Tone Reproduction: From Subject to Print

A photograph is a chain of four transformations and you can only see the last one. Light leaves the subject; some of it is scattered inside the camera before it lands; the emulsion turns what lands into density; the paper turns that density back into a tone; and an eye in a room decides what the tone means. Change anything anywhere and everything downstream moves.

The four-quadrant diagram is the tool for holding all of that in one picture, and this page builds it from the numbers the rest of Part XIII has established. It also owns the course’s tone-reproduction virtual laboratory, and it is written so that an interactive version can be made from the explanation without rewriting a word of it.

The first quadrant: what the subject offers

Everything starts with a ratio you can measure with the meter you already own.

Subject luminance range is the ratio between the luminance of the brightest thing you care about and the darkest thing you care about — not the brightest and darkest things in the frame, which are usually a specular highlight and the inside of a letterbox, and neither of which you intend to render.

A spot meter reports luminance in EV, and one EV is a factor of two, so the arithmetic is the arithmetic of stops.

Subject log-luminance range = 0.301 × (EV_high − EV_low)

Subject range in log units

A scene reading EV 6 on the important shadow and EV 13 on the important highlight is seven stops, which is 2.11 in log units, and that number is the input to everything that follows. This page uses it throughout as its worked example.

Two cautions carry over from the exposure lesson. Meters disagree about the absolute value and agree about the difference, so a range is far more trustworthy than either end of it. And this course quotes no figure for a “typical” scene: it has not verified a survey it could cite, so seven stops here is a worked example and not a claim about the world. Measure your own.

Flare: the range shrinks before the film sees it

Between the subject and the emulsion sits a lens with air-glass surfaces, a barrel, a mirror box and a film chamber, all of which scatter a little of the light that enters and spread it more or less evenly across the frame. That is veiling flare, and it does something specific rather than something vague.

Flare adds a constant, and a constant matters only where there was almost nothing. Suppose the veil adds an illuminance equal to 1 per cent of the brightest subject luminance. At the highlight, which is already at 100 per cent, adding 1 changes almost nothing. At the shadow, which on a seven-stop subject is at 0.78 per cent of the highlight, adding 1 more than doubles it.

E_image = E_ideal + v · E_brightest

What flare does to the image

Run the arithmetic on the seven-stop subject with v = 0.01. The luminance ratio is 129 to 1. After flare the illuminance ratio at the film is (129 + 1.29) to (1 + 1.29), which is 130.3 to 2.29, or 56.9 to 1. The subject’s 2.11 log units have become 1.76 at the film, a loss of 0.35 — about a stop and a fifth, all of it taken from the shadow end.

Now do it again for a ten-stop subject, 3.01 in log units and 1,023 to 1. The same veil is now 10.2 against a shadow of 1, so the ratio at the film is 1,033 to 11.2, which is 92 to 1: 3.01 has become 1.96, a loss of 1.05 log units — three and a half stops. And once more for a four-stop subject: 1.20 becomes 1.14, a loss of 0.06.

!The flare figure on this page is a declared assumption, not a measurement

The course has not verified a published flare factor for any lens or camera, so no number here is attributed to anyone. v = 0.01 is a value chosen for the worked example, and every flare figure on this page follows from it arithmetically. In the virtual laboratory it is a slider with no units on it.

What the course can say without a source is the shape of the effect, because it follows from the model rather than from a measurement: flare adds a constant, so it compresses the shadows and leaves the highlights alone, and its cost grows steeply with the length of the subject range. Two-tenths of a stop on a flat subject; three and a half stops on a contrasty one. That is why a backlit scene photographed into the sun is not merely difficult but differently difficult, and why a lens hood is a tonal control rather than a tidiness measure.

Measuring your own is not hard and Part XV’s densitometer makes it easy: photograph a step wedge or a grey scale in the scene, and compare the negative densities it produces against the same wedge contact-printed with no lens in the path.

Flare is not only a camera phenomenon. The enlarger has it too, and it works the same way on the negative: a veil of scattered light added to the projected image lifts the darkest parts of the projection, which are the negative’s densest parts, which are the print’s highlights. That is one of the two reasons ILFORD specify their ISO Range figures against the image as projected on the enlarger baseboard rather than against the negative as read on a light box.

