Experiment: Calibrating the Sensitometer

Purpose

To find out what the instrument you have just built can honestly claim, and to write that down on one page in a form somebody else could check.

The hypothesis. That the sensitometer delivers the same exposure to the same step of the same wedge, session after session, to better than 0.02 log H — an eighth of a nominal wedge step — and that the variation actually visible on film is dominated not by the instrument at all but by the processing.

The control. Two of them, and they do different jobs. An unexposed strip from the same emulsion batch, processed in every tank alongside the exposed strips, fixes base plus fog for that development, because every density on this page is measured above it. And a reference strip exposed at one fixed setting and developed in every session, exactly as Part IX established, which is what lets a change be attributed to the instrument rather than to the developer.

The one variable that changes is different in each of the three arms, and that is the whole design: in the repeatability arm nothing changes at all, which is what makes it a measurement of the instrument’s own noise; in the reproducibility arm the only thing that changes is the day; in the drift arm the only thing that changes is the number of minutes since the lamp was switched on.

This is the page the part exists for. Parts XV and XXVII and the capstone all want to make quantitative claims about developers, films and processes, and an instrument whose uncertainty is unknown cannot support any of them. What you produce today is not a better instrument. It is the same instrument with a number attached to it.

!Every table on this page is blank, and that is the point

The course has not built this sensitometer and has therefore measured nothing on it. Printing a plausible repeatability figure would be inventing a measurement, which is the one thing this course does not do. What is given here is the method, the arithmetic and the form of the answer. The numbers are yours, and the certificate at the end is a certificate for your instrument and nobody else’s.

Learning objectives

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

• say what the instrument’s relative log exposure axis actually rests on, and why you cannot check the wedge with the instrument the wedge defines;
• compute an absolute log H for every step from an illuminance reading and a time, and state which part of that number is a measurement and which part is a hope;
• convert a density difference between two strips into a log exposure difference, and say why dividing by the gradient is not optional;
• design a reproducibility test that is honest about latent-image keeping instead of quiet about it;
• measure drift from switch-on on the monitor and on film, and say what the film can show that the monitor cannot;
• overlay a sensitometer curve on an enlarger curve, predict the offset between them from published reciprocity factors before you look, and account for what is left;
• build an error budget with every term named, each one sized, the axes kept apart, and the total combined by a rule you can state;
• write an instrument certificate, and read somebody else’s for the claim it cannot support.

Prerequisites

The enclosure and exposure stage, complete, with its uniformity map measured and its light-leak test passed. A calibration of an instrument that leaks is arithmetic about a mistake.

The LED light source and exposure timer, with its three bench tests done: the independent timing check, the warm-up curve and the ten-exposure repeatability of the monitor.

Part II on measurement and uncertainty, which owns how uncertainty travels in this course and rules that the terms are combined as a bound rather than statistically. This page does not re-derive that rule; it uses it and says where a metrology text would do something different.

Part XIII, in full, for the characteristic curve, the speed criterion, the contrast-index convention and the three ways of reading a strip that the course has before it owns a densitometer.

Safety classification

Level A, on the rubric’s criteria for the substances handled and the energies present. The chemistry is one or two ordinary film developments at working dilutions — developer at 1+1, stop at 1+19, fixer at 1+4 — in a few hundred millilitres each; nothing is heated above 50 °C; nothing mains-voltage is built or modified; and the waste is spent developer and silver-bearing fixer that can be collected. The instrument runs from the certified USB supply chosen on the electronics page.

What is not a hazard here, and why. No reagent on this page is handled at a concentration above its working dilution, so there is no splash of anything corrosive, no dust, no weighing and no vapour: the concentrates were diluted in Part VIII and in the stock SOP, and this session only pours what those made. The bright emitter that made the previous two pages careful is now behind an opal panel inside a closed box for every exposure in this session, which is what the enclosure was for. The enlarger used in the cross-check is a purchased, certified appliance used as its maker directs; nothing is opened.

What is present, and is worth naming because it is easy to forget in a session about numbers: several hours of repeated handling of developer and fixer, which is a cumulative skin-contact exposure rather than an acute one. That is what the gloves are for, and it is the reason they go on at the start of the wet work rather than when something is spilled.

Hazards

The processing hazards are those of Part XIII’s step-wedge lab and are not restated here: developer as a skin sensitiser and irritant at working strength, fixer as an irritant with a silver-bearing waste stream, and the stop bath as a dilute acid.

Three hazards belong to this page rather than to that one.

Working in the dark, repeatedly, for two hours. Every arm of this experiment loads film in total darkness, and the failure mode is not chemical: it is a hand on a hot heatsink, a foot on a cable or a graduate knocked into a tank. Set the bench out before the lights go off, and put the module’s heatsink where a hand reaching for the lid will not find it.

The enlarger, in the cross-check. It is mains equipment and it gets hot. The lamp house is not opened, the negative carrier is empty, and the head is left on between exposures rather than switched repeatedly, which is both a photometric decision and the one that keeps you away from a hot lamp.

Time pressure. The drift arm runs for an hour and the reproducibility arm for three days. A session run late and hurried is where a strip gets confused with another strip, and an unlabelled strip is a strip that was never made.

Required PPE

Nitrile gloves and eye protection whenever solutions are handled, which the Level A controls require and which this page has more occasions for than most, because the strips go through the tank in several batches. Change gloves rather than rinse them if fixer gets on the outside: a trace of fixer carried back to a developer is the contamination ILFORD warn about, and on this page it would appear as instrument noise.

Nothing else is specified, and the absence is a decision. No respiratory protection, because nothing is weighed and nothing is sprayed. No splash goggles beyond the Level A pair, because nothing is more concentrated than a working bath. The glove page is the authority on what the published permeation data support.

Ventilation

The standard for manual film development, as on Part XIII’s lab: general ventilation with a through draught, not a sealed cupboard. The wrinkle on this page is that the loading has to happen in the dark, and a light-tight room is often an airtight one. Ventilate between loadings rather than during them, and if the only dark space you have is a windowless one, work in short spells with the door open in between.

