Optics: Technical Reference¶
From 8×10 Inches to 40×7 Feet¶
Prepared for: The Big Shoebox Project (TBS-001) Date: April 2026 Status: Technical Reference
How to Read This Document¶
This report is structured in two layers. Each section opens with a plain-language explanation, followed by the underlying mathematics and citations. Skip or read the math sections based on your need. Every formula used in the calculation tables traces to a cited source.
Part 1: The Physics of Pinhole Photography¶
How a Pinhole Forms an Image¶
A pinhole camera works on a simple optical principle: light travels in straight lines. When light from a scene passes through a very small hole in an opaque wall, each point in the scene sends a narrow cone of light through the hole, projecting a small circle of light onto the opposite wall. Because each point in the scene projects to a different location on the wall, an image forms — inverted and reversed, but geometrically faithful.
There is no lens. The pinhole does not bend or focus light. The image forms purely by geometry.
Plain language: Think of light as millions of tiny flashlights, each aimed in a different direction from every point in the scene. The pinhole lets through only the one beam from each flashlight that travels directly through the hole. The wall behind collects those beams into a picture.
Source: Young, M., "Pinhole Optics," Applied Optics, Vol. 10, No. 12, 1971, pp. 2763–2767. DOI: 10.1364/AO.10.002763 Young describes the pinhole as "a useful and practical device which offers freedom from distortion and virtually infinite depth of field."
Part 2: The Competing Forces That Determine Sharpness¶
There are two physical effects working against each other. Understanding them leads directly to the design equations.
Effect 1: Geometric Blur (Too Large a Hole)¶
If the pinhole is very large, each point in the scene projects a circle of light roughly the same diameter as the hole itself. The image becomes blurry because multiple points in the scene overlap. Making the hole smaller tightens this circle and sharpens the image.
The geometric blur disk diameter ≈ d (the pinhole diameter)
Effect 2: Diffraction (Too Small a Hole)¶
Light is not only a particle — it is also a wave. When a wave passes through a very small opening, it bends and spreads (this is called diffraction). The smaller the hole, the more the light spreads. Below a certain size, making the pinhole smaller actually makes the image blurrier, not sharper.
The spread due to diffraction is described by the Airy disk:
B_diffraction = 2.44 × λ × f / d
Where:
- λ = wavelength of light (0.00055mm for green light at 550 nm)
- f = focal length (distance from pinhole to image plane, mm)
- d = pinhole diameter (mm)
Plain language: Light waves bend around the edges of the hole. Very small holes cause the most bending. There's a sweet spot where the two blurs are balanced.
Source: Born, M. & Wolf, E., Principles of Optics, 7th edition, Cambridge University Press, 1999, §8.6. This textbook is the most authoritative modern treatment of diffraction and aperture theory.
Part 3: The Optimal Pinhole Diameter Formulas¶
The Lord Rayleigh Formula (1891)¶
Lord Rayleigh (John William Strutt, 3rd Baron Rayleigh) used Fresnel zone analysis — a mathematical method for counting how many concentric waves of light fit inside the aperture — to derive the optimal pinhole size. His criterion: a pinhole containing approximately 1.8 Fresnel half-zones yields the best balance between geometric and diffraction blur.
Rayleigh Formula:
d = 1.9 × √(f × λ)
Source: Lord Rayleigh (J.W. Strutt), "On Pin-hole Photography," Philosophical Magazine, Series 5, Vol. 31, 1891, pp. 87–99. Taylor & Francis — Philosophical Magazine, Ser. 5.
The Geometric Minimization Formula (Petzval Criterion)¶
A different approach: instead of Fresnel zones, simply find the pinhole diameter where the total blur disk (geometric + diffraction combined in quadrature) is minimized mathematically:
B_total = √(d² + (2.44 × λ × f / d)²)
Setting dB/dd = 0 and solving:
d = 1.56 × √(f × λ)
Source: Born, M. & Wolf, E., Principles of Optics, 7th ed., §8.6. The derivation showing the two criteria (Rayleigh and Petzval) answer slightly different questions is treated rigorously here.
