Gamma, Contrast Index and Average Gradient

A characteristic curve is a shape, and a shape cannot be put in a table, compared between two developers or plotted against development time. So the industry reduces it to a single number: the slope, which is what “contrast” means once you are being precise about it.

There are three such numbers in common use, they are built differently, and they do not agree with one another on the same curve. This page constructs all three, shows them disagreeing on one published dataset, and then fixes the convention that the rest of this course — Parts XIV and XV, the printing parts and the capstone — will measure against. That convention is stated once, here.

What a slope actually buys you

Take two tones in a subject one stop apart. One stop is 0.30 in log exposure, so on the film they land 0.30 apart along the horizontal axis. What separates them on the negative is 0.30 multiplied by the local slope.

Δ density = slope × Δ log exposure

Slope is a multiplier

At a slope of 1.0, one stop of subject difference becomes 0.30 of density difference: the negative reproduces the subject’s ratios exactly. At a slope of 0.6, the same stop becomes 0.18 of density. The negative is a compressed copy — deliberately so.

Why compress at all? Because the negative is not the picture. A subject may span seven stops, which is 2.1 in log luminance. At a slope of 1.0 that becomes a negative density range of 2.1, and no ordinary printing paper can take it: the ISO Range figures ILFORD publishes for its Multigrade papers run from 190 down to 40, which is a log exposure range of 1.90 at the softest filtration and 0.40 at the hardest. At a slope of 0.6 the same subject becomes a range of 1.26, which lands comfortably among the middle grades. The film’s job is to fit the world onto the paper, and the slope is the gearing that does it.

That is also why a single slope figure is worth so much argument. Get it wrong by 0.1 on a seven-stop subject and the negative density range moves by 0.21 — which on that same ILFORD table is a whole grade step at the soft end and two of them at the hard end.

Gamma: the slope of the straight line

Gamma, γ, is the oldest of the three and the simplest. It is the gradient of the straight-line portion of the curve: pick two points on the straight part, divide the difference in density by the difference in log exposure.

Hurter and Driffield introduced it, though not under that name at first — they called it the development factor and the development constant, and measured it as the tangent of the angle of inclination of the straight portion, found by drawing a line parallel to it through 1000 on their exposure scale and reading where it cut the density scale. They also established the fact that makes it useful: altering the time of development changes the inclination of that straight line, and it can be driven to values greater or less than one.

Kodak’s workbook gives the modern arithmetic on its sample curve. Point A on the straight line has density 0.64 at log H 1.5; point B has 1.58 at log H 3.0. So

γ = (1.58 − 0.64) ÷ (3.0 − 1.5) = 0.94 ÷ 1.5 = 0.63

Gamma from two points on the straight line

Gamma’s weakness is that it assumes there is a straight line to measure. Sheppard and Mees put their finger on this in 1907: where the unexposed plate’s opacity is large the gradient is nearly constant over a long stretch and Hurter and Driffield’s straight-line method works well, but where it is small the straight portion becomes very short and the slope has to be taken from the tangent at the inflection point instead. Many modern films have very little straight line, and a number measured on a short and partly notional stretch is a number two careful people will disagree about.

Worse, gamma ignores the toe entirely — and the toe is where a pictorial negative keeps its shadows. A film could have identical gamma and quite different shadow rendering, and gamma would not know.

✕Gamma is also a word for something else

“Gamma” is used loosely across photography and imaging to mean contrast in general, and in digital imaging it means the exponent of a transfer function, which is a different quantity with a different definition. In this course it means one thing only: the gradient of the straight-line portion of a characteristic curve. Where a page needs the general idea it says contrast or slope.

Contrast index: a slope that includes the toe

Kodak’s answer to gamma’s weakness is the contrast index. It is still a slope, but of a line drawn between two points chosen so that the lower one lands on the toe. The shape of the toe therefore affects the number, which is exactly the intent: a pictorial negative uses the toe, so the contrast measure should too.

The construction, as Kodak’s sensitometry workbook prints it, is mechanical and needs no algebra.

1. Plot the curve on equal scales, so that 0.30 of density occupies the same distance as 0.30 of log exposure.
2. Find D-min and draw a horizontal line at that density.
3. Mark the edge of a strip of paper at 0.0, then at 0.2 further along, then at 2.2, the marks measured in the graph’s own units along the edge.
4. Slide and rotate the straightedge until the 0.0 mark sits on the D-min line and the 0.2 and 2.2 marks both touch the curve.
5. Draw along the edge. The slope of that line is the contrast index.

