Capstone Stage 1: The Instrument, Its Calculation and Its Commissioning

Purpose

To turn requirement 1 into an engineering task with a verdict at the end of it, and requirement 2 into a sheet of arithmetic checked against a hole you measured.

The task has five parts and the fifth is what makes it engineering rather than making:

1. A written performance goal with a number in it, dated before any work begins.
2. A measurement of the starting state, by a method you can describe and with an uncertainty you can quote.
3. The work, with every change made during it recorded and reasoned.
4. A measurement of the finished state, by the same method.
5. A statement of whether the goal was met — and the statement is worth nothing unless the answer could have been no.

A build that met no stated goal has not been commissioned; it has been completed, which is a different and smaller thing. The object you finish with is evidence. The design record and the instrument certificate are the deliverable.

Nothing on this page teaches you how to build anything. Every route in the menu below is an instrument Parts VI, XIV, XV, XVI or XVII already builds, and the pages that build them are linked. What this page adds is the discipline of doing it against a goal, and the calculation that every capstone owes whatever it builds.

Learning objectives

By the end of this stage you will be able to:

• write a performance goal that a measurement could refuse, and say what measurement would refuse it;
• measure a starting state before changing anything, and resist the temptation to skip it because the answer seems obvious;
• carry out the full pinhole calculation — optimum diameter, effective f-number, geometric blur, diffraction limit, their crossing, angle of view, coverage and corner falloff — and check every step against a measured hole and a real negative;
• set commissioning pass criteria before testing, in the units the test reports;
• write an instrument certificate that says what the instrument may and may not be used to claim;
• state the mains boundary correctly, including what the course looked for and did not find;
• record a missed goal as a result and diagnose it, rather than revising the goal.

Prerequisites

The project plan, with its performance goal already written, and the specification’s requirement 1 test read.

From Part VI, designing the modular camera, the build, pinhole geometry and field of view, diffraction and the optimum pinhole and making and measuring pinholes. The last of those owns the measurement your calculation is checked against.

From Part XIV, low-voltage electronics for the darkroom, and from Part XVII, switching lamps safely. Between them they own the boundary this page restates and does not soften.

The permitted menu, and what each demands

Nine routes. Every one is an instrument the course has already taught, and the page that teaches it publishes the commissioning criteria this stage reuses rather than replacing.

Route	What it demands	Where its pass criteria live
A pinhole camera in a new format or focal length	A design decision argued from coverage and blur, and a first negative against a calculated exposure	Part VI’s commissioning session
A substantial modification to the Part VI modular camera — a curved plane, a roll-film back, a second pinhole station	A before-and-after on the property you changed, not on the camera in general	Part VI
A contact printing frame, or its light source	Gap closure across the field, and a uniformity map of the source	Part XVI’s frame page
An LED safelight	The fog test, on the paper you actually use	Part XVI’s fog test
A UVA exposure unit	An enclosure or interlock, a dose measurement and a uniformity map	Part XVI’s UV pages
An LED enlarger head, or an existing enlarger converted to one	Alignment, uniformity, corner sharpness and exposure repeatability	Part XVI’s enlarger commissioning
The exposure timer	Timing accuracy against an independent reference, and repeatability	Part XVII’s calibration
An improvement to the sensitometer or the densitometer, with a measured reduction in uncertainty	The old certificate and the new one, on the same arms	Part XIV and Part XV
An emulsion coating station or a drying box	A measurable property: coating weight spread, or dust settled on a test sheet	Part V’s coating station

Choose one. Two builds is not twice as good a capstone; it is one build’s worth of measurement spread over two objects, and the requirement is about depth of evidence rather than quantity of apparatus.

!Reusing a published criterion rather than inventing a second one

Where the originating page publishes a pass criterion, use its wording, and cite the page. The enlarger’s uniformity criterion is that opposite corners agree within 0.04 in density and that stopping down two stops improves them; its repeatability criterion is that the standard deviation of ten identical exposures is below half the smallest exposure increment you actually use, which is about 3 per cent if that increment is a twelfth of a stop. The safelight’s criterion is Kodak’s and ILFORD’s: no density change between the unexposed area and the longest safelight exposure on a light grey test area, with ILFORD adding that a change of about 0.04 in density after one minute means the conditions are inadequate.

