Assignment: Panorama, Curved Plane and Multiple Pinholes

The intention

Make one panorama on the curved back in which you chose, in advance, which lines would stay straight and which would bow; and one multiple-pinhole negative whose overlap bands you computed and placed before the shutter opened. Both are pictures that only this camera can make, and both are ruined by being discovered rather than planned.

Part VI measured what the curved insert and the multi-hole plates do. This page spends those measurements on pictures. The arithmetic is already done and cited there; what is new here is deciding what to point it at.

Learning objectives

By the end of this session you should be able to:

• Predict, for any subject line, whether it will stay straight on a cylindrical back, and place the camera so that the ones you want straight are.
• Compute the width and the exposure of every overlap band on a multi-hole plate before exposing, and choose which band the exposure is correct for.
• State what the curved back buys in even illumination, in stops, and in which direction only.
• Compute a zone plate’s geometry from Part VI’s Fresnel-zone result and design the one exposure that measures how much of its predicted speed gain actually arrives.
• Read a distorted negative and say which parts of the distortion are the projection and which are the maker’s decision.

Prerequisites

Night, the Very Long Exposure and Solargraphy precedes this page in the sequence. The essential prerequisite is Part VI’s curved plane and multiple pinhole experiments, which derives every geometric result used here and measures several of them; and its diffraction lesson, which derives the Fresnel zone radii the zone plate depends on. If you have not done that experiment, do it before this assignment rather than during it: this page assumes you have your own falloff table and your own measured hole separations.

Safety classification

Level A. No new chemistry. The one new physical operation is cutting a foil mask, which the pinhole lab already covered.

• Substances. Paper developer, stop and rapid fixer at working dilution, indoors, as before.
• Energies. The sun, for an outdoor session. A craft knife and thin metal, for the optional mask.
• Procedures. A tripod in a public place; a curved paper insert loaded in the dark.
• Waste. Used fixer is silver-bearing and is collected; foil offcuts go to metal recycling, not to the bin, because they are thin and sharp.

What is not a hazard here, and why. The curved insert and the multi-hole plates introduce nothing chemically or energetically new: they are card and metal, and the camera is as inert with three holes in it as with one. Even the zone plate — which sounds exotic — is a piece of printed film or pierced foil, and it neither concentrates energy nor emits anything. The single genuine risk on this page is the knife, and it is exactly the risk the pinhole lab already assessed: a fresh blade, a cutting mat, a straight edge, and cuts made away from the hand that steadies the work.

Hazards

Thin metal edges. Shim cut with a knife or scissors leaves an edge that is sharp in a way that does not look sharp. Deburr with fine abrasive paper, handle offcuts with the same care as the piece you are keeping, and collect them immediately rather than leaving them on the bench.

Working in public. The panorama wants a wide subject, which usually means a street, a square or a shoreline. The Highway Code’s rules 1 and 2 apply — pavements where provided, and where there is none, keep to the right-hand side so you can see oncoming traffic — and section 137(1) of the Highways Act 1980 makes wilful obstruction of a highway an offence in England and Wales. Leave a clear passing width and stay with the camera.

Sun. ICNIRP’s shadow rule applies to any long outdoor session: shadow shorter than you means the ultraviolet is at its strongest, which under clear skies in late spring and summer is the four hours around midday.

Required PPE

• A straight edge and a cutting mat are the protective measures for the mask-cutting step; they are what keeps the blade going where it was aimed.
• Sun protection — hat, sleeves, sun cream and shade between sheets — for the outdoor half.
• Indoors afterwards: nitrile gloves, eye protection and one pair of tongs per tray.

Ventilation

Not among the outdoor controls, and not among the mask-cutting controls either, since cutting thin metal with a knife produces no dust or vapour. Indoors, an openable window or an extractor rather than a sealed cupboard, which is ILFORD’s general instruction for the three baths.

