The same film path can accept or reject depending on the phase-flip target. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Dark with one phase flip closes at the whole-order target

The film path stays four metres. The mode is dark and the phase-flip bit is 1, making the target 4 m. The row is accepted.

P=221 m=4 mT=(2+0)2 m=4 mA=1P=2\cdot2\cdot1\ \text{m}=4\ \text{m}\quad T=\left(2+0\right)2\ \text{m}=4\ \text{m}\quad A=1
Thin-film phase boundary rowThe film path, mode, phase-flip bit, target, and acceptance bit are checked.thicknessrefractiveIndex=2thickness=1 mopticalPath=4 mwavelength=2 mphaseFlipBit=1 bitmode=darkorder=2 countacceptedBit=1 bit

Dark without the flip shifts to a half-order target

The film path stays four metres. The mode is dark and the phase-flip bit is 0, making the target 5 m. The row is rejected.

P=221 m=4 mT=(2+12)2 m=5 mA=0P=2\cdot2\cdot1\ \text{m}=4\ \text{m}\quad T=\left(2+\frac{1}{2}\right)2\ \text{m}=5\ \text{m}\quad A=0
Thin-film phase boundary rowThe film path, mode, phase-flip bit, target, and acceptance bit are checked.thicknessrefractiveIndex=2thickness=1 mopticalPath=4 mwavelength=2 mphaseFlipBit=0 bitmode=darkorder=2 countacceptedBit=0 bit

Bright without the flip returns to the whole-order target

The film path stays four metres. The mode is bright and the phase-flip bit is 0, making the target 4 m. The row is accepted.

P=221 m=4 mT=(2+0)2 m=4 mA=1P=2\cdot2\cdot1\ \text{m}=4\ \text{m}\quad T=\left(2+0\right)2\ \text{m}=4\ \text{m}\quad A=1
Thin-film phase boundary rowThe film path, mode, phase-flip bit, target, and acceptance bit are checked.thicknessrefractiveIndex=2thickness=1 mopticalPath=4 mwavelength=2 mphaseFlipBit=0 bitmode=brightorder=2 countacceptedBit=1 bit