Making and Measuring Pinholes

Purpose

The two lessons before this one produced a number: for the focal distance you have chosen, the best hole lies somewhere between about 1.4√(λf) and 1.9√(λf). This session turns that number into metal, and then does the harder half — finds out what you actually made.

Making a pinhole is easy and making a known pinhole is not. A needle pushed through foil leaves an opening whose diameter you do not know to better than a factor you would be embarrassed to write down, surrounded by a burr that both narrows the useful angle and scatters light. So the session has two halves of equal weight. In the first you pierce a graded set of four holes and work each one until it is round and the metal around it is thin. In the second you measure every one of them three independent ways, disagree with yourself by a few per cent, and write the disagreement down. The output is a pinhole register: a table you will use for the rest of this part and the whole of Part VII.

Learning objectives

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

1. Choose a plate material for a stated hole diameter, using the t ≤ d/5 rule from the geometry lesson rather than by habit.
2. Pierce and de-burr a hole to a target diameter within about ten per cent, by a controlled cycle rather than by luck.
3. Measure a small hole by scanning, by a calibrated eyepiece and by laser diffraction, and state the uncertainty of each method with the arithmetic that produced it.
4. Use the first dark ring of an Airy pattern as a measuring instrument, and say why that is a direct test of the previous lesson.
5. Recognise, under magnification, a burred, torn or elliptical hole, and predict what each will do to a negative.
6. Compute and record the effective f-number of every hole at every focal distance you plan to use.
7. Handle a Class 2 laser pointer under the controls a public-health authority actually recommends.

Prerequisites

• Diffraction and the optimum pinhole, which supplies the target diameter and the 1.22 λ/d relation the laser method depends on.
• Pinhole geometry and field of view, for N = f/d and for the tunnel-effect rule that sets the plate thickness.
• Measurement and uncertainty, which owns everything this page does with uncertainty. None of it is re-derived here.
• Laboratory safety and protective equipment, for the standing habits, though the hazards here are mechanical and optical rather than chemical.

Safety classification

Level A. The criteria of the classification rubric that decided it:

• Substances and quantities. None. Nothing is dissolved, mixed, heated or poured. The only materials present are metal sheet, abrasive paper, and a small quantity of matt black paint or ink applied to the finished plates.
• Energy. No heating, no flame. One battery-powered Class 2 laser pointer, which is a visible source in the 400–700 nm band; HSE’s guidance on the Artificial Optical Radiation Regulations places Class 1M, 2 and 2M lasers — naming low-power laser pointers as the example — among the sources that can harm only if used inappropriately, and begins its list of hazardous sources at Class 3B.
• Electrical. A purchased, battery-powered pointer and, optionally, a purchased USB microscope or flatbed scanner. Nothing is built, wired or modified.
• Waste. Metal offcuts and used abrasive paper. Nothing silver-bearing, nothing needing neutralisation.

What is not a hazard here, and why

There is no photographic chemistry on this bench at all. No developer, no fixer, no silver. That is unusual for a Level A page in this course, and it is worth saying explicitly rather than leaving the reader to infer it from an empty section: the reason the Chemicals section below has no table is that there is nothing to put in it, not that the table has been omitted.

Metal dust is not respirable dust here. Sanding a piece of shim with wet-and-dry paper produces a few milligrams of coarse swarf that stays on the paper and on the bench. It is not the fine airborne dust that makes wood and MDF cutting a respiratory question in the build session (build-the-modular-pinhole-camera). Wipe it up with a damp cloth rather than blowing it, which is a habit worth having for the eyes rather than the lungs.

Chemical brass blackening is deliberately not part of this session. Commercial brass-blackening and gun-blue solutions are commonly based on selenium compounds. The aggregated ECHA notifications on PubChem classify selenous acid as H301, toxic if swallowed in 100 per cent of reports, H331, toxic if inhaled in 99.1 per cent, and H410, very toxic to aquatic life with long lasting effects in 99.6 per cent. Acute toxicity of that order is outside what Level A admits, and HSE’s first control measure is to use a safer substance where one will do the job. Matt black paint does the job. That is the whole argument, and it is a worked example of how the classification in this course is arrived at.

What is left is what the Hazards section names: three sharp things, one bright thing, and a paint tin.

Hazards

Puncture wounds from the needle. A sewing needle driven at a sheet of metal that then gives way is the classic workshop puncture. The control is geometry: the plate lies flat on a hardwood or cutting-mat surface, the needle is held near its point in a pin vice or a cork, and no part of your other hand is ever on the far side of the plate. HSE’s general knife principles transfer directly: work on a stable surface, keep the tool sharp so it needs less force, put it away in a block or a cork when you stop, and never try to catch it if it falls.

Cuts from sheared metal edges. A drinks can cut open with scissors leaves an edge that behaves like a blade. Cut the blank oversize, file or fold every edge before handling it further, and collect offcuts in a tin rather than letting them lie on the bench.