Inventing a second standard here would leave the course saying two things about one instrument, and a capstone that scores itself against its own private criterion is scoring itself against nothing.

Safety classification

Level B, and the level is set by the most hazardous route the page permits rather than by the mildest. Two criteria of the rubric apply: ultraviolet and high-brightness optical sources, if the chosen route is a UVA unit or an LED enlarger head; and low-voltage electronics construction, if the route involves soldering and a supply.

A purely mechanical route is Level A work and may be run as such. A camera, a contact frame, a coating station or a drying box involves cutting tools, adhesives, paint and drilling, and nothing else. If that is your route, the Level B controls stay in the cupboard and the page’s own level for your session is A. Say which in the design record, because the classification is a property of what you did rather than of what the page permits.

What is not a hazard here, and why. There is no chemistry in the build at all: nothing is weighed, nothing is dissolved, no vapour is produced, and the only liquids present are an adhesive and a paint used at room temperature with the window open. That is unusual in this course and it is worth naming, because the same materials in another context are not benign — a solvent-based adhesive in a sealed cupboard is a vapour problem, and the same LED emitter run at full current with the optics off is a photobiological one. What removes the hazard here is the quantity, the ventilation and the enclosure, not the substances. The commissioning half of the session does handle chemistry, and it is ordinary Level A tray processing of test sheets under the controls Part XVI and Part XIX already state.

One step may be raised above the session’s level and it is named here rather than in the procedure. If your route is a UVA unit, its first power-on is done with the enclosure closed and the interlock proved, and if the enclosure is not yet finished the emitter is not energised at all. That is not a Level B step inside a Level A session; it is a step that does not happen until its control exists.

Hazards

Cutting and drilling. A scalpel or craft knife used towards a cutting mat and away from the hand holding the work; a drill bit grabbing thin sheet and spinning it. Eye protection when drilling, and the work clamped rather than held.

Soldering. The iron is the commonest injury in this half of the course. A stand, eye protection, and ventilation for the flux fume — soldering flux produces a respiratory sensitiser, which is why the fume is extracted or blown away rather than breathed.

High-brightness LEDs. Bright enough to be an optical hazard before they are uncomfortable, which is the whole problem: the aversion response that protects you from a bright lamp is slower than the damage from a focused emitter. Align with the emitter off or heavily attenuated, and read the maker’s own photobiological and thermal data rather than a general claim.

Ultraviolet. A UVA array is enclosed or interlocked so that direct exposure of eyes and skin is impossible, and is never run open on a bench. The assessment is made on the source, not on your intentions about looking at it.

Dust. Cutting board, sanding and drilling all produce it, and it is done away from film, paper and coated plates. A capstone that fogs its own paper stock with plywood dust has lost more than it built.

The chemistry of the commissioning sheets. Ordinary paper processing: developer, stop and fixer at working dilution, at 20 °C, with nothing heated and nothing volatile.

Required PPE

Eye protection whenever anything is cut, drilled or soldered, and whenever a bright emitter is powered. Nitrile gloves for the adhesive and for the commissioning trays; tongs rather than fingers in the trays. For a UVA route, the enclosure is the control and personal protection is the backup rather than the other way round — if the answer to “what stops the light reaching my eyes” is a pair of glasses, the build is not finished.

Ventilation here is for adhesive vapour and solder flux fume, not for a chemical bath: work at an open window or with an extractor running, and do not do either job in a sealed room. The commissioning trays need the ordinary darkroom provision — an openable window or an extractor — because a stop bath and a fixer are open in the room.

Parts

Route-dependent, and every route’s own build page carries its bill of materials. What this stage adds to that list is the same for all of them:

Part	Quantity	Why this stage needs it
The design record	1	Dimensioned sketch, decisions, rejected alternatives, changes made during the build
A bill of materials tied to planner items	1	So the cost in the plan and the cost in the record are the same number
Test targets for the commissioning arm	Route-dependent	A uniformly lit sheet, a detailed negative, an opaque cap, a grey test area
The instrument certificate form	1	Part XV’s format, reused rather than varied

Tools

The tools of the originating build page, plus the measuring instruments this stage depends on: the densitometer for any uniformity or fog measurement expressed as density, a caliper or a measuring microscope for the pinhole, a stopwatch or the timer for repeatability, and a thermometer you have checked. None of them is consumed and none appears in the consumables table below.

