Experimental Design for the Darkroom

You are about to run a series of tests in which the answer you want is worth about eight per cent, and your reading error is worth about seven. That is the real situation in a home darkroom without a densitometer, and no amount of care with the chemistry rescues an experiment whose design does not account for it.

This page is the design. It settles what a hypothesis has to say to be testable, what must be held still while one thing moves, how many strips to spend and on which cells, how to get a number out of a strip of film with nothing but a lightbox and a flatbed scanner, and — the part most readers skip — how to write it down so it is still evidence next year.

The shape of an experiment, in seven parts

Every experiment page in this course carries the same skeleton, and it is worth naming the bones before the flesh goes on.

1. The hypothesis. A statement that could turn out to be false, about a direction and if possible a magnitude. “Bromide affects development” is not a hypothesis; it forbids nothing. “Adding 1 g/L of potassium bromide to D-76 moves the threshold step by at least two steps and lowers base plus fog” is one, because a strip can contradict it.
2. The prediction. What you expect to see, in the units you will actually read. The hypothesis is about the world; the prediction is about your strips. Writing it down before you develop anything is the single cheapest guard against reading your expectations into the result.
3. The control. The unchanged comparison. Not a good result, not a reference from a datasheet — a strip from the same film, the same exposure and the same session that differs from the test strip in exactly the thing you changed.
4. The procedure. Written before the session, in the order it will happen, with the quantities on the page rather than in your head. If it cannot be followed by somebody else it cannot be repeated, and an unrepeatable result is an anecdote.
5. The observations. What you saw, including the things you were not looking for. A tank knocked, a thermometer that drifted, a strip dropped.
6. The data. The numbers, in a table drawn before the session and filled in during it.
7. The interpretation, and then the conclusion. These are separate on purpose. The interpretation says what the mechanism from Part VIII predicts and whether the data agree; the conclusion says what you now believe and — this is the useful half — what you would have to do to be wrong.

📓One variable at a time, and what that costs

Two changes in one session buy you nothing but a question. If you raise the pH and add bromide and the contrast rises, you have learned that the pair of them raises contrast, which you already believed, and you cannot say what either did alone or whether one partly cancelled the other.

The discipline is cheap to state and expensive to keep, because holding a variable still is work. Every experiment in this part spends most of its procedure not on the variable but on the eleven things that are not allowed to move.

The dozen inputs, and how each one is held still

Development is not a single-input process. Here is what is actually acting on the density of a strip, what each one is worth, and what holds it.

Where variation enters a test strip, and what stops it

1. 1Exposure — lamp, warm-up, distance, timing, film flatness — held by one shared exposure batch
2. 2Developer — formula, batch, age, volume per strip — held by one mix, one version number, one-shot use
3. 3Temperature — water bath; Kodak states that more than 0.3 °C of drift affects process control
4. 4Time and agitation — one clock convention, one agitation script; continuous agitation is worth about 15 per cent of the time
5. 5Stop and fix — fresh baths, separate vessels, separate tongs — fixer in developer is a named process failure
6. 6Wash and dry — all strips together, the same way; density is read dry

Only one box in this chain is allowed to differ between the strips of an experiment, and which one it is changes from page to page. Everything else is procedure.

Read that list of magnitudes and one thing should be uncomfortable: the errors are the same size as the effects. Fifteen per cent of development time, which is what a casual change of agitation is worth, is more than the difference between two adjacent development times in the worked example below. This is not a reason to give up. It is the reason the procedure sections in this part are long.

The two variables nobody lists

Latent image keeping. A strip exposed today and developed in three weeks is not the same strip as one developed this evening. That is why every session in this part develops a shared reference strip from the same exposure batch under the same standard condition: the reference measures drift instead of assuming it away.

Your own eyes. They adapt, they tire, and they are extremely good at finding what you told them to look for. Both are dealt with below.

The sample: a step-wedge contact strip

The standard sample of this part is a strip of film about 135 mm long, exposed by contact through a 21-step transmission wedge under a fixed lamp. A Stouffer T2115 carries 21 steps at a nominal 0.15 density increment to a maximum of 3.05, on a piece 12.7 × 127 mm. Three facts follow, and all three matter.