Because the marks are measured along the straightedge rather than horizontally, the construction is really a pair of arcs of radius 0.2 and 2.2 struck from a point on the D-min line, and it only works if the two axes are drawn to the same scale. This is where the equal-scale rule stops being cosmetic.

Kodak’s workbook also records what moves the number: time, temperature, agitation and developer are the four factors it names, which is the same list Part VIII spent a whole part on.

Average gradient: the slope between two points you name

The third measure gives up on finding a canonical construction and simply says which two points it used. Average gradient, written G with the two densities as subscripts, is the slope of the chord between any two stated points on the curve, and Kodak’s workbook defines it exactly that way — with the note that if both points happen to lie on the straight line, average gradient and gamma are the same number.

On the workbook’s sample curve, the chord from the point at density 0.18 to the point at density 1.70 gives

G(0.18 to 1.70) = (1.70 − 0.18) ÷ (3.30 − 0.30) = 1.52 ÷ 3.00 = 0.51

Average gradient between two named densities

Its virtue is honesty: it cannot be misread, because the definition travels with the number. Its vice is that G(0.18–1.70) and G(0.25–1.50) are different quantities, so nothing can be compared unless both sides used the same pair.

Average gradient is ILFORD’s working measure, written Ḡ and spelled Gbar in its own sheets, where contrast index is Kodak’s. ILFORD publishes development times against it as a matter of routine: the powder-developer sheet for PERCEPTOL, ID-11 and MICROPHEN says its times should produce negatives of normal contrast, typically around a Gbar of 0.62; the Delta 400 sheet marks the times that give normal contrast, Gbar 0.62, in bold; and the Ortho Plus sheet goes furthest, printing a development table indexed by target Gbar with the note that Gbar 0.62 to 0.70 would be considered normal for in-camera use, alongside separate tables reaching 0.80, 1.00 and 1.2 for other work.

!What this course could not verify about Ḡ

ILFORD uses Ḡ constantly and publishes targets in it, and this course cites those figures as ILFORD’s. What the course has not found, anywhere in the manufacturer literature it holds, is an ILFORD document that defines Ḡ — that names the two points on the curve the gradient is taken between. Without those two points a Ḡ figure cannot be reproduced from a curve, only recognised on a datasheet.

What ILFORD does define is the contrast measure in its film process control system, where the monitored variables are speed (LD), contrast computed as HD minus LD, and minimum density (Dmin): a density difference between two defined control-strip steps, which is an average-gradient construction in all but name and units.

So this page teaches average gradient from the source that defines it in general, Kodak’s workbook; quotes ILFORD’s published Ḡ targets as ILFORD’s own figures; and declines to print a definition of Ḡ it cannot source. That gap matters for one specific purpose only — comparing an ILFORD Ḡ figure with a number you measured yourself — and the honest handling is to say the two are the same kind of measure and not to assume they are the same measure.

The course’s contrast-index convention

Everything above is other people’s constructions. This section is the course’s own, and it is stated here once because Parts XIV and XV, the printing parts and the capstone all depend on it. Later pages cite this section rather than restating it.

!Why the course states its own convention instead of quoting a standard

The relevant International Standards are sold rather than published, and purchasing one would not grant the right to reproduce it — so the pages would read the same either way. The course therefore does not buy them. It states its convention in full, cites the standard by number as the thing the convention is modelled on, and marks every figure derived under it as its own measurement under its own criterion. A published criterion a student can check is worth more than an appeal to a document they cannot read.

The construction below follows the one printed in Kodak’s publication H-740, a freely available manufacturer document this course may describe at length, and it is modelled on the contrast condition of ISO 6, cited by number and quoted nowhere.

The definition

Pure Silver contrast index (CI). Plot diffuse density against log exposure on equal scales. Determine base-plus-fog from an unexposed strip of the same material processed alongside. CI is the gradient of the chord that cuts the curve at two points 2.00 units apart measured along the chord, and whose backward extension reaches the base-plus-fog level 0.20 units before the lower of those two points.

That is the straightedge construction, written as a definition rather than as an instruction.

