Build: The Densitometer Optical Head (Transmission and Reflection)

Purpose

To build the half of the densitometer that decides what its readings mean: a diffuse light path in contact with the film, an aperture that defines the patch being read, and a detector close enough and shrouded well enough that almost nothing reaches it except light that went through that patch. Then to add a second head, at 45° to the print’s normal, so that the instrument can measure a print — which nothing else in this course can do.

Nothing is soldered here. The electronics arrive already built: the module from Part XIV’s LED page drives the lamp and reads the photodiode well enough to commission the head, and the electronics and firmware page that follows in this part replaces its converter with one that can reach 3.0 D. That order is deliberate. A head whose stray-light floor you have not measured does not deserve a better converter, and you can measure the floor with the converter you already own, because the floor is a ratio.

You finish this session holding a head, a measured stray-light fraction, a measured ambient-leakage figure, and a spread over ten replaced readings of one wedge step. Those three numbers are the instrument’s first specification.

Learning objectives

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

• explain why the aperture plate must be thin, and compute the largest angle a bore of a given diameter and thickness will admit;
• choose an aperture from the step size of the wedge you own rather than from a preference;
• set an LED’s drive current from the optical power the detector needs, and say why the answer is milliamps rather than the hundreds of milliamps the sensitometer uses;
• build a light path in which the only opening is the one you intend, and prove it with a blank;
• measure a stray-light floor and convert it into the maximum density your instrument can report;
• distinguish a leak of room light from a leak inside the head, by a test that separates them;
• state why a 45° illumination and a normal collection are the whole of a reflection measurement, and why a glossy and a matt print are the pair that reveals a head that has got it wrong;
• say what your head does not conform to, in specific terms, and why the reading is still worth having.

Prerequisites

Photodiodes, ADCs and measuring light over three decades, in full. This page assumes the stray-light equation, the density-per-count arithmetic and the dark-current discussion, and re-derives none of them.

Density depends on how you look, for the two decisions this build implements without re-arguing: diffuse geometry with the diffuser in contact, and a 2 mm sampling aperture from the wedge’s own step size.

The sensitometer enclosure and exposure stage, for the light-tightness discipline, the tape-and-board construction method and the adhesive and paint guidance, all of which apply here unchanged and are not repeated.

The module from Part XIV, working, with its serial terminal to hand. And a 21-step wedge whose serial number you have written down, because from this page onwards it is part of the instrument.

Safety classification

Level A. The classification rubric places a procedure at Level A when the substances handled are at most irritant or harmful in home quantities, when nothing is heated above 50 °C, when there is no mains-voltage construction or modification and the equipment is purchased and certified, and when the waste can be collected ordinarily. All four hold. The work is measuring, cutting, drilling one hole, gluing and blackening; the electricity is a module built and tested on an earlier page, running from a certified USB supply at 5 V.

The criterion that had to be argued. Level B names high-brightness LED sources among its criteria, and Part XIV’s LED build was classified B partly for that reason. This page stays at A because the emitter is a different animal. The arithmetic in build stage 1 shows that the detector needs a few microwatts, so the LED runs at a few milliamps — an indicator, not a lamp — and it spends the whole session either off, or behind an opal diffuser, or inside a closed head. If you substitute a high-power emitter because you have one in the drawer, you have moved your own session to Level B and Part XIV’s controls apply: lowest usable current, emitter below eye level, never looked into.

What is not a hazard here, and why. This page handles no photographic chemistry at all. There is no developer, no fixer, no silver salt, no solution — so no splash risk, no glove-selection problem, no eye-irrigation requirement and no liquid waste stream, and saying so plainly matters because the reflex after twelve chemical parts is to import controls that do not apply. The only substances present are a few millilitres of water-based PVA and a little water-based matt black acrylic paint, both household products used as their labels direct.

Nor is there a shock hazard in the ordinary sense: nothing exceeds 5 V, and five volts across dry skin drives a current far below anything a person can feel, because skin resistance is measured in tens of kilohms. What five volts can still do is push a great deal of current into a short circuit, which is a heating question rather than a shock one, and is why the supply is a certified charger or power bank and never a bare cell.

The same materials in a different session would be assessed differently. Spray paint instead of brushed acrylic brings a vapour and an outdoor operation with it; a sawn plywood housing instead of cut board brings Part VI’s wood-dust controls. The level belongs to this procedure, not to the objects.

Hazards

Cuts, from the knife and from cut metal. The aperture plate is thin brass or aluminium, and a freshly cut or drilled edge in 0.5 mm sheet is sharp enough to open a finger. Deburr every edge with a file or a countersink bit before handling it again. For knife work, the discipline is the enclosure page’s: three light passes rather than one heavy one, a steel rule and never a plastic one, the stroke moving away from the hand holding the work. For a cut, NHS guidance is pressure to stop the bleeding, rinse clean, cover with a sterile dressing, and no attempt to remove anything embedded.

Eye injury from swarf. Drilling a 2 mm hole in metal throws a spiral of hot swarf, and it lands where you are looking. Spectacles on for every hole, and the swarf is picked up with tape rather than brushed with a hand.

Burns, if you solder after all. Nothing on this page needs a soldering iron, but a flying lead will tempt you. If you pick one up, Part XIV’s controls come with it — the tip runs at about 350 °C and a joint stays at solder temperature for seconds after the iron leaves. The NHS instruction for a burn is cool running water for 20 minutes, as soon as possible; remove clothing and jewellery near the area but nothing stuck to it; cover the cooled injury by laying cling film over it rather than wrapping.

Adhesive. PVA is the adhesive here and the control is ordinary care and washed hands. If you reach for cyanoacrylate instead, the enclosure page carries the hazard statements and the warning that it bonds skin; keep the work below the level of your face.

Outgassing, near sensitised material. FOMA instruct that unexposed film be stored away from harmful vapours and gases — a manufacturer stating that vapours can damage sensitised material. Whether a particular paint outgasses enough to fog film held against it is not documented anywhere this course has found, so what follows is a precaution rather than a finding: leave every painted surface in a warm airy place until it is hard and odourless, and let the first thing that sits on the aperture plate for an hour be a scrap rather than an archived strip.

