Designing the Modular Camera

Two lessons and a laboratory session have produced a set of numbers: a blur circle, a cos-fourth table, an optimum hole diameter with a hundred-and-seventy-year-old argument attached to it, and a register of holes you made and measured. This page turns those numbers into a drawing with dimensions on it. By the end you should have a cutting list you could hand to somebody else, and be able to say, for every figure on it, which formula it came from.

The camera is modular, and that word is doing experimental work rather than marketing work. Five pages from now you will run a pinhole-diameter series, a focal-distance series and a flat-against-curved comparison. Each of those changes one variable and holds the rest still. A camera whose hole is a hole in its own front panel cannot do that: changing the hole means building a second camera, and a second camera differs from the first in a dozen ways nobody intended — a different squareness, a different interior finish, a different film plane. Modularity is not a convenience feature. It is the only way one instrument can run a controlled series. Every design decision below is made twice: once for what it does to the picture, and once for whether it lets you change one thing at a time.

Choosing the format

The format decides the back, and the back is the hardest part to change afterwards, so it is decided first. Four candidates are worth considering, and their dimensions come from the sizes photographic materials are actually sold in.

Format	Size at the film plane	Diagonal	What it implies for the back
4 × 5 in paper	101.6 × 127 mm	162.6 mm	Flat back with paper stops and a pressure plate; a curved insert is possible
5 × 7 in paper	127 × 177.8 mm	218.5 mm	The same back, half again as large, and a body that needs a longer focal distance for the same corner behaviour
4 × 5 in sheet film	nominally 4 × 5 in, masked smaller by the holder	measure it	A spring frame that seats on a standard double dark slide, and a film plane you cannot assume
Student-coated plate or paper from Part V	whatever you coat	as cut	The flat back, with the plate held by the same stops

Inch sizes convert exactly, because the inch is defined as 25.4 mm: 4 × 5 inches is 101.6 × 127 mm, and 5 × 7 is 127 × 177.8 mm. The sheet-film row is the one that will not behave. A sheet of film in a holder is masked by the holder’s rebates, so the recorded area is smaller than the nominal size, and the emulsion sits some distance behind the holder’s outer face. This course has not obtained a manufacturer’s drawing for the standard 4 × 5 inch holder pattern, and it does not invent one: the instruction is to measure the holder you own by the rod method in the geometry lesson, and to put the measured figures in the register.

The course’s reference camera is 4 × 5 inch. It is chosen because photographic paper is cheap enough to waste, because 4 × 5 sheet film and second-hand holders exist for the same format so one back change moves you from paper to film, and because at that size the whole camera is small enough to be carried and stiff enough to stay square. Everything that follows can be recomputed for 5 × 7: the formulas are the same and only the numbers move.

📷Why paper, and why it changes the optics

A paper negative is an ordinary enlarging paper exposed in the camera. ILFORD state that their MULTIGRADE RC papers have “approximately an equivalent Film ISO of 3-6”, which is roughly seven stops slower than a normal film, and their spectral sensitivity chart shows the blue-sensitive response of an undyed silver halide emulsion. Both facts feed straight back into this design. The slow speed makes the exposures long, which is why the shutter has to be usable one-handed for minutes at a time. The blue sensitivity means the optimum hole is computed at 450 nm rather than 550 nm, which is where the diameters in the next section come from.

The focal-distance set, computed rather than chosen

A pinhole camera on one format needs more than one focal distance, for the same reason a lens photographer owns more than one lens. The question is which three, and the answer follows from the falloff table rather than from taste.

Take the normal first. The geometry lesson’s practical rule is to keep the corner field angle at or below 45°, where the cos-fourth law costs exactly two stops. The corner sits at arctan(half-diagonal / f), so a 45° corner means the focal distance equals the half-diagonal:

f_normal = half-diagonal = √(w² + h²) / 2

The two-stop-corner focal distance

For 4 × 5 inch that is 81.3 mm, which rounds to a buildable 80 mm. Notice what this “normal” is not: the photographic convention of a focal length equal to the whole diagonal, 163 mm, which would give a 53° picture. The pinhole’s normal is half that, because the pinhole’s constraint is corner brightness rather than the eye’s comfortable angle.

The wide is 50 mm, which is where the corners go to 3.7 stops down and the picture takes on the dark-cornered look pinhole photographs are known for. The long is 120 mm, half again as long as the normal, where the corners come back to a stop. Three settings, each a deliberate point on one curve.

	Wide	Normal	Long
Focal distance f	50 mm	80 mm	120 mm
Angle of view, short side	90.9°	64.8°	45.9°
Angle of view, long side	103.6°	76.9°	55.8°
Angle of view, diagonal	116.8°	90.9°	68.2°
Corner field angle	58.4°	45.5°	34.1°
Corner loss, cos⁴ alone	3.73 stops	2.05 stops	1.09 stops
Optimum d at 450 nm, 1.41√(λf)	0.211 mm	0.268 mm	0.328 mm
Optimum d at 450 nm, 1.56√(λf)	0.234 mm	0.296 mm	0.363 mm
Optimum d at 450 nm, 1.90√(λf)	0.285 mm	0.360 mm	0.442 mm
Plate chosen from the register	0.25 mm	0.30 mm	0.40 mm
Effective f-number	f/200	f/267	f/300
Exposure relative to the wide setting	—	+0.83 stop	+1.17 stops

Every hole chosen sits inside the 1.41-to-1.90 band the diffraction lesson establishes, which is the test that matters; none of them is exactly the 1.56 value, because the graded set from the pinhole laboratory comes in steps of 0.05 to 0.1 mm and there is no point pretending otherwise. The 0.40 mm plate at 120 mm is the loosest fit, sitting above the equal-blur value and therefore slightly in the geometry-dominated half of the curve — very slightly softer than the ideal, and half a stop faster than a 0.363 mm hole would be. That is a trade you are now able to make on purpose.