The same thing as arithmetic, for use on a table

The graphical version needs a plotted curve. Working from tabulated densities — which is what the assignment later in this part asks for, and what a spreadsheet does — the definition reduces to a single unknown. Let ΔD be the density difference between the two points and D₀ the measured base-plus-fog. Then:

D₁ = D₀ + 0.1 ΔD and D₂ = D₀ + 1.1 ΔD

The two points

log H(D₂) − log H(D₁) = √(4 − ΔD²)

The condition that fixes ΔD

CI = ΔD ÷ (log H(D₂) − log H(D₁)) = ΔD ÷ √(4 − ΔD²)

And the answer

Read those three lines slowly, because they are the whole convention. The first says where the two points sit: at fixed fractions of the density rise above the measured base. The second says the chord between them must be exactly 2.00 units long, so its horizontal run is the Pythagorean remainder. The third is just the slope. One unknown, one condition; solve it by trying three values of ΔD and interpolating, or with a solver in one line.

How the course quotes a number derived under it

Three rules, and they are not stylistic.

A figure produced by this construction is written as a course measurement. “Contrast index 0.62, measured under the criterion defined in Part XIII.” Never “the ISO contrast index”, which is not a thing, and never a bare “CI 0.62” on a page that has not said which construction it used.

A manufacturer’s published figure is written as theirs. “Kodak’s starting-point times for Tri-X are intended to produce a contrast index of 0.56.” That is Kodak’s number under Kodak’s construction, and the course does not silently merge it with its own.

The two are comparable but not identical. Kodak’s construction and this one are the same construction; the difference is that this one is stated arithmetically so that two people working from the same table get the same answer, where a straightedge on a hand-drawn curve gives a spread. Expect agreement to about 0.02, and say so when it matters.

And the link to cite is /part-13-sensitometry/gamma-contrast-index-and-average-gradient/#the-courses-contrast-index-convention. A later page that needs a contrast index points at that anchor; it does not restate the construction, because two statements of a convention are two conventions the moment one of them is edited.

What the convention does not claim

It does not claim to be a standard, and it does not claim conformance to one. It is a stated, reproducible criterion, published so that a reader can check it, and it is modelled on a published construction and on the contrast condition of a standard cited by number.

It does not make a home measurement into an absolute one. The exposure axis still depends on a nominal wedge and a lamp that is not a sensitometric illuminant; the density axis still depends on whatever geometry your reading method has. What the convention buys is that your contrast index today is comparable with your contrast index next month, and with any other figure produced by the same construction — which is the whole of what a contrast target needs to be good for.

And it does not settle which measure is right. Gamma, contrast index and average gradient are three answers to three slightly different questions, and the reason two manufacturers picked differently is that they were solving different problems. Kodak’s contrast index is built for a photographer choosing a development time for pictorial negatives, so it deliberately reaches into the toe where the shadows live and it hides its construction behind a straightedge anyone can use. A two-point density difference of the kind ILFORD monitors in process control is built for somebody watching a machine for drift, so it wants two fixed control-strip steps, an unambiguous subtraction, and no construction at all. Gamma survives because it is the only one of the three that means the same thing to a physicist. None is wrong; each is fit for its own purpose, and the harm comes only from quoting one and being read as another.

The three measures, on one curve

Here is why any of this pedantry earns its place. Kodak’s workbook tabulates eleven densities for one sample film and one development, and works two of the three measures on it. The third follows from the convention above. Same curve, same eleven numbers, three answers.

One published dataset, three constructions

• Measured densities, Kodak H-740 sample film
• Gamma, straight line only: 0.63
• Contrast index, this course criterion: 0.62
• Average gradient 0.18 to 1.70: 0.51

Show the numbers behind this plot

Eleven measured density points rise from 0.18 at log exposure 0.30 to 1.70 at 3.30, with a toe up to about log exposure 1.2 and a nearly straight run above it. Three straight lines are drawn across them. The gamma line joins the two straight-line points at density 0.64 and 1.58 and has a gradient of 0.63. The contrast-index chord runs from density 0.29 at log exposure 0.91 to density 1.33 at 2.61 and has a gradient of 0.62, and its backward extension reaches the base-plus-fog level of 0.18 at log exposure 0.74. The average-gradient chord joins the lowest and highest measured points, density 0.18 to 1.70, and has the shallowest gradient of the three at 0.51, because it includes the flat foot of the toe.

