Calculator Inputs
Formula used
Temporal coherence length is the distance over which the phase remains correlated. A common definition uses the coherence time τc and the phase velocity v = c/n:
- Lc = v τc = (c/n) τc
- When a frequency bandwidth Δν is available, this calculator uses a selectable model: τc = k/Δν, where k can be 1, 1/π, or 1/(2π).
- If you enter wavelength bandwidth Δλ at central wavelength λ0, it applies the small-bandwidth approximation: Δν ≈ (c/λ0²) Δλ. This implies Lc ≈ (k/n) λ0²/Δλ.
Notes: Δλ→Δν conversion assumes Δλ is small relative to λ0, and uses vacuum wavelengths.
How to use this calculator
- Select an input mode that matches your data (Δλ, Δν, or τc).
- Choose a coherence-time model from your reference or measurement setup.
- Set refractive index n for the medium (air/vacuum ≈ 1.0).
- Enter values with units, then press Calculate.
- Use CSV or PDF export to save results for reports.
Example data table
| Case | Input mode | Inputs | n | Model | Coherence length (approx.) |
|---|---|---|---|---|---|
| 1 | Δλ | λ0 = 632.8 nm, Δλ = 0.001 nm | 1.0 | τc = 1/Δν | ~0.40 m |
| 2 | Δν | Δν = 1 GHz | 1.0 | τc = 1/(πΔν) | ~0.095 m |
| 3 | τc | τc = 2 ps | 1.5 | Direct | ~0.40 mm |
Tip: If you need very high accuracy, use measured linewidth definitions consistent with your instrument.
Coherence Length Guide
1) Why coherence length matters
Coherence length describes how far an optical field remains phase-correlated along propagation. In practical terms, it sets the maximum path-length mismatch that still produces stable interference fringes. Interferometers, fiber links, holography, OCT, and precision spectroscopy all rely on adequate coherence.
2) Coherence time and propagation speed
This calculator uses Lc = (c/n)τc. The refractive index matters because the phase travels more slowly in glass and liquids. For example, using n = 1.50 reduces coherence length by one third compared with vacuum for the same coherence time.
3) Bandwidth to coherence: the key trade-off
A narrow spectrum typically yields longer coherence. If the frequency bandwidth is Δν, many references approximate τc ≈ k/Δν with a model constant k that depends on linewidth definition and spectral shape. That is why the tool offers multiple model options.
4) Using wavelength bandwidth inputs
When you only know wavelength width Δλ at a central wavelength λ0, the calculator converts it using the small-bandwidth relation Δν ≈ (c/λ0²)Δλ. This is accurate when Δλ ≪ λ0, such as most lasers. For very broad sources, consider entering frequency width directly when available.
5) Typical scales you can expect
Broadband LEDs and superluminescent diodes may have bandwidths of tens of terahertz, giving coherence lengths on the order of micrometers to tens of micrometers. In contrast, stabilized single-frequency lasers can have linewidths in the kilohertz range, corresponding to coherence lengths from many meters to kilometers.
6) Interferometer design checkpoints
In a Michelson or Mach–Zehnder setup, ensure the optical path difference stays comfortably below Lc for strong visibility. If you are measuring thin films or short-delay interferometry, a short coherence length can be beneficial because it rejects unwanted reflections outside the coherence gate.
7) Measurement data and model selection
Linewidth might be quoted as FWHM in frequency, as an angular frequency width, or as a decay constant from a correlation function. The model selector aligns with common conventions: 1/Δν, 1/(πΔν), and 1/(2πΔν). Choose the form that matches your datasheet or experiment to keep results consistent.
8) Reporting results with units
The output shows coherence length in meters, centimeters, and millimeters, plus coherence time in seconds. Use the CSV export for lab notebooks and the PDF export for quick attachments in reports. When documenting a setup, record λ0, bandwidth, n, and the chosen model so others can reproduce your calculation.
FAQs
1) Is coherence length the same as coherence time?
They are linked: coherence time is a temporal measure, while coherence length is spatial. This calculator uses Lc = (c/n)τc to convert between them for a chosen refractive index.
2) Which model should I pick for τc from Δν?
Use the definition used by your reference or instrument. If linewidth is quoted as a simple FWHM and no other detail is given, τc = 1/Δν is a common starting estimate.
3) Can I use this for fiber optics?
Yes. Set n to your fiber’s effective refractive index (often near 1.45). The output then reflects the reduced propagation speed and gives a more appropriate coherence length in the medium.
4) Why does Δλ produce different results at different λ0?
Because the conversion to frequency depends on λ0. The tool uses Δν ≈ (c/λ0²)Δλ, so the same wavelength width corresponds to a smaller frequency width at longer wavelengths.
5) What if my source is extremely broadband?
If Δλ is not small compared with λ0, the approximation may degrade. Enter frequency bandwidth directly when known, or use coherence time if you measured it from an interferogram.
6) Does dispersion change coherence length?
Dispersion can broaden pulses and affect interference visibility in real systems. This calculator focuses on basic temporal coherence from bandwidth and refractive index, so treat dispersion as an additional design factor.
7) How do I compare two sources fairly?
Use the same bandwidth definition and the same model option. Record the medium index n and central wavelength. Then compare coherence length values under consistent assumptions and measurement conditions.