Materials

Item	Quantity	Note
Film, one emulsion batch	16 strips of 135 mm	Twelve exposed — three for repeatability, three for reproducibility, four for drift, two for the cross-check — plus one unexposed control strip for each of the four tanks. One batch for the whole page, and the batch number goes in the certificate
The 21-step transmission wedge	1	The same physical piece for the whole page, and its serial number is part of every result
Opaque card	a strip 15 × 40 mm	Masks the tail of every strip so each carries its own base-plus-fog patch
Negative filing sheets and card label slips	14	Every strip is labelled before it goes in the tank, not after
A light-tight tin	1	For the reproducibility arm’s exposed, undeveloped strips

Chemicals

Nothing is weighed on this page. Every solution is diluted from a stock or a concentrate following the stock SOP.

Chemical	Quantity	Form
D-76 or ID-11 stock, from Part VIII’s lab — metol, hydroquinone, sodium sulfite, borax	600 mL over the whole page	Solution, diluted 1+1 immediately before each tank and discarded after it, as Kodak’s J-78 sheet directs
Stop bath, citric acid type	600 mL at 1+19	Solution
Rapid fixer, ammonium thiosulfate type, or a sodium thiosulfate fixer	600 mL at 1+4	Fixed for twice the clearing time, measured on a scrap of the same film
Wetting agent	600 mL at 1+200	Final rinse

Equipment

The instrument, with its build record, and the module’s serial terminal open on a computer so that every exposure’s measured_us and monitor reading is logged as it happens. An exposure that is not logged cannot be excluded later, and excluding a bad exposure is half of what the monitor is for.

A lux meter reading to at least 0.01 lx at the levels the film plane sees — around 0.8 lx for the film route — or the module’s monitor photodiode on a flying lead. Whichever you use, the same one for the whole page.

A reading method for density, from Part XIII’s three: lux-meter densitometry, spot-meter densitometry or visual matching against the wedge. Use at least two, because the difference between them is itself a measurement of your reading floor. Part XV’s densitometer will replace all three and this page’s method is written so that its tables can be filled in again when it does.

The wet bench: tank, graduates, a thermometer reading to 0.1 °C checked by the balance and thermometer SOP, a water bath, and a light box with an even, colour-stable source.

An enlarger, for the cross-check only, with an empty carrier and a measured head height.

Estimated cost

Cost band £. Everything expensive on this page was bought for an earlier one: the wedge, the instrument, the meter. What this session spends is about fourteen strips of film and four dilutions.

The laboratory planner carries the dated figures. It carries none for the 21-step wedge, which it records as a price gap, and none for the electronics.

Estimated consumables cost

Film is counted at twelve 135 mm strips to a 36-exposure cassette, the course’s own working figure and its caveats being set out on the enclosure build.

Consumed	This session	Sourced price	Cost this session
Film, one emulsion batch	16 strips of 135 mm, about one and a third 36-exposure cassettes	£6.37–£11.40 per one 35 mm roll, 36 exposures	£8.49–£15.20
D-76 or ID-11 stock, from Part VIII	600 mL over three or four tanks, diluted 1+1 and discarded after each	Costed in Part VIII’s mixing lab	—
Rapid fixer concentrate	120 mL, to make 600 mL at 1+4	£21.05–£25.98 per 1 L of ammonium thiosulfate concentrate, diluted 1+4 for film	£2.53–£3.12
Stop bath concentrate	30 mL, to make 600 mL at 1+19	£10.66–£12.18 per 500 mL of citric acid concentrate, diluted 1+19	£0.64–£0.73
Wetting agent	3 mL, for 600 mL at 1+200	£28.70 per 1 L of concentrate, diluted 1+200	£0.09
Negative filing sheets and label slips	14 pockets, 14 slips	None. A named price gap: sleeving that passes the Photographic Activity Test	—

The priced rows come to £11.75 to £19.14 for one run of this page, at the ranges dated 5 September 2026 in the planner. That is a floor rather than a total: one of the six rows carries no dated price and is counted as nothing here, and it is not free. The wedge, the meter and the instrument are equipment and stay out of the table, because none of them is consumed.

Waste streams

Three, kept apart, each labelled per the container SOP and routed per the general waste SOP: spent developer, which is alkaline and carries nearly all the metol and hydroquinone that went into it because a few small strips reduce very little silver; spent fixer and its first rinse, which are silver-bearing and go to the silver stream; and the rest of the wash water. The chemistry and the reason the answer is jurisdictional are on the disposal page, and local regulation governs what may actually be done with them — check your local regulations before the first pour.

Alternative route

Two facilities are needed and each has a different answer.

The darkness. A changing bag is enough for every loading step, as it is on the enclosure page: the strips are short and the fences can be found by feel. Practise the assembly in daylight with a scrap first.

The enlarger, for the cross-check. There is no substitute that gives the same comparison, and the page says so rather than pretending otherwise. If you have no enlarger, drop the cross-check and record that you dropped it on the certificate, which then makes no claim about agreement with an independent light source. What is lost is worth naming: the cross-check is the only step on this page that tests the instrument against something outside itself, and without it every number here is internally consistent and externally unchecked. Two partial substitutes exist — a second builder’s instrument, with strips from a shared emulsion batch developed together; or one strip exposed in daylight through the wedge at a metered illuminance, which is a poor light source and a genuinely independent one.

Preparation

A week before. Mix or check the developer stock. This session is not the place to discover a mixing error, and a fresh stock and a three-month-old stock are not the same developer — which is a fact this part’s next page is entirely about.

The day before. Cut the strips, all of them, from one batch, and notch or label each one. Fourteen identical strips in the dark is how a session goes wrong; fourteen labelled strips is how it does not. Put the reproducibility arm’s strips in the light-tight tin.

An hour before. Bring every solution to 20.0 °C in the water bath and leave it there. Kodak’s own process-control literature is blunt about how tight this has to be: temperature variations greater than ±0.3 °C in the developer will affect process control and image quality. That is a factory’s standard and it is the right one to aim at here, because on this page a temperature error would be counted as instrument noise.

Twenty minutes before. Switch the instrument on and let it warm up for the time your own warm-up curve established. Open the serial log.

📓Write the predictions down before the first exposure

Four of them, in the notebook, dated, before anything is loaded.

