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Sandbox Physics

Optics 064 · Diffraction, Fourier optics, and computational imaging

PSF–OTF–MTF Imaging Lab

An independently initialized three-dimensional apparatus connects Pupil-to-PSF, OTF and MTF, Image convolution and sampling. Two dimensional physical controls, direct probe dragging, a detector trace, and three quantitative checks are recalculated from the stated equation.

Interactive modelPSF–OTF–MTF Imaging Lab
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 PSF–OTF–MTF Imaging Lab

BackgroundPSF–OTF–MTF Imaging Lab is one independently initialized apparatus with three linked investigations: Pupil-to-PSF, OTF and MTF, Image convolution and sampling. Its two controls—Normalized frequency and Wavefront rms—feed the governing relation OTF(ν)=F{PSF(r)}\mathrm{OTF}(\boldsymbol\nu)=\mathcal F\{\mathrm{PSF}(\mathbf r)\}. Scalar, paraxial, or sampled-field assumptions are stated by the validity indicator; vector and nonparaxial effects are outside that boundary.

Why it mattersHow do pupil shape and wavefront error become blur, contrast loss, and an image transfer curve?

Start with the essentials

Focus question
How do pupil shape and wavefront error become blur, contrast loss, and an image transfer curve?
One-sentence intuition
The detector curve and all three numerical readouts are recomputed from OTF(ν)=F{PSF(r)}\mathrm{OTF}(\boldsymbol\nu)=\mathcal F\{\mathrm{PSF}(\mathbf r)\}. 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

OTF(ν)=F{PSF(r)}\mathrm{OTF}(\boldsymbol\nu)=\mathcal F\{\mathrm{PSF}(\mathbf r)\}

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: Pupil-to-PSF

    Select Pupil-to-PSF. Sweep Normalized frequency, hold Wavefront rms 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: OTF and MTF

    Select OTF and MTF. Sweep Normalized frequency, hold Wavefront rms 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: Image convolution and sampling

    Select Image convolution and sampling. Sweep Normalized frequency, hold Wavefront rms 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.