The wedge itself. The one irreplaceable object on the bench is the calibrated wedge, and the hazard is to it rather than from it. Handle it by its ends, never by its steps, keep it in its sleeve between readings, and do not clean it with anything you have not read the label of.

Required PPE

Safety spectacles with side protection, for all knife work, all filing and every hole drilled. The drilled hole is the reason: 2 mm swarf leaves the work at eye height.

A steel rule and a cutting mat, which are protective equipment on this page rather than conveniences. A plastic rule lets a blade climb its edge and into the hand holding the work.

Nothing else is specified, and the reason is stated rather than assumed. Gloves are not among the controls: there is no chemical to keep off the skin, and a glove between your fingers and a small metal plate you are filing makes the handling worse by dulling the feedback that keeps fingers out of the way. A respirator is not among them either, because on the recommended route nothing is sprayed, sawn or sanded. Wash your hands before eating; a bench is a bench.

Ventilation

Ventilation is not among the controls for the construction itself, and the reason is that the recommended materials produce no vapour — PVA is a water-based emulsion, black card is card, and tape is tape. An open window is enough, and it is enough because there is nothing to extract.

If you paint. Water-based matt black acrylic is a household product used as its label directs, at a bench with a window open. If you use an aerosol of any kind — and matt black spray is genuinely blacker than brushed acrylic — that becomes an outdoor operation, out of the wind, with nobody downwind, and the part is left outside to cure for a day before anything photographic goes near it. The course’s preference is flocked black card, because it is blacker than either and produces nothing at all.

Parts

Two lists, because the reflection head is an attachment and a reader may build the transmission head first and come back.

The transmission head

Part	Quantity	What it does	Substitutes and notes
Moulded ABS project box, about 120 × 90 × 60 mm	1	The body: lamp chamber below, stage on top	A box of cut and taped black board works exactly as well and is easier to modify. The box is chosen for being black inside already and for having no seams that light finds
Opal acrylic sheet, 3 mm, cut about 40 × 40 mm	1	The diffuser, in contact under the aperture	Opal acrylic is sold for light panels and signage. The course has obtained no supplier’s transmission or diffusion figure for it and quotes none; the diffuser is specified below by what it must do and accepted by measurement. Opal glass is the traditional part and the one ISO 5-2 names for this job
Shim brass or aluminium, 0.4 to 0.6 mm, about 40 × 40 mm	1	The aperture plate	The thickness is not a preference — see stage 2. A tin lid or a feeler-gauge blade is the same material free. Not 2 mm plate, and not a washer of unknown bore
Green LED, 5 mm through-hole or a small surface-mount part on a board	1	The source	The course names no part. Check four figures on whatever you buy: dominant wavelength (515 to 545 nm), spectral half-width, forward voltage at your current, and viewing angle. Cree’s XP-E2 datasheet is the worked example of where those figures live, not a mandate
Second identical LED, and a third	2	Blue and, later, the UV variant	Optional. The blue is what a printing density is read with; buy it now and fit it later
OPT101 photodiode with integrated amplifier, 8-pin DIP	1	The detector	Or a BPW34 with an op-amp on the next page. The OPT101’s 2.29 × 2.29 mm active area is a third smaller than the BPW34’s 7.02 mm² and needs no layout; the BPW34 collects more and gives you the feedback resistor back
Second photodiode, any type	1	The monitor: watches the LED inside the lamp chamber	Optional and strongly recommended; see stage 6. A BPW34 is the obvious choice because it is cheap and its exact response does not matter for a ratio
Black flocked card, or matt black acrylic paint	one A5 piece, or 20 mL	Every interior surface above the diffuser	Flocked card is blacker than paint and produces no vapour. Matt black acrylic is the fallback. Gloss black is worse than white, because it makes a mirror
White card, matt	one A6 piece	Lines the lamp chamber below the diffuser	Matt only. A gloss wall images the LED onto the diffuser as a bright patch
Aluminium or plastic angle, 10 mm, two 90 mm lengths	2	Registration fences for film and wedge	Two strips of 3 mm board glued down work as well
Small brass hinge, or a strip of gaffer tape	1	The detector arm’s pivot	Tape is a legitimate hinge here and is easier to adjust. A stiff hinge is better than a loose one; a loose one is what the repeatability test will find
Brass or aluminium spacer, 3.0 mm	2	Sets the detector gap, and is the stop the arm closes onto	Two stacks of tape shims, measured with a rule, do the same thing. It must be the same on both sides or the arm tilts
Closed-cell foam strip, 3 mm	200 mm	Light seal around the shroud skirt	Draught-excluder tape. It must compress evenly, or it lifts one side of the arm
Black photographic or gaffer tape, 25 mm	1 roll	Sealing joints, blacking edges, making the hinge	The structural fastener of the board route
PVA adhesive	a few millilitres	Fences and linings	Priced in the planner
Opaque metal blank, about 20 × 20 mm	1	The stray-light test target	Any piece of the shim stock, painted matt black on the side that faces the diffuser. This is a test standard, so make it once and keep it labelled
Self-adhesive labels	a few	Serial number, orientation, aperture size, build date	Written before assembly
A 21-step transmission wedge	1	The ruler	Stouffer T2115 or equivalent. Its serial number is part of the instrument

The reflection attachment

Part	Quantity	What it does	Substitutes and notes
Second small box or board frame, about 80 × 80 × 50 mm	1	The reflection head body	It replaces the transmission head above the stage; the same detector and cable move across
Two LEDs matched to the transmission one	2	The two opposed 45° sources	Buy them from the same reel if you can. An annular ring of six to eight LEDs is the commercial arrangement and is the better one in principle; the two-source pair is specified here because its symmetry can be checked by switching one off
Port aperture plate, shim stock, 4 mm bore	1	Defines the sampled patch on the print	Larger than the transmission aperture because reflected light is scarce. The same thin-plate rule applies
White reference tile, ceramic or opal, about 40 × 40 mm	1	The top-of-scale anchor	The planner could price no certified tile and the course specifies none. An uncertified tile is usable — see stage 8 — and makes the reflection scale explicitly relative. Never handle it on its measured face; never store it in light
Black trap: a tube or box at least 5 × its opening diameter deep	1	The zero	A 20 mm length of 20 mm black tube with a matt black plug at 45° in the bottom. A piece of black card is not a black trap and stage 8 measures the difference
Two small prints on different surfaces, glossy and matt or pearl, at similar density	1 pair	The geometry check	Use prints you already have from Part XIII’s paper sensitometry. Only make new ones if you have no pair

🛠Three-dimensional printing, and why this page ships no files

Every dimension on this page can be printed in one piece, and a printed head would be more repeatable than a taped one. This course publishes no STL or STEP files, because it has printed and tested none, and publishing untested geometry under a licence that invites people to build from it would be inventing an object and then teaching it.

