Moveable Film Plane — Optical Distortion Analysis

Scope note — this is the optical-distortion analysis

What this document is. The optical-distortion derivation for the moveable four-corner film plane: the physics of tilted-/swung-plane projection (§5), the movement envelope (§3), and the per-configuration effects (§4). The plane is a fixed-size rigid rectangle (4,389 × 2,094mm) that tilts and swings as a true rigid-body rotation — envelope tilt ±40° / swing ±28° (single-axis). The optics depend only on that rigid-rotation geometry.

Mechanism, hardware, and BOM are governed by film-plane-mechanism-report.md — the current 6061 Al U-channel + acetal skate + 304 flat-bar cross-slide + Belden U-joint corner design — and the muslin clamp by film-clamp-mechanism-report.md. This analysis covers only the optics; for any hardware, quantity, or price, use those reports.

1. Purpose

The Giant Pinhole Camera uses a 20ft ISO shipping container as its light-tight body. In the default configuration the photosensitive film plane is flush against one of the 20ft long-side walls. It rides a view-camera-style moveable film plane — a mechanism with four corners driven in coordinated pairs (TL, TR, BL, BR) carrying a fixed-size rigid plane that changes only its angle, allowing tilt, swing, and limited combined movements comparable to a large-format view camera's rear standard. This document analyzes the optical distortion those movements produce; the mechanism itself is described in film-plane-mechanism-report.md.

---

2. Container Reference Geometry

Dimension	Value	Notes
Interior length	5,893mm (19 ft 4 in)	Film plane spans this direction
Interior width	2,362mm (7 ft 9 in)	Optical axis = focal length
Interior height	2,388mm (7 ft 10 in)	Container height; the active film plane is 2,094mm (mechanism-limited by the corner slides + walkway clearance)
Pinhole position	Center of one 20ft long-side wall
Nominal film plane	Opposite 20ft long-side wall	flush to wall
Structural ribs	Every 457mm (18 in) along length	Rail mounting points

---

3. Movement Axes

The four-corner mechanism supports all view-camera movements. Corners are labeled TL (top-left), TR (top-right), BL (bottom-left), BR (bottom-right) — where left/right refers to the rail span direction and top/bottom to the 7 ft 10 in height direction.

Axis	Corners Controlled	Max Travel	Effect
Tilt (top)	TL + TR together	100–2,262mm	Perspective convergence, keystone
Tilt (bottom)	BL + BR together	100–2,262mm	Perspective convergence, keystone
Swing (left)	TL + BL together	100–2,262mm	Left-right perspective skew
Swing (right)	TR + BR together	100–2,262mm	Left-right perspective skew
Combined	All 4, kept coplanar	≤±40° tilt + ≤±28° swing	Limited simultaneous tilt+swing — the plane stays a flat rectangle (no twist)
Back focus	All 4 together	100–2,262mm	Uniform magnification change
Rise / Fall	All 4 together, offset vertically	±200mm	Horizon shift
Shift	All 4 together, offset horizontally	±300mm	Left/right perspective offset

Maximum tilt angle (single-axis): ±40° — set by the corner cross-slide Z travel (~250mm); the depth rails alone would allow a steeper angle.

Maximum swing angle (single-axis): ±28° — set by the rail depth available over the 4,389mm span.

(Swing angle is smaller than tilt angle because the active film plane is 4,389mm wide — the left rail sits at X=260mm and the right rail at X=4,649mm. The same Y-axis depth difference over a wider span produces a shallower angle.)

Because the plane is a fixed-size rigid rectangle, its physical height stays 2,094mm at every angle — it does not grow. The corner cross-slides absorb the in-plane arc travel that a rigid rotation forces on each corner, so a single rigid backing panel suffices.

---

4. Tilt Configurations

The plane is always flat, so every achievable pose is a single tilt or swing (or a limited combination). Corner depths below are about the mid-rail center (1,181mm); the film height is constant because the plane is rigid.