The Class 2 laser pointer. UKHSA describe a Class 2 product as visible radiation between 400 and 700 nm that is safe for short exposures because of the natural blink and aversion response, but hazardous for deliberate staring into the beam, and warn that dazzle and afterimages can follow even a brief exposure in a dim room. They also publish the finding that matters most here: consumer pointers marked Class 2, or marked as under 1 mW, are commonly measured as Class 3B or Class 4 — five to five hundred times, or more than five hundred times, the marked output — and that eye injuries, especially to children, have occurred from incorrectly labelled pointers. There is no test a non-specialist can perform to find out which sort you have bought.

Treat every pointer, therefore, as though it might be worse than its label:

• Never look into the beam, and never point it at anyone. UKHSA’s advice for consumer lasers up to Class 3R is that the beam should never be pointed at people at all.
• Keep the whole beam path below eye level for everyone standing or sitting in the room, and terminate it on a matt wall or a sheet of matt card.
• Remove every reflective surface from the path — glass, a phone screen, a steel rule, a shiny pinhole plate you have not yet blackened. The pinhole plate itself is the trap: you are aiming a laser at a piece of polished brass.
• Work alone in the room, or with everyone briefed and behind the pointer.
• Do not use a green pointer if a red one will do. Green pointers of the common diode-pumped design can emit unfiltered infrared, which you cannot see and cannot blink at.

Paint and ink. Water-based matt black acrylic applied with a brush is the course’s default, because it introduces no solvent and no aerosol. If you use an aerosol instead, follow its own label and safety data sheet, spray outdoors or at a wide-open window, away from any flame, and let the plates dry fully before they go anywhere near photographic material.

Required PPE

The protective equipment on this page is mechanical and optical, not chemical.

• Safety glasses to a recognised impact standard, worn whenever piercing or sanding. The risk is a fragment of metal or a snapped needle point, not a splash.
• A hard flat working surface — a cutting mat over a bench, or a hardwood offcut — which is a control rather than equipment but does more for your hands than anything you can wear.
• Nothing on the eyes for the laser step, and nothing that could reflect the beam. There is no eyewear specified for a Class 2 pointer; the control is the beam path and the blink reflex, not a filter. Remove a watch, and take off reflective rings, before you handle the pointer.
• Gloves are not worn while piercing, because a glove that catches on a needle moves your hand where you did not intend. Wear a nitrile glove for the painting step if you would rather not have black fingers.

Ventilation

Ventilation is not among the controls for the piercing, sanding and measuring steps, because none of them releases a vapour, a gas or an airborne dust: the swarf is coarse and stays where it falls. The one step that does raise the question is blackening. Brush-applied water-based acrylic in the quantity used here — enough to cover two square centimetres, four times over — is used at an open window as a matter of habit rather than of necessity. An aerosol is a different proposition, and if you choose one, the ventilation it needs is what its own label and safety data sheet specify, which in practice means outdoors or at a wide-open window with the room door shut behind you.

Materials

Item	Quantity	Notes
Brass shim or shim steel	one small sheet	Sold by stated thickness, which is the point of buying it: you know t before you start. Choose the thinnest stocked grade.
Aluminium from a drinks can	one can	The free option. The wall is thin and soft and pierces beautifully; the thickness is not specified by anyone, so you must measure it.
Copper foil	optional	Softer than brass, tears more readily, blackens well. A reasonable third comparison.
Bought laser-drilled pinhole	optional, one	The reference standard for the measuring half of the session. Buy one only if the budget allows; it is not required.
Stiff card or thin aluminium for carriers	enough for five plates	Every hole is mounted in an identical carrier so that swapping holes changes only the hole.
Wet-and-dry abrasive paper, about 600 and 1200 grit	one sheet of each	The 600 takes the burr down, the 1200 finishes.
Matt black acrylic paint, or a black permanent marker	a few millilitres	For both faces of each finished plate.
Sewing needles, assorted sizes	a packet	A range of shank diameters is what gives you a graded set.
Adhesive tape, black	a small roll	For mounting and for masking.

Chemicals

This session uses no chemicals, and no chemical table appears here because there is nothing to put in one. Inventing a row so the section looks complete is precisely what this course forbids.

What is present, and stays present, is worth inventorying instead. Brass is an alloy of copper and zinc; shim steel is steel; drinks-can wall is aluminium with a thin internal polymer lacquer and a printed external one. All three are handled as solid metal at room temperature, none is dissolved, heated or abraded to a respirable powder, and none leaves the bench in any form but offcuts. The only substance that changes state at all is the water-based acrylic paint, which dries by evaporation of its water and coalescence of its binder; treat it as the household product it is and read its own label. There is no chemical waste stream from this page.

Equipment

A pin vice or a cork to hold needles; a small engineer’s square or steel rule; scissors or tin snips; a fine file; a hardwood block or cutting mat; a bright desk lamp.