Materials

Item	Quantity	Notes
Variable-contrast RC paper	10 sheets	Fibre-based paper takes the curve more willingly if you have any.
The curved insert from Part VI	1	Radius equal to the wide focal distance, checked at centre and both edges.
Two-hole and three-hole plates	1 each	With their separations measured, not nominal.
Card masks	3	To open the holes of a multi-hole plate in sequence.
Zone plate or sieve mask	1, optional	Printed transparency or cut foil; see the caution in section 5.
A tape measure	1	Subject distances are inputs to the displacement arithmetic.
Prediction sheet, folded	2	Predictions on the left, observations on the right.

Chemicals

Chemical	Quantity	Form
Paper developer concentrate	100 mL	Diluted 1+9 to make 1 L; 60 seconds at 20 °C for RC paper.
Stop bath concentrate	50 mL	Diluted 1+19 to make 1 L. A citric acid stop.
Rapid fixer concentrate	200 mL	Diluted 1+4; 30 seconds for RC paper. An ammonium thiosulfate fixer.
Water	about 12 L	Dilution and washing.

Equipment

The camera at its wide setting, f = 50 mm, because the curved insert’s radius equals that focal distance and the geometry breaks if it does not; the curved insert; the flat back for the comparison; the plate register; a tripod with a level; a timer; and the processing kit.

Estimated cost

Cost band £. Ten sheets and a session’s chemistry, plus a few pence of foil or one sheet of transparency film if you take the zone-plate option. Dated prices live in the laboratory planner.

Waste streams

Three streams leave this session. Used fixer carries dissolved silver as a thiosulfate complex, and so does the first change of wash water; both go into the labelled collection container. Developer and stop carry none. Foil offcuts are metal, and go to metal recycling rather than to the bin. Where the collection container goes afterwards is governed by local regulation, which differs between authorities.

Preparation

1. Choose the subject from the mapping, not the other way round

Part VI derives the mapping and this page uses it. A pinhole is a central projection: every straight line in the world, together with the hole, defines a plane, and the image of that line is where that plane cuts the recording surface. A plane cuts a plane in a straight line, which is why a flat back is rectilinear. A plane cuts a cylinder in a conic, which is a curve, and stays a curve when the cylinder is unrolled — with exactly two exceptions.

1. Every vertical stays straight and parallel, provided the camera is level and the wrap is horizontal, because the plane through the hole containing a vertical also contains the cylinder’s axis, and a plane through the axis cuts a cylinder in straight generators.
2. One horizontal stays straight: the one at the height of the pinhole. Its plane is perpendicular to the axis, cuts the cylinder in a circle, and a circle unrolls to a straight line — landing on the centre line of the sheet.

Everything else bows, away from the centre line above the hole’s height and towards it below, increasingly with distance from centre height.

That gives a rule for choosing a subject that is a rule rather than a preference. Point a curved back at something whose verticals matter and whose horizontals do not — a colonnade, a row of houses, a line of trees, masts, a crowd — and place the pinhole at the height of the one horizontal you want kept straight. A shoreline, a parapet, a kerb, the line where a wall meets the ground: pick one, and set the tripod so the hole is level with it.

🧮DO THE MATHS: how much a horizontal actually bows, and where

The bow is easy to quantify because the mapping is. On the cylinder, a point at wrap angle φ and axial angle ψ lands at arc position f φ across the sheet and f tan ψ along it.

Take a horizontal line at height h above the pinhole, at distance u. Straight ahead, at φ = 0, it sits at f h/u above the centre line. At wrap angle φ, the same line is further away — its perpendicular distance from the axis is u/cos φ — so it sits at f h cos φ / u.

So a horizontal’s height on the sheet falls as cos φ, and the bow is f h(1 − cos φ)/u.

Worked. A gutter line 3 m above the pinhole on a terrace 12 m away, at f = 50 mm. Straight ahead it is 50 × 3/12 = 12.5 mm above the centre line. At the edge of a 127 mm sheet wrapped on a 50 mm radius, φ = 72.8°, cos φ = 0.296, so there it is only 3.7 mm above the centre line. The gutter drops 8.8 mm across the sheet — about 7 per cent of the frame width — which is a plainly visible swoop and the whole reason the picture looks like a panorama.

And the control that follows. Halve the height difference by raising the camera 1.5 m and the bow halves with it. The bow is proportional to how far the line is from the pinhole’s own height, so tripod height is the panorama’s principal compositional control. That is a thing you can act on, and it is not obvious.