1. What spread you expect between three strips exposed identically, in density and in log H.
2. Whether you expect the day-to-day spread to be larger, and by how much.
3. Which direction the drift series will go and how big it will be, from the warm-up curve you already have.
4. What offset you expect between the sensitometer curve and the enlarger curve, computed from ILFORD’s published reciprocity factor for your film at the enlarger exposure you used.

A prediction written afterwards is not a prediction, and the fourth of these is the one this page can actually check against a manufacturer’s number.

Procedure

Five parts. Parts 1 to 4 are one bench session of about 150 minutes; part 2 spans three days and is mostly waiting.

Part 1 — Fix the relative scale, and be honest about the circle

The instrument’s log exposure axis is the wedge’s densities, subtracted from whatever the clear step delivers. Kodak’s workbook does exactly this subtraction in its own worked example.

log H(k) = log H₀ − D_wedge(k)

Log exposure at wedge step k

log H₀ is the log exposure reaching bare film in the exposure time, and D_wedge(k) is the density of wedge step k. Everything on the horizontal axis of every curve you will ever plot with this instrument comes out of the second term.

So write down which of two things you have.

A calibrated wedge. Then D_wedge(k) is a measured value for your individual piece, and Stouffer state what stands behind it: the calibrated parts are read against NIST Standard Reference Material 38120C on a densitometer conforming to ANSI PH2.19-1986. Copy your certificate’s twenty-one numbers into the notebook and use them. That is traceability, and it is the only place in this whole instrument where the course can point at a chain that ends somewhere outside itself.

An uncalibrated wedge. Then D_wedge(k) = 0.05 + 0.15(k − 1) is a manufacturing specification, not a measurement of your piece. Stouffer are unusually straight about this: calibrated and uncalibrated guides come from the same batches and are made with the same control, and what the money buys is that each step is read on a densitometer and the readings recorded. Part IX established that the increment is nominal rather than certified, Part XIII inherited it, and this page inherits it again: every absolute figure derived through an uncalibrated wedge carries that unquantified systematic error, and the certificate must say so in those words.

!The circle, named rather than hidden

The obvious move is to check the wedge with the instrument: expose a strip, read the densities, work backwards. It does not work, and the reason is worth being precise about. The instrument’s log exposure axis is defined by the wedge’s densities. Using the instrument to measure the wedge measures the film’s response and the wedge’s densities together, in one product, with no way to separate them.

Breaking the circle takes an independent density measurement of the wedge itself — a densitometer, which is Part XV, and which will in turn have been calibrated against a reference of its own. The chain either ends at a calibrated artefact or it does not end.

There is one thing you can do today that is not circular, and it is worth doing. Read the wedge on a lux meter, step by step, as Part XIII’s lux-meter densitometry does, and compare the differences between neighbouring steps with the nominal 0.15. That will not give you accurate densities — the meter’s floor at the dense end is far too high — but it will find a grossly wrong step, a scratch or a fingerprint, which is a different and useful question.

And one honest gap. Stouffer name the reference material and the densitometer standard, but this course has found no statement from them of the measuring aperture or the status condition under which the calibrated readings are taken. ISO 5-2, cited by number, is the standard that specifies geometric conditions for transmittance density. A density is not a property of a piece of film alone; it is a property of the film and the geometry it was read in, and a certificate that does not say which is quoting a number without its units.

Part 2 — Repeatability, reproducibility, and the compromise between them

Three strips in one session, three strips on three days. The arithmetic is the same; what differs is what varies.

The repeatability arm, in one sitting. Warm up. Expose three strips at the design exposure, one after another, at a fixed cadence — use the cadence your bench tests showed the lamp is stable at. Develop all three together in one tank with one unexposed control. Nothing at all has changed between them, so whatever spread appears is the instrument’s own noise plus the film’s plus the reading’s.

The reproducibility arm, over three days. Here there is a real design choice and it is worth ten minutes before you cut film.

Two ways to run three days, and what each one confounds

1. 1Design A — expose on three days, develop together — measures instrument reproducibility, with latent-image keeping counted into it
2. 2Design B — expose once, develop on three days — measures processing reproducibility, with latent-image keeping counted into it
3. 3The shared confound — latent-image keeping, which neither design can separate; both figures are therefore upper bounds

Run both. Neither is clean, and the pair brackets the answer from opposite sides.

Say plainly what neither design fixes. Part IX named latent-image keeping as its one unavoidable compromise and mitigated it structurally rather than pretending it away, and the same compromise is here. A strip exposed on Monday and developed on Wednesday is not the same strip as one exposed and developed on Wednesday, and ILFORD’s own instruction for FP4 Plus is to process exposed film as soon as practical. Neither design separates it. What each design does is charge it to a different account: design A charges it to the instrument, design B charges it to the process. Both figures are therefore upper bounds rather than estimates, and the error is in the conservative direction — your instrument is at least as good as the number you get, never worse.

Three mitigations, and they are the same ones Part IX used. Keep the interval short: three days, not three weeks. Keep the strips cold, dark and dry in the tin. And run the reference strip in every tank, from the same archived pre-exposed batch, so drift is measured rather than assumed.

Part 3 — Drift from switch-on

The bench test on the LED page measured the lamp. This measures the instrument, which is not the same thing: between the emitter and the film sit a diffuser that warms, a chamber whose walls warm, and an air column that does both.

From cold, switch on and expose one strip at 0, 10, 30 and 60 minutes, logging the monitor reading with each. Develop the four together with one control. Plot two things against elapsed time: the monitor reading, and the density of one mid-scale step on the film.

What the film can show that the monitor cannot. The monitor watches the lamp; the film sees whatever arrives at the film plane. If those two disagree — a flat monitor trace and a drifting film series — something between them is moving, and the candidates are a diffuser changing with temperature, a mount relaxing, or the module shifting on its spacers. That is a fault the monitor is structurally unable to find, which is exactly why the drift arm is run on film as well.

Part 4 — The absolute scale

Two methods, and neither of them is as good as the arithmetic looks.

🧮Working an absolute log H, and then working what it is worth

The measurement. With the lid off, in a darkened room, put the lux meter’s sensor at the film plane at the centre of the field. Warm up, run a long exposure so the meter settles, and read. Suppose it reads 0.83 lx, and the firmware reports the exposure interval as 0.5004 s.

