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Sandbox Physics

Optics 068 · Diffraction, Fourier optics, and computational imaging

Phase Retrieval Challenge

An independently initialized three-dimensional apparatus connects Support-constrained recovery, Multiplane diversity, Stagnation and ambiguity. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelPhase Retrieval Challenge
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 Phase Retrieval Challenge

BackgroundPhase Retrieval Challenge is one independently initialized apparatus with three linked investigations: Support-constrained recovery, Multiplane diversity, Stagnation and ambiguity. Its two controls—Iteration count and Support radius—feed the governing relation Uk+1=PSF−1PIFUkU_{k+1}=\mathcal P_{\mathrm S}\mathcal F^{-1}\mathcal P_{\mathrm I}\mathcal F U_k. Scalar, paraxial, or sampled-field assumptions are stated by the validity indicator; vector and nonparaxial effects are outside that boundary.

Why it mattersCan intensity-only measurements recover a complex field despite ambiguity and noise?

Start with the essentials

Focus question
Can intensity-only measurements recover a complex field despite ambiguity and noise?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from Uk+1=PSF−1PIFUkU_{k+1}=\mathcal P_{\mathrm S}\mathcal F^{-1}\mathcal P_{\mathrm I}\mathcal F U_k. 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

Uk+1=PSF−1PIFUkU_{k+1}=\mathcal P_{\mathrm S}\mathcal F^{-1}\mathcal P_{\mathrm I}\mathcal F U_k

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: Support-constrained recovery

    Select Support-constrained recovery. Sweep Iteration count, hold Support radius 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: Multiplane diversity

    Select Multiplane diversity. Sweep Iteration count, hold Support radius 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: Stagnation and ambiguity

    Select Stagnation and ambiguity. Sweep Iteration count, hold Support radius 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.