What is published instead is the whole of what a file would have to hit, in stage 2 and stage 3: an aperture bore of 2.0 mm through no more than 0.6 mm of material, a detector gap of 3.0 mm set by a hard stop, a diffuser seat that holds the opal in contact with the underside of the aperture plate, a shroud skirt that meets the stage all the way round, and an arm that closes to the same place every time. Model those and the head is the same head. Two printing notes that follow from the physics rather than from experience with any particular printer: print the light path in black filament, since a translucent one is a light pipe, and do not print the aperture plate, because a printed 2 mm bore through a printed wall is neither thin nor black nor round. That part is metal.

Tools

Tool	For	Notes
Craft knife, steel rule, cutting mat	Board, card, foam	Three light passes through 3 mm board
Drill, 2.0 mm and 4.0 mm bits, and a countersink or a file	The apertures and their deburring	Spectacles on. Back the shim with a scrap of hardwood so the bit does not tear the metal
Steel rule reading to 0.5 mm, and a vernier or digital caliper if you own one	Every dimension, and the gap	The caliper is the one tool that makes stage 3 easy; a rule and care will do it
Engineer’s square	Setting the fences and the 45° arms	A square that is not square puts a taper in the light path
Fine file and abrasive paper	Deburring the bore	A burr on the bore is a scattering edge inside the measurement
The Part XIV module, with its serial terminal	Every measurement on this page	Bring its read_monitor routine; you will use nothing else
A small torch	Finding leaks from the inside	Shine it inside the closed head in a dark room and look for the light getting out; the path works both ways
Multimeter	Setting the LED current	Series with the LED, once, then written on the label

Estimated cost

Cost band ££, and as on the sensitometer, almost all of it is the wedge. The head itself is a project box, a square of opal acrylic, a square of shim and two LEDs.

This page quotes prices only where the laboratory planner carries a dated one. It carries none for project boxes, opal acrylic, shim stock, LEDs, photodiodes, flocked card, tape or reference tiles; the planner’s own gap list names the electronics and the enclosure hardware as unpriced, and records separately that no United Kingdom price for a 21-step transmission wedge could be confirmed. What is durable and belongs on the page instead of a price is the specification: an aperture of 2.0 mm through 0.5 mm of metal, a 3.0 mm gap and a shroud that seals will still be right when every quotation here has expired.

The one line that can genuinely double the total is the certified white reference tile, and stage 8 tells you how to do without it and what you give up.

Estimated consumables cost

Almost nothing in this session is consumed. The head is capital — it is meant to be recalibrated rather than replaced, and every part in it survives a rebuild. What one run actually uses up is a little adhesive, a little paint and some tape.

Consumed	This session	Sourced price	Cost this session
PVA adhesive	about 5 mL	£11.99–£14.29 per 5 L, which prices a shelf rather than a session	—
Matt black acrylic paint, or a piece of flocked card	about 5 mL, or one A5 piece	None. The planner carries no line for either	—
Black photographic tape	about 1.5 m	None. The planner carries no line for it	—
Opal acrylic, 3 mm	one 40 × 40 mm piece, usually an offcut	None. The planner carries no line for it	—
Shim brass or aluminium, 0.5 mm	two 40 × 40 mm pieces	None. The planner carries no line for it	—
White and black card	one A6 and one A5 piece	None. The planner names enclosure hardware as a price gap	—
Two RC prints on different surfaces, only if you have no pair to hand	2 sheets, 5 × 7 in	£0.45–£0.64 a sheet, dated 5 September 2026	£0.90–£1.28

The single priced row gives £0.90 to £1.28, and only for a reader who has to make the glossy-and-matt pair rather than pull it from a folder. That is a floor and not a total: six of the seven rows carry no dated price, are counted as nothing here, and none of them is free.

Two honest notes about that table. The planner’s paper line is for variable-contrast RC paper and does not distinguish glossy from matt — which is precisely the distinction the reflection test needs, so even the one priced row is priced against a product description that cannot tell you whether you can buy what the page asks for. And the chemistry to process those two sheets is Part XIII’s, costed there, and is not re-counted here.

Equipment stays out of the table on purpose: the caliper, the drill, the module, the wedge and the reference tile are not consumed. A second run — because the ambient test failed and you rebuilt the shroud — spends the tape and the glue again and nothing else.

Alternative route

Nothing on this page needs a darkroom, a UV source or mains equipment, so the facility question does not arise. The question that does is what a reader who cannot build it should do, and there are two real answers.

Buy a light-to-digital sensor module and build only the mechanics. A TSL2591 or VEML7700 board is about the size of a postage stamp and replaces the photodiode, the amplifier and the converter. The optical head around it is unchanged — same diffuser, same aperture, same gap, same shroud — because the head is what sets the geometry and the stray light, and those are the limits. This is the route the design lesson says loses you access to the middle of the signal chain, and it loses you nothing else.

Buy a second-hand commercial densitometer. Then read this page anyway, because the tests in Testing and calibration are exactly the ones that tell you whether a twenty-year-old instrument with an unknown history is still an instrument. A machine with a dirty diffuser and a perished lamp has a stray-light floor and a drift figure like anything else, and neither is written on its case.

Both routes still owe you a reflection capability, and neither of them provides one at hobby cost: the 361T’s own reflection heads were separate purchased units. If you take either route, build the 45/0 attachment from stage 7 anyway and mount your bought sensor in it.

Waste streams

Small, and mostly solid. Offcuts of board, card, foam and acrylic go to ordinary waste or to the relevant recycling stream where your authority takes them; metal offcuts and swarf go to metal recycling, and swarf is collected with tape rather than swept, because it ends up in fingers and in feet. Washings from an acrylic paint brush are a household paint waste and go on a rag into ordinary waste rather than down a drain, where the pigment and binder load has no business being. Local regulation governs all of this, and it varies more than any of it deserves to; check your own.