Which Formula to Use?¶
| Formula | Coefficient | Approach | Tends to favor |
|---|---|---|---|
| Rayleigh | 1.9 | Fresnel zone analysis | Slightly larger holes — marginally better resolution |
| Petzval / Geometric | 1.56 | Minimize total blur | Slightly smaller holes — marginally tighter geometry |
| Practical range | 1.2–2.0 | Various | Both are valid |
For this project, the Rayleigh formula (d = 1.9√fλ) is used as the primary design target, with the Petzval value shown as a lower bound. The true optimum lies between them and will depend on the specific emulsion grain structure of the chosen photosensitive material.
Source: Renner, E., Pinhole Photography: Rediscovering a Historic Technique, 4th edition, Focal Press, 2009. Renner discusses the range of valid coefficients and the practical effect of choosing within the 1.2–2.0 range.
Part 4: F-Number¶
The f-number (also called f-stop) describes how much light the pinhole admits relative to the focal length. It is defined as:
f-number = f / d
A lower f-number means more light enters, and exposures are shorter. A higher f-number means less light and longer exposures.
For comparison: A typical camera lens operates between f/1.4 and f/22. Pinhole cameras at the sizes covered here operate between f/400 and f/2500 — between 25 and 150 times dimmer than even the smallest conventional aperture.
Each doubling of f-number requires 4× longer exposure (because area scales as the square of the diameter):
t₂ = t₁ × (f-number₂ / f-number₁)²
Source: Hecht, E., Optics, 5th edition, Pearson Education, 2017, Chapter 5. The relationship between aperture, f-number, and exposure is derived in §5.2.
Part 5: Exposure Time Calculation¶
The Sunny-16 Rule (Reference Baseline)¶
In bright, full sunshine, a correctly exposed photograph at f/16 requires an exposure of approximately 1/ISO seconds. For ISO 100 film: 1/100 second at f/16.
Source: Peterson, B., Understanding Exposure, 4th edition, Amphoto Books, 2016. The Sunny-16 rule is a well-established field estimation tool for photographic exposure.
Scaling to Any F-Number¶
t_pinhole = t_reference × (f-number_pinhole / f-number_reference)²
Using ISO 100 film at f/16, 1/100 sec as the reference:
t_pinhole (seconds) = (1/100) × (f-number / 16)²
Worked example — f/1000 (an indicative pinhole aperture, close to TBS-001's f/1088), ISO 100 film, bright sun:
t_film = (1/100) × (1000 / 16)² = (1/100) × 62.5² = (1/100) × 3,906 ≈ 39 seconds
This 39-second bright-sun film baseline is what the paper and cyanotype calculations below scale from.
Photographic Paper Speed¶
Photographic printing paper is much less sensitive to light than film. Silver gelatin enlarging paper (e.g., Ilford Multigrade RC) has an effective speed of approximately ISO 6 in daylight (green-yellow light sensitivity), compared to ISO 100 film. To correct:
t_paper = t_film × (ISO_film / ISO_paper) = t_film × (100 / 6) ≈ t_film × 16.7
Worked example — f/1000, continuing from the 39-second film baseline:
t_paper = 39 sec × 16.7 ≈ 650 sec ≈ 11 minutes (calculated, before reciprocity)
Silver-gelatin paper suffers reciprocity failure at these exposure lengths, so the actual time is longer: applying the Part 6 correction (≈2.3× in this range, p = 0.85) gives roughly 25 minutes.
Source: Stroebel, L., Compton, J., Current, I., Zakia, R., Basic Photographic Materials and Processes, 3rd edition, Focal Press, 2009, Chapter 8. ISO-equivalent speeds for photographic papers are discussed in the context of exposure and sensitometry.
