Coherence Length⚠ unverified
Physics / Optics · Compute the coherence length from the spectral width
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| lambda_ | λ_ | m | 1.0 | Central wavelength of the light |
| delta_lambda | Δλ | m | 1.0 | Spectral width (bandwidth) of the light |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Lc | m | Coherence length, in metres (m). Returns positive infinity when the spectral width is zero (perfectly monochromatic) |
The science & history
Understanding the Parameters
- $\lambda$ — shorter wavelength → shorter $L_c$ at fixed relative bandwidth.
- $\Delta\lambda$ — broader spectrum → shorter coherence (white light: micrometres; lasers: long).
- $L_c$ — order-of-magnitude; exact prefactors depend on lineshape definition.
Derivation (Approaching a Proof)
Fourier relation between spectrum and autocorrelation: coherence time $\tau_c \sim 1/\Delta\nu$ with $\Delta\nu \approx c\Delta\lambda/\lambda^{2}$, and $L_c = c\tau_c \sim \lambda^{2}/\Delta\lambda$.
History
Coherence length is central to interferometry, OCT, and holography source requirements.
Related Concepts: Youngs Double Slit, Optical Path Length, Thin Film Thickness
Notes: Registry calculator coherence-length (unverified). Approximate transform-limited form.