Config	Name	TL	TR	BL	BR	Tilt	Swing	Film Height
C0	Flat	1181	1181	1181	1181	0°	0°	2,094mm
C1	Mild tilt	977	977	1385	1385	11.0°	0°	2,094mm
C2	Strong tilt	622	622	1740	1740	31.5°	0°	2,094mm
C3	Max tilt	494	494	1868	1868	40.0°	0°	2,094mm
C4	Mild swing	923	1439	923	1439	0°	6.6°	2,094mm
C5	Strong swing	412	1950	412	1950	0°	20.0°	2,094mm
C6	Max swing	125	2237	125	2237	0°	28.0°	2,094mm

Depths measured from the pinhole wall about the mid-rail center. Tilt = asin(2·Δd_top-bottom / FP_H) about the plane center (FP_H=2094); swing = asin(2·Δd_left-right / FP_W) (FP_W=4389). Rail positions: left X=260mm, right X=4,649mm.

A compound twist (diagonal, non-coplanar) is not achievable — a rigid plane cannot form a ruled surface. Combined tilt+swing is available only as a flat rotation within the ±40° / ±28° envelope.

---

5. Optical Distortion Analysis

Physics of Tilted-Plane Projection

In a pinhole camera, every scene point projects through the pinhole aperture onto the film plane. When the film plane is flat and perpendicular to the optical axis, the projection is standard central perspective:

film_x = −X · f / D
film_y = −Y · f / D

where f is the perpendicular distance from pinhole to film, and D is subject distance.

When the film plane is tilted (top edge at depth d_top, bottom edge at d_bot), the effective focal length varies continuously with height on the film:

f(v) = d_bot + (d_top − d_bot) · v      (v = 0 bottom, v = 1 top)

When the film plane is swung (left edge at depth d_L, right edge at depth d_R), the effective focal length also varies with horizontal position:

f(u) = d_L + (d_R − d_L) · u            (u = 0 left, u = 1 right)

In the compound case (tilt + swing simultaneously), the depth varies across the entire film surface as a bilinear interpolation of all four corner depths:

f(u, v) = d_BL·(1−u)(1−v) + d_BR·u(1−v) + d_TL·(1−u)v + d_TR·u·v

This varying effective focal length is the source of all the distortion effects described below.

Distortion Effects by Configuration

C0 — Flat (reference): Standard central projection. Vertical lines remain vertical, horizontal lines remain horizontal. The checker pattern is a regular perspective view.

C1 — Mild tilt 11°: Subtle keystone. The top of the image is slightly compressed. Useful for compensating converging verticals when photographing tall subjects close to the camera.

C2 — Strong tilt 30°: Dramatic keystone. Top of image has f ≈ 800mm — three times more compression than the bottom. Buildings appear to flare outward toward the base.

C3 — Maximum tilt 40°: Extreme effect. Top edge 100mm from pinhole wall — a 22× difference in effective focal length between top and bottom. The checkerboard transforms from squares at the bottom to near-horizontal slivers at the top.

Recommended for: wide open landscapes, aerial-perspective scenes, dramatic urban canyons.

C4 — Maximum tilt down (reverse) 40°: The inverse of C3. Ground plane is compressed, sky dominates. Standing subjects elongate dramatically toward the bottom of the frame.

C5 — Both edges near (uniform close): The entire film plane is 100mm from the pinhole. Effective focal length drops from 2,362mm to ~100mm — a 23.6× reduction. Field of view becomes enormous.

C6 — Compound tilt + swing: a diagonal twist (a ruled surface) is not producible — a rigid plane can only rotate flat, so there is no twist render; combined tilt+swing appears only as a flat rotation within the envelope (§3).

Summary Comparison

The six achievable flat configurations on a checker grid (D = 8,000mm):

---

6. Source References

1. Film Plane Mechanism Report — the current four-corner mechanism, hardware, and bill of materials.
2. Muslin Clamp System — the muslin spring-clip mechanism and its parts list.
3. Tilt-Swing Front Board Report — front board mechanism for combined distortion analysis.
4. Equipment Layout Report — rail positions and shadow-free zone verification.