🧮DO THE MATHS: check the square-root law against your own set

The diffraction lesson says the optimum hole grows as √f, so the f-number grows as √f and the exposure grows in proportion to f. Test that against the three settings above.

Predicted, from N ∝ √f: going from 50 mm to 80 mm should cost log₂(80/50) = 0.68 stop, and from 50 mm to 120 mm log₂(120/50) = 1.26 stops.

Actual, from the plates you have: (267/200)² = 1.78, which is 0.83 stop; and (300/200)² = 2.25, which is 1.17 stops.

The two disagree by about a sixth of a stop in each direction, and the disagreement is entirely the rounding of the hole to an available plate. That is the right size of error to find, and finding it is how you know both calculations were done rather than one of them copied. If your own set gives a larger discrepancy, the register is where to look first.

The normal setting: 80 mm on a 4 × 5 inch sheet

The rays are computed from the element positions, so the inversion and the image scale are the geometry's. Only the ratio of the two distances is drawn to scale; the real subject distance is twenty-five times the focal distance.

The set is built as one body plus two frames. The body alone gives 50 mm. A 30 mm frame takes it to 80 mm. Both frames together, 30 plus 40, take it to 120 mm. Two parts, three settings, and no duplicated body.

Body routes: what you can cut decides what you build

Three routes reach the same optical specification. Choose by the tools and the space you have, not by ambition, because a badly made plywood box is worse than a well made card one.

	Plywood	Mount board or foam board	Tin
Material	6 mm birch ply, 4 mm for the back	2 mm greyboard, or 3–5 mm black foam board	A rectangular biscuit or confectionery tin
Tools	Saw, square, clamps, drill, sandpaper	Craft knife, steel rule, cutting mat, square	Tin snips, file, drill
Rigidity	High; stays square for years	Moderate; corners need internal fillets	High, but the lid seal is the weak point
Light-tightness	Good once painted and taped	Unverified — must be tested	Unverified — must be tested
Time to build	4–6 hours	2–3 hours	1–2 hours
Takes stacking frames?	Yes	Yes, with care	Not without rebuilding the back
Cost band	££	£	£ or free

Plywood, with rebated joints, is the reference route. A rebate — a step cut along the edge of one part so the mating part sits into it — does three things a butt joint does not: it registers the parts square while the glue goes off, it triples the glued area, and it puts a corner in the light path so that even a joint that opens slightly does not open a straight line. Birch ply is chosen over medium-density fibreboard deliberately. HSE classify all wood dust as hazardous to health, capable of causing asthma, dermatitis and irritation of the eyes, nose and throat, with hardwood dust also able to cause a rare nasal cancer; sawing and sanding are named as the high-exposure operations; and the workplace exposure limits are 3 mg/m³ for hardwood and 5 mg/m³ for softwood as eight-hour time-weighted averages, with the hardwood figure applying to any mixture. Composite boards are within that guidance, they cut to a fine dust readily, and they take a screw or a T-nut badly in the edge. Plywood is the better material here on both counts, and the build page carries the dust controls.

Board is the route for a kitchen table. It reaches the same internal dimensions with a knife and a steel rule, and it can be finished in an evening. It has two weaknesses, and both are addressable: butt joints in board are weak, so every internal corner gets a fillet strip; and this course has not measured whether black mount board or black foam board is light-tight in the thicknesses sold. That is a real gap, not a hedge. Some black board is black on the surface with a grey or white core, and a grey core passes light. The design therefore assumes it does not, lines the interior, and settles the question by the dark-adapted inspection in the build page — which is the correct way to answer it anyway, since it depends on the board you bought.

A tin is the fastest route to a photograph. It is rigid, it is already opaque, and it costs nothing. Its problem is the lid: a press-fit lid is a light path with one turn in it and no seal, and this course has found no documented measurement of whether a biscuit-tin lid is light-tight. Treat it as leaking until the inspection says otherwise, tape it, and accept that the tin route gives you one focal distance — the depth of the tin, measured — rather than three.

🛠The one dimension all three routes share

Whatever the walls are made of, the interior is the same: 135 mm wide × 110 mm high × 50 mm deep at the wide setting. The width takes the sheet’s 127 mm dimension with 4 mm of clearance each side; the height takes its 101.6 mm dimension with the same; and the depth is the wide focal distance. Landscape is the default orientation and portrait is got by turning the whole camera on the tripod, which costs nothing and saves a second back.

Keeping the interior identical across the routes is what makes the frames, the backs and the carrier interchangeable between them. If you build the board camera first and the plywood one later, the parts you already made still fit.

Flare: why a shiny interior is an optical fault

Flare is light that reaches the film without carrying any image information. It does not make a picture; it adds a layer of uniform or slowly varying exposure on top of one, which raises the shadow densities, compresses the bottom of the tonal scale and takes the contrast out of the negative. On a paper negative, which has a short scale to begin with, a little of it goes a long way.

Where does it come from in a box with no glass in it? Four places, and all four are consequences of the wide angles this camera works at.

