelFactor=3/5parallelField=6 V/mperpendicularField=8 V/macceptedBit=1 bit

Crossed axis passes zero field component

Crossed orientation changes the projection factor to 0, so the axis component is 0 volts per metre.

E∥=10 V/m⋅0=0 V/mE_{\parallel}=10\ \text{V}/\text{m}\cdot0=0\ \text{V}/\text{m}
Projection scan rowThe crossed row makes the zero component explicit.incidentField=10 V/maxisMode=crossedparallelFactor=0parallelField=0 V/mperpendicularField=10 V/macceptedBit=1 bit