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=40⋅43=30
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=24⋅21=12
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.