1. The side walls. At the wide setting the cone from the hole to the corners spans 116.8°, so the light that will form the corners of the picture passes within a few millimetres of the walls and strikes anything it touches at grazing incidence. Grazing incidence is where surfaces that look matt behave increasingly like mirrors, so this is the worst geometry in the camera and it is the one a pinhole camera is always in.
2. The inner face of the pinhole plate. Light that reaches the film and is not absorbed by the emulsion — and photographic paper reflects a good deal of it — travels back up the box and lands on the front panel. The plate’s inner face is the one surface in the camera that sits at the exact centre of the picture’s geometry, so whatever it sends back goes into the middle of the frame. This is why the pinhole laboratory paints both faces of the plate.
3. The extension-frame walls. At 120 mm the box is a tube more than twice as long as it is deep at the wide setting, and every extra millimetre of wall is another millimetre of grazing-incidence surface.
4. The edges of the sheet and the back’s inner surfaces, including the pressure plate, the paper stops and the dark-slide slot’s mouth.

The remedy has been standard practice for more than a century. Wall’s 1912 Dictionary of Photography states it flatly under Blacking: “The interior of all cameras, dark slides, and lens tubes should be coated with a dead black to prevent the reflection of light and consequent fog on the plate.” Two words in that sentence are the whole design. Dead means matt: a matt surface scatters what it does reflect over a whole hemisphere instead of concentrating it into a beam, so no single part of the negative receives a bright patch. Black means low reflectance: less comes back at all.

Where non-image light comes from, and what flocking does about it

1. 1Grazing ray on a bare wall — the wide-angle cone runs close to the walls; grazing incidence is where matt surfaces reflect most
2. 2Return from the film to the plate — paper reflects; the plate is at the centre of the geometry, so its inner face veils the middle of the frame
3. 3Sheet edge and slot mouth — small area, but close to the emulsion
4. 4Fibre pile — traps light in a cavity: several absorbing bounces before it can leave

Drawn to show the paths, not to scale. The test that settles whether your own interior is dark enough is the flare exposure in the commissioning experiment, not this drawing.

Flocking beats paint, and the reason is geometry rather than pigment. A flock or felt surface is a pile of upright fibres. Light that enters between them has to reflect several times before it can find its way back out, and each reflection removes the same large fraction again, so the pile behaves as a light trap in miniature. Paint gets one absorption; a pile gets several. The place to spend felt is therefore the walls that face the film at grazing incidence, and the place to spend care is the pinhole plate’s inner face.

This course could not source a published reflectance figure for hobby matt black paint or for flocking material, and so quotes none. The claim above is a mechanism, not a measurement. The measurement you can make is the flare exposure in the commissioning experiment: a bright source just outside the field of view, with and without a hood, read against a control.

🧮Whether a baffle will fit, and where

A baffle is a ring or a pair of ledges standing proud of the wall to intercept grazing light before it reaches the film. It only works if it stands outside the image cone, and a pinhole camera’s cone is wide, so the first question is whether there is any room at all.

At a distance x behind the hole, the cone that just fills the format has half-height x h / 2f, where h is the format dimension in that direction. The interior half-height is H/2. So the greatest a baffle may project inwards, before it starts eating the corners, is

p_max = H/2 − x h / 2f

Greatest safe baffle projection

Put in the reference camera’s numbers — H = 110 mm interior height, h = 101.6 mm format height — and take the baffle at the middle of the box, x = f/2. The second term becomes 25.4 mm at every focal distance, because x/f is fixed at one half. The interior half-height is 55 mm. So p_max = 29.6 mm, and with a 5 mm margin for the fact that your box is not perfectly square, a baffle may project about 24 mm at mid-box in any of the three settings.

Two things follow. A baffle is possible, which is more than intuition suggests for a 117° camera. And it must be placed and dimensioned by that formula rather than by eye, because at the film plane itself the same sum gives 55 − 50.8 = 4.2 mm, and a ledge any deeper than that would crop the negative.

Light traps: blocking light without a precise fit

Every joint that has to open — the back, the frame stack, the shutter, the dark-slide slot — is a gap. You cannot make a gap disappear. Wood moves with humidity, board compresses, and a joint tight enough to be light-proof by pressure alone is a joint you will eventually force and break. The answer is not a better fit; it is a light trap, and the principle is the one physical fact this whole part rests on: light travels in straight lines.

Arrange the gap so that no straight line runs from outside to inside, and no direct light gets through, whatever the clearance. What remains is light that has scattered off the walls of the passage, and that is dealt with separately by making those walls matt black. A passage with one right-angle turn needs at least one bounce; a labyrinth with two turns needs at least two, and each bounce removes the same large fraction again.

Spigot and socket: the light trap used on the back, the frames and the slot

1. 1Overlap L, at least 8 mm — with a clearance g of about 0.5 mm, only rays within arctan(g/L) = 3.6° of the gap could run straight down it
2. 2First turn, 90° — past the body’s rear edge; no straight line survives it
3. 3Second turn, 90° — into the film chamber; two absorbing bounces minimum
4. 4Shoulder — the stop that sets how far the part goes on, and therefore the focal distance

Drawn with the clearance exaggerated about ten times so that it can be seen; at true scale the gap is a line.

The rule that comes out of it is short enough to work to: overlap at least eight millimetres, clearance about half a millimetre, one right-angle turn minimum and two where you can get them, and every surface in the passage matt black. With those numbers, the steepest ray that could run straight down the gap is at arctan(0.5/8) = 3.6° to the wall — and that gap runs along the outside of the camera, pointing away from the film, so even those rays go nowhere.