One strip is a whole exposure series. Twenty steps of 0.15 is 3.00 log units of exposure — ten stops — recorded on one piece of film in one instant. Everything that would otherwise vary between frames of a bracketed series is identical across the steps of one strip, because they were made at once. That is why the strip and not the frame is the unit of evidence.

A step is 0.15 log units, so two steps are exactly one stop. That single equivalence does most of the arithmetic in this part.

E₂ / E₁ = 10^(0.15 n)

Changing the exposure by a known number of steps

E₁ and E₂ are the exposures before and after, and n is the number of wedge steps you want the threshold to move. For n = 2, the factor is 10^0.30 = 2.00, one stop. For n = 1, it is 1.41, half a stop. If a pilot strip puts the threshold three steps away from where you want it, multiply the exposure time by 10^0.45 = 2.8 — provided the exposure is short enough that the reciprocity law still holds, which ILFORD gives as one second or less, and provided nothing else changed.

A nominal increment is not a calibration. Stouffer states that its calibrated parts, the T2120CC and T1530CC, are the ones measured against NIST Standard Reference Material 38120C on a densitometer conforming to ANSI PH2.19-1986. An ordinary T2115 is manufactured to the increment, not certified to it. Everything this part computes from 0.15 is therefore relative, and the course says so every time rather than quietly forgetting.

A test strip, and everything on it that is not the picture

1. 1Datum notch — one square cut at the head, so head, tail and emulsion side are readable by touch in the dark
2. 2Identity nips — a count of one to five along the top edge — the strip’s cell within this session
3. 3Steps 1 to 21 — step 1 is the clearest wedge step and so the densest film; nominal 0.15 log units apart
4. 4Masked patch — covered during exposure: base plus fog for this strip in this developer
5. 5Threshold step — first step distinguishable from the masked patch — a speed reading
6. 6Last separable step — where further exposure stops adding visible density — the shoulder

The masked patch is the reason each strip carries its own floor. A base-plus-fog figure borrowed from another strip, or from a datasheet, would import that strip's developer into this one's reading.

Reading a strip without a densitometer

Three readings, in increasing order of what they cost and what they buy.

The threshold step, which is a speed reading

Lay the strip on an evenly lit box, cover everything but the clear end, and find the first step you can tell apart from the masked patch. That step number is the threshold.

This is the oldest quantitative reading in photography and it is quantitative for a reason Hurter and Driffield gave in the 1890s. Having first defined the inertia of a plate by a density high up the curve, they changed their minds and came to regard it as “the smallest exposure necessary to produce the slightest deposit on the plate representing the deepest shadow of the original” — and the reason they give is the useful part: very slight deposits are little altered by continued development. Kodak’s sensitometry workbook says the same thing from the other end a century later, observing of a family of curves at three development times that most of the change is in the straight line and the shoulder and that the toe remains basically the same.

So the threshold step is nearly independent of how long you developed, which makes it a reading about speed and not about contrast. Two Tier-1 sources, ninety years apart, agreeing about a foot of a curve is about as solid as this course’s evidence gets.

The step count, which is not quite a contrast reading

Count from the threshold inward to the last step you can distinguish from its neighbour. Call that run the scale length, S, in steps. Multiply by 0.15 and you have the log exposure range the strip resolved.

It is tempting to call a short S “high contrast” and stop there. Be careful. The average gradient over that run is

Ḡ = (D_max − D_min) / (0.15 × S)

Average gradient from a step count

where D_max is the density of the densest separable step, D_min is the masked patch, and S is the scale length in steps. A by-eye reading gives you S and gives you neither density. So a step count converts to a contrast only if you are willing to assume that the two strips you are comparing reached the same maximum density from the same base — which is reasonable for two strips of one film from one exposure batch developed to completion, and unreasonable the moment fog or a shortened development moves either end. Step counting measures the exposure scale. It measures contrast only by assumption, and the assumption has to be stated.

