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Sandbox Physics

Optics 069 · Diffraction, Fourier optics, and computational imaging

Coded-Aperture Camera

An independently initialized three-dimensional apparatus connects Pinhole array, Uniformly redundant array, Random-mask reconstruction. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelCoded-Aperture Camera
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 Coded-Aperture Camera

BackgroundCoded-Aperture Camera is one independently initialized apparatus with three linked investigations: Pinhole array, Uniformly redundant array, Random-mask reconstruction. Its two controls—Mask open fraction and Photon noise—feed the governing relation g=Hf+η\mathbf g=\mathbf H\mathbf f+\boldsymbol\eta. Scalar, paraxial, or sampled-field assumptions are stated by the validity indicator; vector and nonparaxial effects are outside that boundary.

Why it mattersHow can a patterned shadow encode a scene without a conventional lens?

Start with the essentials

Focus question
How can a patterned shadow encode a scene without a conventional lens?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from g=Hf+η\mathbf g=\mathbf H\mathbf f+\boldsymbol\eta. 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

g=Hf+η\mathbf g=\mathbf H\mathbf f+\boldsymbol\eta

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: Pinhole array

    Select Pinhole array. Sweep Mask open fraction, hold Photon noise 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: Uniformly redundant array

    Select Uniformly redundant array. Sweep Mask open fraction, hold Photon noise 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: Random-mask reconstruction

    Select Random-mask reconstruction. Sweep Mask open fraction, hold Photon noise 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.