Coherence Length Calculator

Calculate temporal coherence properties of laser sources for interferometry, holography, and precision measurement applications. Analyze coherence length, coherence time, and spectral characteristics of laser systems.

🌊 Coherence Analysis Tool

Coherence Parameters

Choose your input parameter type
Central emission wavelength
n
Medium refractive index (1.0 for air/vacuum)
FWHM spectral linewidth in wavelength
Statistical definition of linewidth

Application Analysis

Optical path difference for visibility calculation
Application-specific analysis

Coherence Results

Primary Results

Coherence Length 632.8 μm
Coherence Time 2.11 ps
Quality Factor 632,800 Q

Spectral Properties

Spectral Linewidth 1.00 pm
Frequency Bandwidth 237 MHz
Fringe Visibility 95.1 %

Coherence Classification

High Coherence

Excellent for interferometry and precision measurements

Application Suitability

Interferometry Excellent
Holography Good
Spectroscopy Very Good
Max Path Difference 316 μm

Formula and Theory

Coherence Length

L_c = λ²/(n·Δλ) = c·τ_c/n

Temporal coherence length in medium with refractive index n

Coherence Time

τ_c = 1/Δν = λ²/(c·Δλ)

Temporal duration of coherent field correlation

Quality Factor

Q = ν₀/Δν = λ₀/Δλ

Ratio of center frequency to bandwidth

Fringe Visibility

V = exp(-π·ΔL/L_c)

Interference visibility for Gaussian spectral profile

Understanding Coherence

  • Temporal Coherence: Correlation between electromagnetic field at different times
  • Coherence Length: Distance over which interference effects remain visible
  • Spectral Linewidth: Frequency spread that limits coherence properties
  • Quality Factor: Higher Q indicates better spectral purity and longer coherence
  • Interference Visibility: Decreases exponentially with path difference
  • Medium Effects: Refractive index affects coherence length in dispersive media

Applications

🔬

Interferometry

Design optical interferometers for precision measurements, ensuring adequate coherence length for desired path differences.

📸

Holography

Determine coherence requirements for holographic recording and reconstruction with optimal object size and geometry.

📊

High-Resolution Spectroscopy

Analyze spectral resolution capabilities for atomic spectroscopy and precision frequency measurements.

📏

Precision Metrology

Calculate measurement uncertainty and range limitations for laser-based length measurements and dimensional metrology.

🌐

Optical Communications

Analyze phase noise and linewidth requirements for coherent optical communication systems.

🎯

LIDAR Systems

Determine coherent detection capabilities and range resolution for laser radar applications.