Interactive Plot
Sensitivity curve updates with your inputs.Calculator Inputs
Example Data Table
Typical broadband sources yield short coherence lengths.| Source type | λ0 (nm) | Δλ (nm) | Model | n | Approx. Lc (mm) |
|---|---|---|---|---|---|
| SLD (OCT) | 1310 | 50 | Gaussian | 1.00 | ~5.0 |
| SLD (high bandwidth) | 850 | 80 | Gaussian | 1.00 | ~1.3 |
| Narrow-line laser | 1550 | — | Lorentzian | 1.45 | Depends on Δν |
Calculation History
| Timestamp | Method | Shape | n | λ0 (nm) | Δλ (nm) | Δν (GHz) | τc (ps) | Lc (mm) |
|---|---|---|---|---|---|---|---|---|
| No calculations yet. Submit the form to build a history. | ||||||||
Formula Used
How to Use This Calculator
- Select the method based on what you measured: Δλ, Δν, or τc.
- Choose a spectral model. Broadband emitters are often closer to Gaussian.
- Enter refractive index n for the medium where coherence is evaluated.
- Provide the relevant inputs, then press Calculate.
- Review the summary shown below the header and above the form.
- Use CSV or PDF export to save results and history.
Bandwidth-driven OCT performance
For broadband sources, coherence length decreases as FWHM bandwidth grows. With λ0 = 1310 nm and Δλ = 50 nm, the Gaussian estimate gives Lc ≈ 5.0 mm in air and ≈ 3.6 mm at n = 1.38. A common axial envelope metric is Δz ≈ Lc/2, so this case corresponds to about 1.8 mm in tissue. Increasing Δλ to 80 nm at the same λ0 shortens Lc to ≈ 3.1 mm in air, tightening depth gating.
Linewidth comparisons for lasers
Laser sources are often specified by Δν. Using the Lorentzian factor, Δν = 1 GHz at n = 1.45 yields Lc ≈ 65.8 mm, while Δν = 100 MHz extends Lc to ≈ 658 mm. At Δν = 10 kHz, Lc exceeds 6.5×106 mm, and vibration can dominate. These comparisons help when sizing fiber delays and deciding on phase stabilization.
Coherence time as a timing metric
Time-domain measurements map directly to Lc. A coherence time τc = 10 ps corresponds to Lc ≈ 2.07 mm at n = 1.45. At τc = 1 ns, Lc rises to ≈ 207 mm, matching long-path interferometers. The calculator also reports an equivalent Δν ≈ 31.8 GHz from 1/(π·τc), useful for cross-checking linewidth claims against autocorrelation data.
Role of refractive index
Lc scales approximately as 1/n for a fixed vacuum spectrum. In tissue-like media (n ≈ 1.33–1.40), the same source coherence length shortens by 24–29% compared with air. For example, a 5.0 mm air estimate becomes ≈ 3.6–3.8 mm. In glassy optics (n ≈ 1.45–1.50), the reduction approaches one third. If you have group index data, using it improves agreement.
Spectral shape factor impact
Gaussian and Lorentzian assumptions differ by about 28% in the wavelength method (0.441 vs 0.318). For λ0 = 850 nm and Δλ = 80 nm, Gaussian gives ≈ 1.33 mm in air, while Lorentzian gives ≈ 0.96 mm. In frequency form, the same constants apply to c/(n·Δν), so spectral-shape choice can shift design margins. When unsure, compare both and bracket the expected coherence window.
Practical validation workflow
Use the plot to test sensitivity: sweep Δλ or Δν by ±20% and note the proportional change in Lc. This quantifies tolerance to aging and temperature drift. Export CSV to document iterations, then PDF for review packages with the result and history. Confirm units, keep FWHM convention, and validate with interferogram scan quickly.
FAQs
1) What coherence length range is typical for OCT sources?
Broadband SLD sources often yield millimeter-scale coherence lengths. For example, λ0 = 1310 nm with Δλ = 50 nm gives roughly 5 mm in air, and shorter in tissue due to higher refractive index.
2) Should I use phase index or group index for n?
Use group index when available because coherence and envelope propagation depend on group delay. If you only have phase index, it is a reasonable engineering approximation for quick checks, especially in weakly dispersive regions.
3) Why do Gaussian and Lorentzian results differ?
They assume different spectral and temporal correlation shapes. The model changes the proportionality constant, so the same bandwidth can produce coherence lengths that differ by roughly 20–30% depending on the chosen shape.
4) How is Δλ converted to Δν in the calculator?
It uses the small-bandwidth approximation Δν ≈ (c/λ0²)·Δλ. This is accurate when Δλ is much smaller than λ0. For extremely wide spectra, a full frequency-domain calculation is preferred.
5) Can dispersion change the effective coherence length?
Yes. Dispersion broadens the interferometric envelope, effectively reducing usable coherence in the measurement bandwidth. Using group index and managing dispersion compensation improves real-world performance compared with a simple vacuum estimate.
6) Which input method should I trust most?
Trust the method closest to your measurement. If you measured a spectrum, use Δλ. If your vendor specifies linewidth, use Δν. If you measured temporal coherence directly, τc gives the most direct mapping.