The other reason is the Callier effect, which pushes the other way: a condenser head’s directional beam loses the light the silver scatters, so the projected range is longer than the measured one. ILFORD quantify it as about an extra grade, and note that it depends on the amount of silver left in the negative, being small for very pale flat negatives and for a dye image. Enlarger flare shortens the projected range and the Callier effect lengthens it, by different amounts on different machines, and the honest position is that the number to match against a paper’s range figure is the one measured at the baseboard.

The four quadrants

Here is the whole chain in one diagram. Four plots share their axes at the centre, so that the output of each becomes the input of the next and you can walk a single subject tone all the way round.

The four-quadrant tone-reproduction diagram, walked with three subject tones

1. 1Bottom right: flare — subject log luminance in, log exposure at the film out; the bend at the dark end is the shadow lift
2. 2Bottom left: the negative — log exposure in, negative density out; the film curve, rotated so its exposure axis is shared
3. 3Top left: the paper — negative density in, print reflection density out; short, steep, and it stops at maximum black
4. 4Top right: the reproduction curve — composed, not drawn: subject log luminance against print density, and the only quadrant you actually look at
5. 5A shadow traced round — subject 0.10 → exposure 0.30 → negative 0.26 → print 2.12, which is maximum black
6. 6A mid-tone traced round — subject 1.05 → exposure 0.99 → negative 0.56 → print 1.68
7. 7A highlight traced round — subject 2.00 → exposure 1.90 → negative 1.09 → print 0.19, nearly paper white

Curves computed from the model this page states, not measured from any material: a veiling flare of one per cent, a negative of contrast index 0.62 with its shadow at the criterion point, and a paper at ILFORD's published maximum density of 2.15 and range figure of 90. Walk any subject tone down, left, up and right, and where it lands in the top-right quadrant is the tone the print will carry.

Read it as a walk. Pick a subject tone on the horizontal axis to the right of centre. Drop down to the flare curve: that is the exposure the film receives. Move left at that height to the negative curve: that is the density the negative carries. Move up at that position to the paper curve: that is the density the print carries. Move right at that height, and where you cross the vertical through your starting tone is the point on the reproduction curve.

The fourth quadrant is the one nobody draws directly, because it draws itself. It is the composition of the other three, and it is the only one that answers the question you actually asked.

The worked chain, in numbers

Stage	What it does	The worked figures
Subject	Sets the range everything else must handle	7 stops, 2.11 log
Camera flare	Adds a constant; compresses the shadows	v = 0.01 → image range 1.76
Negative	Multiplies by its slope; the toe eats some of it	CI 0.62, shadow at the criterion point → density range 0.91, from 0.25 to 1.15
Paper	Maps the negative’s range onto its own scale	Filter 2, published range figure 90 → log range 0.90; published Dmax 2.15
Print	What is left to look at	Highlight 0.12, shadow 2.12, range 2.00
Overall	Print density range ÷ subject log range	0.95

Two of those rows repay a second look.

The negative delivers less than its contrast index promises. Multiplying 0.62 by 1.76 gives 1.09, and the model gives 0.91. The difference is the toe. The shadow was placed at the criterion point, which is 0.10 above base plus fog, and that point is by construction on the toe, where the local slope is well below the contrast index. Placing shadows at the speed point costs you about a sixth of the density range the straight line would have given — and the alternative, exposing more generously to lift the shadows onto the straight line, costs grain and highlight room. That trade is what an exposure index is for.

The overall gradient is 0.95, and it was not chosen. Nobody set out to make it 0.95. It fell out of matching the paper’s range to the negative’s, and that leads to the most useful structural fact on this page.

🧮Grade matching fixes the overall gradient, and nothing else you do changes it

Suppose you match the grade properly: you pick the paper whose log exposure range equals the negative’s density range. Then, by construction, the negative’s shadow lands at the bottom of the paper’s scale and its highlight at the top, so the print uses the paper’s whole density range, whatever that is.

Overall gradient ≈ (paper density range) ÷ (subject log-luminance range)

The consequence

The numerator is fixed at about 2.1 by the paper — ILFORD publish 2.15 for the current MULTIGRADE RC DELUXE — and in practice a little less because the extreme ends are not used. The denominator is the scene. So:

Subject	Log range	Overall gradient with the grade matched
4 stops, a flat misty morning	1.20	1.67
5 stops	1.51	1.32
6 stops	1.81	1.10
7 stops, the worked example	2.11	0.95
8 stops	2.41	0.83
9 stops	2.71	0.74
10 stops, sun and deep shade	3.01	0.66

Flare, development and grade do not change this. They change which grade you need and how much you have to develop to need it — but once you have matched, the overall gradient is decided by the two ranges alone. That is why a short scene inevitably prints with more contrast than it had and a long one inevitably prints with less, and it is not a failure of technique. It is arithmetic.