The only item worth a note of its own is the LED and the photodiode at end of life, which are electrical and electronic equipment and belong in that stream rather than in a bin, whatever their size.

Build

Nine stages, about three hours, of which stages 4 and 5 are the ones people skip and the ones the instrument’s specification actually comes from.

Stage 0 — Write down the four numbers (15 minutes)

Before cutting anything, put these on the first page of the build record. Three of them are decisions and the fourth is a measurement you have not made yet.

Number	Where it comes from	Typical
Aperture diameter	The step size of your wedge; stage 2	2.0 mm
Aperture plate thickness	The acceptance-angle rule; stage 2	0.5 mm
Detector gap	As small as your film handling allows; stage 3	3.0 mm
LED drive current	Set on the bench in stage 5, to put the zero reading near two-thirds of full scale	a few mA

Then write your LED’s dominant wavelength and its spectral half-width from its datasheet beside them, because those two numbers are the whole of your instrument’s spectral condition and you will be asked for them on the certificate.

Stage 1 — The lamp chamber, and how little light you need (25 minutes)

Line the lower compartment of the box with matt white card, mount the LED at the bottom facing up, and leave 35 to 45 mm between the emitter and where the diffuser will sit. Nothing about that distance is critical — this is not the sensitometer, where a 127 mm wedge had to be lit evenly. Here the illuminated area is 2 mm across, and any diffuser will manage that.

What is worth doing carefully is the current, and it is worth doing by arithmetic rather than by eye.

🧮How much light the detector actually needs

The OPT101 gives 0.45 V per microwatt at 650 nm through its internal 1 MΩ resistor, and on a 3.3 V supply its output cannot exceed about 2.0 V, because the datasheet limits the output high to the supply minus 1.15 to 1.3 V. Set the clear-film reading at 2.0 V and the optical power arriving at the die is

2.0 V ÷ 0.45 V/µW ≈ 4.4 µW

and rather more than that at 525 nm, where silicon’s responsivity is well below its 650 nm value. Call it ten microwatts. Ten microwatts, onto an area of five square millimetres, through a 2 mm hole.

A 5 mm indicator LED at 20 mA radiates on the order of a milliwatt, spread over a wide angle, of which the aperture and the diffuser will pass a small fraction — but “a small fraction of a milliwatt” and “ten microwatts” are the same order, which is the whole point. You do not need a lamp. You need an indicator, run gently.

Three things follow, and they are why the current is set low deliberately rather than accepted lazily. Less current is less junction heating, and a cooler junction is a more stable dominant wavelength and a more stable output. Less current is less light bouncing around inside the head looking for a way to the detector that does not pass through the film. And a few milliamps is not a high-brightness LED source in the rubric’s sense, which is what holds this page at Level A.

Wire the LED to the Part XIV module’s constant-current output, set to the lowest current the driver will hold, and bring the monitor photodiode’s leads out too — you will fit it in stage 6. Do not set the final current yet; that happens in stage 5, when the whole path exists.

Stage 2 — The diffuser and the aperture plate (35 minutes)

This is the stage that decides what the instrument measures.

Cut the opal acrylic to sit flat in the top of the lamp chamber, recessed so that its upper face is level with the surrounding stage rather than standing proud of it. The aperture plate then lies directly on the opal, in contact, and the film lies directly on the plate. Three surfaces, touching, and nothing standing up to hold the film off any of them. The reason is ISO 5-2’s own reasoning: a diffuser in contact with the specimen reproduces the inter-reflection that happens under a contact print, and a gap does not.

Drill the plate 2.0 mm, dead centre, backed by hardwood so the bit does not tear through. Deburr both faces until a fingernail finds no edge. Blacken the upper face and — this matters more — the bore itself, with a black marker worked into the hole and left to dry, or by a wipe of matt black paint on a cocktail stick. A bright bore is a ring-shaped mirror sitting in the middle of your measurement.

!Why the plate must be thin, with the arithmetic

A hole is not a hole; it is a short tube, and a tube has an acceptance angle. Light entering the bottom of a bore at one edge and leaving the top at the other edge has travelled the bore’s diameter sideways while travelling its thickness upwards, so the largest angle from the normal that gets through is

θ_max = arctan(d ÷ t)

Acceptance half-angle of a bore

where d is the bore diameter and t the plate thickness. Put the numbers in.

Plate thickness t	θmax for a 2.0 mm bore	What the illumination has become
0.5 mm	76°	Very nearly hemispherical — diffuse
1.0 mm	63°	Still broadly diffuse
2.0 mm	45°	Neither one thing nor the other
3.0 mm	34°	Directional; you have built a projection densitometer by accident

A 3 mm plate does not make a slightly worse diffuse instrument. It makes a different instrument, one that reads the Callier-inflated number instead of the diffuse one, and it does so silently, with no symptom you would notice. This is the single easiest way to build a head that works perfectly and measures the wrong quantity — which is why the parts list specifies shim stock and refuses a washer of unknown bore.

Choosing the diameter. A Stouffer T2115 is 12.7 × 127 mm in 21 steps, so one step is 127 ÷ 21 ≈ 6.0 mm long by 12.7 mm wide. A 2 mm aperture centred on a step leaves 2.0 mm of margin at each end of it and 5.35 mm at each side — generous even for a hand-placed wedge. A 3 mm aperture still fits, with 1.5 mm at each end, and passes 2.25 times the light, which is worth having at the dense end; take it if your registration is good. The X-Rite 361T offers 1, 2 and 3 mm and an optional 0.5 mm, and the reason the small ones exist is fine detail rather than better densitometry: halving the aperture quarters the signal while leaving every leak unchanged.