For measuring, all three of the following if you can, and at least two:

• A flatbed scanner capable of a stated optical resolution of 2400 dpi or better. The interpolated figure on the box is irrelevant; interpolation computes intermediate values from samples already taken and cannot recover detail the optics did not resolve.
• A reticle loupe or a USB microscope with a calibration slide. A loupe with a 0.1 mm graticule is the classic tool; a USB microscope is cheaper and needs a stage micrometer or a printed calibration target to be worth anything at all, because its magnification is not a known quantity.
• A Class 2 laser pointer of stated wavelength, a tape measure that reaches 3 m, and a matt light-coloured wall.

A digital calliper or micrometer is useful for measuring plate thickness, which matters as much as diameter, but it cannot measure a hole this small.

Estimated cost

Cost band £. A drinks can is free, a packet of needles and a sheet of wet-and-dry are pocket money, and the only items with real prices are the optional ones: a reticle loupe or USB microscope, a laser pointer, and a bought laser-drilled pinhole. Dated prices live in the laboratory planner rather than in this page, so that they can be corrected without rewriting the text.

Estimated consumables cost

Five plates from a drinks can, a packet of needles and two sheets of abrasive. The band above says this is pocket money and the table says why: the only rows with real prices are the optional measuring instruments, and those are equipment.

Consumed	This session	Sourced price	Cost this session
Brass or steel shim, thinnest stocked grade	one small sheet, several plates	None. A named price gap: pinhole-making stock — shim, wet-and-dry abrasive paper, a pin vice and a bought laser-drilled pinhole	—
Aluminium from a drinks can	one can — the free option	Household	—
Wet-and-dry abrasive paper, 600 and 1200 grit	one sheet of each	None. A named price gap: pinhole-making stock — shim, wet-and-dry abrasive paper, a pin vice and a bought laser-drilled pinhole	—
Sewing needles, assorted sizes	a packet; a needle that has been through metal is no longer a fine point	None. craft-knife carries a cost band and no dated figure	—
Matt black acrylic paint or a black marker	a few millilitres, both faces of five plates	None. matt-black-paint carries a cost band and no dated figure	—
Stiff card or thin aluminium for carriers	enough for five identical carriers	None. card-and-paper-stock carries a cost band and no dated figure	—
Black adhesive tape	a small roll	None. tape-and-adhesives carries a cost band and no dated figure	—

Not one row in that table has a sourced price, so this session has no consumables figure at all — only a list of what it consumes. 6 of the 7 rows carry no dated price at all. A priced entry is a dated range to plan against, never a quotation.

The planner names the reason directly: pinhole-making stock is one of the gaps it names. A bought laser-drilled pinhole, a reticle loupe, a USB microscope and a Class 2 laser pointer are all optional instruments rather than consumables and belong to the band above; the same gap covers the bought pinhole.

Waste streams

Three, all solid. Metal offcuts and swarf: brass, steel and aluminium, all recyclable as scrap metal but too small and too sharp to put loose in a household recycling stream. Used abrasive paper, which carries the swarf with it. A brush and a rag with a little dried acrylic on them. No liquid leaves this bench.

Preparation

1. Decide your target diameters before you cut anything. From the previous lesson, work the optimum for each focal distance you intend to build, at 450 nm if you will expose paper. Write the range down. The standard graded set of roughly 0.2, 0.3, 0.4 and 0.5 mm brackets almost any focal distance between 25 and 100 mm, which is why the course uses it.
2. Measure the plate thickness with a micrometer or calliper, or by stacking ten pieces and dividing. Check it against t ≤ d/5 for your smallest intended hole. If the material is too thick, plan on dishing it (step 4 of the procedure) rather than looking for thinner metal.
3. Cut five identical carriers — four holes plus a spare — from card or thin aluminium, each with a window about 6 mm across, and mark a registration corner on every one so that they go into the camera the same way round every time.
4. Cut five plate blanks about 20 × 20 mm. Deburr every edge with the file before you go further.
5. Clear and brief the room for the laser step, even though it comes later. It is easier to move a mirror now than with a pointer in your hand.

Procedure

Station 1 — Pierce a hole (about 15 minutes per hole)

The method is dimple, pierce, sand, re-pierce, repeated. It works because you are never trying to make the final hole; you are always opening a slightly-too-small one by a controlled amount.

The four-step cycle, in section through the plate

1. 1Dimple — press, do not break through: it thins the metal and stops the point wandering
2. 2Pierce — the metal is displaced, not removed; the burr is the displaced metal
3. 3Sand both faces — removes the burr and thins the plate locally — the tunnel-effect fix
4. 4Re-pierce, a little further — open the hole in small increments; then go back to step 3

One cycle. Four or five cycles take a hole from nothing to a target diameter without ever overshooting, which matters because there is no way to make a hole smaller again.

