Coherence length

The coherence length is in the optical path length or the maximum delay time difference, may have the two light beams from the same source, so that still creates a ( spatially and temporally ) stable interference pattern in their superposition. The coherence length is the result of the temporal coherence, and corresponds to the optical path length traveled by light during the coherence time.

To understand it is important to understand that real, not idealized light sources are considered in this context in particular. In this economy, that they emit not absolutely monochromatic light waves that have a time-constant polarization and phase relationship to each other. In absolute monochromatic light, the coherence length is infinite. Lasers produce light with a large to very large coherence length (up to several kilometers ). In natural light (sunlight, flame, heat, radiation, etc.), the concept is hardly applicable, a coherence length here would be in the region of the central wavelength ( order of 10 -6m ). This reflects visible interference pattern only to slim light beams, the coherence length can reach a few meters.

Simple Explanation

Coherence length is defined as the distance at which one can predict or ensure the positions of the zero crossings in the wave field, if you know the distance between two adjacent zero crossings. You can do this with an example from the crystallography compare: For example, when silicon is known in a single crystal of the crystal orientation of a few atoms of the seed crystal and the exact atomic distances in it, you can predict the position of very distant atoms exactly in silicon up to several meters. This safe distance, the coherence length.

Example

The upper curve shows many regular oscillations between A and B. The path difference in an interference experiment must be shorter than the distance between A and B, so that the beginning and end of the train of oscillations overlap and just give a visible interference pattern.

The wave form below has a much shorter coherence length, it also consists of individual oscillation trains, which are separated by phase jumps. Assume that the path length difference of the interference experiment is the same length as the distance DE. Then this wave produces a fortiori, no pattern, shorter (such as FG). In contrast, EF and GH can just create interference patterns. Overall, a poorly visible pattern is found, because the constantly re- appearing anywhere on interference maxima provide ( for example, between the last end of EF and the start of GH with undefined phase relationship) an increasing background brightness.

There are several causes for finite coherence length:

• When solids are as many different energy levels of the atomic shell that no longer separate spectral lines can be observed. The coherence length is only in the range of nanometers, resulting, according to Fourier analysis to a very large frequency and wavelength blur.
• Shortly after the " show" begins a neighboring atom unabgesprochen with its own broadcast on the same frequency with different phase positions. Even if both individual consignments proceed undisturbed, resulting in the sum of three phase jumps.

Laser light, however, is considered the best producible monochromatic light at all and has the largest coherence length ( up to several kilometers ). A helium -neon laser, for example, produce light with coherence lengths of about 1 km, frequency-stabilized laser to achieve a multiple. However, not all laser monochromatic ( eg titanium - sapphire laser Δλ ≈ 2 nm - 70 nm). LEDs are less monochromatic ( Δλ ≈ 30 nm) and therefore have shorter coherence times than most monochromatic lasers. Since a laser across its entire aperture has the same phase, laser light having a very high spatial coherence.

Effect of the coherence length in the double slit experiment

The reason is that the brightness on the right measuring point is not much different (target point in the image above x ) from the brightness of the surroundings. The reasoning follows from the image below:

• The upper waveform relatively short coherence length reaches the measurement point from the direction of the upper gap.
• The lower waveform is derived from the same light source and has the same coherence length. He comes a little late to the measuring point, because it comes from the lower gap and therefore must travel to? S a longer path.
• If one were to select the measurement point a little higher or lower? S would be larger or smaller.

Are added at the measuring point, the amplitudes of both wave trains, while the result may be greater or less than the amplitude of each partial wave alone. Red periods in the picture mean Constructive interference, so maximum brightness. This is because of the small coherence length only while about 70 % of the total time of the event. During the remaining time, the brightness at the measuring point is lower. But then increases the brightness of any neighboring point occurs in the short-term constructive interference. Where this point lies exactly, depends on the value of the phase jump.

As a result of declining coherence length, the average brightness of all measuring points equal to. For very short moments, there can be at any point of constructive interference and a sequence of images of extremely short exposure time would show chaotic umherhüpfende points of light. With increasing coherence length of the dwell times at certain points are getting longer, the familiar interference pattern of regularly spaced bright dots occurs increasingly evident. For infinitely long coherence length would be measured in some ( regularly arranged ) measurement points constant high brightness, the sections in between were constant unlit.

Basics

The figure at right shows the effect of the coherence length on an interference signal. Curve (3 ) is the intensity of the interference signal in dependence on the path length difference. The coherence length is in this illustration, the width of the envelope curve (1) at half the amplitude.

, The relationship between coherence length and coherence time is given by the following equation:

It is the speed of light in vacuum, and the refractive index of the medium in which the wave propagates.

Applications

Both large and small coherence lengths for use in various optical measuring methods. Large coherence lengths are used in laser interferometers, the special properties of a small coherence length may be exploited in the white light interferometer.