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Sandbox Physics

Optics 066 · Diffraction, Fourier optics, and computational imaging

Schlieren Flow Viewer

An independently initialized three-dimensional apparatus connects Knife-edge schlieren, Shadowgraph, Background-oriented schlieren. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelSchlieren Flow Viewer
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 Schlieren Flow Viewer

BackgroundSchlieren Flow Viewer is one independently initialized apparatus with three linked investigations: Knife-edge schlieren, Shadowgraph, Background-oriented schlieren. Its two controls—Index gradient and Knife position—feed the governing relation θx≈1n0∫∂n∂x dz\theta_x\approx\frac{1}{n_0}\int\frac{\partial n}{\partial x}\,\mathrm dz. Scalar, paraxial, or sampled-field assumptions are stated by the validity indicator; vector and nonparaxial effects are outside that boundary.

Why it mattersWhich optical cutoff makes temperature, density, and shock gradients visible?

Start with the essentials

Focus question
Which optical cutoff makes temperature, density, and shock gradients visible?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from θx≈1n0∫∂n∂x dz\theta_x\approx\frac{1}{n_0}\int\frac{\partial n}{\partial x}\,\mathrm dz. 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

θx≈1n0∫∂n∂x dz\theta_x\approx\frac{1}{n_0}\int\frac{\partial n}{\partial x}\,\mathrm dz

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: Knife-edge schlieren

    Select Knife-edge schlieren. Sweep Index gradient, hold Knife position 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: Shadowgraph

    Select Shadowgraph. Sweep Index gradient, hold Knife position 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: Background-oriented schlieren

    Select Background-oriented schlieren. Sweep Index gradient, hold Knife position 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.