Three applications, all the same joint. The back is a tray that slips over the body’s rear shoulder. Each extension frame is a collar with a socket at one end and a shoulder at the other, so frames stack like a telescope. The dark-slide slot is a felt-lined mouth: here the felt is doing the trapping as well as the sealing, because the slide has to move through it.

The pinhole carrier

The hole must change without anything else changing, and it must sit in the same place every time. That is a mechanical requirement with an optical consequence, and it decides the design.

The register from the pinhole laboratory already gives you plates of identical outline with the hole centred in a 6 mm window and a registration corner marked. The carrier is the slot they drop into: a track on the inner face of the front panel, made from two strips 3 mm thick and 8 mm wide, spaced to take the plate with about 0.3 mm of side play, with a stop at one end and a light-trapping overlap at the other. The plate slides in from the side, seats against the stop, and is held there by a small magnet or a leaf of springy card.

Centred on the format, not on the panel. Those are different points if the box is not perfectly square, and they are different points by design if you ever cut the front panel oversize. Set out the carrier from the film aperture: mark the centre of the back’s opening, project it forward, and put the stop so that the hole lands there.

🧮How big the front-panel window has to be

The carrier sits against the inner face of the front panel, so the panel’s own thickness stands in front of the hole and the window through it is a short tunnel — the same geometry the pinhole plate’s thickness gives, at a much larger scale. A window of width W in a panel of thickness T passes light out to a half-angle of arctan(W/2T), and that has to exceed the corner field angle or the panel will vignette the picture before the hole does.

At the wide setting the corner sits at 58.4°, and tan 58.4° = 1.63, so with 6 mm plywood the window must be at least 2 × 6 × 1.63 = 19.5 mm across. Twenty millimetres is the minimum, and the drawing specifies 40 mm so that a slightly off-centre carrier, a thicker panel or a wider format still has room. On the tin route the wall is a few tenths of a millimetre thick and the condition is met by any window you can cut.

Check it for your own camera: it is the one dimension on the front panel that a wide-angle pinhole camera can get wrong without the fault looking like anything but bad vignetting.

The shift position is a second stop, 20 mm to one side of the first, on the long axis. Offset the hole and the whole image circle offsets with it, verticals staying vertical, which is the rising front of a view camera and is what lets you photograph a tall building from ground level without tipping the camera up. What limits it is falloff, and the arithmetic is unforgiving:

Setting	Corner loss, no shift	With 20 mm shift	Greatest shift keeping the worst corner at 45°
Wide, 50 mm	3.73 stops	4.54 stops	none — the corner is already past 45°
Normal, 80 mm	2.05 stops	2.64 stops	none — the corner is at 45.5°
Long, 120 mm	1.09 stops	1.47 stops	45 mm

Shift is a long-setting movement. At 50 mm the corner is already 13° past the two-stop line and shifting only makes it worse; at 120 mm you can shift 45 mm and still be inside it. That is not a mechanical limit and no amount of engineering removes it — it is the image circle running out, exactly as it does behind a lens. Part VII, where the shift is used on a building, works to these numbers. Cut the second detent anyway: it costs nothing now and it is a nuisance to add later.

The shutter

Two requirements, and the second one is the one people forget.

It must not leak when closed. A closed shutter is asked to sit in full sun for as long as the camera is being carried and set up, so it is the hardest-worked seal in the design. A blade that simply covers the hole leaks around its edges; a blade that runs in a rebate with an 8 mm overlap does not, by the same argument as every other joint on this camera.

It must not move the camera when operated. Say that precisely, because “vibration” is the wrong word. During an exposure of thirty seconds a vibration lasting a fifth of a second contributes a two-hundredth of the total, which is invisible. What is not invisible is a permanent displacement: if opening the shutter nudges the camera by two millimetres, the whole frame moves by two millimetres and stays moved, and every subsequent second of the exposure records the new position. The requirement is therefore that operating the shutter applies no lasting force to the body — and, for the short exposures you will get on film in bright sun, that it applies no force during the exposure either.

Three shutters in section, and what each does to the camera when you operate it

1. 1Sliding blade in a channel — sideways force; twists the camera about the tripod screw. Use a long tab so the hand is far from the body.
2. 2Hinged flap with magnet catch — no force while open, but it thumps on closing; fine at the end of an exposure, poor at the start
3. 3Magnetic cap, lifted along the axis — nothing touches the camera during the exposure; tether it so it cannot be dropped in the dark

All three are drawn closed. Overlap, not coverage, is what makes a closed shutter light-tight.

The tripod bush is a ¼-inch, 20-threads-per-inch UNC T-nut let into the base from the inside, with its flange glued and its spikes pulled home by tightening a bolt through it. That thread is the near-universal camera-to-tripod fitting and is what tripod heads are supplied with; ISO 1222 is the standard that specifies camera tripod connections, and this course has not been able to read ISO 1222, which is not published free of charge, so it states the thread from the fittings sold for the purpose and does not quote the standard’s text. The larger 3/8-inch 16-tpi thread exists on heavier heads and is normally adapted down with a bushing.

Two placement rules, both practical. Put it under the balance point, not the middle. Assemble the camera in its heaviest configuration — both frames and the film-holder back — balance it across a pencil, and mark where it settles; that is where the bolt goes, and it will be behind the geometric centre. Keep the base flat and free of anything that projects. Pinhole photography lives near the ground, because a 117° camera wants a low viewpoint, and a camera that can be stood on a kerb is worth a tripod you did not have to carry.

Backs

The back is what the format decision turns into wood, and there are three of them.