Choosing a subject for the cylinder: what stays straight, what bows, and where to put the pinhole

1. 1Verticals — straight and parallel everywhere — guaranteed by the geometry provided the camera is level and the wrap is horizontal
2. 2The horizontal at pinhole height — the only straight one — set the tripod so this is the line you most want straight
3. 3A horizontal above the hole — bows down at the edges — height on the sheet falls as cos φ; the drop is f·h(1 − cos φ)/u
4. 4A horizontal below the hole — bows up at the edges — the same rule with the sign reversed, which is why the picture bulges

Derived from Part VI's cylindrical mapping; drawn to show the rule, not traced from a negative. The single most useful consequence is that tripod height controls the amount of curvature.

2. Falloff as a feature, and the honest size of the gain

Part VI derives the cylinder’s illumination law and it is not what most accounts claim.

E(φ, ψ) = E(0) · cos φ · cos⁴ ψ

Illumination on a cylinder concentric with the pinhole

Across the wrap it is one cosine where a flat plane has four. Along the axis it is cos⁴ ψ, exactly the flat law, unimproved — because a cylinder cut by a plane containing its axis is flat in that direction, and there is nothing for the curve to fix.

The numbers for a 127 mm sheet wrapped on a 50 mm radius:

Position on the sheet	Flat back	Curved back	What the curve is worth
Middle of the wrapped edge	2.77 stops down	1.75 stops down	1.02 stops
Middle of the axial edge	2.05 stops down	2.05 stops down	nothing
Corner	3.73 stops down	3.80 stops down	nothing — very slightly worse

Those are Part VI’s figures and its measurement, not new claims. The single most testable prediction on this page is the second row: the cylinder buys nothing vertically. If your curved negative is brighter at the top and bottom edges as well as at the sides, something other than the geometry is doing it — most likely an insert whose radius is not really equal to the focal distance.

So when do you want each back? Use the curved back when the picture has a wide, evenly lit subject across it — a sky, a sea, a rendered wall — where a two-stop drop at the sides would read as a fault. Use the flat back when you want the dark corners: they are the pinhole photograph’s most recognisable signature, and on a subject with texture in the corners they read as vignetting that frames rather than as a failure. Both are decisions. Neither is a defect.

3. Multiple pinholes, with the bands placed before the shutter opens

Part VI gives the displacement between two images from two holes separated by s:

Δ = s (1 + f / u)

Displacement between the images from two holes

At any ordinary subject distance the correction is small — at u = 10 m and f = 50 mm it is half a per cent — so for practical purposes the images are displaced by the hole separation, and the interesting arithmetic is what that does to the sheet.

🧮DO THE MATHS: three holes 15 mm apart on a 180 mm arc

The plate. Three holes in a row, separated by a measured 15.0 mm, at f = 50 mm. The curved back carries 180 mm of arc.

Where the images land. Centred on the plate’s middle hole, the three images sit at −15, 0 and +15 mm. Each covers the full sheet width less its own displacement.

The bands.

• A 150 mm central band receives all three images. Three equal exposures add, so it is log₂ 3 = 1.58 stops brighter than a single image would be.
• Two 15 mm bands, one at each end, receive two of the three: 1.00 stop brighter.
• Nothing on the sheet receives only one image, because the outer displacements are smaller than the sheet is wide.

The tonal step you are actually composing with is therefore 0.58 stop, not 1.58, because the comparison the eye makes is between the middle of the sheet and its ends. That is a subtle band, and subtlety is a design decision: if you want a visible band, separate the holes further. With s = 40 mm the triple band shrinks to 100 mm and the double bands grow to 40 mm each, and the step is still 0.58 stop — the step never changes with separation; only the widths do. To change the step you change the number of holes.

Which band do you expose for? Whichever you want correct. Expose for the triple band and the ends are 0.58 stop over; expose for the ends and the middle is 0.58 stop under. There is no exposure that is right everywhere, and choosing is the real decision a multi-hole plate forces on you.