Cyanotype Speed (Mike Ware New Cyanotype)¶
The TBS-001 image plane is cotton muslin sensitized with the Mike Ware New Cyanotype formula, not silver-gelatin paper. Its effective speed is approximately ISO 2–4, and — being an iron-based process — it does not exhibit Schwarzschild reciprocity failure (Part 6), so no long-exposure correction is applied:
t_cyanotype = t_film × (100 / ISO_cyanotype) [ISO 2–4 → ×25 to ×50; no reciprocity correction]
Worked example — f/1000, continuing from the 39-second film baseline:
t_cyanotype = 39 sec × (25 to 50) ≈ 980–1,950 sec ≈ 16 to 33 minutes (no reciprocity correction)
In the field the baseline runs ~30–45 minutes in full sun (TBS-001 at f/1088), the longer end reflecting real UV and sky conditions below ideal Sunny-16. Because there is no reciprocity penalty to amplify it, this real exposure stays comparable to silver-gelatin paper despite paper's higher nominal ISO — paper's ~2.3× reciprocity multiplier erases its speed advantage. This is the property that makes the giant-camera exposure practical (see the TBS-001 as-built summary in Part 11).
Source: Ware, M., Cyanotype: the History, Science and Art of Photographic Printing in Prussian Blue, 1999 (New Cyanotype process); see Part 12.
Part 6: Reciprocity Failure¶
What It Is¶
The reciprocity law states that the same photographic result is produced by any combination of light intensity (I) and time (t) that gives the same product: H = I × t. In theory, a 60-second exposure at half the light intensity gives the same result as a 30-second exposure at full intensity.
In practice, photographic materials violate this law at extreme exposure times. This is called reciprocity failure (also known as the Schwarzschild effect). At long exposures — typically anything over 1–10 seconds — the material becomes progressively less sensitive, requiring even more exposure than the calculation predicts.
Plain language: The longer you wait, the less efficiently the paper collects light. If the formula says 30 minutes, you may actually need 60–90 minutes.
Source: Schwarzschild, K., "On the Deviation from the Reciprocity Law in Photography," The Astrophysical Journal, Vol. 11, 1900, pp. 89–91. The original discovery and formulation.
The Schwarzschild Law¶
H = E × t^p
Where:
- H = effective photographic exposure
- E = illuminance (intensity of light on the surface)
- t = exposure time (seconds)
- p = Schwarzschild exponent (dimensionless, specific to each material)
For ideal reciprocity: p = 1.0 For real photographic materials at long exposures: p ≈ 0.75–0.90
Corrected exposure time:
t_actual = t_calculated^(1/p)
For p = 0.85 (a representative value for variable-contrast RC paper):
t_actual = t_calculated^1.176
Correction Multiplier Table¶
The correction multiplier = t_actual / t_calculated = t_calculated^(0.176)
| Calculated Exposure | Multiplier (p=0.85) | Actual Exposure |
|---|---|---|
| 10 sec | 1.50× | 15 sec |
| 30 sec | 1.74× | 52 sec |
| 60 sec | 1.87× | 1 min 52 sec |
| 2 min | 2.00× | 4 min |
| 5 min | 2.16× | 10 min 48 sec |
| 10 min | 2.31× | 23 min |
| 20 min | 2.48× | 50 min |
| 35 min | 2.61× | 1 hr 31 min |
| 1 hr | 2.73× | 2 hr 44 min |
| 2 hr | 2.93× | 5 hr 52 min |
Critical caveat: The Schwarzschild exponent
pvaries significantly between photographic products and cannot be reliably predicted without empirical testing. The value p = 0.85 is used here as a starting estimate. Before any large-format exposure, the specific paper lot must be tested at the relevant exposure range and the actual correction determined.Source: Stroebel et al., Basic Photographic Materials and Processes, 3rd ed., Chapter 8. The variability of the Schwarzschild exponent is addressed here in detail.
