Coherence

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Coherence describes the correlation between the phases of a wave at different points in space or time. It determines the ability of light to produce interference patterns.

Types of Coherence

1. Temporal Coherence (Longitudinal)

Correlation between the field at a single point at different times.

  • Related to the spectral bandwidth of the source
  • Coherence time: $\tau_c \approx 1/\Delta\nu$
  • Coherence length: $L_c = c \cdot \tau_c$

Examples of high temporal coherence:

  • Laser sources
  • Narrowband filtered light

2. Spatial Coherence (Transverse)

Correlation between the field at different spatial points at the same time.

  • Related to the spatial extent of the source
  • Perfect spatial coherence: $|\langle u(x_1) u^*(x_2) \rangle| = 1$

Examples of high spatial coherence:

  • Stars (point sources at infinity)
  • Single-mode laser output

Van Cittert-Zernike Theorem

The spatial coherence function of light from an incoherent source is the Fourier transform of the source intensity distribution.