The flat paper back is a tray with four paper stops — 3 mm strips defining an aperture of exactly 101.6 × 127 mm — a pressure plate of foam-faced board behind them, and a dark-slide slot across one end. The stops do two jobs: they locate the sheet, so that the frame you composed is the frame you get, and they hold its edges flat. The pressure plate matters more than it looks. Photographic paper curls, resin-coated paper more than fibre, and a sheet that bows 3 mm in the middle has a focal distance 3 mm shorter there than at its edges — which is 6 per cent at the wide setting, enough to change the local blur and the local f-number. Flat is a measurement, not a tidiness.

The dark slide is a sheet of black polypropylene or painted 0.5 mm aluminium running in a felt-lined slot. Its purpose is to let you load in the darkroom and carry the loaded camera into the light, which is what makes a session of five sheets possible instead of five journeys.

The film-holder back replaces the tray with a spring frame: a hinged panel, sprung by two leaves of springy steel or by a pair of small springs, which presses a standard 4 × 5 inch double dark slide against a seat. The seat must bear on the holder’s own light-trap ridge, the raised rim that the holder’s design already uses to keep light out where the dark slide withdraws. That is the point of the arrangement: you are not sealing the holder, the holder seals itself, and your job is to hold it squarely against a flat face without distorting it.

✕The film plane is not where you think it is, and the course will not guess for you

A sheet of paper taped to the flat back sits where the back is. A sheet of film in a holder does not: its emulsion sits some millimetres inside the holder, behind the dark-slide rails, and the holder’s body stands proud of the camera. This course has not obtained a manufacturer’s drawing or a published standard for the 4 × 5 inch holder pattern, so it gives no figure.

Measure yours. Close an empty holder into the back, withdraw the dark slide, push a straight rod or a strip of stiff card through the pinhole until it just touches the septum where the film would lie, mark the rod flush with the outer face of the pinhole plate, withdraw it and read the length. Subtract the plate’s own thickness. That is your real f for that configuration, and it goes in the register beside the design value; every f-number, angle of view and exposure afterwards uses the measured one.

Get it wrong by 3 mm and at the long setting you have lost 2.5 per cent in f, which is a twentieth of a stop and does not matter. The same 3 mm at the wide setting is 6 per cent, an eighth of a stop, and four degrees of angle of view.

The curved insert is the interesting one, and it is worth the space because the geometry pays a dividend most builders do not expect. Bend the sheet into a cylinder whose radius equals the focal distance and put the pinhole on the cylinder’s axis, and two of the three cosines in the cos-fourth law vanish. Every point on the film is now exactly f from the hole, so the inverse-square term goes; and the film’s normal points straight at the hole everywhere, so the obliquity term goes too. Only the foreshortening of the aperture itself survives:

E(θ) = E(0) · cos θ (in the direction of the wrap)

Falloff on a cylinder with the pinhole on its axis

Falloff across the frame: flat back against curved back, in stops

• Flat back: cos⁴ θ
• Curved back, R = f, hole on the axis: cos θ

Show the numbers behind this plot

Two curves of light loss in stops against field angle from zero to seventy-five degrees. The upper curve is the cos-fourth law of a flat film plane: zero at the axis, 0.20 stop at 15 degrees, 0.83 at 30, exactly 2.00 at 45, 3.73 at the 58.4-degree corner of a 4 by 5 inch sheet at 50 millimetres, exactly 4.00 at 60, and 6.19 at 70. The lower curve is the plain cosine law of a cylindrical film surface whose radius equals the focal distance with the pinhole on its axis: zero at the axis, 0.05 stop at 15 degrees, 0.21 at 30, exactly 0.50 at 45, 0.93 at 58.4, exactly 1.00 at 60, and 1.55 at 70. The gap widens rapidly with angle: at 45 degrees the curved back is one and a half stops better, at 60 degrees three stops better, and at 72.8 degrees, the edge of a 127-millimetre sheet wrapped on a 50-millimetre radius, the flat law would cost 7.0 stops against the cylinder's 1.75.

Series	Field angle from the axis, degrees	Loss, stops
Flat back: cos⁴ θ	0.00	0.00
Flat back: cos⁴ θ	10.00	0.09
Flat back: cos⁴ θ	15.00	0.20
Flat back: cos⁴ θ	20.00	0.36
Flat back: cos⁴ θ	30.00	0.83
Flat back: cos⁴ θ	40.00	1.54
Flat back: cos⁴ θ	45.00	2.00
Flat back: cos⁴ θ	50.00	2.55
Flat back: cos⁴ θ	55.00	3.21
Flat back: cos⁴ θ	58.40	3.73
Flat back: cos⁴ θ	60.00	4.00
Flat back: cos⁴ θ	65.00	4.97
Flat back: cos⁴ θ	70.00	6.19
Flat back: cos⁴ θ	72.80	7.02
Curved back, R = f, hole on the axis: cos θ	0.00	0.00
Curved back, R = f, hole on the axis: cos θ	10.00	0.02
Curved back, R = f, hole on the axis: cos θ	15.00	0.05
Curved back, R = f, hole on the axis: cos θ	20.00	0.09
Curved back, R = f, hole on the axis: cos θ	30.00	0.21
Curved back, R = f, hole on the axis: cos θ	40.00	0.38
Curved back, R = f, hole on the axis: cos θ	45.00	0.50
Curved back, R = f, hole on the axis: cos θ	50.00	0.64
Curved back, R = f, hole on the axis: cos θ	55.00	0.80
Curved back, R = f, hole on the axis: cos θ	58.40	0.93
Curved back, R = f, hole on the axis: cos θ	60.00	1.00
Curved back, R = f, hole on the axis: cos θ	65.00	1.24
Curved back, R = f, hole on the axis: cos θ	70.00	1.55
Curved back, R = f, hole on the axis: cos θ	72.80	1.75

Computed from cos⁴ θ and cos θ; neither curve was measured by this course. The curved-back law follows from the same three-factor derivation as the flat one, with two of the three factors removed by the geometry — the course's own application of the geometry lesson's result, and something the flat-against-curved comparison later in this part sets out to test. The curve is drawn to show the shape, not measured from a real material. Your own materials will differ, and measuring them is what the sensitometry part of the course is for.