Estimated cost

££ on the planner’s bands, and the band is set by the route rather than by the stage. A camera or a frame built from sheet material is the cheap end; an LED enlarger head or a UVA unit with its enclosure is the dear end, and an improvement to the densitometer can be anywhere depending on whether it needs a new photodiode or only a better baffle. The planner carries the capital; the table below carries what one commissioning run uses up.

Estimated consumables cost

Every figure with a source is the planner’s own dated UK price, and every quantity comes from the Parts list and from the commissioning programme below. The worked example is the camera route: a new back for the Part VI modular camera, and a fourteen-sheet commissioning session with four sheets over for finding exposures.

Consumed	This session	Sourced price	Cost this session
Variable-contrast RC paper, 8 × 10 in	18 sheets	£33.50 for 25 to £96.18 for 100	£17.28 to £24.12
Paper developer concentrate	100 mL	£10.52 per 500 mL to £20.03 per 1 L	£2.00 to £2.10
Stop bath concentrate	30 mL	£10.66 to £12.18 per 500 mL	£0.64 to £0.73
Rapid fixer concentrate	60 mL	£21.05 to £25.98 per 1 L	£1.26 to £1.56
Thin hardwood plywood	about a quarter of one sheet	£11.00 to £21.50 a sheet, bought whole	£2.75 to £5.38
PVA adhesive	100 mL	£11.99 to £14.29 per 5 L	£0.24 to £0.29
Pinhole-making stock — shim, abrasive paper, a pin vice	one hole’s worth	Named in the price file’s own gap list as unpriced	—
Camera build hardware — T-nut, magnets, flocking, foam, sheet	one back’s worth	Named in the price file’s own gap list as unpriced	—
Solder and flux, for an electronic route	one build’s worth	The price file could not price it. It is one of the bench and workshop consumables the file names as a gap	—

The priced rows come to about £24.17 to £34.18 for one run of the camera route, and that is a floor and not a total: three of the nine consumables carry no sourced price, and for an electronic or ultraviolet route the unpriced share is far larger, because emitters, drivers, enclosures and optics are all outside the price file. Equipment used and not consumed — the densitometer, the caliper, the drill, the timer, the trays — is in the prose above and deliberately not in this table.

Alternative route

Two obstacles bite on this stage, and both have a route.

No darkroom. The build itself needs none. What needs one is the commissioning: the light-tightness sheets, the uniformity map and the safelight fog test all involve paper handled in the dark. A changing bag loads a camera back or a printing frame, and the paper can then be processed at a sink with the lights on in a daylight tank or a lidded tray — but a uniformity map made that way loses the ability to place a card by hand mid-exposure, which is how the safelight test’s timed steps are made. So: the camera, frame, coating-station and instrument-improvement routes are fully available; the safelight route is not, because a fog test needs a room that can be darkened and there is nothing else the test could be run in. That is stated rather than worked around, and a reader with no darkroom picks a different route from the menu rather than running a weakened version of that one.

No woodworking tools, no bench, no space to cut. Requirement 1’s test is the performance goal, not the fabrication, and the specification says so. Two routes need no cutting at all: an improvement to the sensitometer or densitometer, which is usually a baffle, a better zero routine or a firmware change with a measured reduction in uncertainty; and a modification to bought equipment, which is where an LED conversion of an existing enlarger sits. Both produce a before-and-after that could have failed, which is the whole of what requirement 1 asks.

The pinhole calculation, mandatory for every capstone

Seven quantities, from three measurements, and the point of doing it even when your instrument has a lens or no optics at all is that it is the shortest complete example in the course of optics predicting a photograph and then being checked against one.

