Atomic Spectra Relation Cross Scans

Calibration Channel Three-Row Scan

Three matched line energies show the affine channel map. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Calibration scans energy into detector channel

The matched photon energy is 4 joules. With scale 2 channels per joule and offset 1 channel, the displayed channel is 9.

channel=2⋅4+1=8+1=9channel=2\cdot 4 + 1=8 + 1=9
Calibration rowThe affine channel number is bound to the photon energy.E=4 Jchannel=9scale then offsetlowerupper4

Calibration scans energy into detector channel

The matched photon energy is 5 joules. With scale 2 channels per joule and offset 1 channel, the displayed channel is 11.

channel=2⋅5+1=10+1=11channel=2\cdot 5 + 1=10 + 1=11
Calibration rowThe affine channel number is bound to the photon energy.E=5 Jchannel=11scale then offsetlowerupper5

Calibration scans energy into detector channel

The matched photon energy is 6 joules. With scale 2 channels per joule and offset 1 channel, the displayed channel is 13.

channel=2⋅6+1=12+1=13channel=2\cdot 6 + 1=12 + 1=13
Calibration rowThe affine channel number is bound to the photon energy.E=6 Jchannel=13scale then offsetlowerupper6