H₀ = 0.83 × 0.5004 = 0.415 lux-seconds, so log H₀ = −0.382.

Every step follows: step 1 at D 0.05 receives log H = −0.432, step 11 at 1.55 receives −1.932, step 21 at 3.05 receives −3.432. Kodak’s workbook works the identical sum in millilux-seconds and is worth checking your arithmetic against.

The uncertainty, by Part II’s rule. For a quantity built by multiplying, the relative uncertainties add in the worst case:

ΔH/H ≤ ΔE/E + Δt/t

The timing term is nothing: a few hundred microseconds in half a second is 0.0004, or 0.0002 in log H. The whole of the absolute uncertainty is the meter’s, and this is where the page stops. The course has verified no accuracy specification for any consumer lux meter, from a manufacturer or from a standard, so it quotes no number for ΔE/E and the certificate’s absolute line is left blank with its reason written next to it. If your own meter’s data sheet states an accuracy, that figure is yours to use — write down the meter, the specification and where you read it, and the blank becomes a number for your instrument.

The photodiode route, and why it is not a shortcut. A photodiode with a datasheet responsivity looks like a way round the meter, and it is not, for a reason worth understanding rather than memorising. OSRAM specify the BPW34’s spectral sensitivity as 80 nA/lx — but measured under standard illuminant A at 2856 K, a tungsten spectrum, and the same sheet gives the device’s own peak sensitivity at 920 nm, in the infrared, over a range of 420 to 1120 nm. Silicon’s long-wavelength reach is not an accident of one part: Hamamatsu’s technical note puts the threshold at a cut-off wavelength of 1240 divided by the threshold energy, which lands silicon well beyond the visible. Texas Instruments quote the OPT101 at 0.45 A/W at 650 nm — a radiometric figure at a single wavelength.

None of those three numbers converts a phosphor white LED’s output into lux, because lux is a photopically weighted quantity and none of these detectors is photopically weighted. Without a photopic correction filter, a photodiode measures a number proportional to the light for as long as the spectrum does not change — which makes it an excellent relative instrument and the right choice for the monitor, the uniformity map and the drift series, and the wrong one for an absolute lux figure. Cree publish a chart of relative chromaticity against current and temperature; its existence is the evidence that the spectrum is not fixed, which is why the drift arm reads the film as well.

And the mismatch that no meter fixes. A lux meter weights wavelengths by the human photopic response; a panchromatic film weights them by its own sensitivity, published by ILFORD as a wedge spectrogram to tungsten light at 2850 K. A white LED is neither of those. The course applies no correction for this and states none, which is why every speed figure this instrument yields is quoted under the course’s own criterion, modelled on ISO 6 and never called an ISO speed.

Part 5 — The cross-check against the enlarger

Expose one strip in the sensitometer and one under the enlarger by Part XIII’s method, from the same emulsion batch, and develop both in the same tank with one control. Plot both curves on the same axes against relative log H.

Predict the offset before you look. ILFORD state that exposures of one second or less need no reciprocity compensation and give the correction above that as metered time raised to a film-specific power — 1.26 for FP4 Plus, 1.31 for HP5 Plus. The sensitometer’s 0.5 s exposure needs no correction at all. The enlarger’s does.

🧮What reciprocity alone predicts for the offset

For an enlarger exposure of 8 s on FP4 Plus, the loss in log exposure is

(P − 1) × log₁₀(t) = (1.26 − 1) × log₁₀(8) = 0.26 × 0.903 = 0.235 log H

which is more than one and a half nominal wedge steps, and about ten times the instrument’s whole relative error budget. On HP5 Plus at the same 8 s the figure is 0.31 × 0.903 = 0.280 log H.

So the enlarger strip should sit to the right of the sensitometer strip — needing more exposure for the same density — by roughly that much, before anything else is considered. The other terms all push in directions you can name: a tungsten enlarger and a phosphor white LED are different illuminants for a panchromatic film, the enlarger’s uniformity was measured at about a fifth of a step in Part XIII’s own procedure, and the two exposures were metered by different means.

If your measured offset is close to the prediction, you have learned something real about both instruments. If it is far away, the difference is the thing to chase, and the first suspect is the absolute scale of whichever exposure you metered least carefully.

Expected observations

The three same-session strips should be difficult to tell apart by eye, and the difficulty is the result. A visible difference between two strips exposed three minutes apart at the same setting means the instrument is not yet an instrument, and the drift arm and the light-leak test are where to look.

The three-day strips should be slightly worse, and the gap between the two spreads is the interesting number: it is everything that changes when a day passes, with latent-image keeping counted in.

The drift series should show a shape rather than a number — a change over the first minutes that flattens — resembling the warm-up curve the LED page measured, translated onto film. If the film’s drift is larger than the monitor’s, something between lamp and film is moving.

The two cross-check curves should have the same shape and different positions: the same film in the same developer, offset for the reasons predicted above. A difference in shape is a finding rather than a nuisance. ILFORD note that contrast can rise on long exposures, so a steeper enlarger curve is expected; and a difference at the toe alone points at reciprocity failure falling unequally along the wedge, because the dense end of a 3.0 wedge receives a thousandth of the illuminance the clear end does.

A benchmark worth keeping in view. Hurter and Driffield, working with a standard candle at one metre and a chronograph watch, obtained 0.750, 0.730 and 0.720 on three separate days, and 0.490, 0.490, 0.500 and 0.480 from four different candles. That is the standard the whole science was built on: an instrument that beats it comfortably is doing real work, and one that does not has a fault today’s session is designed to find.

What is happening chemically

Everything above treats the film as a measuring instrument, and it is a chemical one, which is why processing variation arrives dressed as instrument noise.

A density on a strip is the mass of silver reduced per unit area, and that depends on two things you are trying to keep apart: how much light arrived, which is what you are measuring, and how far development was allowed to go, which you are trying to hold constant. Part VIII’s development kinetics owns the mechanism and this page does not re-derive it; the consequence is what matters here. Development is a rate process, so anything that changes the rate — temperature, agitation, the age of the developer, the bromide released by the film already in the tank — moves every density on the strip, and moves the densities in the middle of the curve most, because that is where the gradient is steepest.