Series	Log exposure (millilux-seconds)	Density
Measured densities, Kodak H-740 sample film	0.30	0.18
Measured densities, Kodak H-740 sample film	0.60	0.20
Measured densities, Kodak H-740 sample film	0.90	0.28
Measured densities, Kodak H-740 sample film	1.20	0.45
Measured densities, Kodak H-740 sample film	1.50	0.64
Measured densities, Kodak H-740 sample film	1.80	0.82
Measured densities, Kodak H-740 sample film	2.10	1.01
Measured densities, Kodak H-740 sample film	2.40	1.20
Measured densities, Kodak H-740 sample film	2.70	1.39
Measured densities, Kodak H-740 sample film	3.00	1.58
Measured densities, Kodak H-740 sample film	3.30	1.70
Gamma, straight line only: 0.63	1.50	0.64
Gamma, straight line only: 0.63	3.00	1.58
Contrast index, this course criterion: 0.62	0.74	0.18
Contrast index, this course criterion: 0.62	0.91	0.29
Contrast index, this course criterion: 0.62	2.61	1.33
Average gradient 0.18 to 1.70: 0.51	0.30	0.18
Average gradient 0.18 to 1.70: 0.51	3.30	1.70

The eleven points are Kodak's published densities for its sample film and are plotted as measured; the three lines are constructions on them. The workbook itself gives 0.63 for gamma and 0.51 for the average gradient, and reads 0.61 for contrast index off the printed graph with a straightedge, against 0.62 from the arithmetic form of the same construction.

Solving the convention on this table takes three trials. Base-plus-fog is 0.18.

Trial ΔD	D₁ = 0.18 + 0.1ΔD	D₂ = 0.18 + 1.1ΔD	log H at D₁	log H at D₂	Actual run	Required √(4 − ΔD²)	Verdict
0.90	0.27	1.17	0.863	2.353	1.490	1.786	run too short, raise ΔD
1.00	0.28	1.28	0.900	2.526	1.626	1.732	still short
1.05	0.285	1.335	0.909	2.613	1.704	1.702	matched

So ΔD = 1.05, the run is 1.70, and CI = 1.05 ÷ 1.70 = 0.62.

Set the three side by side: γ = 0.63, CI = 0.62, G(0.18–1.70) = 0.51. Gamma and contrast index are close here because this sample curve has an unusually well-behaved toe. The average gradient is markedly lower because its lower point is the very foot of the toe, where the curve is almost flat, and that flat stretch is included in the average. Quote any of the three without saying which one it is and you have handed the reader a number that could be out by a fifth.

How development steers the slope

The reason contrast is worth measuring at all is that you control it — through development, which is a rate process, and rate processes have a shape.

Sheppard and Mees derived it in 1907 from their work on the dynamics of development, and it is still the form the curves take:

γ = γ_∞ (1 − e^−kt)

Gamma against development time

γ_∞ is the ultimate development factor attainable with infinite development, and it is a property of the plate. k is what they called the velocity constant, and it depends on the plate, the temperature and the concentration of the developer. What the equation says is that gamma climbs steeply at first, then flattens, and approaches a ceiling it never reaches. Doubling the development time from 5 to 10 minutes might take you from 0.51 to 0.67; doubling it again buys far less, and long before you get near γ_∞ the fog is rising faster than the contrast.

That shape is why manufacturers publish contrast-index against time curves rather than tables. Kodak prints them for T-Max 100 for seven developer and dilution combinations, in four processing arrangements — small tank, large tank, rotary tube and tray — at 20 °C, with the densitometry stated as diffuse visual, and the contrast index axis running from 0.3 to 0.9. Tri-X carries the same kind of plot. You read them backwards: pick the contrast index you want, go across to the developer’s curve, drop down to the time.

Kodak’s workbook has the reader do exactly that on a worked plot: a contrast index of 0.70 needs 11 minutes in its Developer A, and 0.58 needs 7.

📓Your own time-CI curve is the deliverable

The whole apparatus of this part exists so that you can plot that graph for your film in your developer at your temperature with your agitation, because those four variables are precisely the ones Kodak names as affecting contrast index and precisely the ones a published curve cannot know about. Three development times, three strips, three contrast indices, a smooth curve through them, and you can read a development time for any contrast you want for the rest of that film’s life. It is the single highest-value measurement in the course.

Choosing a target, honestly

Now the question every reader wants answered: what number should you aim for?

Both manufacturers publish a target, in their own measure. Kodak states, on the Tri-X datasheet, that its starting-point development recommendations are intended to produce a contrast index of 0.56. ILFORD states, on the powder-developer sheet for PERCEPTOL, ID-11 and MICROPHEN, that its published times should produce negatives of normal contrast, typically around a Gbar of 0.62, and its Ortho Plus sheet prints a development table indexed by target Gbar with the note that 0.62 to 0.70 would be considered normal for in-camera use.

