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=2⋅2⋅1m=4mT=(2+0)2m=4mA=1
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=2⋅2⋅1m=4mT=(2+21)2m=5mA=0
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.