Thin Film Phase And Source Audit

thin-film-phase-flip-makes-reflected-dark

A thin-film dark claim is accepted by optical path plus phase-flip bookkeeping. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The film path is twice index times thickness

The reflected rays cross the film thickness twice. The helper records the optical path before applying the phase-flip bit.

2nt=2⋅1 m=4 m2nt=2\cdot1\ \text{m}=4\ \text{m}
Thin-film path setupThe optical path is checked before the dark verdict.thicknessrefractiveIndex=2thickness=1 mopticalPath=4 mwavelength=2 mphaseFlipBit=1 bitmode=darkorder=2 countacceptedBit=1 bit

The phase bit is part of the verdict

The same optical path can change verdict when the phase-flip bit changes. A thicker film is also rejected if it does not match the same dark row.

ntpathflipaccepted21 m4 m1121 m4 m0022 m8 m10\begin{array}{c|c|c|c|c}n&t&\text{path}&\text{flip}&\text{accepted}\\2&1\ \text{m}&4\ \text{m}&1&1\\2&1\ \text{m}&4\ \text{m}&0&0\\2&2\ \text{m}&8\ \text{m}&1&0\\\end{array}

A phase flip can make an integer film path dark

The reflected dark claim is accepted because the optical path and the phase-flip bit are both checked.

path=(2)nt=2⋅2⋅1 m=4 m;accepted=1\text{path}=(2)nt=2\cdot2\cdot1\ \text{m}=4\ \text{m};\quad \text{accepted}=1
Thin-film dark ledgerOptical path and phase flip jointly decide the reflected label.thicknessrefractiveIndex=2thickness=1 mopticalPath=4 mwavelength=2 mphaseFlipBit=1 bitmode=darkorder=2 countacceptedBit=1 bit