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Sandbox Physics

Optics 057 · Diffraction, Fourier optics, and computational imaging

Aperture Diffraction Studio

An independently initialized three-dimensional apparatus connects Slit, circle, and polygon, Babinet complement, Poisson–Arago spot. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelAperture Diffraction Studio
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 Aperture Diffraction Studio

BackgroundAperture Diffraction Studio is one independently initialized apparatus with three linked investigations: Slit, circle, and polygon, Babinet complement, Poisson–Arago spot. Its two controls—Aperture size and Wavelength—feed the governing relation U∞(kx,ky)∝F{A(x,y)}U_\infty(k_x,k_y)\propto\mathcal F\{A(x,y)\}. Scalar, paraxial, or sampled-field assumptions are stated by the validity indicator; vector and nonparaxial effects are outside that boundary.

Why it mattersHow does drawing a new aperture rewrite its entire far-field intensity pattern?

Start with the essentials

Focus question
How does drawing a new aperture rewrite its entire far-field intensity pattern?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from U∞(kx,ky)∝F{A(x,y)}U_\infty(k_x,k_y)\propto\mathcal F\{A(x,y)\}. 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∞(kx,ky)∝F{A(x,y)}U_\infty(k_x,k_y)\propto\mathcal F\{A(x,y)\}

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: Slit, circle, and polygon

    Select Slit, circle, and polygon. Sweep Aperture size, hold Wavelength 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: Babinet complement

    Select Babinet complement. Sweep Aperture size, hold Wavelength 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: Poisson–Arago spot

    Select Poisson–Arago spot. Sweep Aperture size, hold Wavelength 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.