5.3 Partial coherence and its effects on interference
4 min read•Last Updated on July 22, 2024
Light waves aren't always in perfect sync. Partial coherence measures how well they line up in space and time. This affects how light behaves in interferometers and other optical systems.
Understanding partial coherence is key for many applications. It impacts fringe visibility in interferometers, resolution in imaging systems, and even how we measure distant stars. Knowing these effects helps us design better optical devices.
Partial Coherence and Interference
Partial coherence and light properties
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Partial coherence quantifies correlation between phases of light waves at different points in space and time
Light sources exhibit varying partial coherence from completely incoherent to fully coherent
Temporal coherence relates to spectral purity and monochromaticity of light source
Longer coherence time implies more monochromatic source and higher temporal coherence (lasers)
Spatial coherence depends on light source size and distance between considered points
Smaller source size and larger distances lead to higher spatial coherence (stars, distant objects)
Degree of partial coherence affects light waves' ability to interfere constructively or destructively (interference patterns, fringe visibility)
Effects on interference fringe visibility
Partial coherence reduces visibility and contrast of interference fringes in interferometers
Visibility defined as V=(Imax−Imin)/(Imax+Imin), where Imax and Imin are maximum and minimum fringe intensities
Lower coherence results in lower visibility and less distinct fringes (blurred or washed out patterns)
In Michelson interferometers, partial coherence affects fringe sharpness and contrast
Reduced temporal coherence decreases fringe contrast as path difference between interferometer arms increases (white light interferometry)
Fabry-Perot interferometers sensitive to both temporal and spatial coherence
Partial coherence reduces finesse and sharpness of transmission peaks (broadened peaks, reduced resolution)
Partial coherence also affects fringe formation in other interferometric systems (Mach-Zehnder, Sagnac interferometers)
Analysis using coherence functions
Mutual coherence function Γ(r1,r2,τ) describes correlation between electric fields at two points r1 and r2 with time delay τ
Defined as Γ(r1,r2,τ)=⟨E∗(r1,t)E(r2,t+τ)⟩, where E(r,t) is electric field at position r and time t
Complex degree of coherence γ(r1,r2,τ) is normalized mutual coherence function
Given by γ(r1,r2,τ)=Γ(r1,r2,τ)/Γ(r1,r1,0)Γ(r2,r2,0)
∣γ(r1,r2,τ)∣ ranges from 0 (incoherent) to 1 (fully coherent)
Complex degree of coherence quantifies temporal and spatial coherence properties of light sources
Temporal coherence characterized by complex degree of self-coherence γ(τ)=γ(r,r,τ) (autocorrelation)
Spatial coherence characterized by complex degree of mutual coherence γ(r1,r2,0) (cross-correlation)
Applications in interferometric systems
In interferometric system design, light source coherence properties must be considered for desired performance
High-precision measurements often use highly coherent sources (lasers)
Applications requiring reduced coherent noise or speckle may prefer partially coherent sources (LEDs, superluminescent diodes)
Path difference between interferometer arms should be within source coherence length to maintain high fringe visibility
Coherence length related to source spectral bandwidth by Lc=c/Δf, where c is speed of light and Δf is spectral bandwidth
White-light interferometry exploits short coherence length of broadband sources for high axial resolution
Sample scanned through zero path difference position to obtain depth information (optical coherence tomography)