Optical Coherence
Coherence measures the degree of correlation between the phases of a light field at different times or positions, determining whether interference can be observed.
Definition
The statistical correlation of the optical field with itself at different points in space or time, characterized by correlation functions whose magnitude sets the visibility of interference fringes.
Scope
This topic covers the statistical description of partially coherent light. It distinguishes temporal coherence, related to the spectral bandwidth and quantified by the coherence time and length, from spatial coherence, related to the angular size of the source and quantified by the coherence area. It introduces the mutual coherence function and the complex degree of coherence, the link between fringe visibility and the degree of coherence, and the van Cittert-Zernike theorem connecting source geometry to spatial coherence. It treats coherence as the property that controls the observability and contrast of interference and diffraction.
Core questions
- What distinguishes temporal from spatial coherence?
- How do spectral bandwidth and source size limit coherence?
- How is the degree of coherence related to fringe visibility?
- How does the geometry of a source determine its spatial coherence?
Key concepts
- temporal coherence
- spatial coherence
- coherence time
- coherence length
- coherence area
- degree of coherence
- fringe visibility
- van Cittert-Zernike theorem
Key theories
- Mutual coherence function and degree of coherence
- The correlation of the field at two space-time points defines the mutual coherence function; its normalized magnitude, the complex degree of coherence, equals the visibility of the resulting interference fringes.
- Van Cittert-Zernike theorem
- The spatial coherence of light from an extended incoherent source is given by the Fourier transform of the source intensity distribution, so larger or more distant sources yield greater coherence area.
Clinical relevance
The short coherence length of broadband light sources is exploited in low-coherence interferometry and optical coherence tomography to localize reflections from specific tissue depths, enabling micrometre-scale cross-sectional imaging of the eye and other organs.
History
The modern statistical theory of coherence was developed in the mid-twentieth century, building on van Cittert's and Zernike's work on spatial coherence in the 1930s. Wolf formulated a unified framework of correlation functions that became standard, later extended to the quantum domain with Mandel.
Key figures
- Emil Wolf
- Frits Zernike
- Pieter van Cittert
Related topics
Seminal works
- bornwolf1999
- mandelwolf1995
Frequently asked questions
- What is the difference between coherence length and coherence time?
- Coherence time is the interval over which the phase of the wave stays predictable, and coherence length is the corresponding distance the light travels in that time; both shrink as the source's spectral bandwidth increases.
- Why is laser light so coherent?
- A laser emits a narrow band of wavelengths from a single mode, giving it a long coherence length, and its output emerges as a well-defined beam, giving it high spatial coherence, which is why it produces sharp, high-contrast interference patterns.