Matching, which does buy a density

Put the strip and the wedge side by side on the lightbox, touching, and find the wedge step whose grey matches a given step of the strip. The wedge step’s nominal density is then that step’s density, and you have converted a position into a number. Do it for four or five steps across the scale and you can plot something that behaves like a characteristic curve.

The glossary is blunt about what this is: visual matching against a calibrated step wedge is the same measurement a densitometer makes, done by eye. Three limits, all of them real.

• The wedge is nominal, not calibrated, unless you bought a CC part. Your densities inherit that.
• You are matching two different greys. The wedge is a manufactured neutral; your strip is developed silver, which scatters as well as absorbs and may not be neutral in colour. The Callier effect is the formal name for the part of this that also troubles real instruments.
• Adjacency is everything. The eye compares well only when two patches touch and are lit alike. Move the wedge away from the strip and the match falls apart.

The flatbed scanner as a rough densitometer

A scanner is a light source, a lens and a detector, which is most of a densitometer, and it is already on the desk. What it is missing is the part that makes a densitometer an instrument: a defined geometry, a defined spectral band, and a calibration.

Use it like this.

1. Turn everything off. Automatic exposure, automatic tone, colour management, sharpening, dust removal, backlight correction. Every one of them is a function applied to your data that you cannot see and cannot invert.
2. Scan every strip of an experiment in one pass, at one setting, in one session, laid out together. Numbers from two passes are not comparable, and there is no reason to make them be.
3. Put the wedge itself in the scan. This is the important one. The wedge is a ladder of known nominal density steps, so scanning it alongside the strips gives you the scanner’s own transfer function over the range you care about, measured on the day, on that machine.
4. Read a fixed area at the centre of each step, the same size every time — the sampling aperture, which decides whether you get the local grain as noise or an average that may not exist anywhere on the step.
5. Convert to relative density as −log₁₀(V / V₀), where V is the mean code value of the step and V₀ is the mean code value of the clear film base beside it.

!Why those numbers stay relative, and what would fix it

The course has not verified a published figure for the density range or the linearity of any particular flatbed scanner, and manufacturers’ maximum-density claims are not made under a stated standard. So no number in this part is presented as an absolute density.

That is not a dead end. Plot your scanned code values against the wedge’s nominal densities and you have measured your own scanner’s response: where it is straight, where it flattens at the dense end, and how far up the density scale it can still separate two steps. That is a measurement you can make in ten minutes, it is specific to your machine, and it tells you exactly how far to trust the rest of the numbers. Part XIII and Part XIV replace it with an instrument built for the job.

The honest summary is that the scanner is worth having for two things: it separates differences a little finer than the eye does, and it produces a record that can be re-examined after the strip is filed. It is not worth having as a source of density, and every plot in this part that came from one says so in its caption.

How many strips, and where to spend them

Here is the arithmetic that decides the design of every experiment in the part.

Read one strip’s threshold twice, an hour apart, and you will not always get the same step. Call the spread across identically treated strips your resolution limit: the smallest difference you are entitled to call real. It is not a number the course can give you, because it is a fact about your lightbox, your eyes and your rig — which is precisely why the test-negative lab processes a control set of several identically exposed and identically developed strips before anything else happens. Those strips have one job: to measure the floor.

Now the spending decision. Replicating a cell — running three strips in the carbonate developer instead of one — narrows the uncertainty of that cell’s mean as 1/√n, so three strips buy a factor of 1.7. Replicating the control tells you the resolution limit itself, which is the number you apply to every cell in the experiment. The activity-series experiment has seven cells; replicating each three times would need twenty-one strips instead of seven, roughly two extra rolls of film, and an afternoon that does not fit in one session.

So this part spends its replication on the control and runs the cells singly, and it accepts the consequence: a difference smaller than the resolution limit is not reported as a result. That is a design decision with a cost, it is written down here rather than buried, and if your control set comes back with a spread of two steps you should redesign the rig before running anything else.

🧮The uncertainty budget, and why Part II owns it

Part II’s measurement page sets out how uncertainty travels through arithmetic, the difference between accuracy and precision, and why the resolution of a display is not the accuracy of the instrument behind it. None of that is re-derived here.