1. Lay the blank on the hardwood block. Dimple: press the needle point into it and rotate the needle a few times without breaking through. You are making a cone-shaped depression, which thins the metal locally and stops the point wandering.
2. Pierce: press and twist until the point just breaks through. Do not push the needle in up to its shank — the hole would then be the shank diameter, and you would have skipped the whole controlled part of the method.
3. Sand: lay the plate face down on the 600-grit paper on a flat surface and rub in small circles until the burr has gone and the plate is flat. Turn it over and do the other face. Finish with 1200 grit.
4. Re-pierce with the same needle, entering a fraction further than last time, and go back to step 3.
5. Repeat until the hole is at your target. Measure between cycles, not only at the end: the loupe is the fastest check and takes ten seconds.
6. Make four holes this way, aiming for the graded set. Record which needle and how many cycles each took; the second plate will be much quicker than the first.

Station 2 — Blacken and mount (15 minutes)

Bare brass is a mirror at grazing incidence, and grazing incidence is exactly what the light around the edge of a wide-angle image circle is doing. Paint both faces matt black — a thin coat, dabbed rather than brushed, so that no paint creeps into the bore — and let it dry hard. Check the hole under the loupe afterwards: if paint has narrowed it, re-pierce gently and touch up.

A black permanent marker is an acceptable substitute for a plate you are going to remake anyway. Blackening by holding the plate in a candle flame appears in hobby writing; this course has found no evidence beyond that as to whether soot sheds inside a camera and settles on the negative, so it records the practice as uncorroborated and does not use it.

Mount each finished plate in a carrier with black tape, hole centred over the window, registration corner aligned. Label the carrier — not the plate — with a single letter.

Station 3 — Measure by scanning (20 minutes)

1. Set the scanner to its highest optical resolution, greyscale, all automatic corrections and sharpening off.
2. Lay the plates on the platen with a steel rule beside them, hole side down, and put a sheet of white paper over the top so the holes are backlit by the scanner’s own reflected light.
3. Scan. Open the image and count pixels across the hole in two directions at right angles, at the half-brightness point of the edge gradient.
4. Convert: at 2400 dpi one pixel is 25.4/2400 = 0.0106 mm; at 4800 dpi, 0.0053 mm.
5. Estimate the uncertainty from the edge. If you can place each edge to within one pixel, the diameter is uncertain by two pixels: ±0.021 mm at 2400 dpi, which on a 0.25 mm hole is ±8.5 per cent; ±0.011 mm, or ±4.2 per cent, at 4800 dpi.
6. Check the rule in the same scan against a real rule. If the scan says the 100 mm marks are 99 mm apart, every diameter you just measured is out by one per cent as well.

Station 4 — Measure by eyepiece (15 minutes)

With a reticle loupe, lay the graticule against the hole and read it, estimating to a fifth of a division: on a 0.1 mm graticule that is ±0.02 mm, or ±8 per cent on a 0.25 mm hole. Read two diameters at right angles and record both — the difference between them is the ellipticity, and it is data, not noise.

With a USB microscope, photograph a calibration slide or a printed scale in the same focus first and again afterwards; the instrument’s magnification is not a specification, it is whatever the focus happens to be, and a measurement without a scale in the frame is worthless.

Comparing the hole against the shanks of known drills or needles laid beside it is a legitimate coarse check and no more: it tells you the hole is between two sizes.

Station 5 — Measure by laser diffraction (30 minutes)

This is the good one, because it measures the hole by the very physics the camera will use, and it gets more precise as the hole gets smaller — the opposite of the other two methods.

⚠Before the pointer is switched on

Beam path below eye level and terminated on a matt wall. Nothing reflective anywhere along it, including the unblackened face of a brass plate. Nobody in the room in front of the pointer. Never look into the beam or at the plate from the far side. If you must adjust the plate, switch the pointer off first.

The laser-diffraction bench

1. 1Class 2 pointer, clamped so it cannot roll — wavelength read off its own label; beam below eye level
2. 2Pinhole plate, upright, hole on the beam axis — blackened face towards the pointer
3. 3Distance L, measured with a tape — 2 to 3 m; must be much greater than d²/λ
4. 4First dark ring, diameter D, measured on the wall — the dark gap outside the central disc

d = 2.44 λ L / D. Everything on the right of that expression is a length you can measure with a rule, plus a wavelength printed on the pointer.

The first dark ring of the Airy pattern lies at sin θ₁ = 1.22 λ/d. At distance L the ring’s radius is L tan θ₁ ≈ L × 1.22 λ/d, so its diameter D is twice that, and rearranging:

d = 2.44 λ L / D

Hole diameter from the first dark ring

1. Clamp the pointer so it cannot roll, aimed at the wall, beam well below eye height.
2. Hold the plate in the beam about 100 mm in front of the pointer, hole on the axis. Nudge it until the pattern on the wall is a clean set of concentric rings.
3. Darken the room. Measure the distance L from plate to wall with a tape, and the diameter D of the first dark ring with a rule held flat against the wall. The dark ring is easier to judge than the bright disc, which is why it is the quantity used.
4. Compute d. Expected ring diameters, so that you know what you are looking for:

