5.2 Spatial coherence and coherence area

Spatial coherence describes how well light waves from different points in a source maintain their phase relationship. It's crucial for understanding interference patterns and the behavior of light in various optical systems.

The coherence area, determined by source size and distance, affects interference visibility. Smaller sources like lasers have higher spatial coherence, producing clearer fringes, while extended sources like light bulbs result in less pronounced interference effects.

Spatial Coherence and Coherence Area

Spatial coherence and light source properties

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• Spatial coherence describes the correlation between the phases of light waves at different points in space originating from the same source at a given time
  • High spatial coherence occurs when light waves have a strong correlation in their phases across different spatial points (laser beams)
  • Low spatial coherence occurs when light waves have a weak or no correlation in their phases across different spatial points (extended sources like light bulbs or stars)
• The size and angular subtense of a light source directly influence its spatial coherence
  • Smaller source sizes and smaller angular subtenses result in higher spatial coherence
  • Larger source sizes and larger angular subtenses lead to lower spatial coherence
• Angular subtense ($\theta$) represents the angle subtended by the source at the observation point and is calculated as $\theta = \frac{d}{r}$, where $d$ is the source diameter and $r$ is the distance from the source to the observation point

Coherence area calculations and implications

• Coherence area ($A_c$) represents the area over which the light waves maintain a high degree of spatial coherence and is calculated as $A_c = \frac{\lambda^2 r^2}{d^2}$, where $\lambda$ is the wavelength of light, $r$ is the distance from the source to the observation point, and $d$ is the source diameter
• Larger coherence areas enable more pronounced interference effects
  • Interference fringes appear more visible and have higher contrast
• Smaller coherence areas reduce the visibility of interference effects
  • Interference fringes become less visible or may not be observable at all
• The coherence area determines the maximum separation between two points in an interferometer that can still produce observable interference fringes (Young's double-slit experiment)

Spatial coherence in interferometers

• Michelson interferometer
  • High spatial coherence results in clear, high-contrast interference fringes
  • Low spatial coherence leads to low-contrast or no observable interference fringes
• Young's double-slit experiment
  • High spatial coherence is necessary to observe well-defined interference fringes
  • Reduced spatial coherence decreases fringe visibility
• Fabry-Pérot interferometer
  • High spatial coherence is essential for the formation of sharp, high-finesse interference fringes
  • Low spatial coherence reduces the finesse and contrast of the fringes

Spatial coherence of various sources

• Point sources
  • Idealized sources with infinitesimally small size
  • Exhibit high spatial coherence due to their small angular subtense
• Extended sources
  • Sources with finite size (light bulbs, stars)
  • Have lower spatial coherence compared to point sources
  • The degree of spatial coherence depends on the source size and distance
• Laser beams
  • Highly spatially coherent light sources
  • Emit light with a high degree of phase correlation across the beam cross-section
  • Maintain spatial coherence over long distances
  • Enable the formation of high-contrast interference fringes in interferometric setups (Michelson interferometer, Fabry-Pérot interferometer)