What this page adds is where the dominant term lies. In this part it is almost never the balance or the graduate: it is the reading. A strip read to ±1 step is read to ±0.15 log units of exposure, a factor of 1.4 — against 0.5 per cent for a 0.01 g error on 2 g of borax and 1 per cent for a 1 ml error on 100 ml of developer. Two orders of magnitude separate them. Knowing which error dominates is the whole point of a budget, and here it says plainly: improve the reading before you improve the weighing.

Reading blind, because you cannot trust yourself

You know which strip is the carbonate one. You expect it to be denser and foggier. You will find it denser and foggier.

The remedy is standard and costs almost nothing.

1. When the strips come off the drying line, an assistant — or you, using a shuffled set of cards — assigns each one a random two-digit number and writes it on the sleeve.
2. The key, which maps random number to cell, goes in a sealed envelope or a closed notebook page.
3. Every reading is made and written down against the random number, with all the strips of the session read in one sitting, in random order, and read against each other rather than from memory.
4. Only when the table is complete is the key opened.

Two honest caveats. Blinding does not work on a strip that is obviously different — a carbonate strip fogged grey to the edges announces itself — and it does not repair a confounded design. It protects the close calls, which is where the arguments are.

The notebook, and the version number on the bottle

A result whose inputs were not written down is not a result. The lab notebook is the instrument this part leans on hardest, and the fields below are the minimum for a strip that Part XXVII will have to read in a year’s time.

Session header. Date and time; who; room temperature; the water supply; the lightbox and the room light you read by; every instrument used, with its last check against a reference.

Exposure batch. Film name, format and emulsion batch number; the tin or cassette; the lamp, its power and its distance; the exposure time; the wedge’s part number; the date of exposure. Every strip in the part refers back to one of these blocks by name.

The developer, by version. Not “D-76” — a formula version, in the style D76-XX-001, tied to a mixing entry that records the actual masses weighed, the volumes made up to, the water, the mixing date, the measured pH with its temperature, and the bottle. Part VIII’s assignment on reading a formula sets the scheme; this part uses it without inventing a second one.

The cell. Which strip, which notch code, which random reading number, what was changed from the base formula and by how much, the volume of solution and the vessel.

The process. Time from immersion to lift; the temperature at start, middle and end; the agitation script in words; the stop; the clearing time and the fixing time; the wash; how it was dried.

The readings. Threshold step, scale length, base-plus-fog description, matched densities if you took them, scanner code values with the scan settings, and — separately — anything you noticed.

The deviations. Everything that went differently from the written procedure. This section is the one that is worth the most and gets written the least.

Worked example: what the eye cannot get to

Everything above is method. This last section is the demonstration, and it uses published data so that nobody has to run it. Two questions are asked of two manufacturers’ own tables.

Contrast against development time

Kodak’s sensitometry workbook prints a family of characteristic curves for an unnamed film in an unnamed developer — it calls them XYZ and A — at 20 °C with intermittent agitation at 30-second intervals, and its answer key gives the contrast index of each. With the extra data the workbook supplies for the reader’s own exercise, six points are published.

Contrast index against development time, from Kodak's published workbook data

• Film XYZ in developer A, 20 °C, intermittent agitation

Show the numbers behind this plot

Six published points rising from left to right and flattening as they go: contrast index 0.51 at 5 minutes, 0.55 at 6, 0.62 at 8, 0.67 at 10, 0.72 at 12 and 0.73 at 13. The rise between consecutive points falls steadily, from 0.040 of contrast index per minute between 5 and 6 minutes, through 0.035 between 6 and 8 and 0.025 between 8 and 10 and again between 10 and 12, to 0.010 between 12 and 13. Two further points are marked, both read off the same curve by Kodak's own answer key rather than by this course: a contrast index of 0.58 is reached at 7 minutes, and a contrast index of 0.70 at 11 minutes. Both fall on the line drawn through the six data points, which is the internal consistency check the page makes. The published range does not extend far enough to show a true plateau; what it shows is the rising limb and the beginning of its flattening.