And here is what makes it a composition rather than a diagram. On the curved back the sheet’s angular scale is even: 1.15° of subject per millimetre of arc at f = 50 mm. So a 15 mm separation displaces each image by 17.2° of subject. The three images are the same scene shifted by 17°, and where a strong vertical stands in one image it lands 15 mm away in the next. Place a single isolated vertical — a lamp post, a mast, a doorway — and you get three of them, evenly spaced, in a scene that is otherwise a legible single picture. Place it in front of a busy façade and you get mud.

Two holes, one subject, two images: where the displacement comes from

The image belongs to the hole and goes where the hole goes. Δ = s(1 + f/u) is the blur formula b = d(1 + f/u) with the separation in place of the diameter, and that is not a coincidence: a single hole of diameter d is a continuous row of pinholes spanning d.

Opening the holes in sequence layers time as well as space. Mask two of the three with card, expose the first for a third of the total, then open the second, then the third. Each image then carries a different slice of the session — different traffic, different cloud, different people — and the bands record the sum. Write the sequence and the timings down before you start, because a sheet with three overlaid images and no record of which was open when is not readable afterwards.

Three holes on a 180 mm arc: the bands, their exposures, and the opening sequence

1. 1Triple band, 180 − 2s = 150 mm — +1.58 stops over a single image
2. 2Double bands, s = 15 mm each — +1.00 stop; the step across the picture is 0.58 stop
3. 3The opening sequence — each hole carries a different slice of time, and therefore a different density

Widths computed for s = 15.0 mm on a 180 mm arc at f = 50 mm, where 15 mm of arc is 17.2° of subject. Exposure ratios are the base-two logarithms of the number of overlapping images.

4. The anamorphic stretch, and which back removes it

The flat plane places a point at f tan θ and the cylinder at f φ, so the cylinder has a uniform angular scale — equal angles occupy equal widths of paper, everywhere — and the flat plane does not. Part VI puts a number on the difference: on a flat plane the horizontal scale is stretched relative to the vertical by sec θ, which is 1.41 at 45° and 2.00 at 60°.

That is the whole of the anamorphic question, and it settles a common confusion. A face at the edge of a very wide flat-plane frame is widened by that factor, and it looks wrong. The cylinder removes that stretch entirely across the wrap — and pays for it by bending horizontals instead. Neither is a distortion in the sense of a fault: both are exact central projections onto different surfaces, and you are choosing which price to pay.

The compositional use of it is the low, wide horizon. Set the pinhole low and level, and the cylinder gives you a very wide field at even scale with the ground rising towards you and the sky curving away above — a picture with no equivalent on a flat back, because a flat back that wide would stretch the edges into nonsense.

5. Optional: the zone plate, and what the course could not verify

Part VI’s diffraction lesson derives the Fresnel half-period zones: contributions from a ring of radius r arrive late by r²/2f, and the boundaries where successive zones flip sign are at

r_n = √( n λ f )

Fresnel zone radii

A pinhole is an aperture admitting about one zone. A zone plate is the same aperture with every second zone blacked out, so that only the adding zones get through and nothing cancels them — which is why it can be much larger than a pinhole and still concentrate light.

The geometry, which is derivable and therefore given here. At f = 50 mm and λ = 550 nm the first five zone boundaries are at 0.166, 0.235, 0.287, 0.332 and 0.371 mm. A five-zone plate is therefore 0.742 mm across, giving N = 50/0.742 = f/67. The near-optimum pinhole at the same focal distance is 0.259 mm, or f/193. The ratio of areas is (0.742/0.259)² = 8.2, so the geometric prediction is a gain of just over three stops.

✕Three things about zone plates this course has not verified, and will not assert

How much of that three stops actually arrives at the focus. A zone plate diffracts light into several orders, and only some of it lands in the primary focus; the rest spreads as a veil. This course has not read a source giving that fraction for a binary amplitude zone plate, so it makes no claim about the true speed gain. The three stops above is an upper bound from aperture area alone.

Whether the characteristic “glow” is real, and what causes it. It is widely described. The course has not verified it against a source that meets its standard, and the mechanism it would attribute it to — undiffracted and higher-order light veiling the image — is a plausible explanation rather than a cited one.

