Optics 026 · Imaging, instruments, and visual systems

Photography Optics Playground

A 2D full-frame camera workbench links a moving focal-length carriage, entrance pupil, fixed sensor, three depth-resolved ray fans, calculated spot circles, depth-of-field threshold, exposure stops, and diffraction growth without conflating focal length with perspective.

Horizontal field and entrance pupil

\mathrm{FOV}_h,\ D

$0.50$

Depth-of-field interval and defocus circles

D_N,\ D_F,\ c

$50\%$

Airy diameter, exposure, and perspective invariant

d_A,\ \Delta\mathrm{EV},\ \Pi

$0.00\pi$

Model regime $\text{valid model regime}$

Physics tutorial

Audit the physics of Photography Optics Playground

BackgroundA photographic camera combines a conjugate solve with a finite entrance pupil. The focus plane fixes the sensor distance through $\frac{1}{f}=\frac{1}{u}+\frac{1}{v},\qquad D=\frac{f}{N}$ . The sensor stays fixed while rays from every other depth cross before or after it and arrive as a finite spot.

Why it mattersAt a fixed viewpoint, how do focal length and entrance pupil change framing, defocus, depth of field, and diffraction without changing perspective?

Start with the essentials

Focus question: At a fixed viewpoint, how do focal length and entrance pupil change framing, defocus, depth of field, and diffraction without changing perspective?
One-sentence intuition: Tracing the two pupil edges to the fixed sensor gives the paraxial circle of confusion directly: $c=D\left|1-\frac{v_s}{v_o}\right|$ . Focal length changes framing and image scale at a fixed viewpoint; perspective remains a ratio of object distances and changes only when the viewpoint or scene geometry changes.

Core mathematical model

Field of view and entrance pupil

\mathrm{FOV}_h=2\arctan\!\left(\frac{w_s}{2v_s}\right),\qquad D=\frac{f}{N}

The sensor width is fixed at thirty-six millimetres and the sensor distance comes from the finite-focus conjugate solve; it tends to focal length for a distant focus. Changing f-number changes the physical ray bundle diameter.

Depth-of-field convention

H=\frac{f^2}{Nc_0}+f,\quad D_N=\frac{Hu}{H+u-f},\quad D_F=\frac{Hu}{H-u+f}

Near and far limits are not exact boundaries of physical focus. They are the object distances whose geometric blur reaches the declared conventional threshold on this sensor.

Diffraction tradeoff

d_A\approx2.44\lambda N

Stopping down contracts geometric defocus circles but expands the diffraction first-zero diameter. The aperture-sweep trace plots both contributions on one physical sensor scale.

Common difficulties

Claiming focal length changes perspective

Typical misconceptionA wide lens exaggerates near objects and a long lens compresses distance even when the camera never moves.

Better mental modelAt one viewpoint, equal-height image-size ratios depend on object-distance ratios; changing focal length scales both images together and only crops the field differently. The familiar perspective change appears when the photographer moves to restore framing.

Run the experiment

01
Scene 1: Fixed-viewpoint framing
Use fixed-viewpoint framing. Drag focal length and watch the field cone narrow while the displayed perspective invariant remains unchanged.
What to observe: The focused gold bundle always converges to one sensor point independent of pupil height. Foreground and background bundles retain finite spreads of opposite defocus sign.
02
Scene 2: Aperture and defocus
Switch to aperture and defocus. Sweep f-number and compare the nine-blade pupil diameter, five-ray sensor spreads, foreground blur, and background blur.
What to observe: A longer focal length narrows field of view and increases image scale, but the equal-height near-to-far ratio remains fixed because all three object distances are unchanged.
03
Scene 3: Depth-of-field versus diffraction
Enter the depth-of-field versus diffraction scene. Stop down through the marked depth interval and find where reduced defocus no longer compensates for the growing Airy scale.
What to observe: A high f-number can place more scene depths below the conventional confusion threshold while still reducing fine-detail contrast through diffraction. Depth of field and resolving power are not synonyms.