Series	Development time at 20 °C, minutes	Contrast index
Film XYZ in developer A, 20 °C, intermittent agitation	5.00	0.51
Film XYZ in developer A, 20 °C, intermittent agitation	6.00	0.55
Film XYZ in developer A, 20 °C, intermittent agitation	8.00	0.62
Film XYZ in developer A, 20 °C, intermittent agitation	10.00	0.67
Film XYZ in developer A, 20 °C, intermittent agitation	12.00	0.72
Film XYZ in developer A, 20 °C, intermittent agitation	13.00	0.73

Measured: every point is Kodak's, from the workbook's figure and its answer key. The film and developer are deliberately unnamed in the source, so this curve teaches a shape and describes no material you can buy. The two marked points are the workbook's own read-offs; that they fall on the line drawn through its own data is a check worth making on any source.

Three things to take from it.

It flattens. The slope falls from 0.040 of contrast index per minute at the start to 0.010 at the end — a factor of four across eight minutes. That flattening is the reason a development time can be chosen at all: near the plateau, an error of half a minute costs almost nothing, while down on the rising limb the same half minute is worth several per cent of contrast. The published range stops before a true plateau; what it shows is the rising limb and the beginning of the knee.

It is entered from the vertical axis. The workbook says so: the purpose of the graph is to find the development time for a desired contrast index. You decide what negative you want and read off the time. That is the whole of development-time selection, and it is why the gamma-time curve is the most practical diagram in sensitometry.

Only one thing was varied. The workbook’s own answer to “what four factors affect contrast index” is time, temperature, agitation and developer — and its answer to “which one is being varied here” is time. The family of curves is a single-variable experiment, printed as a teaching example, run by somebody with a densitometer.

The temperature coefficient, from a table nobody calls a coefficient

ILFORD publishes a time-temperature compensation chart. Its 8-minute row reads, at 18, 19, 20, 21, 22, 24, 25 and 27 °C: 9:45, 8:45, 8:00, 7:15, 6:30, 5:30, 5:00 and 4:15.

Take the rate of development to be inversely proportional to the time needed to reach the same result, and normalise to 20 °C.

Temperature	Published time	Time, seconds	Relative rate
18 °C	9:45	585	0.82
19 °C	8:45	525	0.91
20 °C	8:00	480	1.00
21 °C	7:15	435	1.10
22 °C	6:30	390	1.23
24 °C	5:30	330	1.45
25 °C	5:00	300	1.60
27 °C	4:15	255	1.88

The temperature coefficient is conventionally quoted as Q₁₀, the factor by which the rate rises for ten degrees. Take the two ends of the row, which are nine degrees apart and least affected by the chart’s rounding to the nearest fifteen seconds:

Q₁₀ = (1.88 / 0.82)^(10/9) = 2.29^1.11 ≈ 2.5

Q₁₀ from the ends of a published time-temperature row

Now use it to predict a value the chart also contains, which is the only way to find out whether the derivation is worth anything. At 22 °C, two degrees above the reference:

t = 480 s ÷ 2.5^(2/10) = 480 ÷ 1.20 = 400 s = 6 min 40 s

Predicting a development time from the coefficient

ILFORD’s own figure is 6:30. The prediction is 10 seconds long, about 2.5 per cent, on a chart explicitly rounded to the nearest 15 seconds. The derivation survives its own test.

⚗What Q₁₀ ≈ 2.5 is telling you about the chemistry

Part III’s kinetics page owns the relation between rate and temperature and the activation energy behind it, and Part VIII’s development kinetics owns what it means for a developer. Neither is re-derived here.

The one thing worth carrying forward is that the coefficient belongs to that developer, and ILFORD offers the chart as a guide for all film and developer combinations while publishing separate figures elsewhere for its own products. A coefficient derived from one maker’s chart and applied to a metol-sulfite bath you mixed yourself is an extrapolation. Say so in the notebook, and treat the first strip as a datum rather than a correct result — exactly as Part VIII’s mixing lab does for D-23’s development time.