A third number arrives from a different direction and lands in the same place. The speed criterion on the next page requires the density to rise 0.80 over 1.30 of log exposure, which is an average gradient of 0.80 ÷ 1.30 = 0.62, and the ±0.05 tolerance Kodak’s workbook allows on the 0.80 makes that a window of 0.58 to 0.65. Three independent routes — Kodak’s starting points, ILFORD’s stated aim and the development condition attached to speed — all put a normally developed pictorial negative in the region of 0.56 to 0.70. That convergence is worth noticing, and it is not a coincidence: all three are answers to the same question, which is what slope puts an ordinary subject onto an ordinary paper.

What the course cannot source is a target band tied to a viewing or printing system. Kodak says its T-Max starting points suit a diffusion enlarger and tells you to reduce development for a condenser, shifting one column to the left in its adjustment table; ILFORD quantifies the enlarger difference as about a grade. But no document in this course’s corpus states a contrast-index band for scanning, or a general band for condenser work. So the honest formulation is: the makers’ own aims cluster between 0.56 and 0.70 in whichever measure they use, a diffusion enlarger wants more contrast in the negative than a condenser does, and your own target is a measurement you make rather than a number you look up.

Why enlarger type matters at all is the Callier effect. A silver image scatters light as well as absorbing it. A condenser enlarger sends a fairly directional beam through the negative, so light scattered out of that beam is lost and the effective density is higher; a diffusion head illuminates from all directions, so much of the scattered light is recovered. Since scattering grows with density, the condenser raises the dense parts more than the thin ones — which is an increase in contrast. ILFORD puts the size of it plainly: condenser enlargers give about an extra grade of contrast compared with a diffuser, and the difference depends on how much silver is left in the negative. That last clause is the tell that this is a scattering effect and not a property of the lamp.

Slope and developer chemistry

Everything Part VIII established about developers now has a number attached to it. Four levers move the time needed to reach a given contrast index, and they move it for different reasons.

Activity. A more active developer — higher pH, a more energetic agent pairing — reaches a given gamma sooner, because it raises k in the Sheppard and Mees relation. Part VIII’s alkali and pH lesson is where that comes from, and superadditivity is why a metol and hydroquinone pair behaves as it does.

Dilution. Diluting a developer slows it, so a given contrast index takes longer — and because the developer is being locally exhausted while it works, dilution also changes the shape slightly, not only the timing. Part VIII’s acutance and compensation lesson is the mechanism, and it is why a dilute developer can hold highlights back while shadows continue.

Temperature. Rate processes follow the Arrhenius relation, so k rises steeply with temperature; Part III’s kinetics page gives the form and Part VIII gives the photographic consequence.

Solvent action. Sulfite dissolves silver halide as well as preserving the developer, and Part VIII’s solvent lesson shows what that does to grain and covering power. Its sensitometric signature is subtler than the others: it alters density per unit silver rather than the rate, so it can move the whole curve down slightly without changing how fast contrast builds.

The one thing none of them does is move the toe much. Exposure places the shadows; development sets the slope. Everything on this page is about the second half of that sentence.

From slope to a paper grade

Here is the bridge the printing parts will walk across.

Negative density range ≈ CI × subject log-luminance range

Negative density range

A subject measured at seven stops between the important shadow and the important highlight spans 7 × 0.301 = 2.11 in log luminance. Develop to CI 0.60 and the negative should span about 0.60 × 2.11 = 1.27 in density.

ILFORD then tells you what to do with that figure. Its Multigrade RC sheet gives ISO Range figures for each filter and instructs the printer to take the effective negative density range, multiply by 100, and choose the nearest range figure; its own worked example takes an effective density range of 1.32 log exposure units, multiplies to 130, and sends you to the corresponding filter. So a negative at 1.27 lands near an ISO Range of 130 — one of the softer filtrations, and a sane place to be.

Two caveats, both of which the paper lesson later in this part takes up properly. ILFORD says effective density range and specifies the image as projected on the enlarger baseboard, which means the figure already includes the Callier effect of your enlarger and its flare — so it is not quite the number your densitometer reads from the negative on a light box. And joining a film contrast index to a paper range figure is this course’s own inference from two manufacturers’ documents that were not written to be read together. It is a good working inference and the arithmetic is sound, but it is an inference, and the course says so rather than presenting it as either maker’s advice.

