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Sandbox Physics

Optics 051 · Interference, coherence, cavities, and metrology

Low-Coherence Interferometry & OCT

An independently initialized three-dimensional apparatus connects Coherence envelope, Layered A-scan, Raster B-scan. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelLow-Coherence Interferometry & OCT
Primary prediction P1\mathcal P_10.500.50
Physical scale P2\mathcal P_250%50\%
Limit check V\mathcal V0.00π0.00\pi
Model regimevalid model regime\text{valid model regime}

Physics tutorial

How to investigate Low-Coherence Interferometry & OCT

BackgroundLow-Coherence Interferometry & OCT is one independently initialized apparatus with three linked investigations: Coherence envelope, Layered A-scan, Raster B-scan. Its two controls—Center wavelength and Spectral bandwidth—feed the governing relation ℓc≈2ln⁡2πλ02Δλ\ell_{\mathrm c}\approx\frac{2\ln2}{\pi}\frac{\lambda_0^2}{\Delta\lambda}. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersHow does a short coherence gate turn reflected light into a depth-resolved image?

Start with the essentials

Focus question
How does a short coherence gate turn reflected light into a depth-resolved image?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from ℓc≈2ln⁡2πλ02Δλ\ell_{\mathrm c}\approx\frac{2\ln2}{\pi}\frac{\lambda_0^2}{\Delta\lambda}. Geometry and glow are presentation encodings; the equation, units, conservation or limit check, and validity indicator are the quantitative evidence.

Core mathematical model

Governing relation

ℓc≈2ln⁡2πλ02Δλ\ell_{\mathrm c}\approx\frac{2\ln2}{\pi}\frac{\lambda_0^2}{\Delta\lambda}

The implementation evaluates this relation with dimensional inputs and an executable analytic or numerical benchmark. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Common difficulties

Mistaking glow for measured power

Typical misconceptionA brighter cinematic trail must represent proportionally more optical power.

Better mental modelUse the detector and normalized readouts for comparison. Glow is deliberately nonlinear so weak structure stays visible.

Run the experiment

  1. 01

    Scene 1: Coherence envelope

    Select Coherence envelope. Sweep Center wavelength, hold Spectral bandwidth fixed, and then reverse the roles. Drag the stage probe to repeat the first sweep directly.

    What to observe: Read the primary prediction, physical scale, limit check, and validity indicator together. Record where the approximation boundary changes.
  2. 02

    Scene 2: Layered A-scan

    Select Layered A-scan. Sweep Center wavelength, hold Spectral bandwidth fixed, and then reverse the roles. Drag the stage probe to repeat the first sweep directly.

    What to observe: Read the primary prediction, physical scale, limit check, and validity indicator together. Record where the approximation boundary changes.
  3. 03

    Scene 3: Raster B-scan

    Select Raster B-scan. Sweep Center wavelength, hold Spectral bandwidth fixed, and then reverse the roles. Drag the stage probe to repeat the first sweep directly.

    What to observe: Read the primary prediction, physical scale, limit check, and validity indicator together. Record where the approximation boundary changes.