Which leaves the real question. If the overall gradient is decided for you, what is the photographer deciding? The answer is the whole art of it: where in the scale that gradient is spent. A curve with an overall gradient of 0.66 can be flat everywhere, or steep in the mid-tones and crushed at both ends, or open in the shadows and compressed in the highlights. The shapes of the film’s toe, the paper’s toe, and every local control in the printing parts are what distribute it.

Overall gradient against subject range, with the grade matched

• Overall gradient = 2.00 ÷ subject range
• Exact reproduction, gradient 1.00

Show the numbers behind this plot

A falling curve of overall gradient against subject log-luminance range, computed as a print density range of 2.00 divided by the subject range. At a subject range of 1.20, four stops, the gradient is 1.67. At 2.11, seven stops, it is 0.95. At 3.01, ten stops, it is 0.66. A horizontal line marks a gradient of 1.00, which the curve crosses at a subject range of 2.00, a little under seven stops. Everything to the left of that crossing is expanded by the print and everything to the right is compressed, and the photographer does not choose which: the print's fixed density range and the scene's range decide it between them.

Series	Subject log-luminance range	Overall gradient (magnitude)
Overall gradient = 2.00 ÷ subject range	1.20	1.67
Overall gradient = 2.00 ÷ subject range	1.51	1.32
Overall gradient = 2.00 ÷ subject range	1.81	1.10
Overall gradient = 2.00 ÷ subject range	2.11	0.95
Overall gradient = 2.00 ÷ subject range	2.41	0.83
Overall gradient = 2.00 ÷ subject range	2.71	0.74
Overall gradient = 2.00 ÷ subject range	3.01	0.66
Exact reproduction, gradient 1.00	1.20	1.00
Exact reproduction, gradient 1.00	3.01	1.00

Computed from the chain on this page, not measured: a print density range of 2.00, which is a little less than ILFORD's published maximum of 2.15 because the extreme ends of the paper's scale are not used. Where the curve crosses 1.00 is the only subject a print can reproduce at its own contrast. 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.

Objective and subjective reproduction

The reproduction curve in the fourth quadrant is an objective description: measured print density against measured subject luminance. It says what the print is.

It does not say what the print looks like, and the gap between the two is not small.

A print is not viewed in the scene’s light. The scene was outdoors at thousands of lux; the print is on a wall at a few hundred. The eye adapts to the print’s own level, so the print is judged against itself rather than against the original — which is the only reason a photograph works at all, since no print has ever come close to a sunlit scene’s absolute luminances.

A print is surrounded by something. The same print reads darker against a white mount and lighter against a black one, and reads differently again on a screen-lit desk and in a gallery. Simultaneous contrast is a property of vision, not of the paper.

The eye’s response is not the print’s density. A tone’s apparent lightness is not a simple function of its reflection density, and the relation depends on adaptation, surround and the observer.

Subjective tone reproduction is the study of what people actually prefer given all of that, and its central finding — reported consistently in the literature that follows Jones — is that a preferred reproduction is not the geometrically exact one: viewers prefer a little more contrast through the mid-tones than an exact copy would give.

⁇What this course can and cannot attribute to Loyd A. Jones

The four-quadrant diagram is universally credited to Loyd A. Jones of the Kodak Research Laboratories, and this course uses it and names him. It must also say what it has and has not verified, because the difference matters.

What the corpus supports. Eder’s history records that George Eastman installed a research laboratory at Rochester in 1912 under C. E. Kenneth Mees, and names L. A. Jones among the scientists Mees gathered there; that Jones contributed to the first volume of the laboratory’s Abridged Scientific Publications, 1913–14; and that work of L. A. Jones, E. Huse and V. C. Hall in 1926 on the theory of photographic density built on Kron’s. So Jones was at Kodak Research from its earliest years and was publishing on density theory by the mid-1920s. That much is Tier 1 and verified.

What the corpus does not support. This course holds none of Jones’s own papers, and has therefore verified no date, no title and no journal for the tone-reproduction work itself, nor for the Jones and Condit scene-luminance surveys that are often quoted for “typical” subject ranges. It quotes no number from any of them, and it does not date the four-quadrant diagram.

