Coherence 1 1

Concept of coherence is related to stability or predictability of phase Spatial coherence describes the correlation between signals at different points in space. Temporal coherence describes the correlation between signals at different moments of time.

A laser beam with high spatial coherence, but poor temporal coherence. Electric field distribution around the focus of a laser beam with perfect spatial and temporal coherence. A laser beam with high spatial coherence, but poor temporal coherence. A laser beam with poor spatial coherence, but high temporal coherence. 3

Wave train Band of frequencies = Many sinusoidal nearby frequencies Quantifying Coherence Physically, monochromatic sources are fictitious. Band of frequencies = Wave train Many sinusoidal nearby frequencies are needed to construct the above

y(t) = [Sin t + Sin(1.01 t) + Sin (1.02 t)

Temporal coherence: Coherence time: Coherence length: Quantifying Coherence Temporal coherence: The coherence time is the time over which a propagating wave may be considered coherent. In other words, it is the time interval within which its phase is, on average, predictable. Coherence time: : Spectral width of the source in units of frequency. Coherence length: The coherence length is the coherence time times the vacuum velocity of light, and thus also characterizes the temporal (not spatial!) coherence via the propagation length (and thus propagation time) over which coherence is lost.

Red Cadmium = 6438 Å 30 cm = 10 Yellow Sodium = 5893 Å = 10 3 cm Hz, Yellow Sodium = 5893 Å 10 = 10 3 cm Hz, He-Ne Laser = 6328 Å 6 300 m = 10 Hz,

A plane wave with an infinite coherence length. Since there are two transverse dimensions, we can define a coherence area (Ac).

A wave with a varying profile (wavefront) and infinite coherence length.

The spatial coherence depends on the emitter size and its distance. A wave with a varying profile and finite coherence length. The spatial coherence depends on the emitter size and its distance. where d is the diameter of the light source and D is the distance.

The wave with finite coherence length is passed through a pinhole The wave with finite coherence length is passed through a pinhole. The emerging wave has infinite coherence area. The coherence length (or coherence time) are unchanged by the pinhole.

Double slit: A closer look Curves of equal-path difference are Hyperboloids of revolution

http://fp. optics. arizona http://fp.optics.arizona.edu/milster/505%20Lecture/Lecture%20Notes%20and%20Slides/Chapter%204-%20Basic%20Interference/OLD%20NOTES/Basic%20Interference%20-%20Part%20B%20.pdf

Transverse Section: Straight fringes

Longitudinal section: Circular fringes