The visible phase signal is an ideal count multiplied by coherent fraction. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Coherent fraction scales the ideal signal

The first row keeps 60 coherent shots out of 80. Multiplying ideal visible count 40 by fraction 3/4 gives 30.

Nvisible=4034=30N_{\text{visible}}=40\cdot\frac{3}{4}=30
Visible signal scan rowThe coherent bar sets the visible fraction.3/4coherent1/4dephasedvisible fringe

One half coherence halves the visible signal

The second row has 30 coherent and 30 dephased shots, so the coherent fraction is 1/2. The visible count is 12.

Nvisible=2412=12N_{\text{visible}}=24\cdot\frac{1}{2}=12
Visible signal scan rowThe dephased half does not enter visibility.1/2coherent1/2dephasedvisible fringe

Lower coherence reduces the same style of count

The final row keeps 40 coherent shots out of 100, so only 2/5 of the ideal count remains visible. The result is 20.

Nvisible=5025=20N_{\text{visible}}=50\cdot\frac{2}{5}=20
Visible signal scan rowThree rows show visibility as count scaling.2/5coherent3/5dephasedvisible fringe