And this is precisely what a step wedge read by eye cannot give you

Both of the results above are slopes of density against log exposure. Look at how Kodak’s contrast index is actually constructed: a straightedge marked 0.0, 0.2 and 2.2, laid on the curve so that the 0.0 mark sits on the minimum-density line and the 0.2 and 2.2 marks both touch the curve, with the slope of that line being the answer. The construction needs the shape of a curve and two density values 2.0 log units apart — which is 13⅓ wedge steps, landing nowhere near a step boundary.

A by-eye reading returns step numbers. It cannot return either density, so it cannot return the slope. And the arithmetic of how close it gets is worth doing once.

Suppose the two strips you are comparing do reach the same maximum density and the same base, so that the scale length S is a fair inverse measure of gradient. A reading repeatable to ±1 step, on a scale length of about 13 steps, is a gradient known to about ±8 per cent. On the published curve above, the difference between 8 minutes and 10 minutes of development — contrast index 0.62 against 0.67 — is also about 8 per cent.

So the effect and the error are the same size. The by-eye method can just about separate a two-minute change in development at eight minutes, on one strip, with nothing to spare, and can separate nothing finer. That is the honest boundary of everything in Part IX, it is why every experiment here reports a resolution limit alongside its results, and it is why every strip is archived rather than thrown away: Part XXVII puts them on a densitometer, and the same strips then answer the question this method could only point at.

Recap

• An experiment is a hypothesis, a prediction, a control, a procedure, observations, data, an interpretation and a conclusion — written in that order, and the prediction written before the development.
• One variable moves; the other eleven are held by procedure, and holding them is most of the work.
• The sample is a step-wedge contact strip. Two steps are one stop. Every strip carries its own masked patch, so base plus fog is measured rather than borrowed.
• The threshold step is a speed reading and is nearly independent of development time; the scale length is an exposure-scale reading and becomes a contrast reading only under a stated assumption; matching against the wedge buys relative densities and inherits the wedge’s nominal calibration.
• A flatbed scanner separates a little more finely than the eye and records what it saw. Scan the wedge with the strips, turn every automatic function off, and call the numbers relative.
• Replication goes on the control, to establish the resolution limit. Differences smaller than that limit are not results.
• Read blind, write everything down, and put a version number on the bottle.

Check your understanding

Question 1. A pilot strip puts the threshold at step 20, and you want it at step 17. By what factor should the exposure time change, and in which direction?

• Multiply by 3, because it is three steps
• Multiply by 10^0.45 ≈ 2.8, giving more exposure
• Divide by 10^0.45 ≈ 2.8, giving less exposure
• Multiply by 1.5, because each step is half a stop

Show the answer and why

Answer: Multiply by 10^0.45 ≈ 2.8, giving more exposure

Each step is 0.15 log units, so three steps are 0.45 log units and the exposure factor is 10 to that power, about 2.8 — a little under one and a half stops. The direction follows from which end of the wedge is which: step 20 is nearly the densest step, so the threshold sitting there means only the very clearest steps put anything on the film, and the film needs more light, not less. The check that catches the sign error is that two steps are exactly one stop, so three steps must be between one and two stops.

Question 2. Why does this part put its replicate strips on the control rather than on the experimental cells?

• Because the control is the most important strip
• Because replicating a cell narrows that cell’s mean as 1/√n, while replicating the control measures the resolution limit that applies to every cell in the experiment — and film and session time are finite
• Because a control must always be run in triplicate
• Because the cells are too variable to replicate usefully

Show the answer and why

Answer: Because replicating a cell narrows that cell’s mean as 1/√n, while replicating the control measures the resolution limit that applies to every cell in the experiment — and film and session time are finite

It is a spending decision with an explicit cost. Three strips per cell would improve each cell’s mean by a factor of 1.7 and would turn a seven-cell experiment into twenty-one strips, about two extra rolls and an afternoon that does not fit. Replicating the control instead yields one number — the spread across identically treated strips — which is then applied to every single-strip cell as the threshold for calling a difference real. The consequence has to be accepted openly: any difference smaller than that limit goes unreported.

Question 3. Hurter and Driffield abandoned a high density as their speed criterion in favour of the smallest exposure producing the slightest deposit. What is the practical reason, and what does it license you to do?