Read one number for scale. Part II worked it from ILFORD’s published time-temperature chart: a 1 °C temperature error is worth about 9 per cent of development time. Kodak’s process-control literature is stricter still and asks for ±0.3 °C in the developer. Against that, a timing error of a few per cent is small and an exposure error of 0.02 log H is smaller.

So the two controls do different chemical jobs and neither substitutes for the other. The unexposed control strip fixes base plus fog for that particular development, which is the floor every density is measured above and which moves with the developer’s age and the film’s storage. The reference strip fixes the development level, because it is a known exposure carried unchanged from tank to tank: if the reference has moved, the developer has moved, and every other strip in that tank is quoted relative to a different zero.

That is the mechanism behind a sentence that is otherwise just good advice. Processing is not in the instrument’s error budget at all — it is a density error, not an exposure error — and the control strip is what keeps it out.

Data to record

Everything below goes in the lab notebook, with the curve work on the curve-plotting sheets and the instrument’s own line in the calibration records.

Per session. Date and time; room temperature; the instrument’s serial; the module’s firmware version and drive current; warm-up time given; the wedge’s serial and whether it is calibrated; the film’s emulsion batch; every solution’s dilution, temperature at start, middle and end, and the agitation script in words.

Per exposure. Strip number; requested interval; the firmware’s measured_us; the monitor mean and its spread; the minutes since switch-on; and anything unusual, written at the time.

Per strip, after processing. Base plus fog from the control; the density of every step by whichever reading method, with the method named; and the reading floor you measured for that method that day, by reading one dense step five times and taking the spread.

The one derived quantity to compute at the bench, because it is the number the rest of the page turns on:

Δ log H = Δ D ÷ G

Turning a density difference between two strips into a log exposure difference

ΔD is the density difference between the two strips at the same step, and G is the local gradient of the characteristic curve there — the slope of density against log exposure, read off your own plot from Part XIII. Dividing is not optional and it is where most of the mistakes on this page live: on a straight-line section with G = 0.60, a density difference of 0.03 is 0.05 log H, which is a third of a wedge step, and the same 0.03 out on the shoulder where G = 0.15 is 0.20 log H, which is more than a whole step. A density difference means nothing until it is divided by the slope where it was measured.

Analysis

Four numbers, then a budget, then a certificate.

1. Repeatability. At each of five well-spread steps, take the three same-session densities, compute the mean and the standard deviation, and convert the standard deviation to log H with the local gradient.

Step	D strip 1	D strip 2	D strip 3	Mean	s (density)	G here	s (log H)
4
8
11
14
17

Then quote the straight-line figure, not the largest one, and the plot below is why. The density spread is roughly the same at every step, because it comes from the reading method and from the process. The log exposure spread is that number divided by the local gradient, so it balloons wherever the curve is flat — at the shoulder, where the clear steps have run into maximum density, and much worse at the toe, where the dense steps are barely above base plus fog. A repeatability of 0.6 log H read off step 20, where the gradient has fallen to about 0.04, is not a statement about the instrument at all; it is a statement about the film’s toe. Record the toe and shoulder figures, because they tell you which steps are worth reading, and put the straight-line figure on the certificate.

The same density spread, converted to log exposure at every step

• Spread in density, s(D)
• Same spread as log H, s(D) ÷ G

Show the numbers behind this plot

Two traces plotted against wedge step number from 2 to 20. The first, the spread in density between three identically exposed strips, is a nearly flat line at about 0.025 across the whole range, because it comes from the reading method and from the processing rather than from where on the curve the step falls. The second, the same spread converted to log exposure by dividing by the local gradient of the characteristic curve, is a deep U: it is high at step 2, about 0.17, because the clear steps sit on the shoulder where the curve is flat; it falls to a broad minimum of about 0.04 between steps 8 and 14, which is the straight-line portion where the gradient is around 0.6; and it then rises steeply, reaching about 0.08 at step 16 and 0.21 at step 18, because the dense steps sit on the toe where a large change in exposure produces almost no change in density; step 20 is left off the drawing because at a gradient of about 0.04 it lands near 0.63 and would flatten everything else. Two guide lines mark the 0.02 log H design target and the 0.15 of a nominal wedge step. The drawing's point is that the instrument's repeatability must be quoted from the flat bottom of the U, and that a figure taken from either end describes the film's curve rather than the instrument.

Series	Wedge step (1 is the clear end, 21 the dense end)	Spread between three identical strips
Spread in density, s(D)	2.00	0.03
Spread in density, s(D)	4.00	0.03
Spread in density, s(D)	6.00	0.02
Spread in density, s(D)	8.00	0.03
Spread in density, s(D)	10.00	0.03
Spread in density, s(D)	12.00	0.03
Spread in density, s(D)	14.00	0.03
Spread in density, s(D)	16.00	0.02
Spread in density, s(D)	18.00	0.03
Same spread as log H, s(D) ÷ G	2.00	0.17
Same spread as log H, s(D) ÷ G	4.00	0.07
Same spread as log H, s(D) ÷ G	6.00	0.04
Same spread as log H, s(D) ÷ G	8.00	0.04
Same spread as log H, s(D) ÷ G	10.00	0.04
Same spread as log H, s(D) ÷ G	12.00	0.04
Same spread as log H, s(D) ÷ G	14.00	0.05
Same spread as log H, s(D) ÷ G	16.00	0.08
Same spread as log H, s(D) ÷ G	18.00	0.21

Drawn on an assumed constant density spread of 0.025 and a plausible gradient profile, to show the shape of the conversion; it is not a measurement of any instrument. What is real in it is that the two traces have completely different shapes, and that only one of them is about the box. The curve is drawn to show the shape, not measured from a real material. Your own materials will differ, and measuring them is what the sensitometry part of the course is for.

2. Reproducibility. The same table for the three-day strips, in both designs if you ran both. Report the two figures separately and never average them: they are answers to different questions.

3. Drift. Plot monitor reading and mid-scale density against minutes from switch-on. Report the excursion over the first 10 minutes, the residual slope after settling per 10 minutes, and both in log H. Then write your warm-up rule as a sentence, because that sentence goes on the certificate.

4. The cross-check. The offset between the two curves at the criterion density, in log H, beside the reciprocity prediction, with the residual named.