The numbers are startling. At 45° the flat back is 2.00 stops down and the cylinder 0.50. At 60° the flat back is 4.00 stops down and the cylinder exactly 1.00. And because the sheet now wraps instead of standing across, the same sheet sees a wider angle: 127 mm of paper bent to a 50 mm radius subtends 127/50 = 2.54 radians, which is 145.5°, against the flat back’s 103.6° at the same focal distance.

There is a price, and it is not brightness. A plane cuts a cylinder in an ellipse, so straight lines in the world no longer render straight unless they are parallel to the cylinder’s axis. Verticals stay vertical if the wrap is horizontal; everything else bows. That is a choice about mapping, and it is the whole subject of the curved-plane experiment later in this part.

🛠Whether the curved insert fits, worked for both settings

The insert has to go inside a box built for a flat back, so check the chord before you cut anything. For an arc of length s on a radius R, the half-angle is s/2R, the chord is 2R sin(s/2R) and the depth is R(1 − cos(s/2R)).

Wide setting, R = 50 mm, the 127 mm dimension wrapped. Half-angle 72.8°, wrap 145.5°, chord 95.5 mm, depth 35.2 mm, and the leading edges of the sheet stand 14.8 mm behind the pinhole plate. The chord fits the 135 mm interior with 20 mm to spare and the depth fits inside 50 mm. It fits.

Normal setting, R = 80 mm, the same 127 mm wrapped. Half-angle 45.5°, wrap 91.0°, chord 114.1 mm, depth 23.9 mm. That still fits the 135 mm interior — but only just, and it needs the 30 mm frame in place to give the depth. Wrap the short side instead, 101.6 mm on a 80 mm radius, and the chord falls to 94.9 mm and the depth to 15.6 mm, at the cost of a 72.8° wrap rather than 91°.

The insert is therefore cut for one radius, and the course cuts it for the wide setting, where the gain over the flat back is largest and the fit is easiest. Note also what curling does: RC paper is stiffer than fibre paper and resists a 50 mm radius harder, so the insert needs edge clips as well as a back stop, and fibre paper is the easier material on a tight curve.

Extension frames, and keeping the register honest

An extension frame is a plain collar: interior 135 × 110 mm to match the body, a socket at one end and a shoulder at the other, matt black inside, felt on the two walls that face the film. Two of them, 30 mm and 40 mm, give 50, 80 and 120 mm from one body.

Three rules make them worth having rather than a source of error.

The mating faces butt. The frame’s contribution to the focal distance is the distance between the face that meets the body and the face the next part sits on — that is, the collar’s own length — and nothing else. If the frame seats on its spigot rather than its shoulder, the contribution becomes whatever the spigot happens to be, and it will differ each time you assemble it.

Every frame is labelled with its measured contribution, not its nominal one. Cut to 30 mm and you will get 29.6 or 30.4; write what you measure on the outside of the frame in white pencil, and write it again in the register.

The register records the whole configuration, not the parts. Body alone; body plus A; body plus A plus B — three rows, each with its measured f, its f-number for every plate in the pinhole register, its angle of view and its corner loss. That table is what you will actually work from in the field, and building it now is the difference between a camera and a box.

📓The check that catches most build errors

Recompute, do not re-measure, and see whether the two agree. Take the measured f of a configuration, divide by the adopted diameter from the pinhole register, and compare the f-number with the design value. Then take the same measured f, compute 2 arctan(162.6/2f), and compare the diagonal angle with the design value. A single mis-cut frame shows up as a consistent offset in both; a mis-recorded pinhole diameter shows up in the f-number only. Two independent checks on one measurement is the cheapest quality control in the whole part.

The drawing, and the cutting list

A design is finished when every computed number appears somewhere you can cut to. Here is the reference camera, plywood route, with the interior fixed at 135 × 110 × 50 mm.

The reference camera, exploded, with the dimensions that come from a formula marked

1. 1Magnetic cap shutter, 60 × 60 mm — overlap ≥ 8 mm; matt black inner face; tethered
2. 2Front panel, 147 × 122 × 6 mm ply — 40 × 40 mm window; carrier track with centred and +20 mm shift stops
3. 3Pinhole plate in its carrier — from the register; d = 0.25 / 0.30 / 0.40 mm for the three settings
4. 4Body: interior 135 × 110 × 50 mm — depth = the wide focal distance; T-nut at the balance point; felt on the long walls
5. 5Extension frames, 30 mm and 40 mm — 50 + 30 = 80; 50 + 30 + 40 = 120; label each with its measured length
6. 6Back: tray 15 mm deep — stops at 101.6 × 127 mm, pressure plate, felt-lined dark-slide slot
7. 7Curved insert, R = 50 mm — alternative to the flat back at the wide setting; 145.5° wrap, chord 95.5 mm, depth 35.2 mm

Exploded along the optical axis in assembly order. Every dimension marked in the key is either a format size, a computed optical distance or the 8 mm light-trap overlap; nothing on this drawing was chosen because it looked right.

