In Quantum Optics, the two-photon interference is popularly known as Hong Ou Mandel interference. The visibility of this interference is calculated using the formula V = (C_max -- C_min)/(C_max + C_min). Where C_max and C_min are the minimum and maximum of the co-incidence counts.
But in some of the research articles, people use a modified form of this formula which is like this (C_max -- C_min)/C_max.
The second formula will give us a higher value of the visibility with the same value of the coincidence counts. Which one is correct?
Dear Sandeep,
In my opinion, the second definition is more natural when 0
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As long as they’re definitions of visibility, it doesn't make sense to ask which is the correct expression. It’s a matter of convention.
I agree with Stam.
Finally, you need to compare different visibilities with each other. Any description you use, the final comparison will be the same.
Describimg these type of concepts looks like the description of phase. Phase by iotself is meaninglesse, the only meaningful term is "phase difference".
I know I am a year late, but I wanted to explain the way I understand it for anyone else having the same question. This is also pretty much Miccola's answer with more details.
The most generic formula for interference visibility is V=Amplitude/Average of your signal's intensity. Normally, this is for wave interference but it takes a different form when you measure single photon interference (which is what the HOM measures).
If your signal is oscillating (similar to a sine/cosine function), then your Amplitude=(Max-Min)/2, and your Average=(Max+Min)/2. Hence, interference Visibility=(Max-Min)/(Max+Min). This is the typical formula for wave interference.
On the other hand, in a HOM measurement, your coincidence detection drops due to the HOM effect only when the delay between events is ~0. This behavior is similar to a delta function. In this case, your Amplitude=Max-Min (the depth of your valley), and your Average≅Max (since the coincidences are consistently at their Max except for a small area near the zero delay). Hence, HOM Visibility=(Max-Min)/Max.
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