What the course uses, and why. The diagram is used as a construction — four transfer functions chained through shared axes — which stands or falls on its own arithmetic and needs no authority. Every number in it is computed from this page’s stated model or taken from a manufacturer sheet cited by name. Attribution to Jones is given as the settled convention of the field and flagged as unverified in its particulars, and closing that gap needs a copy of the papers, which is a research task rather than a judgement.

The older half of the argument the course can source, and it is worth seeing how early it starts. Hurter and Driffield defined a theoretically perfect negative as one whose opacities are directly proportional to the intensities of the light that produced them, identified the straight portion of their curve as the “period of correct representation” where that proportionality holds, and then went on — in the same body of work — to the relation between negatives and their positives. That is the whole tone-reproduction idea in its first form: treat the negative and the print as one chain, and ask what the chain does rather than what either half does. What the twentieth century added was flare, the paper’s curve, and the eye.

📷Why exact reproduction is not the aim, in one paragraph

It is not achievable for most scenes: the plot above shows the overall gradient is fixed by two ranges you do not control together, and it equals 1.00 for exactly one subject range and no other.

It is not desirable even when it is achievable: the print is seen at a fraction of the scene’s luminance, in a surround the scene did not have, by an eye adapted to the room, and a geometrically exact copy under those conditions looks flat.

And it is not what anybody wants: a photograph is a statement about a subject. The useful question is not “how close is this to the scene?” but “where did I spend the contrast I had?” — which is a question with a numerical answer and an aesthetic one, and this page is about making them the same question.

Steering the chain

Four controls, in the order they occur, each doing something the others cannot.

Exposure places the subject on the film’s curve. It slides the whole subject range left or right along the log exposure axis without changing its length or the curve’s shape. Get it wrong to the left and the shadows fall off the bottom of the toe and record as nothing; get it wrong to the right and the highlights climb into the shoulder and compress. Kodak’s workbook has the construction exactly: draw the subject range as a bar of fixed length on the exposure axis, place its foot at the speed point, and the slack between the bar and the ends of the curve is your latitude, divided between under- and over-exposure.

Development sets the slope. It rotates the negative’s curve about its toe, because — as Kodak observe of a real family of curves and Hurter and Driffield observed of slight deposits — the toe stays put while the straight line and the shoulder move. That is what makes exposure and development genuinely separable controls, and it is the sensitometric fact the Zone System is built on.

Paper grade matches the ranges. It chooses the length of the paper’s exposure axis so that the negative’s density range fits it.

Local printing controls redistribute what is left. Burning, dodging and split-grade work change the exposure of parts of the print, which is the only way to give two areas of one print two different placements on the paper’s curve. That is Part XIX’s subject, and this page hands it over deliberately: this page owns the diagram and the numbers; Part XIX owns the practice.

📓Which control to reach for, from the symptom

What you see	What has gone wrong in the chain	The control
Shadows undifferentiated, mid-tones fine	The subject range fell off the bottom of the toe	Exposure — more of it
Highlights blocked, shadows fine	The range climbed into the shoulder, or development ran too long	Exposure down, or development down
Everything present, print flat and grey	Negative density range shorter than the paper’s exposure scale	A harder grade; next time, more development
Everything present, print harsh, no separation at either end	Negative density range longer than the paper’s scale	A softer grade; next time, less development
Highlights right, shadows grey, at every test-strip band	The two ranges do not match at all	Grade, not exposure — no exposure fixes a mismatch
Whites not white, everything else fine	A veil somewhere: safelight fog, enlarger flare, or a base fog	Find the veil; none of the four controls repairs it

The Zone System, read against the diagram

Adams and Archer’s Zone System is the practitioner’s version of everything above, and it is a good one. It converts the same sensitometry into two instructions a person can carry out in a field with a meter.

Zones are stops. The scale runs from Zone 0, maximum black with no detail, to Zone X, paper white, with Zone V the mid-tone a reflected-light meter assumes. One zone is one stop, which is 0.30 in log exposure, so a zone is a unit on the horizontal axis of the second quadrant. That single equivalence is what makes the whole scheme translatable.

You place, and then things fall. Meter the important shadow and decide which zone it should occupy — Zone III is the conventional choice for a textured dark tone — and set the exposure so that it lands there. Then meter the important highlight and see where it falls. It is not placed; it falls, because the subject range decides it once the shadow is fixed.

Development moves what fell. If the highlight fell on Zone VIII, normal development is right. If it fell on Zone IX, one zone too high, develop less — N−1 — so that it comes down to VIII. If it fell on Zone VII, develop more: N+1.