Hole	D at 2.0 m, 650 nm	D at 3.0 m, 650 nm	D at 3.0 m, 532 nm
0.20 mm	15.9 mm	23.8 mm	19.5 mm
0.25 mm	12.7 mm	19.0 mm	15.6 mm
0.30 mm	10.6 mm	15.9 mm	13.0 mm
0.40 mm	7.9 mm	11.9 mm	9.7 mm
0.50 mm	6.3 mm	9.5 mm	7.8 mm

5. Check that the far-field condition holds. The arithmetic above assumes L is much greater than d²/λ. At 650 nm that quantity is 0.06 m for a 0.20 mm hole and 0.39 m for a 0.50 mm one, so a 2 m throw is comfortable for the small holes and only five times the limit for the largest; use 3 m for the 0.4 and 0.5 mm plates.
6. Estimate the uncertainty. If you can read the ring diameter to ±1 mm on a 12.7 mm ring, that is ±8 per cent. The wavelength contributes about ±1.5 per cent if the pointer is honestly labelled “650 nm”. Combining in quadrature, about ±8 per cent, dominated entirely by reading the ring. Move the wall further away and that shrinks; the method has no fixed resolution limit, which is what makes it different from the other two.

Expected observations

• The first two or three cycles produce nothing that looks like a hole — a dimple, then a jagged slit. This is normal, and stopping here is the commonest way to end up with a torn aperture.
• The burr is on the far face, and it is much bigger than you expect: hold the plate up to a lamp and it looks like a volcano. It sands away in a few seconds.
• A finished plate is visibly thinner around the hole than at its edges, and dished if you hold it to the light. That is the tunnel-effect fix, and it is the point.
• The scan shows a hole with a soft edge two or three pixels wide, not a hard one. That gradient is the reason you cannot measure to one pixel.
• The laser pattern is startlingly large and clean from a good hole. A poor hole gives a pattern that is not concentric: rings that are elongated, or a bright fan across the middle.
• Your three measurements will not agree. Five to ten per cent spread is a normal, honest result and is what the register is designed to record.

What is happening chemically

Almost nothing, and the interesting part of this session is what is happening mechanically and optically instead. Saying so plainly is more useful than manufacturing a reaction.

At the needle, the metal is not cut and not removed; it is pushed. Brass, aluminium and copper all deform plastically under a point long before they fracture, so the first thing a needle does is stretch and thin the sheet into a cone. The hole appears when that thinned cone finally tears, and the material that used to fill the hole is still there, folded outwards as the burr. That is why sanding is not tidying-up: it removes a piece of the plate that is otherwise part of the aperture, and it is also why a slow, many-cycle approach gives a rounder hole than one hard push. Each cycle tears only a little new metal, and a small tear follows the thinned cone; a large one follows whatever grain happens to be weakest.

At the wall, the physics is the previous lesson’s, used backwards. The pattern you are measuring exists because the wavelets from every part of the hole arrive at the wall with different phases, and the first dark ring is where the phases cancel completely. That the ring’s size gives back the hole’s diameter, to within a few per cent of what a scanner says, is not a coincidence to be noted in passing — it is an experimental confirmation of the 1.22 λ/d relation that the whole optimum-hole argument rests on. If the two methods agree, you have verified the theory on your own bench. If they do not, one of them is wrong and the register is where you say which.

The only genuine chemistry within reach is the tarnish on a bare brass plate — the copper in the alloy oxidising slowly in air — which is a reason to blacken the plate with paint rather than a reason to do anything about it.

Data to record

The pinhole register is the deliverable. One row per plate, and it is used for the rest of the part.

The pinhole register: one row per plate

1. 1Identity — plate letter (on the carrier), material, measured thickness t
2. 2Three measurements — each with its own uncertainty and the raw readings behind it
3. 3Adopted diameter — the one number the rest of the course uses, and why you chose it
4. 4Derived — t/d, and N = f/d at every focal distance you will build

Keep the raw readings, not just the answers: L and D for the laser, pixels and dpi for the scan. A register you cannot recompute is a register you cannot correct.

Also record, for the session as a whole: the needle used for each plate, the number of cycles, the scanner make and the optical resolution you set, the pointer’s labelled wavelength, and the room temperature if you are being thorough. And a sketch or a photograph of each hole under magnification.

Analysis

Reconcile the three methods. For each plate, write the three diameters with their uncertainties and ask whether the intervals overlap. A 0.25 mm hole measured as 0.243 ± 0.021 by scan, 0.26 ± 0.02 by loupe and 0.251 ± 0.020 by laser is three measurements that agree, and the right adopted value is somewhere near their middle. If one sits three of its own uncertainties away from the other two, something is wrong with that method on that plate, and the usual culprits are a mis-set scanner resolution, an uncalibrated microscope, or a laser ring you measured while the plate was tilted.