The relation the course uses, from Part VI:

d_opt = k √(λ f)

Optimum pinhole diameter

d_opt is the hole diameter, λ the wavelength, f the focal distance — the hole-to-plate distance you measured, not the one you designed — and k the constant. The course uses 1.56, the equal-blur criterion, and states the range 1.41 to 1.90 rather than a single number, because the constant is where the historical disagreement lives: 1.41 is Petzval’s minimised summed blur and Rayleigh’s quarter-wave criterion arriving at the same figure by different arguments, and 1.90 is Rayleigh’s own measurement on his own plates, back-calculated to an effective wavelength of 420 nm. Anyone who quotes 1.90 as “the Rayleigh criterion” has conflated a measurement with a phase criterion.

🧮DO THE MATHS: the whole sheet, worked at 80 mm on 4 × 5

Given. Focal distance f = 80 mm, measured. Pinhole diameter d = 0.30 mm, measured by the method in making and measuring pinholes, with that method’s own precision recorded beside it. Format 4 × 5 in, sheet 102 × 127 mm. Design wavelength λ = 550 nm, the conventional figure for panchromatic film.

Optimum diameter. λf = 5.5 × 10⁻⁴ × 80 = 0.0440 mm²; √ = 0.2098; × 1.56 = 0.327 mm. At 450 nm, the blue-sensitive figure, it is 0.296 mm — and 1.41 at 550 nm gives 0.296 mm too, which is worth noticing: changing the wavelength from blue to green moves the answer by less than the disagreement between authors does.

Against the hole you have. 0.30 mm against an optimum of 0.327 mm. Your hole is 8 per cent small, which puts you on the diffracted side of the crossing.

Effective f-number. N = f / d = 80 / 0.30 = f/267.

Geometric blur, for a distant subject, is the hole itself: 0.30 mm.

Diffraction blur, as the Airy diameter, is 2.44 λ f / d = 2.44 × 5.5 × 10⁻⁴ × 80 / 0.30 = 0.358 mm.

Where they cross. Equal when d = √(2.44 λ f) = √0.1074 = 0.328 mm, which is the optimum above, as it must be. The summed blur at your 0.30 mm hole is 0.658 mm; at the optimum it is 0.655 mm. Three thousandths of a millimetre. That is the useful result of the whole calculation: being 8 per cent off the optimum costs you almost nothing, and a capstone that agonises over the last 0.02 mm of a hole is optimising the wrong thing.

Angle of view. The sheet diagonal is √(102² + 127²) = 162.9 mm, so the diagonal angle is 2 arctan(81.45 / 80) = 91.0°. Across the short side, 65.0°; across the long side, 76.9°.

Coverage. A pinhole has no image circle in the lens sense — it illuminates everything in front of it — so coverage is decided by how much falloff you will accept rather than by an optical edge. State your own limit and where it came from.

Corner falloff. The corner sits at 45.5° off axis. cos⁴ 45.5° = 0.241, which is −log₂ 0.241 = 2.05 stops down. Two stops at the corner, from geometry alone, before the plate’s own thickness adds anything.

Then check it against the negative, which is the half that makes it a calculation rather than an exercise. Three checks, and each can fail:

• The exposure. Did the sheet exposed at the time computed from f/267 come out where the calculation said? A systematic error here means the focal distance, the hole diameter or the meter reading is wrong, and the bracket tells you which way.
• The corner. Read the corner and the centre of a uniformly lit sheet on your densitometer and convert the difference to stops. Part VI states that real falloff is generally worse than cosine-fourth because of the tunnel effect of a plate with thickness, and that it found no published measurement of the excess. So record the excess over 2.05 stops with your plate thickness beside it, and do not compare it with a limit, because the course has established none.
• The sharpness. Does the blur in the negative match the 0.66 mm the sum predicts, at the magnification you will print at? Part VI’s diameter series is the comparison: three holes at matched exposure, indistinguishable in density and different in sharpness.

Build

Four things happen here and only two of them involve tools.

Before anything is cut: write the goal down, dated. One sentence, a number, and the method that will measure it. “Opposite corners of the new back’s field will agree within 0.10 in density at f/267 on a uniformly lit sheet, read on instrument serial NNN; they currently differ by 0.31.” That sentence is the whole of requirement 1’s first two parts, and it is impossible to write honestly afterwards.