Reciprocity Failure by Process Type¶
| Process | Reciprocity Failure | Notes |
|---|---|---|
| Silver gelatin RC paper | Moderate | p ≈ 0.80–0.90; test required |
| Silver gelatin FB paper | Moderate to severe | Generally worse than RC at long exposures |
| Cyanotype | Minimal | Iron-based process — does not exhibit classical Schwarzschild failure; response is more linear at long exposures |
| Digital (CMOS sensor) | None | No reciprocity failure; linear response at any exposure |
Part 7: Resolution¶
Rayleigh Resolution Criterion for Pinholes¶
The minimum resolvable separation on the image plane is determined by the Airy disk radius:
r_min = 1.22 × λ × f / d
Converting to line pairs per millimeter (lp/mm):
Resolution (lp/mm) = d / (2 × 1.22 × λ × f)
This is the physical diffraction limit — the sharpest image the pinhole can produce regardless of how well it is manufactured.
For context: - Human vision at 25 cm (comfortable reading distance): ~8–10 lp/mm - Human vision at 3 m (across a room): ~0.5–1 lp/mm - Human vision at 10 ft: ~0.3 lp/mm - Human vision at 20 ft: ~0.15 lp/mm
Large-format pinhole images are viewed from large distances. A 20-foot-wide print is not examined at arm's length. The required resolution for comfortable large-format viewing is much lower than for a small print, and the physical diffraction limit is sufficient.
Source: Born, M. & Wolf, E., Principles of Optics, 7th ed., §8.8. Young, M., Applied Optics, Vol. 10, No. 12, 1971.
Part 8: Field of View¶
The angle of view depends on the ratio of the image dimension to the focal length:
Angle of view (horizontal) = 2 × arctan(image_width / (2 × f))
When focal length ≈ image diagonal, the angle of view is approximately the same as normal human vision (~50–53° diagonal) — this is the "normal" perspective.
When focal length < diagonal: wide-angle (more of the scene visible) When focal length > diagonal: telephoto (narrower field, magnified)
Practical note for large cameras: A focal length equal to the image diagonal requires a camera depth equal to that diagonal. For a 40' × 7' image, this means a camera approximately 40 feet deep — impractical. Using a shorter focal length (e.g., equal to the image height of 7 feet) creates a wide-angle view in a much more manageable structure, with the trade-off of a larger optimal pinhole and shorter exposure times.
Part 9: Calculation Tables¶
Notes on the Tables¶
Focal length assumption: All calculations below use focal length = image diagonal, which produces a "normal" (approximately 53°) angle of view. For large formats, alternative focal lengths may be more practical — see the discussion at the end of this section.
Light condition: "Bright sun" = Sunny-16 rule conditions; "Overcast" = approx. 3–4 stops less light (4–8× longer exposure, approximately).
Schwarzschild correction: Tables show both the calculated exposure (no correction) and the estimated actual exposure with p = 0.85. These corrected values are estimates and must be verified by testing with the actual material used.
Abbreviations: - d = pinhole diameter (mm) - f = focal length (mm) - f/N = f-number - lp/mm = line pairs per millimeter (resolution) - ISO 100 = standard photographic film - Paper = silver gelatin enlarging paper (~ISO 6)
Table 1: Small and Medium Format (8"×10" to 30"×40")¶
These sizes represent conventional large-format photography through oversized darkroom work. At these scales, Ilford roll paper handles each size within a single sheet.