The transmission head in section, with the dimensions that matter

1. 1Green LED, a few milliamps, facing up — constant-current drive from the Part XIV module; current set in stage 5, not guessed
2. 2Lamp chamber lined in MATT WHITE card — white for efficiency below the diffuser; matt, because a gloss wall images the emitter onto the diffuser as a bright patch
3. 3Black baffle ring, about half way up — stops light grazing the walls from reaching the diffuser edge and creeping round the aperture plate
4. 4Opal acrylic diffuser, 3 mm, recessed so its upper face is level with the stage — in contact with the aperture plate above it — the contact is the geometry, not a convenience
5. 5Aperture plate: 0.5 mm shim, 2.0 mm bore, blackened on top AND inside the bore — thin, because arctan(d ÷ t) is the acceptance angle; a 3 mm plate builds a projection densitometer by mistake
6. 6Film, emulsion downward, on the plate — emulsion to the diffuser, as the standard specifies for the analogous arrangement
7. 7Registration fences at a right angle — the wedge goes back in the same place; a millimetre of drift is a different patch of film
8. 8Photodiode facing down, 3 mm above the film — active area larger than the aperture, so the receiver region exceeds the diaphragm — close and wide is what makes it diffuse
9. 9Two hard spacers of equal height, clear of the light path — the arm closes onto these and nowhere else; unequal spacers tilt the detector and the tilt is a drift you will chase for weeks
10. 10Shroud skirt, matt black, with a foam seal at the stage — the only thing standing between your reading and the room
11. 11Hinge — a tape strip is legitimate — stiff is better than free; the repeatability test finds a floppy arm before you do

Drawn readable rather than to scale: the 2 mm bore and the 3 mm gap are shown far larger than their true proportion to the 40 mm chamber. Build from the key and the dimensions, not from the picture.

Stage 3 — The detector arm (30 minutes)

The arm’s whole job is to put the photodiode in the same place every time, close to the film, with nothing but blackness around it.

Mount the photodiode facing down, its die centred over the bore. Centring by eye is good enough at this gap; centring badly is not, because the die is 2.29 mm across and the aperture is 2.0 mm, so there is very little margin before you are clipping the cone.

Set the gap with hard spacers, not with the hinge. Two spacers of the same height, standing on the stage clear of the light path, are what the arm closes onto. Three millimetres is the target and the reason is a trade: closer collects more of the widely scattered light, which is what makes the geometry diffuse, but leaves no room for a curled strip of film. Anything from 2 to 5 mm works if it is the same every time; what ruins a densitometer is a gap that varies.

Hang a shroud skirt from the arm, all the way round, down to the stage, with a strip of closed-cell foam at its lower edge so it seals against a slightly uneven surface. Everything inside the shroud — skirt, arm underside, spacer sides — is matt black. Flocked card is best; matt black paint is acceptable; bare black plastic is usually shinier than it looks and should be flocked or painted.

✕The detector-side aperture stop: what it is for, what it costs, and when to fit it

A blackened tube between the film and the photodiode, restricting the detector’s field of view to the aperture and a little beyond, is the classic answer to light that has got inside the shroud. The base build deliberately does not have one, and the reason is that it would change the measurement.

A detector that sees only a narrow cone is a directional receiver. Fit a tube and you have moved the head away from the diffuse geometry it was designed for and part of the way towards a projection geometry — quietly, with the same symptom as no change at all, until you compare readings with someone else. The whole argument of the design lesson was that the diffuse quantity is the one this course needs.

So the rule is conditional and the condition is a measurement. If your ambient-leakage test in Testing and calibration fails, fix the shroud first. Only if it still fails, fit a stop — and then fit it before you calibrate, never after, and record on the instrument’s certificate that it is there, because from that moment your instrument and an unstopped one are measuring two different things.

Stage 4 — Blacken and baffle, which is most of the instrument (30 minutes)

The design lesson showed that the maximum density is −log₁₀ of the stray-light fraction, and nothing else in the build touches that number. This stage is where you earn it.

Work through the list, and treat the whole of the volume above the diffuser as one problem:

1. Everything above the diffuser is matt black: the aperture plate’s upper face, its bore, the fences, the stage surface, the skirt, the arm’s underside. If you can see a highlight on it under a desk lamp, it is not matt enough.
2. The chamber below the diffuser stays matt white, and the boundary between the two is the diffuser itself. Getting this backwards — a black lamp chamber and a shiny stage — is a common and expensive mistake, costing light where it is free and gaining leakage where it is fatal.
3. Seal every seam of the box with black tape, inside and out, including the joint between the two halves and every screw hole you are not using.
4. Bring the cable in through a grommet or a foam plug, not through an open hole, and dress it so that the hole is never in line of sight with anything luminous.
5. Blank off the second and third LED positions while they are unused. An empty LED hole in a chamber wall is a window.
6. Check with a torch, from the inside. Close the head, take it into a dark room with your eyes adapted, put a small torch inside the lamp chamber and look for where the light gets out. Every path works in both directions, and this test finds in two minutes what the blank test will otherwise report as a number you cannot explain.

✦The cheapest ten-fold improvement on this page

Black flocked card — the self-adhesive velvet-textured card sold for camera interiors and for display — is dramatically blacker than matt black paint, because it traps light in a pile of fibres rather than reflecting a few per cent of it off a smooth surface. It costs a few pounds for a sheet, needs no curing time, and outgasses nothing.

If you line only one surface with it, line the underside of the detector arm, which is the surface directly facing the detector’s own field of view and the one that returns light straight back into the die.

Stage 5 — First light, and setting the current (30 minutes)

Connect the OPT101 to the Part XIV module’s ADC input and run its read_monitor routine. You are about to make four readings and each one means something.

1. Lamp off, head closed. This is your dark reading — the amplifier’s offset plus whatever the converter contributes. Expect a few hundred counts and not zero.
2. Lamp on, head closed, nothing on the stage. This is your air reading, the instrument’s zero. Adjust the LED current until it sits near two-thirds of the converter’s full scale — high enough to use the range, low enough that a warm lamp does not clip it. Write the current on the label.
3. Lamp on, wedge step 1 in place. The clearest step of a Stouffer T2115 is a nominal 0.05 D, so this should read about 89 per cent of the air reading. If it reads 60 per cent, the wedge is not where you think it is.
4. Lamp on, wedge step 21. Nominal 3.05 D, so about a thousandth of the air reading. On the Part XIV module’s 12-bit converter, this is where the last lesson’s arithmetic arrives in your hands: from a two-thirds-scale zero of roughly 2 700 counts you should see two or three counts. Not a poor reading — an absent one.