Measure the starting state. Even where the answer seems obvious. The commonest reason a capstone fails requirement 1 is not that the modification did nothing; it is that nobody measured the state it started from, so the improvement has no size. If the instrument does not yet exist — a new camera rather than a modification — the starting state is the instrument it replaces, or the calculated prediction, and you say which.

Build it, recording as you go. The design record is a deliverable and it has four parts:

1. What was decided, and the numbers it was decided from.
2. What was rejected and why. At least one rejected alternative, with the reason. A design record with no rejected alternative is a description rather than a record, because it does not show that a choice was made.
3. The dimensioned sketch, and the bill of materials tied to planner items.
4. Every change made during the build, with its reason. These are the entries that matter in three years. “Moved the light trap 4 mm inboard because the back would not seat with the original spacing” is the sentence that explains why the drawing and the object disagree.

And stop before testing. Write the pass criteria down now, in the units the test will report, before a single reading exists. A limit chosen after the numbers are seen is not a limit; it is a preference.

Testing and calibration

Six kinds of commissioning test. Run the ones your route has, and skip the ones it does not — with a line in the record saying which and why, because a skipped test that is not recorded is indistinguishable from a failed one.

The commissioning sequence, and why it is in this order

1. 11 — Light-tightnessAn extended exposure on paper with the aperture capped, against a control sheet that was never exposed and was processed in the same session. Everything downstream is corrupted by a leak, so this goes first.
2. 22 — Uniformity, mapped rather than judgedA uniformly lit sheet read at the centre and at points across the field, in density. The criterion is stated as a density difference, and for the enlarger route the published one is 0.04 between opposite corners.
3. 33 — Alignment, where there is an optical axisA grid negative printed square, or a laser and a mirror. Misalignment produces a gradient that looks exactly like a uniformity fault, so the two are separated by changing one thing at a time.
4. 44 — Repeatability, where there is a timer or a sourceTen identical exposures; the criterion is a standard deviation below half the smallest increment you actually use.
5. 55 — Thermal behaviour, where an LED runs at powerOutput against time from cold, from the maker's own derating data rather than from a general claim, giving the warm-up rule that goes on the certificate.
6. 66 — A first negative against a calculated exposureFor a camera route only, and it tests the optics and the arithmetic together — which is why it comes last and why a failure here is diagnosed against the five tests above.

The order is not a preference. A leak corrupts every measurement after it; uniformity has to be known before a corner can be read honestly; and there is no point measuring the repeatability of an instrument that has already failed the first three.

Then write the instrument certificate, in the format Parts XIV and XV established, and do not introduce a variant. Six fields:

Field	What goes in it
What was measured	Each arm, named, with the quantity it reports
With what	The instrument, its serial and its own certificate date — a measurement is only as good as the thing that made it
Against what reference	A calibrated wedge, a certified tile, an independent timebase, or “none, so the scale is relative”, said plainly
With what uncertainty	By band where the quantity has bands, not one figure for the whole instrument
On what date	Because the certificate is a claim about a day, not about an object
What it may and may not be used to claim	The field that stops the certificate being a rosette. “Repeatable to 0.01 D between 0.0 and 2.0 with the sample replaced; the scale above 2.5 is limited by stray light and is not quoted.”

📓The sentence that has to be on every certificate this course produces

Where a scale is anchored to something you did not buy a certificate for, say so on the face of the certificate. A reflection scale is relative to your white tile, identified by its serial. An exposure scale from an uncalibrated wedge is relative to the wedge’s manufacturing specification rather than to a measurement. A commercial benchmark exists — the published figures for a bench densitometer are repeatability of ±0.01 D, linearity of ±0.02 D and zero stability of ±0.02 D per eight hours — and it is worth reading your own numbers against it, as a comparison and never as a claim to have met it.

The mains boundary

This is the page where a reader is most tempted to cross it, so the course’s line is restated in full and it does not move.

Everything you build stays at extra-low voltage. Anything at mains potential is a bought, certified, sealed appliance, plugged in, used as its maker directs, and never opened. HSE put extra-low voltage at 50 V ac and below; 230 V ac is in the band that kills, and the everyday phrase “low voltage” belongs to the second band rather than the first.