Read against the four quadrants, that is exactly the two controls this page just described. Placing the shadow is exposure, sliding the bar along the film’s exposure axis. N and its variants are slope, rotating the curve so that a subject of a different length still delivers the negative density range the paper wants.

N, N+ and N− as contrast-index targets

The translation is arithmetic, and it is the course’s own inference rather than anybody’s published table. Since the aim of a development adjustment is to deliver the same negative density range from a different subject range:

CI(target) = CI(normal) × R(normal) ÷ R(subject)

Development target for a non-normal subject

R is a subject log-luminance range. Take the worked example’s normal as a seven-stop subject developed to CI 0.62 — which is where ILFORD’s published Ḡ target and Kodak’s contrast-index starting points both sit — and the family follows:

Development	Subject it is for	Subject log range	Contrast-index target
N+2	5 stops	1.51	0.87
N+1	6 stops	1.81	0.72
N	7 stops	2.11	0.62
N−1	8 stops	2.41	0.54
N−2	9 stops	2.71	0.48

Now put that table beside the time-against-contrast-index plot from the assignment, or better, beside the one you made from your own step wedge, and the Zone System’s development instructions become development times you can read off a graph. That is the whole payoff of Part XIII and it is worth stopping to notice: “N−1” was a word, and now it is eleven minutes.

!Three things the course cannot verify about the Zone System, and how it handles them

The attribution and date. The scheme is universally credited to Ansel Adams and Fred Archer, and commonly dated to about 1939–41 at the Art Center School in Los Angeles. This course holds no Tier-1 or Tier-2 source for that attribution or that date, having searched its corpus and found none. It therefore names Adams and Archer as the settled convention of the field, prints no date, and flags this sentence as the flag.

The trademark position. The course has not established whether “Zone System” carries any trademark or attribution constraint. It uses the term descriptively, claims no endorsement, and reproduces no text or diagram from any Zone System publication.

The numbers above are the course’s own. No published table of contrast-index targets against N numbers was found. The five figures are derived from one equation stated on this page, from a normal contrast index that manufacturers do publish, and from a definition of “normal” — a seven-stop subject — that this course chose and states. Your normal is your paper, your enlarger and the subjects you actually photograph, and recomputing the table with your own R(normal) takes one line of arithmetic.

What it gets right, and where it simplifies

Right, and importantly right. It puts exposure and development in the correct causal order and gives each its own job — the single most valuable idea in practical sensitometry, and one most photographers never arrive at unaided. It measures rather than guesses. It insists on placing the shadow, which is correct because the toe is where information is irrecoverably lost. And its unit is the stop, which is the unit the equipment already speaks.

Simplifications, all of them benign until they are not. Zones are drawn as equal steps of print tone, which the paper’s curve does not deliver — the top and bottom zones are compressed by the paper’s toe and its ceiling, so Zone VIII to Zone IX is a smaller step of print density than Zone V to Zone VI. It treats development as rotating the curve cleanly, and development also moves fog and the shoulder. It says nothing about flare, which by the arithmetic above has already taken a stop or more off the range before the film sees it, and taken all of it from the shadow you are so carefully placing. And it attaches no paper to “normal”, although the whole meaning of a normal negative is the paper it is normal for.

None of that makes it wrong. It makes it a model, like the one on this page, and knowing which approximations a model makes is the difference between using it and believing it.

Latitude and range, revisited

The characteristic-curve lesson defined latitude as a property of the curve and the subject together: the amount you can misplace the exposure and still fit the subject inside the useful range. The four quadrants add the rest of the chain, and the picture changes.

Latitude is decided in the second quadrant, but spent in the third. A film may offer 3.0 of useful exposure range and your flare-reduced subject may occupy 1.76 of it, leaving 1.24 of slack — four stops, split between under and over. That is real latitude and it is why negatives are forgiving. But the print has no latitude at all: its range is 2.1 and the negative’s range has to fit the paper’s scale or one end is lost. Latitude protects the placement, not the match.

Which scenes fit. With the grade matched, any subject fits — but the overall gradient it gets is 2.1 divided by its own range, and past about eight stops that is a visible flattening. Beyond ten it is severe, and the honest options are the ones photographers have always used: change the light, change the framing, expose for one end and let the other go, or use development and grade to compress knowingly and then reopen the mid-tones locally in the print.

