Interferometric visibility

The interferometric visibility (also known as interference visibility and fringe visibility, or just visibility when in context) is a measure of the

wave superposition

. Examples include as optics, quantum mechanics, water waves, sound waves, or electrical signals. Visibility is defined as the ratio of the

interference pattern

to the sum of the powers of the individual waves. The interferometric visibility gives a practical way to measure the

degree of coherence

, using the notion of correlation.

Generally, two or more waves are

interferometer

.

Visibility in optics

In linear optical

fringes. Under these circumstances, the interferometric visibility is also known as the "Michelson visibility" ^[1] or the "fringe visibility." For this type of interference, the sum of the intensities (powers) of the two interfering waves equals the average intensity over a given time or space domain. The visibility is written as:^[2]

\nu =A/{\bar {I}},

in terms of the amplitude

envelope

of the oscillating intensity and the average intensity:

A=(I_{\max }-I_{\min })/2,

{\bar {I}}=(I_{\max }+I_{\min })/2.

So it can be rewritten as:[3]

\nu ={\frac {I_{\max }-I_{\min }}{I_{\max }+I_{\min }}},

where I_max is the maximum intensity of the oscillations and I_min the minimum intensity of the oscillations.

I_{max}=I_{1}+I_{2}+2*{\sqrt {I_{1}*I_{2}}}*|\gamma |,

I_{min}=I_{1}+I_{2}-2*{\sqrt {I_{1}*I_{2}}}*|\gamma |,

If the two optical fields are ideally

monochromatic (consist of only single wavelength) point sources of the same polarization

, then the predicted visibility will be

\nu ={\frac {2{\sqrt {I_{1}I_{2}}}|\gamma |}{I_{1}+I_{2}}},

where $I_{1}$ and $I_{2}$ indicate the intensity of the respective wave. $\gamma$ indicates the phase relationship of the original electric field. Any dissimilarity between the optical fields will decrease the visibility from the ideal. In this sense, the visibility is a measure of the