| Format | Dimensions (mm) | Focal Length (mm) | Rayleigh d (mm) | Petzval d (mm) | f-number | Resolution (lp/mm) |
|---|---|---|---|---|---|---|
| 8 × 10 in | 203 × 254 | 325 | 0.80mm | 0.66mm | f/406 | 1.84 |
| 11 × 14 in | 279 × 356 | 452 | 0.95mm | 0.78mm | f/476 | 1.57 |
| 16 × 20 in | 406 × 508 | 651 | 1.14mm | 0.94mm | f/571 | 1.31 |
| 20 × 24 in | 508 × 610 | 794 | 1.26mm | 1.03mm | f/630 | 1.19 |
| 24 × 30 in | 610 × 762 | 976 | 1.40mm | 1.15mm | f/697 | 1.07 |
| 30 × 40 in | 762 × 1,016 | 1,270 | 1.59mm | 1.31mm | f/799 | 0.94 |
| Format | f-number | ISO 100 film, bright sun | Photo paper calculated | Photo paper corrected (p=0.85) |
|---|---|---|---|---|
| 8 × 10 in | f/406 | 6.4 sec | 1 min 47 sec | 4 min 4 sec |
| 11 × 14 in | f/476 | 8.9 sec | 2 min 28 sec | 6 min |
| 16 × 20 in | f/571 | 12.8 sec | 3 min 34 sec | 9 min 12 sec |
| 20 × 24 in | f/630 | 15.6 sec | 4 min 20 sec | 11 min 34 sec |
| 24 × 30 in | f/697 | 19.1 sec | 5 min 19 sec | 14 min 30 sec |
| 30 × 40 in | f/799 | 25.0 sec | 6 min 57 sec | 20 min 9 sec |
Table 2: Large Format (4'×5' to 10'×7')¶
At these scales, a single sheet of photographic paper cannot cover the image plane. Multiple panels are required, or liquid emulsion must be applied to a continuous substrate. Exposures lengthen significantly; reciprocity failure becomes a major design factor.
| Format | Dimensions (mm) | Focal Length | Rayleigh d | f-number | Resolution (lp/mm) |
|---|---|---|---|---|---|
| 4 × 5 ft | 1,219 × 1,524 | 1,952mm (6.4 ft) | 1.97mm | f/991 | 0.76 |
| 5 × 7 ft | 1,524 × 2,134 | 2,625mm (8.6 ft) | 2.28mm | f/1152 | 0.65 |
| 8 × 7 ft | 2,438 × 2,134 | 3,250mm (10.7 ft) | 2.54mm | f/1280 | 0.58 |
| 10 × 7 ft | 3,048 × 2,134 | 3,721mm (12.2 ft) | 2.72mm | f/1369 | 0.55 |
| Format | f-number | ISO 100 film, bright sun | Photo paper calculated | Photo paper corrected (p=0.85) |
|---|---|---|---|---|
| 4 × 5 ft | f/991 | 38 sec | 10 min 39 sec | 33 min 20 sec |
| 5 × 7 ft | f/1152 | 51 sec | 14 min 14 sec | 46 min |
| 8 × 7 ft | f/1280 | 64 sec | 17 min 47 sec | 59 min |
| 10 × 7 ft | f/1369 | 73 sec | 20 min 24 sec | 1 hr 11 min |
Table 3: Very Large Format (20'×7' to 40'×7')¶
At this scale, the calculated focal length (= image diagonal) requires an impractically deep camera structure. See the alternative focal length options below.
| Format | Dimensions (mm) | Focal Length (diagonal) | Rayleigh d | f-number | Resolution (lp/mm) |
|---|---|---|---|---|---|
| 20 × 7 ft | 6,096 × 2,134 | 6,459mm (21.2 ft) | 3.58mm | f/1804 | 0.41 |
| 30 × 7 ft | 9,144 × 2,134 | 9,389mm (30.8 ft) | 4.31mm | f/2181 | 0.34 |
| 40 × 7 ft | 12,192 × 2,134 | 12,377mm (40.6 ft) | 4.96mm | f/2497 | 0.30 |
| Format | f-number | ISO 100 film, bright sun | Photo paper calculated | Photo paper corrected (p=0.85) |
|---|---|---|---|---|
| 20 × 7 ft | f/1804 | 2 min 7 sec | 35 min 18 sec | 1 hr 32 min |
| 30 × 7 ft | f/2181 | 3 min 6 sec | 51 min 48 sec | 2 hr 21 min |
| 40 × 7 ft | f/2497 | 4 min 3 sec | 1 hr 7 min | 4 hr 52 min |
Note on 40' × 7' at f/2497: A ~5-hour corrected paper exposure in a single outdoor session is at the outer edge of practical feasibility. This argues strongly for either: (a) using a shorter focal length (wider angle) to increase the f-number down to f/1000–f/1500, or (b) using a faster medium such as liquid emulsion on a custom substrate with higher effective ISO, or (c) using digital capture.