Compression and expansion are not symmetrical. Compressing a long scene works, because the paper has range to spare at the ends and the eye tolerates flattened extremes. Expanding a flat one has a harder limit: raising the negative’s contrast raises grain and fog with it, and past a point the straight line runs out, as the Sheppard and Mees relation says it must.

The art track: choosing an intention, then a number

Everything above is machinery. This is what it is for.

A tone-reproduction intention is a sentence about where you will spend the contrast. It is not “good tones” or “rich blacks”. It is something like: open shadows with texture down to Zone III, mid-tones slightly compressed, highlights held below maximum white so the sky keeps its structure. Or: the whole scene pushed into the upper half of the scale except one small deep black, which is the only thing at Zone I.

Then translate it, and the translation is mechanical once the intention is a sentence.

1. Which end matters? If the shadow does, place it and let the highlight fall. If the highlight does, place it and let the shadow go — and accept that you are choosing to lose the other end.
2. What is the subject range? Meter both ends. That gives R.
3. What negative density range does your paper want? Its published range figure divided by 100, for the grade you intend to print on — and intend is the word: choosing to print on filter 3 is part of the intention, not a consequence of it.
4. So what contrast index? The paper’s range divided by the flare-reduced subject range. That is the development target, and your own time-against-contrast-index curve turns it into minutes.
5. What is left over goes to the print. Burning and dodging are how a global decision gets local exceptions, and the exceptions are usually where the photograph is.

▷Write the intention before you meter, once

On the next scene you photograph seriously, write two sentences in the notebook before taking a reading: what the picture is about tonally, and which end of the scale you are protecting. Then meter, compute, and record the numbers beside the sentences.

Do it a dozen times and something specific happens: you find out that your intentions cluster. Most photographers discover they nearly always protect the same end, and nearly always want a slope a little above or below what the arithmetic offers. That cluster is a working style with a number attached to it, and it is worth more than any published starting point, because the published one was written for somebody else’s subjects.

Viewing conditions, stated as what they are

The fourth transformation has no curve in this course, because the course cannot source one.

What can be said qualitatively is worth saying anyway. A print’s apparent contrast rises with the light it is viewed in, up to a point, so a print judged under a bright darkroom lamp and hung in a dim hallway will look flatter than it did. A print’s apparent lightness depends on its surround, so the mount, the frame and the wall are part of the print. A print is compared to what is next to it, which is why a portfolio sequence changes every print in it. And the eye adapts, so the first print of a session and the twentieth are not judged by the same instrument.

The practical rules follow without any numbers at all. Judge dry prints, in the light they will be seen in, against the mount they will have, after a break. And keep one known print — a reference you made and are sure of — to look at first, so that the instrument is calibrated before the work starts.

The virtual laboratory

The tone-reproduction laboratory implements the transformations in four panels. Its first implementation uses straight-line negative response and hard paper clipping, with the simplifications printed beside every result. Use the fuller curves above to identify what it omits.

Four controls, matching the four things a photographer changes.

1. Subject range, in stops. Sets R, and with it the length of the bar on the exposure axis.
2. Flare, as the dimensionless veil v. Recomputes the image range as described above.
3. Negative slope, as a contrast index. Rotates the second quadrant’s curve about its toe.
4. Paper grade, as a published ISO Range figure. Sets the length of the third quadrant’s exposure axis; the maximum black stays where the paper’s published figure puts it.

What it displays. All four quadrants, chained through shared axes exactly as drawn above; a traced tone the reader can drag; the reproduction curve composing itself in the fourth quadrant; and the four computed numbers — image range, negative density range, print density range and overall gradient — updating as the controls move.

Every relationship it animates is one the course can source or state. Flare adds a constant, which follows from the model stated here. Development rotates the curve about its toe, which Kodak state of a real family of curves and Hurter and Driffield state of slight deposits. Grade sets the paper’s exposure range, which ILFORD publish per filter. Maximum black is fixed by the paper, which ILFORD publish. Anything the course cannot source is left out of the model rather than approximated — which is why there is no viewing-conditions quadrant, and no preferred-reproduction overlay.

!The label this module carries in every view

This is a qualitative educational model. It does not predict the behaviour of any particular film, paper or developer, and no number read off it may be used as a working value in place of the student’s own measurement.

That wording is fixed here and is the course’s canonical form. Part VIII’s companion module — a curve family that moves as the agent, alkali, sulfite and bromide of a developer formula change, which will live on reading a developer formula — carries the same label, in the same words, so that a reader meets one warning rather than two paraphrases of one. The formula designer exposes the sourced directions as text. It does not invent a numerical curve family from them; this section remains the authority for the model limitation.