=What step 21 is supposed to teach you

Two counts is the whole argument for the next page, felt rather than read. The head is fine. The geometry is fine. The lamp is fine. The converter has run out, exactly as the density-per-count equation said it would at three decades from a 12-bit zero, and no amount of averaging will recover information that was never digitised.

Record the number anyway, with the date. When the 16-bit converter is fitted, reading the same step again on the same head is the cleanest before-and-after measurement in this part.

Stage 6 — The monitor channel (20 minutes)

Fit the second photodiode inside the lamp chamber, looking at the LED from the side, well away from the diffuser’s clear path. Bring its output to a second ADC input.

Its purpose is a ratio. The lamp drifts as it warms and ages; so does the detector’s responsivity, but much less. If you divide every sample reading by the monitor reading taken at the same instant, a change in the lamp cancels out of the density entirely, because a density is a ratio of two readings and a common factor disappears from it. That is why the same trick appeared on the sensitometer, and why it is worth twenty minutes here.

What it cannot do. It cannot cancel a change in the lamp’s spectrum, only in its output; a junction that warms shifts its dominant wavelength as well as its brightness, and the monitor reports one number for both. It cannot cancel stray light, which does not come from the monitored path. And it adds one more thing to fail: a monitor that has come loose reads a constant and quietly rescales every density you take. The firmware on the next page logs the monitor value beside every reading for exactly that reason.

Stage 7 — The 45/0 reflection head (35 minutes)

Nothing else in this course can measure a print. That sentence is the justification for the whole attachment, and it is worth spelling out, because a reader may reasonably ask why a densitometer part grows a second head.

!Seven places downstream that need a number this attachment provides

The safelight fog test needs a reflection density difference to say whether a safelight is fogging paper. The contact printer and the enlarger both need a uniformity map across the easel, and a map is a grid of reflection densities. Paper Dmax is a reflection density by definition, and so is dry-down, for which this course has found no manufacturer figure at all and which therefore has to become something the student measures rather than looks up. The print curves of the printing parts are plotted in reflection density against log exposure. Six alternative-process pages state a Dmax. The print-fault figures compare a defect against its surround. And three stages of the capstone quote a paper’s tonal range.

Every one of those is a reflection density, and until this attachment exists every one of them is a judgement by eye. This is the smallest object that closes that gap, and it is here rather than in a printing part because it shares a detector, an amplifier, a cable and a firmware with something you are already building.

The geometry is the measurement, and it is one idea. A print returns two quite different things. The specular component is a mirror reflection from the surface itself; it carries no image information and is simply a picture of the lamp. The diffuse component has entered the emulsion, been scattered by the silver and the paper fibres, and come back out; that is the image. Illuminate at 45° to the print’s normal and collect along the normal, and the specular beam leaves at 45° on the other side and misses the detector entirely.

Get that angle wrong and the instrument stops measuring silver. A glossy paper returns a strong, narrow specular beam; a matt paper scatters its surface reflection over a wide angle. So a glossy and a matt print at the same silver density will read differently the moment any specular light reaches the detector — which makes the pair the perfect diagnostic, and is why the parts list asks for one.

The 45/0 reflection head in section

1. 1Print, face up, flat against the port — flat contact is not optional; a curled print changes the angle and the angle is the measurement
2. 2Port plate, 4 mm bore, thin and blackened — larger than the transmission aperture because reflected light is scarce; the arctan(d ÷ t) rule still applies
3. 3Two LEDs at 45° to the normal, opposed, 25 mm out — switch one off and the reading should halve and not change in density; that is the symmetry check
4. 4Photodiode on the normal, 20 mm up, in a blackened tube — the tube is legitimate here — a reflection measurement is directional on the collection side by design
5. 5Diffuse lobe — the image — light that entered the emulsion, scattered off silver and paper, and came back out
6. 6Specular rays, thrown away at 45° on the far side — each source's mirror reflection leaves towards the other source, not towards the detector — which is why an opposed pair is self-consistent
7. 7White reference tile — the top of the scale; uncertified unless you buy a certificate, which makes the scale relative and the certificate says so
8. 8Black trap, depth at least 5 × its opening — the zero. A cavity, not a card: stage 8 measures the difference and it is large

Drawn readable rather than to scale, but the two illumination lines are at a true 45° to the print normal because that angle is the measurement. The two dashed rays are the whole argument: any construction that lets either of them reach the detector is measuring surface finish, not image.

Build it as follows. Make a body that drops onto the same stage, carrying a thin port plate with a 4.0 mm bore. Mount the two LEDs on opposite sides, each aimed at the centre of the port along a line at 45° from the normal — set the angle with a square and a scrap cut to 45°, not by eye. Mount the photodiode on the normal, 20 mm above the port, in a short blackened tube. Everything inside is matt black except the LED housings.

⁇Annular ring or opposed pair — the course specifies one and has not compared them

The commercial arrangement is an annular ring of LEDs surrounding the detector, and in principle it is better: it averages over the azimuth, so a print with directional surface texture — a fibre-based paper’s grain, a brush-coated alternative print — reads the same whichever way round it is placed. An opposed pair averages over one axis only, and a textured print will read differently rotated 90°.

This course has not measured whether the two arrangements give the same reading on the same sample, and it says so rather than asserting equivalence. What decided the specification here is diagnosability: with two sources you can switch one off, read again, and expect the signal to halve while the density stays the same. If it does not, one arm is misaligned, and you know which. With eight sources in a ring you have no such handle.

Build the ring if you would rather, and then run the experiment neither of us has: a matt fibre print with visible texture, read on both heads, at four rotations.

Stage 8 — The white tile and the black trap (25 minutes)

A reflection reading has no natural zero and no natural top, so the head needs two standards, and they are as much a part of the instrument as the detector.

The white tile anchors the top of the scale. A certified ceramic or opal tile comes with a stated reflectance, and the planner could price none; the course therefore specifies none and tells you what an uncertified one buys you instead. An uncertified white tile of stable material is a perfectly good transfer standard: it lets you return to the same top-of-scale reading next month, which is what repeatability needs. What it cannot give you is an absolute reflection density, so the scale on your certificate is declared relative to this tile, identified by its own serial number, and that is an honest instrument rather than a compromised one. Store it in the dark, in a sleeve, and never touch the measured face — skin oil and yellowing are both real, and both drift slowly enough that you would never notice them happening.