The error budget

This is the deliverable. Every term identified, every one sized, the two axes kept apart, and a stated rule for combining them.

!The budget has two axes and mixing them is the classic mistake

Log exposure terms are errors in where a step sits on the horizontal axis: the wedge, uniformity, drift, timing. They are properties of the instrument.

Density terms are errors in where a point sits on the vertical axis: processing variation, the reading method’s floor, base-plus-fog uncertainty. They are properties of the process and of your densitometry.

A density term can be converted into a log exposure term by dividing by the gradient, and sometimes that is the right thing to do — but only deliberately, and only with the gradient written down beside it. Adding a density and a log exposure because both are “about 0.02” is how a budget becomes fiction.

Term	Axis	How you sized it	Systematic or random	Your figure
Wedge step values	log H	Certificate, if calibrated; otherwise unquantified	Systematic, and common to every strip, so it cancels in a comparison and dominates any absolute claim
Uniformity across the wedge	log H	The map on the enclosure page	Systematic for a fixed geometry; it distorts the shape of the curve rather than shifting it
Lamp and instrument drift	log H	The drift arm above, expressed as log H	Random between sessions if the warm-up rule is followed; systematic if it is not
Timing	log H	The firmware’s measured_us spread over ten exposures	Random, and negligible
Contact and film flatness	log H	Bound it: expose one strip with the glass and one without	Random, and unmeasured until you measure it
Illuminance measurement	log H, absolute only	The meter’s own specification, if it has one you have read	Systematic
Spectral mismatch	log H, absolute only	No correction exists that this course can apply	Systematic, and unquantified
Processing variation	density	The reference strip’s movement between tanks	Random between sessions
Reading floor	density	Five readings of one dense step, spread	Random

Combine the log exposure terms by Part II’s rule: in the worst case the relative uncertainties add, and in log exposure — where multiplying becomes adding — that means the terms simply add. Report the relative figure (uniformity, drift, timing, contact) and the absolute figure (all of those plus the wedge and the illuminance terms) as two separate numbers, because the relative one is what a developer comparison uses and the absolute one is what a speed claim uses.

🧮A worked budget, on numbers that are not yours

Take a wedge uncertainty of 0.02, uniformity of 0.015, timing of 0.002 and drift of 0.01, all in log H.

Part II’s bound: 0.02 + 0.015 + 0.002 + 0.01 = 0.047 log H, which is about a third of a nominal wedge step.

What a metrology text would do: combine independent terms in quadrature, the root of the sum of the squares, giving √(0.0004 + 0.000225 + 0.000004 + 0.0001) = 0.027 log H. That is the more realistic number when the terms really are independent, and it is nearly half the bound.

Which the course quotes, and why. The bound. Part II ruled for it on the grounds that it is arithmetic anyone can check and that a proper treatment of how independent uncertainties combine belongs to a metrology text this course has not read. That ruling stands, and this page does not quietly overturn it: name the root-sum-square figure if you want to, say which rule produced it, and never present the smaller number without the label. The gap between 0.047 and 0.027 is not a rounding difference; it is a statement about whether your terms are independent, and you have not shown that they are.

Which term to attack first. The wedge, at 0.02, and it is the only one on the list you cannot improve by building anything: it is bought. After that, uniformity at 0.015, which is geometry and free. Drift at 0.01 is a warm-up rule, which costs ten minutes a session. Timing at 0.002 is already a hundredth of the total and no amount of work on it will move the answer — which is the point of writing a budget rather than optimising whatever is nearest to hand.

The same budget drawn twice: what each term contributes, and what remains after the obvious fix

• Uncalibrated wedge: 0.020, 0.035, 0.045, 0.047
• Calibrated wedge: 0.002, 0.017, 0.027, 0.029

Show the numbers behind this plot

Two step-shaped cumulative traces against a horizontal axis of four budget terms taken in decreasing order of size: wedge, uniformity, drift and timing. The upper trace, labelled uncalibrated wedge, starts at 0.020 for the wedge term, rises to 0.035 when uniformity is added, to 0.045 when drift is added and to 0.047 when timing is added, ending just under a third of a nominal wedge step. The lower trace, labelled calibrated wedge, starts at 0.002 because the wedge's certificate replaces the manufacturing tolerance with a measured value, rises to 0.017 with uniformity, to 0.027 with drift and to 0.029 with timing. The gap between the two traces is almost entirely established at the first step and never closes, which is the drawing's point: the single largest decision in the budget is made at the moment the wedge is bought, before any construction begins.

Series	Contribution to the log exposure uncertainty	Cumulative total, log H
Uncalibrated wedge: 0.020, 0.035, 0.045, 0.047	1.00	0.020
Uncalibrated wedge: 0.020, 0.035, 0.045, 0.047	2.00	0.035
Uncalibrated wedge: 0.020, 0.035, 0.045, 0.047	3.00	0.045
Uncalibrated wedge: 0.020, 0.035, 0.045, 0.047	4.00	0.047
Calibrated wedge: 0.002, 0.017, 0.027, 0.029	1.00	0.002
Calibrated wedge: 0.002, 0.017, 0.027, 0.029	2.00	0.017
Calibrated wedge: 0.002, 0.017, 0.027, 0.029	3.00	0.027
Calibrated wedge: 0.002, 0.017, 0.027, 0.029	4.00	0.029

Illustrative arithmetic on the worked figures above, not a measurement of any instrument: the axis positions 1 to 4 are the four terms in order. What is real in it is the shape — the first term sets the total, and the last one cannot change it. The curve is drawn to show the shape, not measured from a real material. Your own materials will differ, and measuring them is what the sensitometry part of the course is for.

The instrument certificate

One page. It is the deliverable of this whole part, and every later page that quotes a number from this instrument cites it.