Table 4: Alternative Focal Lengths for Very Large Format Cameras¶
The tables above use focal length = image diagonal for a "normal" angle of view. For large structures, a shorter focal length is often more practical. This table shows the same image plane (20' × 7') at different focal length choices — demonstrating the design trade-off between field of view, camera depth, and exposure time.
Image plane fixed at 20' × 7' (6,096 × 2,134mm)
| Focal Length | Camera Depth | Angle of View (horizontal) | Rayleigh d | f-number | Paper exposure, calculated | Paper exposure, corrected |
|---|---|---|---|---|---|---|
| 6,459mm (21.2 ft) | ~22 ft | 53° (normal) | 3.58mm | f/1804 | 35 min | 1 hr 32 min |
| 4,572mm (15 ft) | ~15 ft | 70° (wide) | 3.01mm | f/1519 | 25 min | 1 hr 1 min |
| 3,048mm (10 ft) | ~10 ft | 90° (ultra-wide) | 2.46mm | f/1239 | 16 min | 37 min |
| 2,134mm (7 ft) | ~7 ft | 110° (extreme wide) | 2.06mm | f/1036 | 11 min | 23 min |
Key insight: Choosing a 7-foot focal length instead of a 21-foot focal length reduces the corrected paper exposure from ~1.5 hours to ~23 minutes — a 4× improvement — by shortening the camera depth from 22 feet to 7 feet. The trade-off is a dramatically wider, more distorted perspective (110° horizontal angle of view vs. 53°).
Part 10: Resolving Power vs. Viewing Distance¶
To determine whether the calculated resolution is adequate, compare the diffraction-limited resolution against the minimum required for the intended viewing distance.
Minimum required resolution:
Required lp/mm = (viewing distance in mm) / (image width in mm × 3438)
Note: 3438 is 1 radian in arcminutes × (1/tan of 1 arcminute) — this simplifies to the formula above for comfortable visual acuity.
Or more practically, the minimum required resolution depends on viewing distance:
| Viewing Distance | Min. Required Resolution |
|---|---|
| 25 cm (reading distance) | 8–10 lp/mm |
| 1 m (close inspection) | 2–3 lp/mm |
| 3 m (gallery distance) | 0.7–1 lp/mm |
| 5 m | 0.4–0.6 lp/mm |
| 10 m | 0.2–0.3 lp/mm |
Comparing against our calculated resolutions:
| Format | Resolution (lp/mm) | Adequate for viewing at |
|---|---|---|
| 8 × 10 in | 1.84 lp/mm | ≥ 2 m viewing distance |
| 16 × 20 in | 1.31 lp/mm | ≥ 2–3 m viewing distance |
| 4 × 5 ft | 0.76 lp/mm | ≥ 3–4 m viewing distance |
| 10 × 7 ft | 0.55 lp/mm | ≥ 4–5 m viewing distance |
| 20 × 7 ft | 0.41 lp/mm | ≥ 5–6 m viewing distance |
| 40 × 7 ft | 0.30 lp/mm | ≥ 7–8 m viewing distance |
Conclusion: The diffraction limit is not the constraint for large-scale pinhole work. A 20-foot print displayed in a large space will be viewed from 5–10 meters or more, and the theoretical resolution is sufficient. The limiting factors in practice are: pinhole manufacturing precision, vibration during exposure, and emulsion evenness.
Part 11: Summary — Key Design Numbers for the 20' × 7' Camera¶
Based on the analysis above, the following parameters are recommended as design targets for a 20' × 7' pinhole camera, with sources cited for each.
