Interferometric visibility

Visibility in optics

In linear optical interferometers (like the Mach–Zehnder interferometer, Michelson interferometer, and Sagnac interferometer), interference manifests itself as intensity oscillations over time or space, also called fringes. Under these circumstances, the interferometric visibility is also known as the "Michelson visibility" 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:

:\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:

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

where Imax is the maximum intensity of the oscillations and Imin 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 coherence between two optical fields. A theoretical definition for this is given by the degree of coherence. This definition of interference directly applies to the interference of water waves and electric signals.

Examples

Visibility in quantum mechanics

Since the Schrödinger equation is a wave equation and all objects can be considered waves in quantum mechanics, interference is ubiquitous. Some examples: Bose–Einstein condensates can exhibit interference fringes. Atomic populations show interference in a Ramsey interferometer. Photons, atoms, electrons, neutrons, and molecules have exhibited interference in double-slit interferometers.

References

References

1. "Fringe Visibility -- from Eric Weisstein's World of Physics".
2. "Fundamentals of Light and Interference - Fringe Contrast".
3. "Coherence".