⚠What the course looked for, what it did not find, and the three routes that remain

An earlier version of this stage’s design assumed a certified enclosed switching module — a sealed appliance with a moulded plug and a socket, taking a low-voltage trigger — as the permitted way to let an instrument you built switch a mains lamp.

Part XVII went looking for one on 5 September 2026, with five criteria written down before anything was looked at: a sealed finished appliance with no conductor to terminate; a genuine certification mark against a named standard; an isolation figure stated by the manufacturer; a current rating covering an enlarger lamp with margin; and a trigger that holds the output on while asserted, so that it carries an interval computed somewhere else. Nothing on the market met them. The devices that take a low-voltage trigger are not sealed appliances, and the sealed appliances — every commercial darkroom timer surveyed — have foot switches that start the host’s own programmed exposure rather than inputs that carry an outside one.

So there are three routes and there is no fourth.

1. Convert the light source to a low-voltage LED head, built in Part XVI. Your own timer switches it directly and nothing is at mains potential. The mains problem is abolished rather than solved.
2. Leave the mains enlarger on its own switch and count the exposure by ear on a metronome. It costs resolution and nothing else.
3. Buy a certified enlarger timer with its own switched socket — £112.20 to £429.00 on 5 September 2026 — which owns the mains while your own instrument keeps the low-voltage heads.

No relay board, no smart plug, no home-built appliance, and no procedure for any of them anywhere in this course. A capstone build that cannot be completed inside those three is not permitted, and the correct response is to change the build.

The survey’s own limit is stated with its result, because a finding that hides its method is not one: a survey by direct supplier reading cannot prove a universal negative, and a listing for a plug-and-socket appliance with a documented hold-while-asserted trigger, a named standard, a stated isolation and a price materially below the cheapest certified timer would reopen the question rather than embarrass it.

When the goal is not met

This is a result, and it is a better capstone outcome than a goal quietly revised.

Record the shortfall as a number. “The goal was 0.10 in density between opposite corners; the measurement is 0.17.” Not “close”, not “much improved” — the number, with the uncertainty of the measurement beside it, because a shortfall of 0.07 measured to ±0.04 is a different situation from one measured to ±0.005.

Diagnose it before deciding anything. Name the single most likely cause and the one test that would confirm it. A corner that is dark on one side only is not the same fault as one dark on all four; a repeatability that fails at short exposures and passes at long ones is a latency, not a timing error.

Then choose, and the choice is between two legitimate answers. Iterate, inside the budget you set at planning time — one attempt, a stated number of evenings — or carry the limitation into the project and account for it. Carrying it is not surrender: it means the negatives are exposed knowing the corner is 0.17 down rather than 0.10, the printing maps carry an edge burn that compensates, and the chemistry report says what the instrument’s limit did to the pictures. That is a complete piece of engineering.

What is not available is revising the goal. A goal moved to meet the result destroys the only property that made requirement 1 meaningful, which is that the answer could have been no. If you find yourself editing the sentence you wrote in week one, stop and write a second sentence instead: the goal, the result, and what you decided.

Handing the instrument to Stage 3

Three things go forward, and they are what Stage 3 will read.

The operating notes. How this instrument is set up, in the order it is done, including the things you will have forgotten by week six: which way round the back seats, how long the source is left to warm up, where the shim goes.

The exposure factors or corrections it introduces. The effective f-number, any bellows or extension factor, any filter factor that belongs to the instrument rather than to the subject, and the corner falloff you measured rather than the one you calculated. These are numbers Stage 3’s exposure arithmetic uses directly.

The line that goes in the exposure log every time it is used. Instrument, configuration, focal distance, hole, and the certificate date under which its numbers are being quoted. A negative made with an instrument whose certificate has since been superseded is still a good negative — but only if the log says which certificate was current when it was made.