| Parameter | Recommended Value | Formula / Source |
|---|---|---|
| Image plane dimensions | 6,096 × 2,134mm (20' × 7') | Project spec |
| Focal length (normal perspective) | 6,459mm (21.2 ft) | f = image diagonal; Renner (2009) |
| Focal length (practical wide-angle) | 2,134–3,048mm (7–10 ft) | Chosen to minimize camera depth |
| Optimal pinhole diameter | 2.5–3.6mm | d = 1.9√(fλ), Rayleigh (1891); d = 1.56√(fλ), Born & Wolf (1999) |
| Pinhole manufacturing tolerance | ±0.05mm | Sufficient at 3mm scale; Lenox Laser standard spec |
| Pinhole material | Blackened SS-302/304 | Lenox Laser product spec |
| f-number (7-ft camera depth) | f/1036 | f = 2,134mm, d = 2.06mm |
| f-number (21-ft camera depth) | f/1804 | f = 6,459mm, d = 3.58mm |
| Exposure on photo paper, calculated | 11–35 min (depending on focal length choice) | Sunny-16 × (f/N ÷ 16)² ÷ 6; Stroebel (2009) |
| RC paper (ISO 6) — reciprocity-corrected | 23 min–1.5 hr | Schwarzschild p=0.85; test empirically |
| Cyanotype on muslin, Ware formula (ISO ~2–4) — no correction | ~30–45 min | Iron-based process; no Schwarzschild failure (see Part 5) |
| Resolution at optimal pinhole | 0.41–0.55 lp/mm | Young (1971); Born & Wolf (1999) |
| Max Ilford paper roll width | 127 cm (50 in) | Ilford product page (verified 2026) |
| Panels needed to cover 20' width | 5 panels (seamed) | 6,096mm ÷ 1,270mm |
| Liquid Light coverage (116 sq ft) | ~78 oz, single coat | Rockland Colloid product spec (~1.5 sq ft/oz) |
TBS-001 As Built (Orientation B)¶
The summary above sizes a generic 20' × 7' camera from the image diagonal. TBS-001 is built differently: in Orientation B (see Container Report §4) the focal length is the container interior width, not the image diagonal. This keeps the structure shallow while the full long wall serves as the image plane — trading a wider angle of view for a much shorter, more practical exposure.
| Parameter | TBS-001 value | Formula / Source |
|---|---|---|
| Focal length | 2,362mm | Container interior width (Orientation B) |
| Optimal pinhole (Rayleigh) | 2.17mm | d = 1.9√(fλ); Rayleigh (1891) |
| f-number | f/1088 | f / d |
| Image plane (full interior long wall) | 5,893 × 2,388mm | One long wall |
| Active film zone (shadow-free) | 4,499 × 2,388mm (~116 sq ft) | Within the long wall |
| Horizontal field of view | 102° | 2·arctan(5,893 / (2 × 2,362)) |
| Resolution at f/1088 | 0.69 lp/mm | d / (2 × 1.22 × λ × f) |
| Baseline exposure (cyanotype) | ~30–45 min | Ware New Cyanotype on muslin, full sun; iron-based — no Schwarzschild correction (Part 6) |
Part 12: Citations and Sources¶
All claims in this document trace to the following sources. Where source content has been verified by direct web fetch or manufacturer document, this is noted.
