Interferometric visibility
The interferometric visibility is a measure of the contrast of interference in any system subject to wave superposition.
Examples include as optics, quantum mechanics, water waves, sound waves, or electrical signals.
Visibility is defined as the ratio of the amplitude of the interference pattern to the sum of the powers of the individual waves.
The interferometric visibility gives a practical way to measure the coherence of two waves. A theoretical definition of the coherence is given by the degree of coherence, using the notion of correlation.
Generally, two or more waves are superimposed and as the phase difference between them varies, the power or intensity of the resulting wave oscillates, forming an interference pattern. The pointwise definition may be expanded to a visibility function varying over time or space. For example, the phase difference varies as a function of space in a two-slit experiment. Alternately, the phase difference may be manually controlled by the operator, for example by adjusting a vernier knob in an interferometer.
Visibility in optics
In linear optical interferometers, 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 of the two interfering waves equals the average intensity over a given time or space domain. The visibility is written as:in terms of the amplitude envelope of the oscillating intensity and the average intensity:
So it can be rewritten as:
where Imax is the maximum intensity of the oscillations and Imin the minimum intensity of the oscillations.
If the two optical fields are ideally monochromatic point sources of the same polarization, then the predicted visibility will be
where and indicate the intensity of the respective wave. 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
Image:visibility.png|left|thumb|Visibility in a Mach–Zehnder interferometer is constant.Image:double slit visibility.png|thumb|Visibility in this double-slit interference is maximum at the center.
Image:HOM visibility.png|thumb|Visibility in Hong–Ou–Mandel interference. At large delays the photons do not interfere. At zero delays, the detection of coincident photon pairs is suppressed.