Whether a mask printed on transparency film is opaque enough in its dark zones. An inkjet or laser black on film is not the same as metal. If the dark zones transmit appreciably, the plate behaves as a large fuzzy aperture rather than as a zone plate, and the picture is simply soft. The course has no measurement of this and offers none.

So the zone plate is offered here as an experiment rather than as a technique, and the comparison exposure in Stage 4 of the making is what turns it into a result for your mask. If you have no mask, skip it: it is the one optional item on this page, and nothing later depends on it.

6. Write the predictions, then fold the sheet

For the panorama: the pinhole’s height above the ground and the one horizontal you levelled on; the predicted bow of two named lines in millimetres; the falloff you expect at the wrapped edge, the axial edge and the corner; and the computed exposure.

For the composite: the measured hole separations; the displacement at your actual subject distance; the width and exposure of every band; which band the exposure is correct for and by how much the others will be wrong; and the opening sequence with its timings.

For the zone plate, if you use it: the zone radii, the plate diameter, the geometric f-number and the predicted gain in stops.

Fold the sheet. Part VI makes the point and it holds here: confirmation bias is a perceptual failing, not a moral one, and the fold is the control for it.

The making

Stage 1 — Load the curved insert and check the radius (25 minutes)

Measure from the pinhole to the paper at the centre and at both wrapped edges. On a correct insert those three distances are equal. If the edges are further away, the radius is too large, the cosine advantage will be smaller than predicted, and you should say so in the log rather than discover it in the negative. Resin-coated paper springs; if you have fibre paper, use it here, and use it for the flat comparison too so the only variable stays the shape.

Stage 2 — The panorama (40 minutes)

Level the camera on your chosen horizontal, set the tripod height deliberately, and expose two sheets: the computed time and one stop over. Then, without moving the tripod, fit the flat back and expose one more of the same scene. That flat sheet is not a picture; it is the control that lets the critique say what the cylinder did.

Stage 3 — The multiple-pinhole composite (40 minutes)

Choose a scene with one strong isolated vertical and an otherwise legible background. Fit the three-hole plate, mask two holes, and run the opening sequence to your written timings. Expose a second sheet with all three open for the whole time, for comparison. Do not move the camera between them.

Stage 4 — Optional: the zone-plate comparison (20 minutes)

Two sheets of one static scene, changing only the mask: the near-optimum pinhole at its computed exposure, and the zone plate at the exposure its geometric f-number predicts. Give the zone plate exactly the predicted time, with no correction and no bracket. The whole value of the exercise is in how far wrong that turns out to be.

Stage 5 — Process everything together (35 minutes)

Developer 1+9 for 60 seconds at 20 °C, stop, rapid fixer 1+4 for 30 seconds, wash. All the sheets in one session at one temperature.

Stage 6 — Measure, then unfold (20 minutes)

Trace, measure and rank before unfolding the predictions.

Expected observations

On the panorama. Verticals straight and parallel. One horizontal straight, on the centre line. Every other horizontal bowed, more the further it is from centre height, and in opposite directions above and below. The sides of the frame noticeably brighter than a flat-back negative’s sides — by about a stop — and the top and bottom edges no brighter at all.

On the flat control. Straight lines everywhere, dark corners, and edges of the frame visibly stretched horizontally relative to the middle.

On the composite. Three copies of the isolated vertical, evenly spaced. A brighter central region with a step down to the ends, at about half a stop. Where the three images fall on the same tone, no band at all is visible — the bands only appear where the images differ, which surprises most people the first time.

On the sequenced sheet. Three images of visibly different density, the first-opened being the densest, and time differences between them if anything moved.

On the zone plate, if you tried it. A soft image, probably with a veiling brightness, and almost certainly not at the density the geometric prediction called for.