| # | Citation | Status |
|---|---|---|
| 1 | Rayleigh, J.W.S. (Lord Rayleigh), "On Pin-hole Photography," Philosophical Magazine, Ser. 5, Vol. 31, 1891, pp. 87–99. | Journal archive: tandfonline.com |
| 2 | Young, M., "Pinhole Optics," Applied Optics, Vol. 10, No. 12, 1971, pp. 2763–2767. DOI: 10.1364/AO.10.002763 | Verified — fetched directly. Abstract confirmed. |
| 3 | Born, M. & Wolf, E., Principles of Optics, 7th ed., Cambridge University Press, 1999. §8.6 "The Pinhole Camera." | Reference text — catalog |
| 4 | Hecht, E., Optics, 5th ed., Pearson Education, 2017. | Reference text — catalog |
| 5 | Schwarzschild, K., "On the Deviation from the Reciprocity Law in Photography," The Astrophysical Journal, Vol. 11, 1900, pp. 89–91. | NASA ADS |
| 6 | Stroebel, L., Compton, J., Current, I., Zakia, R., Basic Photographic Materials and Processes, 3rd ed., Focal Press, 2009. | Reference text — catalog |
| 7 | Renner, E., Pinhole Photography: Rediscovering a Historic Technique, 4th ed., Focal Press, 2009. | Reference text — catalog |
| 8 | Peterson, B., Understanding Exposure, 4th ed., Amphoto Books, 2016. | Reference text — catalog |
| 9 | Ilford Photographic Paper product page. ilfordphoto.com/photographic-paper | Verified — fetched directly. Max roll: 127 cm × 30 m confirmed. |
| 10 | Rockland Colloid Liquid Light product page. rockaloid.com/Liquid-Light-emulsion-half-pint | Partially verified — site refused connection. Spec (~1.5 sq ft/oz) confirmed via B&H listing. |
| 11 | Lenox Laser Pinholes & Apertures. lenoxlaser.com/blog/pinholes-and-apertures/ | Verified via WebSearch — product descriptions and material specs returned. |
| 12 | "The Great Picture" (world's largest pinhole camera), Wikipedia. en.wikipedia.org/wiki/The_Great_Picture | Verified — confirmed via WebSearch; all dimensions and materials cited match. |
| 13 | Ware, M., Cyanotype: the History, Science and Art of Photographic Printing in Prussian Blue, 1999; New Cyanotype process (ISO ~2–4; no reciprocity failure). | Author's reference: mikeware.co.uk |
Appendix A: Quick-Reference Formulas¶
| Variable | Formula | Units |
|---|---|---|
| Optimal pinhole (Rayleigh) | d = 1.9 × √(f × 0.00055) | mm |
| Optimal pinhole (Petzval) | d = 1.56 × √(f × 0.00055) | mm |
| f-number | N = f / d | dimensionless |
| Exposure, ISO 100, bright sun | t = (f_number / 16)² / 100 | seconds |
| Exposure, photo paper (~ISO 6) | t = above × 16.7 | seconds |
| Reciprocity-corrected exposure (silver gelatin) | t_actual = t_calculated^(1/0.85) | seconds |
| Exposure, cyanotype on muslin (Ware formula, ISO ~2–4) | t = above × 25–50 (no Schwarzschild correction) | seconds |
| Resolution limit | R = d / (2 × 1.22 × 0.00055 × f) | lp/mm |
| Airy disk radius | r = 1.22 × 0.00055 × f / d | mm |
| Angle of view (horizontal) | θ = 2 × arctan(width / (2 × f)) | degrees |
Appendix B: Glossary for Non-Technical Readers¶
Airy disk: The circular pattern of light formed when light diffracts through a small circular aperture. Named after the astronomer George Airy who first described it mathematically in 1835.
Diffraction: The bending and spreading of waves (including light waves) when they pass through a small opening or around an edge. The smaller the opening, the more spreading occurs.
f-number (f-stop): A ratio that describes how wide an aperture is relative to the focal length. Lower f-numbers = more light = faster exposure. A pinhole at f/1600 admits 10,000× less light than a lens at f/16.
Focal length: The distance from the pinhole to the image plane (the light-sensitive material at the back of the camera). In a pinhole camera, this is simply the internal depth of the box.
Fresnel zones: Concentric ring-shaped regions on a wavefront that contribute constructively or destructively to a diffraction pattern. Lord Rayleigh used the count of Fresnel zones inside the pinhole to determine the optimal size.
Reciprocity failure: The breakdown of the simple rule that "double the time = double the exposure." At very long exposures, photographic materials become less and less efficient, requiring disproportionately long exposures to compensate.
Resolution (lp/mm): A measure of how much fine detail a camera can capture, expressed as the number of alternating black-and-white line pairs per millimeter that are just distinguishable in the image. Higher = finer detail.
Schwarzschild exponent (p): A number between 0 and 1 that describes how severe a material's reciprocity failure is. p = 1.0 is perfect reciprocity (no failure). Typical photographic paper: p ≈ 0.80–0.90.
Document version: 1.0 — April 2026. Primary sources are listed in Part 12 with links to DOIs, NASA ADS, and publisher or library-catalog records.