• Faint deposits are easier to see, so the reading is quicker
• Very slight deposits are little altered by continued development, so the threshold is nearly independent of development time and can be read as a speed measure even across strips developed differently
• It matches the ISO speed point, so the number is comparable with a datasheet
• It avoids the shoulder, where the curve is unreliable

Show the answer and why

Answer: Very slight deposits are little altered by continued development, so the threshold is nearly independent of development time and can be read as a speed measure even across strips developed differently

Their own reasoning is that the very slight deposits are little altered by continued development, and Kodak’s workbook says the same from the other side, observing that in a family of curves at different times most of the change is in the straight line and the shoulder while the toe remains basically the same. That is what makes a threshold reading a speed reading: it survives a change in development time, which a step count does not. It is not the ISO speed point, which is defined at 0.10 above base plus fog with a further condition on the curve, so the number is not comparable with a datasheet speed.

Question 4. You scan six strips and the wedge together, with every automatic function switched off, and convert code values to −log₁₀(V/V₀). What exactly have you measured?

• Diffuse density, comparable with a manufacturer’s published curve
• A relative density on your scanner’s own uncalibrated response, on that machine, in that pass — useful for ranking the strips against each other and for nothing beyond it
• Nothing, because a scanner cannot measure density
• Contrast index, once the wedge is included

Show the answer and why

Answer: A relative density on your scanner’s own uncalibrated response, on that machine, in that pass — useful for ranking the strips against each other and for nothing beyond it

Including the wedge is what makes the scan worth doing, because it maps the scanner’s response against a ladder of nominal densities on the day. But the wedge itself is nominal rather than certified unless it is a CC part, the course has verified no published linearity or density-range figure for any particular scanner, and the geometry and spectral band are undefined — three reasons the result is a ranking and not a density. Diffuse density is the ISO reference geometry a published curve is plotted in, and a flatbed does not deliver it.

Question 5. Your control set of three identically exposed and identically developed strips reads threshold step 17, 18 and 16. What has the session just told you, before any experiment has been run?

• That the film is faulty and should be replaced
• That the resolution limit is about two steps, so no experimental result smaller than that can be reported, and the rig is worth improving before spending more film
• That the average threshold is 17, which is the number to use
• That the exposure was wrong and should be increased by one stop

Show the answer and why

Answer: That the resolution limit is about two steps, so no experimental result smaller than that can be reported, and the rig is worth improving before spending more film

A spread of two steps is a spread of 0.30 log units, a whole stop, and applying it as the resolution limit would wipe out most of what the part is trying to measure — an 8 per cent contrast change corresponds to about one step. The reading is not evidence about the film; the three strips differed only in ways the procedure was supposed to hold still, so the spread is a fact about the rig, the lightbox and the reader. The useful response is diagnostic: look first at exposure timing, then at the flatness of the film against the wedge, then at how the threshold judgement is being made, and re-run the control set before committing an experiment to it.

Question 6. The ILFORD chart gives 8:00 at 20 °C and 6:30 at 22 °C, and the coefficient derived from the whole row predicts 6:40. Is the 10-second discrepancy a failure of the derivation?

• Yes: the model is wrong and a different one should be fitted
• No: the chart is rounded to the nearest 15 seconds, so a 10-second difference is inside the source’s own stated precision, and the agreement is the evidence that the coefficient is usable across the row
• No, because temperature coefficients are only approximate and precision does not matter
• Yes, but only because Q₁₀ should have been derived from the 20 to 22 °C pair instead

Show the answer and why

Answer: No: the chart is rounded to the nearest 15 seconds, so a 10-second difference is inside the source’s own stated precision, and the agreement is the evidence that the coefficient is usable across the row

A prediction has to be judged against the precision of the thing it is predicting. The chart’s own values are rounded to 15 seconds, so 6:30 stands for anything from about 6:23 to 6:38, and 6:40 sits just outside — close enough that the residual is dominated by rounding rather than by the model. Deriving the coefficient from the widest interval is deliberate for the same reason: over 9 degrees the rounding is a small fraction of the change, while over the 20 to 22 °C pair alone it is a large one, which is why short intervals in this row return coefficients scattered between about 2.5 and 2.8.

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