Field	What goes in it
Instrument and serial	The name you gave it and its number, from the build record
Date of calibration, and by whom	And the date the next one is due
Wedge	Serial number; calibrated or not; if calibrated, the certificate’s own reference
Exposure	Design interval, drive current, firmware version
Warm-up rule	In a sentence, from your own drift curve
Relative log H uncertainty	The figure, the terms in it, and the rule used to combine them
Absolute log H uncertainty	The figure or an honest blank, with the reason written in
Uniformity	Worst deviation across the film area, in log H, and the date of the map
Repeatability	Standard deviation in log H, same session, and how many strips it came from
Reproducibility	The same across three days, and which design produced it
Illuminant	“Phosphor white LED, spectrum not measured”; no colour temperature is claimed
Speed convention	“Measured under the criterion defined in Part XIII, modelled on ISO 6.” Never “ISO speed”
Known limitations	The uncalibrated wedge if that is what you have; the unread meter specification; the spectral mismatch; anything dropped, such as the cross-check
Signature and notebook page	So the certificate points back at the raw data

✕The four claims a certificate must not make

“Accurate to 0.02 log H.” Accuracy and repeatability are different words. Part II keeps them apart and so must this: a repeatable instrument with a wrong wedge is precisely wrong every time.

“ISO 400.” Ruling 3.1 of the course’s open questions settled this: the standards are cited by number and never quoted, and every derived figure is the course’s own measurement under the course’s own criterion.

“Calibrated against a lux meter.” Unless you have read and recorded the meter’s own accuracy specification, that sentence names an instrument rather than a measurement.

“Traceable.” Traceability is an unbroken chain of comparisons, each with a stated uncertainty, ending at a national standard. A calibrated wedge gives you one link of it and the certificate should say exactly that much and no more.

Troubleshooting

What you see	Likely cause	What to do
The three same-session strips differ visibly	Drift, because the warm-up was short or the cadence was too quick; or a light leak that varies with what is happening in the room	Look at the logged monitor readings first — they will show drift and will not show a leak. If the monitor is flat and the film is not, re-run the enclosure page’s fog test with the room lit as it was
Day-to-day spread is enormous compared with the same-session spread	Processing, almost always — temperature, a different agitation, a developer a week older	Read the reference strip. If it moved, the developer moved, and the instrument is not implicated at all
The reference strip has moved but the working strips have not	Something specific to the reference: a mislabelled strip, a different part of the batch, or a strip from an older exposure session	Check the labelling before you conclude anything. This is the failure that most often ends a session with two hours of unusable data
Drift on film but not on the monitor	Something between the emitter and the film plane is moving: the diffuser, its ledge, or the module on its spacers	Repeat with the monitor moved above the diffuser if the lead reaches. A monitor that watches the panel rather than the lamp finds this class of fault
The absolute log H is implausible by a factor of ten	Almost always a units error — millilux for lux, or a meter left on a ×10 range	Work Kodak’s own published example through your own arithmetic; it exists to be checked against
The cross-check offset is much larger than the reciprocity prediction	The enlarger exposure was longer than you recorded, the head height changed, or the two exposures were metered by different means and one is wrong	Re-run the enlarger strip with the time logged at the moment of exposure. Reciprocity error grows fast with time, so a 16 s exposure recorded as 8 s doubles the discrepancy
The cross-check offset is close to zero	Suspect it. Two independent light sources agreeing to better than a wedge step is a result, but so is a strip that was exposed twice in the same instrument	Check the labels, then repeat with the two strips exposed in the opposite order
Every step reads low at one end of every strip	The uniformity map, showing up on film exactly as it should	Nothing is wrong with the session. This is the instrument’s systematic term and it belongs in the budget, not in the troubleshooting

Clean-up

Solutions to their labelled waste containers, never combined. Rinse the tank and reels and leave them to dry completely: ILFORD are firm that a spiral must be dry before the next loading, and a damp reel is what turns a fifteen-minute loading into a ruined strip. Wipe the wedge with a clean dry lens cloth, never a solvent, and put it back in its sleeve. Wash your hands before touching the notebook. Close the laboratory to the SOP.

Storage

The wedge goes back in its own sleeve, flat, away from heat. It is now the most precisely known object in your darkroom and it is a piece of film.

The strips go into labelled sleeves with a card slip carrying the batch, the strip number, the arm, the exposure and the processing — the eight-line slip Part IX’s lab specified. Part XXVII will re-read these strips on a densitometer, and a strip that cannot be identified in six months was never made.

The reproducibility arm’s exposed, undeveloped strips go in the light-tight tin, cool and dry, and the tin is labelled with the exposure date. This is where the compromise named in part 2 lives, and the label is the only reason it can be quantified later.

The certificate goes in the notebook and a copy in the calibration records. Both, because one of them will be lost.

Disposal considerations

The three streams are the ones every processing page in this course produces: alkaline developer carrying the developing agents almost unconsumed; silver-bearing fixer and its first rinse; and rinse water. The chemistry and the general practice are on the disposal page and the silver stream’s handling is in its SOP.

Local regulation governs what may lawfully be done with any of them, and it differs by jurisdiction — check your local regulations. The course describes the chemistry and the general practice and gives no jurisdiction-specific instruction as though it were universal.

Questions

1. Two strips differ by 0.04 in density at step 6, where your own plot gives a local gradient of 0.55, and by 0.04 at step 18, where the gradient is 0.12. Express both as log exposure differences, and say which one you would report as the instrument’s repeatability and why.
2. Your budget has uniformity at 0.018, drift at 0.006, timing at 0.0002 and an uncalibrated wedge. Compute the relative figure by Part II’s bound. Then say, in one sentence each, what the absolute figure is and why the page will not let you write it down.
3. A reader proposes checking the wedge by exposing a strip in the sensitometer and reading the densities. Explain the circularity in terms of what is being multiplied by what, and name the one measurement that would break it.
4. Design A gives a three-day reproducibility of 0.031 log H and design B gives 0.026. Explain why neither figure is the instrument’s reproducibility, say which direction each is biased, and state what you would put on the certificate.
5. Your drift series shows the film density falling for the first eight minutes and then flat, while the monitor is flat throughout. Give two physical explanations, and design the one further exposure that would distinguish them.
6. A certificate you are shown states: “Relative log H uncertainty 0.02, absolute 0.05, traceable to NIST, ISO 400 measured on FP4 Plus.” Identify every claim it cannot support, and say what the honest version of each line would be.

Further experiments

Measure the contact term you had to bound. Expose three strips with the cover glass and three without, developing all six together, and compare the sharpness of the step edges and the densities at the middle of each step. That term sits in the budget above with no number against it, and this is the afternoon that puts one there.

