Calculate coherence length, center wavelength, or wavelength bandwidth from two values using Lc ≈ λ0²/Δλ with metric or imperial units.
Customize This Calculator
Build your own version. Describe what you want changed, added, or compared.
- All Physics Calculators
- All Length Calculators
- Wavelength to Energy Calculator
- Energy to Wavelength Calculator
Coherence Length Formula
The calculator uses the narrowband approximation for coherence length:
It can also rearrange the same relationship to solve for wavelength bandwidth or center wavelength:
- Lc = coherence length
- λ0 = center wavelength of the light source
- Δλ = wavelength bandwidth, or total wavelength spread
The coherence length function calculates how far the light remains predictably phase-related using the entered center wavelength and bandwidth. The bandwidth function finds the wavelength spread needed for a given coherence length. The center wavelength function finds the wavelength that matches a known coherence length and bandwidth.
All entered values are converted to meters before calculation, then converted back to the unit selected for the missing value.
Common Wavelength Units
These conversions are useful when checking the calculator result or comparing values from optics references.
| Unit | Equivalent in meters | Common use |
|---|---|---|
| 1 nm | 1 × 10-9 m | Visible and near-infrared wavelength bandwidths |
| 1 µm | 1 × 10-6 m | Infrared wavelengths and short coherence lengths |
| 1 mm | 1 × 10-3 m | Longer coherence lengths |
| 1 cm | 1 × 10-2 m | Very long coherence lengths |
Typical Coherence Length Ranges
| Light source type | Typical bandwidth | Typical coherence length |
|---|---|---|
| Broadband LED | 10 to 100 nm | A few micrometers to tens of micrometers |
| Filtered LED or superluminescent diode | 1 to 50 nm | Tens of micrometers to less than a millimeter |
| Narrowband laser diode | 0.001 to 1 nm | Millimeters to meters |
| Single-frequency laser | Very small spectral width | Meters to kilometers or more |
Example Problems
Example 1: Find coherence length
You have a light source with a center wavelength of 850 nm and a bandwidth of 10 nm.
The coherence length is about 72,250 nm, which is 72.25 µm.
Example 2: Find wavelength bandwidth
You want a coherence length of 5 mm from a source centered at 1550 nm.
Convert 5 mm to nanometers:
Then solve for bandwidth:
The wavelength bandwidth is about 0.48 nm.
FAQ
What does coherence length mean?
Coherence length is the distance over which a light wave maintains a predictable phase relationship. A longer coherence length means the light can produce interference over a longer path difference. A shorter coherence length means interference disappears more quickly as the path difference increases.
Why does a smaller bandwidth give a longer coherence length?
A smaller bandwidth means the light contains a narrower range of wavelengths. Those wavelengths stay in phase with each other over a longer distance, so the coherence length increases. In the calculator formula, Δλ is in the denominator, so reducing Δλ increases Lc.
Is this formula exact for every light source?
No. The calculator uses the common approximation Lc ≈ λ02 / Δλ, which is most useful for narrowband sources where the bandwidth is much smaller than the center wavelength. Real sources can require correction factors depending on the spectral shape, such as Gaussian or Lorentzian linewidths.