Recap

• Tone reproduction is four transformations chained: subject to image illuminance through flare, image to negative density through the film’s curve, negative to print density through the paper’s curve, and print density to what a person sees.
• The four-quadrant diagram shares its axes, so the fourth quadrant — the reproduction curve — is composed rather than drawn, and a single tone can be walked all the way round.
• Flare adds a constant, so it compresses the shadows and leaves the highlights alone. Its cost grows steeply with subject range: about a fifth of a stop on a four-stop subject and three and a half stops on a ten-stop one, under this page’s declared assumption of a 1 per cent veil.
• The negative delivers less than CI × range, because a shadow placed at the criterion point sits on the toe.
• Matching the grade fixes the overall gradient at roughly the paper’s density range divided by the subject’s log range: 1.67 for a four-stop subject, 0.95 for seven stops, 0.66 for ten. Nothing else you do changes it — only where in the scale it is spent.
• Exact reproduction is neither generally achievable nor wanted, because the print is viewed at a fraction of the scene’s luminance in a surround the scene did not have.
• The Zone System is this sensitometry in a practitioner’s language: place the shadow with exposure, let the highlight fall, and use development to bring it where it belongs. N±n translates to a contrast-index target by one equation, and your own time-against-CI curve turns that into minutes.
• The course names Jones and names Adams and Archer as the field’s settled attributions, and flags both as unverified in their particulars, because it holds none of the primary papers.
• The explorer on this page is a qualitative educational model and carries that label in every view, along with Part VIII’s companion module.

Check your understanding

Question 1. A subject spans ten stops. Under this page assumption of a veil equal to one per cent of the brightest subject luminance, roughly what range reaches the film, and why is the loss so much larger than for a seven-stop subject?

• About 2.7 log units; the loss is the same fraction for every subject
• About 1.96 log units, a loss of 1.05, because flare adds a constant equal to one per cent of the brightest luminance and on a longer subject that constant is a far larger multiple of the shadow
• About 3.01 log units; flare affects only colour films
• About 1.20 log units; flare removes exactly half the range

Show the answer and why

Answer: About 1.96 log units, a loss of 1.05, because flare adds a constant equal to one per cent of the brightest luminance and on a longer subject that constant is a far larger multiple of the shadow

Ten stops is a luminance ratio of 1023 to 1, so a veil of one per cent of the brightest is 10.2 units against a shadow worth 1. The shadow becomes 11.2 and the highlight 1033, a ratio of 92 to 1, which is 1.96 in log units. On a seven-stop subject the same rule gives a veil of 1.29 against a shadow of 1, and the range falls from 2.11 to 1.76. The lesson is that flare is not a fixed tax: it is a constant added to a shadow whose absolute value shrinks as the subject range grows, so it costs a fifth of a stop on a flat scene and three and a half stops on a contrasty one. That is why a lens hood is a tonal control, and why the shadow you are carefully placing may already have been lifted before the film saw it.

Question 2. You match the paper grade correctly to two different negatives: one from a five-stop subject and one from a ten-stop subject. Which statement about the two prints is right?

• Both prints have the same overall gradient, because the grade was matched in each case
• The five-stop subject prints with an overall gradient near 1.3 and the ten-stop subject near 0.66, because matching the grade uses the paper whole density range in both cases and that range is divided by different subject ranges
• The ten-stop print has the higher gradient, because it needed a harder paper
• Overall gradient cannot be computed without knowing the developer

Show the answer and why

Answer: The five-stop subject prints with an overall gradient near 1.3 and the ten-stop subject near 0.66, because matching the grade uses the paper whole density range in both cases and that range is divided by different subject ranges

Matching the grade means choosing the paper whose log exposure range equals the negative density range, which by construction places the shadow at the bottom of the paper scale and the highlight at the top. The print therefore uses the paper whole density range, about 2.0 in practice, whichever negative it came from. Divide that by the subject log range and the answer follows: 2.00 over 1.51 is 1.32 for five stops, and 2.00 over 3.01 is 0.66 for ten. Neither figure was chosen by the photographer and neither can be changed by development or by grade, because those decide which grade is needed rather than what the matched result delivers. What the photographer does decide is where in the scale that fixed gradient is spent, and that is what the shapes of the curves and the local printing controls are for.

