Deeper Grating Scans

Grating Sine Marker Three-Row Scan

Only one sine marker closes the selected spacing, order, and wavelength. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Low sine marker undershoots the target

Spacing 10 m times sine marker 1/5 gives 2 m. Order 2 times wavelength 2 m gives 4 m, so this row is rejected.

10 m⋅15=2 mmλ=2⋅2 m=4 mA=010\ \text{m}\cdot\frac{1}{5}=2\ \text{m}\quad m\lambda=2\cdot2\ \text{m}=4\ \text{m}\quad A=0
Grating relation rowThe grating spacing, sine marker, order, wavelength, and acceptance bit are checked.sinegratingSpacing=10 msineFactor=1/5wavelength=2 morder=2 countacceptedBit=0 bit

Middle sine marker closes exactly

Spacing 10 m times sine marker 2/5 gives 4 m. Order 2 times wavelength 2 m gives 4 m, so this row is accepted.

10 m⋅25=4 mmλ=2⋅2 m=4 mA=110\ \text{m}\cdot\frac{2}{5}=4\ \text{m}\quad m\lambda=2\cdot2\ \text{m}=4\ \text{m}\quad A=1
Grating relation rowThe grating spacing, sine marker, order, wavelength, and acceptance bit are checked.sinegratingSpacing=10 msineFactor=2/5wavelength=2 morder=2 countacceptedBit=1 bit

High sine marker overshoots the target

Spacing 10 m times sine marker 3/5 gives 6 m. Order 2 times wavelength 2 m gives 4 m, so this row is rejected.

10 m⋅35=6 mmλ=2⋅2 m=4 mA=010\ \text{m}\cdot\frac{3}{5}=6\ \text{m}\quad m\lambda=2\cdot2\ \text{m}=4\ \text{m}\quad A=0
Grating relation rowThe grating spacing, sine marker, order, wavelength, and acceptance bit are checked.sinegratingSpacing=10 msineFactor=3/5wavelength=2 morder=2 countacceptedBit=0 bit