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Sandbox Physics

Optics 061 · Diffraction, Fourier optics, and computational imaging

Talbot Carpet

An independently initialized three-dimensional apparatus connects Integer self-image, Fractional carpet, Two-dimensional lattice revival. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelTalbot Carpet
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 Talbot Carpet

BackgroundTalbot Carpet is one independently initialized apparatus with three linked investigations: Integer self-image, Fractional carpet, Two-dimensional lattice revival. Its two controls—Grating period and Distance fraction—feed the governing relation zT=2d2λz_{\mathrm T}=\frac{2d^2}{\lambda}. Scalar, paraxial, or sampled-field assumptions are stated by the validity indicator; vector and nonparaxial effects are outside that boundary.

Why it mattersWhy does a periodic grating reproduce shifted and multiplied copies of itself during propagation?

Start with the essentials

Focus question
Why does a periodic grating reproduce shifted and multiplied copies of itself during propagation?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from zT=2d2λz_{\mathrm T}=\frac{2d^2}{\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

zT=2d2λz_{\mathrm T}=\frac{2d^2}{\lambda}

The implementation evaluates this relation with dimensional inputs and an executable analytic or numerical benchmark. Scalar, paraxial, or sampled-field assumptions are stated by the validity indicator; vector and nonparaxial effects are outside that boundary.

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: Integer self-image

    Select Integer self-image. Sweep Grating period, hold Distance fraction 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: Fractional carpet

    Select Fractional carpet. Sweep Grating period, hold Distance fraction 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: Two-dimensional lattice revival

    Select Two-dimensional lattice revival. Sweep Grating period, hold Distance fraction 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.