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Sandbox Physics

Optics 056 · Diffraction, Fourier optics, and computational imaging

Huygens–Fresnel Propagation Lab

An independently initialized three-dimensional apparatus connects Point-wavelet construction, Fresnel near field, Fraunhofer far field. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelHuygens–Fresnel Propagation Lab
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 Huygens–Fresnel Propagation Lab

BackgroundHuygens–Fresnel Propagation Lab is one independently initialized apparatus with three linked investigations: Point-wavelet construction, Fresnel near field, Fraunhofer far field. Its two controls—Propagation distance and Aperture width—feed the governing relation U(P)=1iλ∬U(Q)eikrrcos⁡θ dAU(P)=\frac{1}{i\lambda}\iint U(Q)\frac{e^{ikr}}{r}\cos\theta\,\mathrm dA. Scalar, paraxial, or sampled-field assumptions are stated by the validity indicator; vector and nonparaxial effects are outside that boundary.

Why it mattersHow does a field evolve continuously from near-field wavelets to a far-field diffraction pattern?

Start with the essentials

Focus question
How does a field evolve continuously from near-field wavelets to a far-field diffraction pattern?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from U(P)=1iλ∬U(Q)eikrrcos⁡θ dAU(P)=\frac{1}{i\lambda}\iint U(Q)\frac{e^{ikr}}{r}\cos\theta\,\mathrm dA. 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

U(P)=1iλ∬U(Q)eikrrcos⁡θ dAU(P)=\frac{1}{i\lambda}\iint U(Q)\frac{e^{ikr}}{r}\cos\theta\,\mathrm dA

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: Point-wavelet construction

    Select Point-wavelet construction. Sweep Propagation distance, hold Aperture width 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: Fresnel near field

    Select Fresnel near field. Sweep Propagation distance, hold Aperture width 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: Fraunhofer far field

    Select Fraunhofer far field. Sweep Propagation distance, hold Aperture width 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.