The black trap anchors the bottom, and it is the part most people get wrong. A piece of black card reflects a few per cent of the light falling on it; a trap reflects a small fraction of one per cent, because light entering it has to escape after several bounces off matt black surfaces at unhelpful angles. The construction rule is depth: at least five times the opening diameter, with a matt black sloping baffle in the floor so that nothing gets a straight run back out.

📓Measure the difference; do not take it on trust

Read your black card and your black trap in turn. The difference between them, expressed as a fraction of the white tile reading, is exactly the stray-light fraction of your reflection head, and by the stray-light ceiling it sets the highest reflection density you may report.

Paper Dmax on a good glossy paper is high enough that the difference between a 0.5 per cent floor and a 0.05 per cent floor is the difference between an instrument that can compare two papers and one that cannot. This is a five-minute measurement that decides whether six later pages have data.

Stage 9 — Sample presentation, and the rules that go on the label (15 minutes)

Reflection readings are ruined by handling more often than by electronics, so the discipline is part of the build.

Flat contact with the port, every time. A print that stands off by a millimetre has changed both the illumination angle and the collection solid angle. Use a weight or a sprung backing plate; do not press with a finger, which tilts.

The same backing behind every sample. Paper is translucent, and light that goes through it, bounces off whatever is behind, and comes back through is indistinguishable from light the image reflected. A white bench and a black bench will give you two different Dmax figures on the same print. Fix one backing — matt black is the sensible choice, because it makes the show-through term as small as possible rather than merely constant — and record it on the certificate.

A wet or damp print is not a measurable print. A wet emulsion is optically a different material, and this is the same phenomenon as dry-down; a print read wet and read again dry gives two honest numbers about two different objects. Dry it fully, flat, and give it the same settling time every session.

Label the head with: the aperture diameter, the plate thickness, the gap, the LED’s dominant wavelength, the drive current, the tile’s serial number, and the build date. Every one of those changes the reading, and an unlabelled instrument is one you will have to characterise again in a year.

Testing and calibration

Five tests, in this order, and none of them takes long. Together they are the instrument’s first specification, and the calibration experiment that follows in this part assumes all five have been passed and recorded.

Commissioning the head, in the order that isolates faults

1. 1T1 — DarkLamp off, head closed. Establishes the offset that every later reading is corrected against. A reading that drifts here is an amplifier or temperature problem, not an optical one.
2. 2T2 — Blank, lamp ONOpaque blank over the aperture. Whatever this reads above T1 is stray light: light from your own lamp reaching the detector without passing through the sample.
3. 3T3 — Blank, room lights ON and OFFThe difference between the two is ambient leakage, which is a shroud problem rather than a stray-light problem. Separating T2 from T3 is why the tests are in this order.
4. 4T4 — Ten replaced readings of one stepLift the arm, move the wedge away, put it back, read again. The spread is mechanical repeatability and it is usually the largest term in the budget.
5. 5T5 — Air, step 1, step 21The first density figures. Compare against the wedge's nominal 0.05 and 3.05 and see where your instrument stops being able to tell you anything.

Run them in this order every time you rebuild anything. A test that fails tells you which stage to go back to, which is only true because each one holds the others fixed.

T1 — The dark reading

Lamp off, head closed, room dark. Take 64 readings and record the mean and the spread. This is the offset that every measurement is corrected against, and the reason the firmware retakes it constantly is the OPT101’s 10 µV/°C offset drift, which the design lesson turned into about 0.02 D at the top of the range for a 10 °C change.

Repeat it after half an hour with the lamp running. If the dark reading has moved appreciably, the head is warming and you have found your warm-up requirement — the 361T’s is two minutes and yours is probably longer.

T2 — The stray-light floor

Put the opaque blank over the aperture, close the head, lamp on, room dark. Subtract the T1 dark reading. What is left is light from your own lamp that has reached the detector without going through the sample: around the aperture plate, through the box seam, off the arm, past the shroud.

f = (blank − dark) ÷ (air − dark) and D_max ≈ −log₁₀ f

The floor, and the ceiling it sets

f is the stray-light fraction and D_max is the highest density the instrument can report, however good the converter. Write both in the build record. This is the single most important number this page produces.

If f is	Your ceiling is	What to do
1 %	2.0 D	Go back to stage 4; something is wide open. Torch test from the inside
0.3 %	2.5 D	Usable for paper work, short for film. Flock the arm underside; re-tape the seams
0.1 %	3.0 D	The design target. Record it and move on
Below 0.05 %	Better than 3.3 D	Excellent, and worth checking that the blank really is opaque

T3 — Ambient leakage

Repeat T2 twice: once with the room lights on and once with them off. The reading should not change. A difference between them is room light finding its way inside the shroud, and it is a different fault from T2 with a different cure — the shroud, its foam seal and the box seams, rather than the blackening of the interior.

This matters because a densitometer lives on a bench, and a fault that only appears when the desk lamp is on is one you would otherwise diagnose as drift for weeks. For scale: a professional instrument in a sealed metal case specifies its ambient interference as a decrease in D of less than 0.25 per cent.

T4 — Mechanical repeatability

Choose a mid-scale step — step 10 or 11 of a 21-step wedge. Read it, lift the arm, slide the wedge away, put it back against the fences, close the arm, read again. Ten times.

Convert the spread of those ten readings into density and record it. This is the number most home-built densitometers are actually limited by, and it has nothing to do with electronics. Common causes, in the order you should suspect them: a floppy arm that does not close to the same place; spacers of unequal height, so the tilt depends on how you press; a wedge that can slide along the fence, so you are reading a different patch; a fence that has come unglued at one end.

Then do it again without lifting the arm — ten readings of an undisturbed sample. That spread is the electronics alone. The difference between the two spreads is the mechanics, and knowing which is which is what tells you where the next hour should go.

T5 — Air, step 1, step 21

Read the air, then the clearest step, then the densest. On the T2115 those steps are a nominal 0.05 and 3.05 — nominal, because Part IX established that an uncalibrated wedge is manufactured to its increment rather than certified to it, and every absolute scale derived through it inherits that.