Question 3. On a scene you meter EV 5 on the important shadow and EV 13 on the important highlight. Taking normal as a seven-stop subject at contrast index 0.62, what development does the Zone System call for and what contrast index does it correspond to?

• N+1, contrast index 0.72
• N-1, contrast index 0.54
• N, contrast index 0.62
• N-2, contrast index 0.48

Show the answer and why

Answer: N-1, contrast index 0.54

Eight stops is one stop longer than normal, so the highlight will fall one zone too high once the shadow is placed, and the development must be reduced by one: N minus 1. The contrast index follows from the requirement that the negative deliver the same density range from a longer subject, so the target is 0.62 multiplied by 2.11 and divided by 2.41, which is 0.54. Two things about that number are worth keeping straight. It is this course own inference from an equation stated on the page, not a published table, and it depends on a definition of normal that the course chose and states. And turning 0.54 into minutes needs your own plot of contrast index against development time, which is exactly what the step-wedge lab exists to let you make.

Question 4. A print shows good separation in the shadows and mid-tones but the whites are slightly grey, and no change of exposure or grade improves it. Where in the chain is the fault?

• The negative is underexposed
• A veil has been added somewhere - safelight fog, enlarger flare or an unusually high base fog - and it lifts the flat foot of the paper curve where the highlights sit, which none of the four main controls repairs
• The paper is too hard
• The developer is exhausted, so maximum black is low

Show the answer and why

Answer: A veil has been added somewhere - safelight fog, enlarger flare or an unusually high base fog - and it lifts the flat foot of the paper curve where the highlights sit, which none of the four main controls repairs

The symptom is specific and it is diagnostic. A small uniform exposure added everywhere matters only where the curve is nearly flat and the tones are separated by very little density, which on a paper is the long toe where the highlights live, so the whites lift and their separation goes while everything else looks normal. Exposure moves the whole scale together and cannot recover a difference that was never recorded; grade changes the length of the exposure axis and does not remove a veil. The controls that do work are all upstream: find the light leak, run the safelight test, hood the enlarger lens, or check the negative base fog against a control strip. An exhausted developer would show as a loss of maximum black at the other end of the scale, which is the opposite symptom.

Question 5. Why does the negative in this page worked chain deliver a density range of 0.91 when its contrast index is 0.62 and it received 1.76 of exposure range?

• Because 0.62 times 1.76 is 0.91
• Because the shadow was placed at the criterion point, which is on the toe, where the local slope is well below the contrast index, so part of the exposure range is recorded at less than full gradient
• Because the developer was exhausted
• Because contrast index is measured in different units from density range

Show the answer and why

Answer: Because the shadow was placed at the criterion point, which is on the toe, where the local slope is well below the contrast index, so part of the exposure range is recorded at less than full gradient

Multiplying 0.62 by 1.76 gives 1.09, and the model gives 0.91, so about a sixth of the expected range is missing. The reason is where the subject was placed. The criterion point sits 0.10 above base plus fog and is by construction in the toe, so the darkest part of the subject is recorded on a stretch of curve whose local slope is a fraction of the contrast index. Exposing more generously would lift the shadow onto the straight line and recover that range, at the cost of more grain and less room before the highlights reach the shoulder. That trade is precisely what a personal exposure index is a decision about, and it is why a contrast index quoted alone never quite predicts the density range a real negative delivers.

Question 6. What does the label on this page virtual laboratory forbid, and why is the same wording used on the Part VIII module?

• It forbids using the module at all without a densitometer
• It forbids using a number read off the model as a working value in place of the student own measurement, and one wording is used across both modules so a reader meets a single warning rather than two paraphrases of it
• It forbids sharing screenshots of the module
• It forbids changing more than one control at a time

Show the answer and why

Answer: It forbids using a number read off the model as a working value in place of the student own measurement, and one wording is used across both modules so a reader meets a single warning rather than two paraphrases of it

The model chains four transfer functions whose parameters are chosen to be plausible and to move in the directions the course can source; it is not fitted to any material, and a development time or a grade read off it would be a guess wearing the costume of a measurement. Encouraging exploration while forbidding extraction is exactly what the label does. Using identical wording on the companion developer-formula module matters for a reason beyond tidiness: two paraphrases of one warning read as two different warnings of uncertain strength, and a reader who has learned to skip one has learned to skip both. One sentence, stated in one place, cited from the other, is the same discipline the course applies to its contrast-index convention and its speed criterion.

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