Troubleshooting

What you see	Likely cause	The test that separates it
The control sheet is grey too	The fault is downstream of the instrument: the loading routine, the holder, the storage box, or fogged paper	Process a sheet straight from the packet without loading it anywhere. If that is grey, the paper or the safelight is the problem, not the build
Every commissioning sheet is grey in the same place	Not a leak — a leak moves with the exposure length. A fixed grey patch is a reflection, a flare path or a fault in the holder	Repeat one sheet at four times the exposure. A leak grows with time; a reflection does not
Uniformity is symmetric but poor	The source, not the alignment. Sources fall off symmetrically; misalignment does not	Move the source’s distance and remap. A source problem scales with distance in a predictable way
Uniformity is worse on one side	Alignment, or mechanical vignetting from something in the path	Rotate the instrument 180° in its mount and remap. If the dark side follows the instrument it is the instrument; if it stays put it is the room
Repeatability is fine at long exposures and poor at short ones	A latency — a fixed delay at the start or end of the exposure, not a proportional error	Plot the measured exposure against the commanded one. A latency shows as an intercept, a scale error as a slope
The first negative is a stop out, consistently	The focal distance or the hole diameter is not what you entered	Remeasure both. An 8 per cent error in the diameter is a quarter of a stop; an 8 per cent error in the focal distance is about the same, and the two are told apart by the corner falloff, which depends on the focal distance and not on the hole
An LED head drifts over the first ten minutes	Thermal, and it is normal rather than a fault	Measure the warm-up curve, put the warm-up rule on the certificate, and obey it. Nothing needs repairing

Questions

1. Your performance goal reads: “The new back will improve corner illumination.” Rewrite it so that a measurement could refuse it, and name the measurement.
2. Your pinhole is 0.26 mm and the optimum for your focal distance is 0.33 mm. Compute the summed blur at each and say, in one sentence, whether the difference is worth remaking the hole for.
3. A uniformity map shows the top-left corner 0.22 in density below the centre and the other three corners within 0.05. Which of alignment, source non-uniformity, lens falloff and mechanical vignetting does that pattern rule out, and why?
4. You measure the corner of a negative at 2.6 stops below the centre. The cosine-fourth prediction for your geometry is 2.05 stops. What may you conclude, and what may you not?
5. Your route is an LED enlarger head and you want your own timer to control it. Trace the decision through the mains boundary and say which of the three permitted routes you are on.
6. Write the “what it may and may not be used to claim” line for an instrument whose reflection scale is anchored to an uncertified white tile.

Further experiments

Measure the falloff excess properly, since nobody has published it. Make three plates of the same diameter in shim of three different thicknesses, expose a uniformly lit sheet through each at the same focal distance, and read the corner and the centre. Plot the excess over cosine-fourth against thickness. That is an original measurement of a quantity this course explicitly could not source, and it costs three sheets.

Cross-check two instruments against one artefact. If another reader has built a densitometer, exchange step wedges and read each other’s. The disagreement is the sum of two uncertainties, and it is the only external check either of you can get without buying a certificate.

Take the crossing seriously. Make five holes spanning 0.6 to 1.6 times the optimum for your focal distance, expose one scene through each at exposures scaled by the square of the f-number so the light is matched, and print them at the magnification you will actually use. Find where you can first see the difference. That is your own resolution threshold, in the only units that matter, and it will almost certainly be wider than you expect.

Rebuild one arm of the sensitometer or densitometer and re-certify it. The strongest version of requirement 1 available to a reader with no space to cut anything: the old certificate and the new one, on the same arms, with the term that shrank identified. An uncertainty reduced from 0.047 to 0.029 log H by fitting a calibrated wedge is a modification with a measured result and no sawdust at all.

Check your understanding

Question 1. Your hole measures 0.30 mm where the optimum for your 80 mm focal distance is 0.327 mm. The summed blur is 0.658 mm against 0.655 mm at the optimum. What is the right conclusion?

• Remake the hole: an 8 per cent error in the most important dimension of the instrument should not be tolerated
• The summed blur is flat near its minimum, so being 8 per cent off costs three thousandths of a millimetre and the effort belongs elsewhere — but record both numbers, because the calculation is evidence that the hole was checked rather than assumed
• The calculation is wrong, because the blur at a non-optimum diameter must be substantially worse
• Change the design wavelength to 450 nm so that 0.30 mm becomes the optimum

Show the answer and why

Answer: The summed blur is flat near its minimum, so being 8 per cent off costs three thousandths of a millimetre and the effort belongs elsewhere — but record both numbers, because the calculation is evidence that the hole was checked rather than assumed

The optimum is a minimum of a sum of two terms, one rising with diameter and one falling, and every such minimum is flat in its neighbourhood — which is exactly why pinhole photographers get away with holes made by hand. The useful output of the calculation is not a instruction to remake anything; it is the knowledge that you are on the diffracted side of the crossing by a margin that does not matter, recorded with the measurement that established it. The last option is the interesting wrong answer: you may indeed design at 450 nm, but choosing the wavelength to make your existing hole come out optimal is fitting the criterion to the result, which is the same error as revising a performance goal after the measurement.