Cutting list — plywood route, 6 mm birch ply unless stated.

Part	Qty	Size	Where the number comes from
Body top and bottom	2	147 × 50 mm	135 interior + 2 × 6 wall; 50 = wide focal distance
Body sides	2	110 × 50 mm	110 = interior height = 101.6 format + 8.4 clearance
Front panel	1	147 × 122 mm	body external; 40 × 40 mm window centred on the format, not the panel
Carrier track strips	2	3 × 8 × 60 mm	plate thickness plus 0.3 mm play; stops at 0 and +20 mm
Rear shoulder collar, 3 mm ply	4	2 × 147 × 12, 2 × 116 × 12 mm	sets how far the back goes on; 8 mm minimum overlap
Extension frame A walls	4	2 × 147 × 30, 2 × 110 × 30 mm	50 + 30 = 80 mm, the two-stop-corner setting
Extension frame B walls	4	2 × 147 × 40, 2 × 110 × 40 mm	80 + 40 = 120 mm, the shift-capable setting
Frame socket collars, 3 mm ply	8	12 mm wide, to suit	light-trap overlap
Back tray, 4 mm ply	1 + 4	panel 156 × 131; walls 2 × 148 × 15 and 2 × 123 × 15	slips over the shoulder with 0.5 mm clearance
Paper stops	4	3 × 6 mm strip, to suit	aperture exactly 101.6 × 127 mm
Pressure plate	1	100 × 125 × 4 mm, foam faced	holds the sheet flat; a 3 mm bow is 6 per cent in f at the wide setting
Dark slide, 0.5 mm sheet	1	150 × 130 mm	runs in a felt-lined slot across the back
Curved insert former, 2 mm ply or card	2 ends + skin	R = 50 mm, 145.5° arc	R equals the wide focal distance; skin 101.6 mm wide
T-nut	1	¼-inch 20 tpi UNC	fitted at the measured balance point
Black felt	—	to line the two long walls and the slot	flare and the dark-slide seal

Board and tin routes take the same interior and the same backs and frames; only the wall thickness and the joint detail change, and the build page carries both.

▷Do this before you cut

Redraw the table above for your format and your register. If you are working 5 × 7 inch, the half-diagonal is 109.2 mm, so the two-stop-corner setting is about 110 mm rather than 80, the optimum holes at 450 nm move to 1.56√(λf) = 0.347 mm there, and the interior becomes 186 × 135 mm. If your smallest measured hole is 0.22 mm rather than 0.25, your wide setting’s f-number is 227 and not 200, which is a third of a stop on every exposure you ever make with it.

Neither of those is a correction to the design. They are the design, done for your camera.

Recap

• The format decides the back, and the back is the part you cannot change later. The course’s reference is 4 × 5 inch, 101.6 × 127 mm, diagonal 162.6 mm.
• The focal-distance set is computed. The “normal” is the half-diagonal, 80 mm, because that is where the corner sits at 45° and loses exactly two stops; 50 mm and 120 mm bracket it. One body and two frames, 30 and 40 mm, give all three.
• Body route follows tools, not ambition. Plywood is the reference; board and tin reach the same interior. Whether black board and a tin lid are light-tight is unverified here and is settled by the dark-adapted inspection.
• Flare is non-image light, worst at grazing incidence, which is exactly where a wide pinhole camera puts it. Matt black scatters what it reflects; flocking absorbs it several times over. A baffle may project about 24 mm at mid-box on this camera, and not a millimetre by guesswork.
• A light trap beats a tight fit, because light travels in straight lines: 8 mm overlap, 0.5 mm clearance, one right-angle turn minimum, everything matt black.
• The carrier is centred on the format with a second stop 20 mm off for shift — a movement only the long setting can afford.
• The shutter must not leak closed and must not displace the camera when operated. A lifted cap applies no force at all during the exposure.
• The curved insert changes cos⁴ θ to cos θ, turning four stops of corner loss into one, at the price of bowing every line that is not parallel to the cylinder’s axis.
• Every dimension on the drawing traces to a formula, a format size or the 8 mm trap rule, and the measured value replaces the design value in the register the moment the part exists.

Check your understanding

Question 1. You decide to build the reference camera on 5 × 7 inch paper (127 × 177.8 mm) instead of 4 × 5. What focal distance puts the corners at exactly 45°, and what is the optimum hole diameter there on the equal-blur criterion at 450 nm?

• 109 mm and about 0.35 mm
• 218 mm and about 0.49 mm
• 80 mm and about 0.30 mm
• 109 mm and about 0.24 mm

Show the answer and why

Answer: 109 mm and about 0.35 mm

Two steps, both from formulas on this page. The corner sits at 45° when the focal distance equals the half-diagonal: the diagonal of 127 × 177.8 mm is √(127² + 177.8²) = 218.4 mm, so the half-diagonal is 109.2 mm. Then d = 1.56√(λf) with λ = 450 nm = 0.00045 mm gives 1.56 × √(0.00045 × 109.2) = 1.56 × 0.2217 = 0.346 mm. Option 2 forgets to halve the diagonal and would give a 53° picture with corners only 0.64 stop down — a perfectly reasonable camera, but a much longer and slower one. Option 3 is the 4 × 5 answer. Option 4 pairs the right focal distance with the 50 mm hole, which is the commonest slip: the hole grows as the square root of the focal distance, so a 2.2-times-longer camera needs a 1.48-times-larger hole.

Question 2. A student builds the body accurately but seats each extension frame on its spigot instead of on its shoulder, so every frame goes on 8 mm further than intended. What happens to the pictures made with both frames fitted?