Decide which method you trust for which size, and write the reason. The scan’s uncertainty is fixed in millimetres, so it gets relatively worse as the hole gets smaller — ±0.021 mm is 8.5 per cent of a 0.25 mm hole but only 4 per cent of a 0.5 mm one. The laser’s uncertainty is fixed as a percentage of the ring diameter, and the ring gets bigger as the hole gets smaller, so laser diffraction gets better exactly where the scan gets worse. That is the finding of this session, and it is worth more than any single diameter in the table.

Compute N for every hole at every focal distance. N = f/d, and this is the table the exposure lesson will read:

d	at 25 mm	at 50 mm	at 75 mm	at 100 mm
0.20 mm	f/125	f/250	f/375	f/500
0.25 mm	f/100	f/200	f/300	f/400
0.30 mm	f/83	f/167	f/250	f/333
0.40 mm	f/62	f/125	f/188	f/250
0.50 mm	f/50	f/100	f/150	f/200

Propagate the uncertainty while you are there: an 8 per cent uncertainty in d is an 8 per cent uncertainty in N, which is 16 per cent in exposure — about a quarter of a stop. That is smaller than the reciprocity corrections coming in the next lesson, which is a useful thing to know before you spend another evening on the loupe.

Compare each hole with the optimum for the focal distances you will use, and mark in the register which plate is the intended working hole at each. Some plates will be nobody’s optimum, and they are still worth keeping: the diameter series in the commissioning experiment needs holes on both sides of the best one.

Four holes at about 40×, and the laser pattern each throws

1. 1Round and clean-edged — concentric rings; the hole the theory assumes
2. 2Burred — lopsided, washed-out rings; dark corners and veiling flare on the negative
3. 3Torn — a fan or cross, no rings; slow like a small hole and soft like a large one — scrap it
4. 4Elliptical — elliptical rings at right angles to the hole; detail has a direction to it

The upper row is what the loupe shows; the lower row is what the same plate throws on the wall from a laser pointer. Drawn to show the signatures, not traced from photographs.

🔬UNDER THE MICROSCOPE: four holes and what each does to the picture

At 40× the difference between a good hole and a bad one is obvious, and each fault has its own signature on the negative.

Round and clean-edged. A circle whose two perpendicular diameters agree within a few per cent, with a sharp dark rim and no bright fringe. Under the laser it gives concentric rings. This is the hole the whole of the previous lesson was about, and its point spread is the disc-plus-Airy-rings the theory predicts.

Burred. A ragged collar of displaced metal standing proud of one face. Optically it is two faults at once: it lengthens the effective bore, so the tunnel-effect cut-off arrives at a smaller angle and the corners go darker than cos⁴ predicts; and its irregular edge scatters light forward into the image as veiling flare, lifting the shadows and flattening the scale. Sanding removes it. There is no reason ever to keep one.

Torn. Not a circle but a star or a slot, made by pushing the needle hard in one go. The aperture now has a long perimeter and a small area, which is the worst combination available: it is slow like a small hole and soft like a large one, and its diffraction pattern has spikes running perpendicular to the tears. Under the laser it is unmistakable — a fan or a cross instead of rings. A torn plate is scrap; start again.

Elliptical. Two perpendicular diameters that differ by more than about ten per cent, usually from entering the needle at an angle. It behaves as two different apertures at once: the image is sharper across the narrow direction and softer across the wide one, so fine detail has a direction to it, most visible on foliage and brickwork. The laser pattern is an ellipse with its long axis at right angles to the hole’s long axis, which is a satisfying thing to see the first time. A mildly elliptical hole is usable if you record both diameters and use their mean; a badly elliptical one is scrap.

Troubleshooting

The hole is already too big after two cycles. You pushed rather than twisted, or used too large a needle to start. There is no way to make a hole smaller; start a new plate with a finer needle and more cycles.

The plate creases when sanded. It is too thin to sand unsupported. Back it with a piece of card or tape it to a flat offcut before rubbing.

The scan shows an oval and the loupe shows a circle. The plate was not flat on the platen, or the scanner’s two axes are not equally calibrated. Rescan with the rule in frame and check both axes against it.

The laser pattern is a bright fan rather than rings. The hole is torn, not round. Look at it under the loupe: you will find a slot or a star. This is the single most useful diagnostic in the session, because the laser sees the fault before your eye does.

The laser pattern is rings but not concentric, and shifts as you move the plate. The beam is clipping the edge of the plate window or hitting the hole at an angle. Re-centre and make the plate perpendicular to the beam.

The three measurements disagree by more than 20 per cent. Check the units first, then the scanner’s optical against interpolated setting, then whether the microscope was calibrated at the same focus it measured at. In this course’s experience the first suspect is the microscope.

Paint has closed the hole. Too thick a coat. Re-pierce gently with the original needle, sand the face lightly, and touch up with a much drier brush.

Clean-up

Sweep swarf into a folded piece of paper and tip it into the offcuts tin; wipe the bench with a damp cloth rather than blowing it. Count the needles back into the packet — a needle left on a bench is the hazard of this session that lasts longest. Wash the brush. Return the pointer to its case with the battery out or the cap on, and put it away where a child cannot reach it.