Question 2. Your capstone instrument is an LED enlarger head, and you want the timer you built in Part XVII to control the enlarger you already own. Which route does the mains boundary leave open?

• Fit a relay module with an optocoupler between the timer and the enlarger, since the optocoupler provides isolation
• Use a smart plug, which is a sealed certified appliance with a moulded plug
• Convert the enlarger to the low-voltage LED head, at which point the timer switches it directly and nothing is at mains potential
• Buy a certified enclosed switching module with a low-voltage trigger input

Show the answer and why

Answer: Convert the enlarger to the low-voltage LED head, at which point the timer switches it directly and nothing is at mains potential

The fourth option is the one an earlier draft of this specification assumed, and Part XVII's market survey found no product meeting the five criteria it set in advance — so it is not a route. A relay board is not a sealed appliance and its optocoupler isolates two circuits rather than protecting a hand at the screw terminals. A smart plug is sealed but has no dry contact that holds the output on while asserted, so it cannot carry your timer's interval. Converting the head abolishes the problem rather than solving it, which is why it is the course's first recommendation; the other two permitted routes are counting by ear and buying a certified timer that owns the mains itself.

Question 3. You set a goal of 0.10 in density between opposite corners. The finished measurement is 0.17, with an uncertainty of ±0.02. What does this specification ask you to do?

• Revise the goal to 0.20, since 0.17 is a substantial improvement on the starting 0.31
• Record the shortfall as a number with its uncertainty, diagnose the most likely cause and name the test that would confirm it, then choose between one bounded iteration and carrying the limitation into the project with the printing maps compensating for it
• Repeat the measurement until one of the readings lands under 0.10
• Report the build as failed and choose a different route from the menu

Show the answer and why

Answer: Record the shortfall as a number with its uncertainty, diagnose the most likely cause and name the test that would confirm it, then choose between one bounded iteration and carrying the limitation into the project with the printing maps compensating for it

A missed goal is a result, and it is worth more in the documentation than a met one that could not have failed. The uncertainty matters here: 0.17 ± 0.02 is genuinely short of 0.10 rather than arguably at it, so the shortfall is real and the diagnosis is worth doing. Both of the legitimate endings are complete pieces of engineering — a bounded iteration, or an accounted-for limitation that the negatives and the printing maps are made in the knowledge of. Revising the goal destroys the only property that made requirement 1 meaningful, and repeating a measurement until it agrees with you is not measurement.

Question 4. Why does the commissioning sequence put light-tightness before uniformity, and uniformity before repeatability?

• Because it matches the order of the Part VI commissioning session
• Because a leak adds density to every later measurement, and an unknown uniformity makes a corner reading uninterpretable, so a failure at either stage corrupts everything downstream of it — and there is no value in measuring the repeatability of an instrument that has already failed
• Because light-tightness is the cheapest test in sheets of paper
• Because repeatability requires the instrument to be warm, and the earlier tests warm it up

Show the answer and why

Answer: Because a leak adds density to every later measurement, and an unknown uniformity makes a corner reading uninterpretable, so a failure at either stage corrupts everything downstream of it — and there is no value in measuring the repeatability of an instrument that has already failed

The order is a dependency chain rather than a convention. A leak is additive and affects every sheet, so a uniformity map made in a leaking camera measures the leak as well as the field. A corner reading taken without a known uniformity cannot be attributed to falloff, alignment or the source. And a repeatability figure for an instrument that fails the first three tests describes how consistently it is wrong, which is not information anybody needs. The same logic is why the first negative against a calculated exposure comes last: it tests the optics and the arithmetic together, so it is only diagnostic once everything it depends on has passed.

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