phase-flip-bit-changes-the-bright-verdict

Flipping the phase-flip bit swaps the bright and dark verdicts, because the half-wave shift changes which path differences constructively combine. The arithmetic is exact only for the stated wavelength, film thickness, refractive index, and phase-flip bit in the ideal thin-film model. Real films add finite bandwidth, thickness variation, imperfect surfaces, angle spread, index dispersion, calibration, and measurement/source uncertainty.

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

highlighted = computed this step

Hold the optical path fixed

Both comparison films use the same optical path. That isolates the phase-flip bit as the change being tested.

\text{path}=3\ \text{m}

Changing only the phase bit changes the verdict

The first two rows have the same path. The accepted bit changes because the phase-flip bit changes, not because the path changed.

\begin{array}{c|c|c|c|c}n&t&\text{path}&\text{flip}&\text{accepted}\\\frac{3}{2}&1\ \text{m}&3\ \text{m}&1&1\\\frac{3}{2}&1\ \text{m}&3\ \text{m}&0&0\\\frac{3}{2}&2\ \text{m}&6\ \text{m}&1&0\\\end{array}

The phase-flip bit changes the bright verdict

Both films have the same optical path, but only the one with the checked phase-flip bit accepts the bright label.

\text{path}=3\ \text{m};\quad \text{flip}=1\Rightarrow1;\quad \text{no flip}\Rightarrow0