Run the wedge end for end. Expose two strips with the wedge the usual way round and two with it reversed, then compare. Any systematic difference between them contains both the uniformity gradient and any asymmetry in the wedge itself — and the two can be separated by turning the box around in the room instead and repeating.

Calibrate the reading methods against each other. Read one strip by lux-meter densitometry, by spot meter and by visual matching, and plot the three against each other step by step. The scatter is your reading floor, method by method, and it is the number that decides how small a difference you are entitled to report before Part XV exists.

Repeat the whole calibration in six months. A calibration is a statement about a date. Run the same three arms on the same instrument half a year later, with a strip from the original film batch if any remains, and see whether the certificate still describes the box. That comparison is the only thing that turns a certificate into a habit, and the review date is on the certificate for exactly this reason.

Check your understanding

Question 1. Two strips, exposed identically and developed together, differ by 0.030 in density at a step where your own plot gives a local gradient of 0.60. What is the difference in log exposure, and how does it compare with a nominal wedge step?

• 0.018 log H, about an eighth of a step
• 0.050 log H, about a third of a step
• 0.030 log H, about a fifth of a step
• It cannot be converted without knowing the absolute scale

Show the answer and why

Answer: 0.050 log H, about a third of a step

Δ log H = ΔD ÷ G = 0.030 ÷ 0.60 = 0.050, and a nominal step is 0.15, so it is a third of a step. Option 3 is the mistake this page exists to prevent: reading a density difference as though it were an exposure difference. Option 1 multiplies by the gradient instead of dividing. Option 4 confuses the two axes — the conversion needs the local slope, which is a property of the curve you already have, and needs nothing about where the horizontal axis has its zero.

Question 2. A budget carries a wedge term of 0.02, uniformity 0.015, timing 0.002 and drift 0.01, all in log H. What does the course quote as the combined relative uncertainty, and why not the smaller figure?

• 0.027 log H, the root of the sum of the squares, because the terms are independent
• 0.047 log H, the bound, because Part II ruled for arithmetic anyone can check and the course has read no metrology text
• 0.02 log H, the largest term, because errors do not add
• 0.0115 log H, the mean of the four terms

Show the answer and why

Answer: 0.047 log H, the bound, because Part II ruled for arithmetic anyone can check and the course has read no metrology text

The bound is 0.02 + 0.015 + 0.002 + 0.01 = 0.047 and it is what Part II tells this course to quote. The quadrature figure really is 0.027 and it really is more realistic when the terms are genuinely independent — but independence is a claim you have not demonstrated, and the smaller number should never appear without the label saying which rule produced it. Option 3 describes a world in which only one thing can go wrong at a time; option 4 is not a rule at all. Note also which term to attack: the wedge, at 0.02, which is bought rather than built.

Question 3. A strip is exposed under an enlarger for 8 s on FP4 Plus, for which ILFORD publish a reciprocity power of 1.26. Roughly how far should its curve sit from a 0.5 s sensitometer curve on the same film, from reciprocity alone, and in which direction?

• About 0.03 log H, with the enlarger strip needing less exposure
• About 0.235 log H, with the enlarger strip needing more exposure
• About 1.2 log H, with the enlarger strip needing more exposure
• There should be no offset, because both strips received the same total exposure

Show the answer and why

Answer: About 0.235 log H, with the enlarger strip needing more exposure

(P − 1) × log₁₀(t) = 0.26 × 0.903 = 0.235 log H, and the loss is a loss of speed, so the enlarger strip needs more exposure to reach the same density and its curve sits to the right. That is more than one and a half nominal wedge steps and about ten times the instrument's whole relative budget, which is why the design lesson put the sensitometer's exposure at half a second in the first place. ILFORD state that exposures of one second or less need no compensation, so the sensitometer strip contributes nothing to the offset. Option 4 is the reciprocity law itself, which is what fails here.

Question 4. Why is a BPW34 photodiode an excellent choice for the uniformity map and the drift series, and a poor one for the absolute scale?

• Because it is not sensitive enough for an absolute reading but is stable enough for a relative one
• Because it is not photopically weighted — its peak is at 920 nm and its stated 80 nA/lx is quoted under a tungsten illuminant — so it tracks changes in one fixed spectrum faithfully but cannot convert a white LED's output into lux
• Because its response is non-linear at low light levels, which averages out across a map
• Because a lux meter has a wider acceptance angle and therefore samples the field better

Show the answer and why

Answer: Because it is not photopically weighted — its peak is at 920 nm and its stated 80 nA/lx is quoted under a tungsten illuminant — so it tracks changes in one fixed spectrum faithfully but cannot convert a white LED's output into lux

A silicon photodiode responds to a band that reaches well past the visible — OSRAM give 420 to 1120 nm with a peak at 920 nm — while lux is a photopically weighted quantity defined on the human response. The 80 nA/lx figure is a conversion valid for the illuminant it was measured under, standard light A at 2856 K, and a phosphor white LED is not that. For a relative measurement none of this matters: the same detector, looking at the same unchanged spectrum, reports a faithful ratio, which is exactly what a uniformity map and a drift series need. Option 1 has it backwards — the device is sensitive enough and the problem is spectral, not photometric magnitude.

Question 5. Your three-day reproducibility comes out at 0.031 log H using design A: expose one strip a day, develop all three together. What has been counted into that figure that does not belong to the instrument?

• Processing variation, because three days of developer ageing are included
• Latent-image keeping, of up to two days, because the day-one strip waited while the day-three strip did not
• Nothing; design A isolates the instrument cleanly
• The wedge's step uncertainty, which changes from day to day

Show the answer and why

Answer: Latent-image keeping, of up to two days, because the day-one strip waited while the day-three strip did not

Design A holds the processing constant by putting all three strips in one tank, which is what it was for, so option 1 is excluded by construction. What it cannot hold constant is how long each latent image waited: two days for the first strip, none for the last. Part IX named that compromise and mitigated it structurally rather than pretending it away, and the same applies here. The figure is therefore an upper bound on the instrument's reproducibility — the error runs in the conservative direction, so your instrument is at least as good as 0.031 and possibly better. Option 4 misreads the wedge term, which is systematic and identical on all three strips and therefore cancels entirely in a comparison between them.

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