Contents

Interferometric visibility

Visibility in optics[edit]

In linear optical interferometers^{[clarification needed]} (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" ^[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]

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

in terms of the amplitude envelope of the oscillating intensity and the average intensity:

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

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

So it can be rewritten as:^[3]

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

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

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

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

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

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

where ${\displaystyle I_{1}}$ and ${\displaystyle I_{2}}$ indicate the intensity of the respective wave. ${\displaystyle \gamma }$ 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[edit]

Visibility in quantum mechanics[edit]

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.

See also[edit]

• Degree of coherence
• Interferometry
• Optical interferometry
• List of types of interferometers
• Hong–Ou–Mandel effect

References[edit]

External links[edit]

• Stedman Review of the Sagnac Effect