Evaluation and reconciliation

1. Measure the bow. On the panorama, measure the height of one named horizontal above the centre line at the middle of the sheet and at both edges. Compare with f h cos φ/u. Report the discrepancy in millimetres.
2. Reconcile the falloff. Judge the density at centre, wrapped edge, axial edge and corner against a grey scale, convert to stops, and compare with the table in section 2. Part VI establishes that by-eye judging resolves about half a stop, so a predicted advantage of 1.02 stops at the wrapped edge is measurable and a predicted advantage of zero at the axial edge is confirmable only as “smaller than half a stop”.
3. Measure the displacement. Find one feature that appears three times and measure the spacing. Compare with s(1 + f/u), and propagate the uncertainties in s and u as Part II’s measurement lesson sets out. Does the measured value lie inside the predicted range?
4. Find the band edges. Can you see them at all? If not, say what that tells you about a 0.58-stop step on a paper negative, and compare with the resolution figure in point 2.
5. The zone plate, if used. How many stops out was the predicted exposure? That number is a measurement of the fraction of the light reaching the focus, and it is yours, for your mask.

The critique

One paragraph per submitted picture, naming causes. The intention as written; which projection produced which feature; whether the exposure landed and by how much; which band or which part of the frame you chose to be correct and whether that was the right choice; and the single change you would make.

Then the comparison this page exists for: say what the panorama gained and what it lost against the flat-back negative of the same subject. Both sheets are in front of you and they differ in exactly two ways — the line mapping and the edge illumination — so this is a critique that can be argued from evidence rather than from taste. Most students find the honest answer includes a loss.

Troubleshooting

What you see	Most likely cause	What to check, and what to change
Verticals curved on the curved-back negative	The camera was not level, or the wrap is not horizontal	Check the level and the insert’s seating; the geometry guarantees straight verticals only when both are right
The edges no brighter than a flat back’s	The insert’s radius is not equal to the focal distance	Measure hole-to-paper at centre and both edges; they must be equal
Top and bottom edges brighter than expected	Something other than the geometry — most likely flare or a leak	The cylinder buys nothing axially; a vertical improvement is evidence of a fault, not of success
The composite unreadable	A busy subject behind three overlaid images	Choose one isolated feature against a plain ground and repeat
No visible bands on the composite	The images are landing on similar tones, or 0.58 stop is below your judging resolution	Both are real answers; say which, from the negative
The sequenced images all the same density	The masks leaked, or the timings were not kept	Card masks must overlap the holes generously; a watch, not a count
A soft image sitting on a grey veil, from the zone plate	Insufficient opacity in the dark zones, or the higher orders	Hold the mask to a bright light and look at the dark rings; this is the failure the section 5 caution names
Paper sprung flat inside the curved insert	RC stiffness	Card tongues at each end of the arc, or fibre paper

Clean-up, storage and disposal considerations

Return the insert flat and dry. Collect every foil offcut. Sleeve the negatives the same day, labelled to the log — and note on the sleeve which back and which plate made each one, because a curved negative and a flat one look sufficiently alike in a sleeve to be confused a month later.

The waste from this session is the waste from every session in this part, and it leaves by the routes already established: the fixer and the first wash water into the silver collection container, the developer and stop with no silver in them, and the foil to metal recycling. The route the collection container takes is set by local regulation.

What to submit

• One panorama, negative and working positive, with the flat-back control sheet alongside it as evidence.
• One multiple-pinhole negative, with the band widths and exposures you computed beforehand.
• The log entries for every sheet, including the measured hole separations and the insert’s three measured distances.
• The folded prediction sheets, unfolded, with observations beside predictions.
• Two critique paragraphs, including the gained-and-lost comparison.

Further work

The two-hole time layering. Two holes, one scene, and a two-hour gap between opening the first and the second: the same place at two times, superimposed and displaced. It is the simplest way this camera can put two moments in one frame, and it costs nothing but a plate you already have.

The horizon sweep. Five panoramas of the same subject at five tripod heights, from ground level to above head height, changing nothing else. The bow of every horizontal changes with the height, and the set is a direct demonstration that the curvature is under your control rather than the camera’s.

Wall’s question, answered on your own negatives. The 1912 Dictionary of Photography observes of the plain box pinhole camera only that “the larger the plate the wider the angle and the greater the distance the larger the image” — the flat-plane trade, stated as a constraint. The cylinder is built to escape exactly that constraint. Write a paragraph saying, from your two negatives, whether it does.