Polarization Boundary and Invariant Scans

Malus Source Scaling Three-Row Scan

A Malus-source-scaling scan varies the source intensity across three rows at a fixed Malus factor, checking that the transmitted intensity I = I0 * cos^2(theta) scales in step with the source row by row. The arithmetic is exact only for the stated source intensities, Malus factors, and rows in the ideal lossless-polarizer model. Real measurements add bandwidth, alignment, detector calibration, polarizer extinction ratio, material dispersion/loss, finite precision, and measurement uncertainty.

A fixed projection factor scales transmitted and blocked intensity. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Fixed projection factor scales the source intensity

The projection factor stays fixed. Increasing only the source intensity scales both transmitted and blocked intensity.

f=45O=50f2=32B=50 − 32=18\begin{array}{c}f=\frac{4}{5}\\O=50f^{2}=32\\B=50\,-\,32=18\end{array}
Malus source-scaling rowThe same projection source is used in each row.projectionSource=boundsourceIrradiance=50 W/m^2projectionFactor=4/5transmittedIrradiance=32 W/m^2blockedIrradiance=18 W/m^2

Fixed projection factor scales the source intensity

The projection factor stays fixed. Increasing only the source intensity scales both transmitted and blocked intensity.

f=45O=75f2=48B=75 − 48=27\begin{array}{c}f=\frac{4}{5}\\O=75f^{2}=48\\B=75\,-\,48=27\end{array}
Malus source-scaling rowThe same projection source is used in each row.projectionSource=boundsourceIrradiance=75 W/m^2projectionFactor=4/5transmittedIrradiance=48 W/m^2blockedIrradiance=27 W/m^2

Fixed projection factor scales the source intensity

The projection factor stays fixed. Increasing only the source intensity scales both transmitted and blocked intensity.

f=45O=100f2=64B=100 − 64=36\begin{array}{c}f=\frac{4}{5}\\O=100f^{2}=64\\B=100\,-\,64=36\end{array}
Malus source-scaling rowThe same projection source is used in each row.projectionSource=boundsourceIrradiance=100 W/m^2projectionFactor=4/5transmittedIrradiance=64 W/m^2blockedIrradiance=36 W/m^2