Storage

Store finished plates in their carriers, flat, in a small box or an envelope with the register letter on it, hole side not rubbing against anything. Brass and steel keep indefinitely; painted aluminium will chip if plates are allowed to slide over one another, so interleave them with card. Keep the register with the plates, not in a separate notebook, or the letters will eventually mean nothing.

Disposal considerations

Metal offcuts and swarf are recyclable as scrap, but loose sharp fragments do not belong in a kerbside recycling stream: collect them in a closed tin and take that to a household recycling centre. Used abrasive paper carries the swarf with it and goes the same way, or to general waste if your centre will not take it. Dried acrylic on a brush or a rag is a solid; a rag with wet solvent-based paint on it is not, and must not be left crumpled. Local regulations govern all of this, and they differ between authorities even within the United Kingdom; check yours.

Questions

1. Your scan says 0.243 mm and your laser says 0.251 mm for the same hole, and the uncertainties are ±0.021 and ±0.020. Are these the same measurement? What single number should go in the register, and what should you write in the “why” column?
2. Why does the laser method get better as the hole gets smaller, while the scan gets worse? Express both as a percentage of the diameter and show the arithmetic.
3. A plate is 0.10 mm thick and its hole is 0.25 mm. What is the tunnel cut-off angle, and is the plate acceptable for a 50 mm camera on 4 × 5 inch paper? What would you do about it?
4. You have measured a hole as 0.30 mm. Compute N at 25, 50, 75 and 100 mm, and say which of those focal distances this hole is closest to optimum for at 450 nm.
5. Why is it worth blackening the inside-facing surface of a pinhole plate as well as the outside?

Further experiments

Measure the same hole ten times by the same method, on ten different days. The spread you get is your Type A uncertainty for that method, measured rather than estimated, and it may well be larger than the ±8 per cent this page assumes.

Buy one laser-drilled pinhole and treat it as a standard. Measure it by all three methods. It will not have a certificate, so it is not a traceable standard — but if your three methods agree on it and disagree on your own plates, the fault is in your plates rather than your measuring.

Vary the throw distance in the laser method. Measure the same hole at 1, 2, 3 and 4 m and plot computed d against L. A horizontal line means the far-field condition holds everywhere; a drift at short L is the Fresnel regime showing itself, and finding the distance where it stops mattering is a neat piece of experimental physics.

Photograph the diffraction pattern. Put a sheet of photographic paper where the wall was, in the dark, and expose it to the pattern directly. Rayleigh measured his apertures under a microscope and tested them photographically; you can do both in one afternoon, and the print of an Airy pattern is a good thing to own.

Check your understanding

Question 1. A first dark ring 24 mm across is measured at 2.0 m from the plate with a pointer labelled 650 nm. What is the hole diameter?

• 0.132 mm
• 0.066 mm
• 0.264 mm
• 1.32 mm

Show the answer and why

Answer: 0.132 mm

Use d = 2.44 λ L / D throughout in metres and then convert: d = 2.44 × 650 × 10⁻⁹ × 2.0 / 0.024 = 1.322 × 10⁻⁴ m = 0.132 mm. Option 2 uses 1.22 rather than 2.44, which is the commonest slip — 1.22 λ/d is the angular radius, so it belongs with the ring radius, and the diameter needs the factor of two. Option 3 doubles it in the other direction. As a sanity check, 0.132 mm is a small hole, and small holes give big rings, so a 24 mm ring at only 2 m is exactly what you would expect.

Question 2. The laser pattern from one of your plates shows a bright fan across the middle instead of round rings. What will the loupe show, and what should you do?

• A perfectly round hole; the fan comes from the pointer and can be ignored
• A torn hole — a slot or a star rather than a circle. The plate is scrap; start again with a finer needle and more pierce-and-sand cycles
• A burred hole; sand it and re-measure
• An elliptical hole; record both diameters and use their mean

Show the answer and why

Answer: A torn hole — a slot or a star rather than a circle. The plate is scrap; start again with a finer needle and more pierce-and-sand cycles

A diffraction pattern is the aperture turned inside out: a long straight edge in the hole produces a bright streak at right angles to it, so a fan or a cross means the aperture has straight tears in it. An elliptical hole gives elliptical rings, not a fan, and a burr shows up as scatter and asymmetry rather than as a spike. A torn hole has a long perimeter and a small area, which makes it slow like a small hole and soft like a large one; nothing can be done to it, and the fix is method rather than repair — a finer needle, more cycles, and a proper dimple before the first pierce.

Question 3. Why does laser diffraction get more precise as the hole gets smaller, while a scan gets less precise?