• Nothing measurable; 16 mm is within the tolerance of a home-made camera
• The focal distance is 104 mm instead of 120, so the angle of view is wider than predicted, the true f-number is f/260 instead of f/300 and the frames are overexposed by about a quarter of a stop if the old figure is used
• The focal distance is 136 mm, the pictures are narrower than predicted and underexposed
• The focal distance is unchanged, because the spigot is inside the socket

Show the answer and why

Answer: The focal distance is 104 mm instead of 120, so the angle of view is wider than predicted, the true f-number is f/260 instead of f/300 and the frames are overexposed by about a quarter of a stop if the old figure is used

Seating on the spigot means each frame contributes 8 mm less than its length, so two frames lose 16 mm: 120 − 16 = 104 mm. Every quantity that depends on f moves with it. The diagonal angle of view becomes 2 arctan(162.6/208) = 76.0° rather than 68.2°. The f-number with the 0.40 mm plate becomes 104/0.4 = f/260, not f/300, so the camera is really (300/260)² = 1.33 times faster than assumed — about 0.4 stop of overexposure on every sheet, applied consistently, which is exactly the kind of error that gets blamed on the paper. The remedy is not more careful assembly but the measurement: measure the true pinhole-to-emulsion distance for each configuration and label the frame with what you measured.

Question 3. Why does a labyrinth seal keep light out even when the parts fit loosely, while a flat butted joint of the same clearance leaks?

• Because the longer path gives the light more time to be absorbed
• Because the labyrinth compresses a felt strip and the butt joint does not
• Because light travels in straight lines, so a passage with a right-angle turn in it admits no direct light at any clearance; what is left has to scatter off the passage walls, and matt black walls remove a large fraction at every bounce
• Because the labyrinth diffracts the light back out again

Show the answer and why

Answer: Because light travels in straight lines, so a passage with a right-angle turn in it admits no direct light at any clearance; what is left has to scatter off the passage walls, and matt black walls remove a large fraction at every bounce

This is the same straight-line optics the whole part is built on, used defensively. A butt joint of clearance g is a straight tube: any ray aimed down it gets through, and the only defence is to make g small enough that the total flux is negligible — which needs a fit that wood and board will not hold. Put one right-angle turn in the passage and no ray can traverse it without touching a wall, whatever g is. The remaining transmission is scattered light, and that is what the matt black surfaces are for: two bounces off a surface of reflectance R transmit of order R², so the paint and the geometry are doing two different jobs. This is also why the rule specifies overlap rather than tightness: 8 mm of overlap against 0.5 mm of clearance means even a straight gap only accepts rays within 3.6° of the wall, and those point along the outside of the camera rather than at the film.

Question 4. The curved insert turns cos⁴ θ into cos θ. Which of the three factors in the cos-fourth derivation survive on a cylinder whose radius equals the focal distance with the pinhole on its axis, and why?

• The inverse-square factor survives, because the corners are still further away
• The aperture foreshortening survives, because the round hole is still seen obliquely from a point off the axis; the inverse-square and film-obliquity factors vanish because every point on the cylinder is exactly f from the hole and its normal points at the hole
• All three survive but are each reduced to a quarter
• The film-obliquity factor survives, because the paper is bent and therefore not flat

Show the answer and why

Answer: The aperture foreshortening survives, because the round hole is still seen obliquely from a point off the axis; the inverse-square and film-obliquity factors vanish because every point on the cylinder is exactly f from the hole and its normal points at the hole

Take the three factors in turn. The slant-distance factor, cos²θ, existed because a corner of a flat sheet is f/cos θ from the hole rather than f; on a cylinder of radius f centred on the hole, every point is at f, so that factor becomes one. The film-obliquity factor, cos θ, existed because the beam met the flat sheet at an angle and was spread over more area; on the cylinder the surface normal at every point passes through the axis, which is where the hole is, so the beam arrives square and that factor also becomes one. The aperture foreshortening, cos θ, is a property of the hole and not of the film — the round opening is seen as an ellipse from any off-axis point wherever that point is — so it is untouched. One factor of cos θ survives. That is why the curved back is worth 3 stops at the 60° mark, and why the cost is not brightness but the bowing of straight lines, which comes from a plane cutting a cylinder in an ellipse.

Question 5. On the reference camera at the wide setting, would a baffle standing 30 mm proud of the wall at the middle of the box improve the flare, and what would it do to the negative?

• Yes, and it would have no optical cost at all
• It would help the flare, but it projects past the safe limit of about 24 mm and would crop the corners of the frame
• No, because baffles do not work in lensless cameras
• It would crop nothing, because at the middle of the box the image cone is only 25.4 mm high

Show the answer and why

Answer: It would help the flare, but it projects past the safe limit of about 24 mm and would crop the corners of the frame

Work the formula. At x = f/2, the image cone that just fills the format has half-height x·h/2f = (f/2)(101.6)/(2f) = 25.4 mm, independent of the focal distance, and the interior half-height is 55 mm. So the greatest projection that touches nothing is 55 − 25.4 = 29.6 mm. A 30 mm baffle is just past that, and because a real box is not perfectly square and the sheet is not perfectly centred, the working limit is about 24 mm. The last option quotes the cone correctly but forgets that the baffle projects inwards from a wall at 55 mm, not outwards from the axis. What the over-deep baffle does to the negative is worth naming: it removes light from the corners only, which looks exactly like worse vignetting, so a student who fits it to cure dark corners will make them darker.

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