Skip to main content
Sandbox Physics

Optics 055 · Interference, coherence, cavities, and metrology

Moiré & Fringe Metrology

An independently initialized three-dimensional apparatus connects Moiré magnification, Phase-shifting projection, Deflectometry and unwrap. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelMoiré & Fringe Metrology
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 Moiré & Fringe Metrology

BackgroundMoiré & Fringe Metrology is one independently initialized apparatus with three linked investigations: Moiré magnification, Phase-shifting projection, Deflectometry and unwrap. Its two controls—Pitch mismatch and Surface phase—feed the governing relation ϕ=atan2⁡(I4−I2,I1−I3)\phi=\operatorname{atan2}(I_4-I_2,I_1-I_3). The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

Why it mattersHow can coarse fringe motion amplify and recover tiny displacement or surface shape?

Start with the essentials

Focus question
How can coarse fringe motion amplify and recover tiny displacement or surface shape?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from ϕ=atan2⁡(I4−I2,I1−I3)\phi=\operatorname{atan2}(I_4-I_2,I_1-I_3). 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

ϕ=atan2⁡(I4−I2,I1−I3)\phi=\operatorname{atan2}(I_4-I_2,I_1-I_3)

The implementation evaluates this relation with dimensional inputs and an executable analytic or numerical benchmark. The validity indicator marks the paraxial, lossless, weak-field, or steady-state assumption used by this apparatus.

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: Moiré magnification

    Select Moiré magnification. Sweep Pitch mismatch, hold Surface phase 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: Phase-shifting projection

    Select Phase-shifting projection. Sweep Pitch mismatch, hold Surface phase 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: Deflectometry and unwrap

    Select Deflectometry and unwrap. Sweep Pitch mismatch, hold Surface phase 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.