• Because lasers are more accurate than scanners in general
• Because the scan's uncertainty is a fixed number of millimetres set by the pixel pitch, so it grows as a percentage when the hole shrinks; while the laser's uncertainty is a percentage of the ring diameter, and the ring grows as the hole shrinks
• Because diffraction does not occur at large holes
• Because the scanner interpolates and the laser does not

Show the answer and why

Answer: Because the scan's uncertainty is a fixed number of millimetres set by the pixel pitch, so it grows as a percentage when the hole shrinks; while the laser's uncertainty is a percentage of the ring diameter, and the ring grows as the hole shrinks

At 2400 dpi one pixel is 0.0106 mm and a two-pixel edge judgement is ±0.021 mm whatever you are measuring: 8.5 per cent of a 0.25 mm hole but 4.2 per cent of a 0.5 mm one. The laser turns the problem round, because the ring diameter is 2.44λL/d — inversely proportional to the hole — so a 0.20 mm hole throws a 24 mm ring at 3 m while a 0.50 mm hole throws only 9.5 mm, and reading either to ±1 mm is 4 per cent for the small hole and 11 per cent for the large one. The two methods are therefore complementary rather than rival, and the register should say which was adopted for which plate.

Question 4. A plate is 0.10 mm thick with a 0.25 mm hole, intended for a 50 mm camera on 4 × 5 inch paper. Assess it.

• Acceptable: t/d = 0.4, cut-off at 68°, well outside the 58° corner angle
• Marginal: the cut-off at 68° is outside the 58° corner, but the partial vignetting at 58° already costs about two stops on top of the cos-fourth loss. Sand a dish around the hole to bring t down
• Unusable: the corner is beyond cut-off and will record nothing
• Irrelevant: plate thickness affects diffraction, not illumination

Show the answer and why

Answer: Marginal: the cut-off at 68° is outside the 58° corner, but the partial vignetting at 58° already costs about two stops on top of the cos-fourth loss. Sand a dish around the hole to bring t down

The cut-off is arctan(d/t) = arctan(2.5) = 68.2°, and the corner of a 4 × 5 sheet at 50 mm is at 58.4°, so light does still reach the corner — but cut-off is not the criterion, partial vignetting is. At 58.4° with t/d = 0.4 the two circle openings overlap over only about 23 per cent of the bore, which is 2.1 stops on top of the 3.7 stops cos⁴ already costs, for a corner nearly six stops down. The geometry lesson's rule of t ≤ d/5 would want 0.05 mm here. Sanding a shallow dish around the hole reduces t locally while leaving the plate stiff, which is exactly what the pierce-and-sand cycle does anyway.

Question 5. Which statements about handling the Class 2 pointer in this session are correct?

• A pointer marked Class 2 may in fact be Class 3B or Class 4, and there is no test a non-specialist can do to find out
• The unblackened face of a brass pinhole plate is a reflective surface in the beam path and should be treated as one
• Class 2 means the beam is safe to look into briefly, so a quick check down the axis to align the plate is acceptable
• The beam should be kept below eye level and terminated on a matt surface

Show the answer and why

Answer: A pointer marked Class 2 may in fact be Class 3B or Class 4, and there is no test a non-specialist can do to find out, The unblackened face of a brass pinhole plate is a reflective surface in the beam path and should be treated as one, The beam should be kept below eye level and terminated on a matt surface

The first, second and fourth are the controls this page is built on. UKHSA publish the finding that consumer pointers marked Class 2 or under 1 mW are commonly measured as Class 3B or Class 4, five to five hundred times the marked output or more, and that there is no simple test for a non-specialist; that is precisely why the beam-path controls do not depend on the label being true. The third is the dangerous one. Class 2 is defined as relying on the blink and aversion response for short exposures, and UKHSA describe it as hazardous for deliberate staring; deliberately looking down the axis to align something is deliberate staring, and if the pointer is mislabelled the aversion response is not fast enough to protect you. Align by moving the plate in the visible spot on the wall, with the pointer off while your hands are near the axis.

Question 6. Your three measurements of one plate are 0.243 ± 0.021 mm (scan), 0.26 ± 0.02 mm (loupe) and 0.251 ± 0.020 mm (laser). What goes in the register?

• The smallest value, 0.243 mm, because a smaller hole is sharper
• The laser value alone, because diffraction is the most fundamental method
• An adopted value near 0.25 mm, with all three raw measurements, their uncertainties and a stated reason for the choice kept beside it
• The mean, 0.251 mm, quoted to three decimal places

Show the answer and why

Answer: An adopted value near 0.25 mm, with all three raw measurements, their uncertainties and a stated reason for the choice kept beside it

The three intervals overlap comfortably, so these are three measurements of the same quantity and no one of them is "the" answer. Adopt a round value in the middle — 0.25 mm — and record why, because that is the number every later exposure calculation will use and a future you will want to know how much to trust it. What matters more than the choice is keeping the raw readings: the pixel counts and the dpi, the ring diameter and the throw. A register you cannot recompute is a register you cannot correct. And note the last option's error of precision: quoting 0.251 to three decimals claims a resolution of one micrometre from methods whose uncertainty is twenty.

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