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Sandbox Physics

Optics 060 · Diffraction, Fourier optics, and computational imaging

Diffractive Lens Workshop

An independently initialized three-dimensional apparatus connects Amplitude zone plate, Binary phase plate, Multilevel Fresnel lens. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelDiffractive Lens Workshop
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 Diffractive Lens Workshop

BackgroundDiffractive Lens Workshop is one independently initialized apparatus with three linked investigations: Amplitude zone plate, Binary phase plate, Multilevel Fresnel lens. Its two controls—First zone radius and Phase levels—feed the governing relation rm≈mλfr_m\approx\sqrt{m\lambda f}. Scalar, paraxial, or sampled-field assumptions are stated by the validity indicator; vector and nonparaxial effects are outside that boundary.

Why it mattersHow do zone placement and phase quantization trade focal efficiency against chromatic behavior?

Start with the essentials

Focus question
How do zone placement and phase quantization trade focal efficiency against chromatic behavior?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from rm≈mλfr_m\approx\sqrt{m\lambda f}. 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

rm≈mλfr_m\approx\sqrt{m\lambda f}

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: Amplitude zone plate

    Select Amplitude zone plate. Sweep First zone radius, hold Phase levels 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: Binary phase plate

    Select Binary phase plate. Sweep First zone radius, hold Phase levels 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: Multilevel Fresnel lens

    Select Multilevel Fresnel lens. Sweep First zone radius, hold Phase levels 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.