So this test does not tell you your instrument is accurate. It tells you three other things, all useful: that the light path works, that the sign and rough magnitude of your density calculation are right, and where your instrument runs out. Compare step 21 against your D_max from T2. If the ceiling is 2.5 and the step is nominally 3.05, you have just learned that the top four steps of your wedge are outside your instrument’s range, and reporting them would be reporting your stray light.

T6 — Commissioning the reflection head

Four readings and one comparison.

1. The white tile. Set the LED current so this sits near two-thirds of full scale, and record it.
2. The black trap. Compute the reflection stray-light fraction as in T2, and its ceiling.
3. A black card, for comparison. The gap between card and trap is what a trap is worth, in your own numbers.
4. The symmetry check. Read a print, then switch one LED off and read again. The signal should fall by about half and the density should not change. A density that shifts means one arm is misaligned or one LED is dimmer, and the ratio of the two single-arm readings tells you which.
5. Glossy against matt. Read the glossy print and the matt one. Then tilt each by a few degrees and read again. The glossy print should move much more than the matt one — that asymmetry is the specular component finding the detector, and if the glossy reading is stable under tilt while the matt one is not, something is wrong with the geometry that is not what you assumed.

Troubleshooting

Symptom	Most likely cause	What to do
Air reading changes when you close the lid a second time	Arm not closing onto the spacers; hinge binding or spacers unequal	Measure both spacers with a caliper. Make the hinge stiffer, not looser
Densities read consistently low at the dense end only	Stray light. This is its signature: faithful for two decades, then bending over	Re-run T2. Torch test from the inside. Flock the arm underside
Densities read low across the whole scale by a similar fraction	A scale error, not a range error: wrong reference, a gain misread, or a wedge whose increment is not what you assumed	Calibration problem; the calibration experiment fixes it. Do not reach for the black paint
Reading changes when the desk lamp is switched on	Ambient leakage through the shroud, not stray light	T3. Fix the foam seal and the box seams; blackening the interior will not help
Reading creeps steadily for the first twenty minutes	Lamp warm-up, detector warm-up, or both	T1 repeated after half an hour separates them. Then write a warm-up rule and obey it
Step 21 reads the same as a completely opaque blank	You have hit Dmax; the instrument is reporting its own floor	Nothing is broken. Reduce the floor, or state the range honestly and exclude those steps
Readings jump when you touch the cable	Connector or a cracked joint at the photodiode	Strain-relieve the cable at the arm; a moving lead near a high-impedance input is a fault
Two adjacent wedge steps read identically	Aperture straddling the boundary, or the wedge slipping along the fence	Check the aperture is centred within the step; add an index mark to the fence
Everything is noisy and nothing is stable	The detector is not centred over the bore, so you are on the edge of the cone	Look through the head with the arm open and the lamp on; the bore should be a bright disc centred under the die
Glossy and matt prints of the same density differ by a lot	Specular light reaching the reflection detector	Re-set the 45° angles with a square; check the port plate is thin and the detector tube is blackened

Questions

1. Your aperture plate turns out to be 1.6 mm thick rather than 0.5 mm. Compute the acceptance half-angle for the 2.0 mm bore, compare it with the 0.5 mm case, and say in one sentence what quantity your instrument is now measuring. Then say whether recalibrating against a wedge would hide the problem or reveal it.
2. T2 gives a blank reading of 41 counts, a dark reading of 12 counts and an air reading of 2 780 counts. Compute f and D_max. Then say how much of the T2115’s 21 steps lies inside that range, given a nominal 0.15 increment from 0.05.
3. Your ten replaced readings of step 11 have a spread of 0.9 per cent of the mean, and your ten undisturbed readings have a spread of 0.15 per cent. Express both as densities. Say which term you would attack first, and name two specific mechanical causes you would check before touching the electronics.
4. You are offered a 6 mm aperture plate, free, in the right metal. Give two independent reasons to refuse it for a T2115, one geometric and one about the bore, and then give the one condition under which a 6 mm aperture would actually be the right choice.
5. A friend fits a blackened tube between film and photodiode on their head and reports that their stray-light floor improved from 0.4 per cent to 0.08 per cent. They then compare readings with you and find a systematic disagreement that grows with density. Explain the disagreement without invoking any fault in either instrument, and say what each of you must write on your certificate.
6. Your reflection head reads a glossy print at 1.94 and a matt print of visually identical density at 2.11. Give the two explanations that are consistent with a correctly built head and the one that is not, and describe the single test that separates them.
7. The monitor photodiode’s reading falls by 3 per cent over a session while the sample readings fall by 3 per cent too. Explain why the reported densities are unaffected, and then give one kind of lamp change that this ratio would not protect you against.

Further experiments

Measure your own Callier coefficient. The design lesson refused to quote one because the course has sourced none. Read a full wedge on your diffuse head, then fit a long blackened tube between film and detector so the collection cone is narrow, and read it again. Plot the ratio against diffuse density and you have measured, for your own film in your own developer, the quantity every textbook tabulates for somebody else’s. Ware’s observation gives you the control: because there is no Callier effect in contact printing, a step tablet’s exposure scale read by contact should agree with your diffuse numbers and not your specular ones.

Find the aperture at which grain appears. Make three aperture plates — 3 mm, 2 mm and 1 mm — and take twenty undisturbed readings of the same mid-scale step through each. The spread should be roughly independent of aperture until the sampled area gets small enough for the film’s own granularity to matter, and then it should rise. Where it starts rising is your film’s answer to a question the standards answer generically.

Map your own stray light. Instead of one blank reading, take blanks with black card masking successive parts of the head: the seam, the cable entry, the arm’s underside, the space around the aperture plate. Each mask that improves the blank tells you how much of the floor that path was worth. It is a tedious half-hour and it is the difference between guessing and knowing which surface to flock.

Read Part XIII’s archived strip. It has been waiting for this. Read every step, plot your densities against the ones you obtained by lux meter, spot meter and visual matching, and look at both the slope and the scatter. The slope is the calibration of your interim method; the scatter is its precision. Part XIII promised you that measurement and this is the first day you can take it.