Do the maths

🧮Three measures and a development time

The ten readings below are constructed for this exercise, not measured from any material: they are a set of numbers with a plausible toe and a straight run, chosen so the arithmetic can be checked by hand. Base-plus-fog on the control strip reads 0.12.

log H	0.30	0.60	0.90	1.20	1.50	1.80	2.10	2.40	2.70	3.00
D	0.12	0.14	0.22	0.38	0.56	0.74	0.92	1.10	1.28	1.44

1. Gamma. Take differences first: 0.02, 0.08, 0.16, then five steps of 0.18, then 0.16 again. The straight run is therefore log H 1.20 to 2.70, and everything outside it is toe or shoulder. γ = (1.28 − 0.38) ÷ (2.70 − 1.20) = 0.90 ÷ 1.50 = 0.60.

2. Average gradient over the whole strip. G(0.12–1.44) = (1.44 − 0.12) ÷ (3.00 − 0.30) = 1.32 ÷ 2.70 = 0.49. Lower than gamma, for the usual reason: the flat foot is inside the average.

3. Contrast index. Try ΔD = 1.00, so D₁ = 0.12 + 0.100 = 0.22 and D₂ = 0.12 + 1.100 = 1.22. From the table, D = 0.22 falls at log H 0.90 exactly, and D = 1.22 falls between 1.10 at 2.40 and 1.28 at 2.70, so log H = 2.40 + 0.30 × (0.12 ÷ 0.18) = 2.60. The run is 2.60 − 0.90 = 1.70, and the requirement is √(4 − 1.00) = 1.73. Close; the run is slightly short, so nudge ΔD up. Try ΔD = 1.02: D₁ = 0.222, D₂ = 1.242, log H 0.904 and 2.637, run 1.733, requirement √(4 − 1.0404) = 1.720. Now the run is slightly long, so the answer is between. CI ≈ 0.59.

4. What that tells you. Gamma 0.60, CI 0.59, average gradient 0.49. The first two agree closely because this strip has a short toe; the third does not, because it swallows the flat foot. Do not expect the first agreement on a long-toe film, and do not assume it — the whole reason to state which construction you used is that it is not guaranteed.

5. Predict the print. Your subject measured EV 6 in the important shadow and EV 13 in the important highlight — seven stops, 2.11 in log luminance. At CI 0.59 the negative density range should come out near 0.59 × 2.11 = 1.24, which multiplied by 100 is 124, nearest to ILFORD’s range figure of 130.

6. Get to a different contrast. You want a negative density range of 1.05 instead, for a harder paper. That needs CI = 1.05 ÷ 2.11 = 0.50. On your own time-CI curve, find where 0.50 falls; if you have only this one point, 0.59 at 6 minutes, you cannot interpolate honestly yet — which is the point of plotting three times rather than one, and the reason the assignment in this part exists.

Recap

• Contrast is the slope of the characteristic curve, and slope is a multiplier: a subject difference in log luminance times the slope is a density difference on the negative.
• Gamma is the gradient of the straight-line portion. It is the oldest measure, it descends from Hurter and Driffield’s development factor, and it is unreliable on films with little straight line.
• Contrast index deliberately includes part of the toe, by a construction that places one point 0.20 units along a chord from the base-plus-fog line and the other 2.00 units further.
• Average gradient is the slope between two points you name, and the names are part of the number. It is ILFORD’s working measure, written Ḡ, and ILFORD publishes targets in it — but no document this course holds says which two points ILFORD takes it between.
• The course’s convention is fixed on this page and stated arithmetically: the two points sit at D₀ + 0.1ΔD and D₀ + 1.1ΔD, the chord is 2.00 long, and CI = ΔD ÷ √(4 − ΔD²). Later parts cite this section.
• On one published curve the three measures give 0.63, 0.62 and 0.51. Always say which you used.
• Development steers the slope along γ = γ_∞(1 − e^−kt), which is why makers publish contrast index against time, and why your own such curve is worth more than any of theirs.
• The makers’ own aims cluster between 0.56 and 0.70: Kodak’s Tri-X starting points at contrast index 0.56, ILFORD’s published times at Gbar 0.62, ILFORD’s Ortho Plus sheet calling 0.62 to 0.70 normal for in-camera use, and the speed criterion implying 0.58 to 0.65. A condenser enlarger wants a softer negative than a diffuser by about a grade, because of the Callier effect. Your own target is still a measurement rather than a lookup.

Check your understanding

Question 1. A film curve has base-plus-fog 0.10. A strip developed to your target gives density 0.20 at log H 1.00 and density 1.30 at log H 2.75. Is the chord between those two points a valid contrast-index chord under this course convention?

• Yes, because the density difference is 1.10 and the run is 1.75
• No, because the chord length is 2.06 rather than 2.00 and the lower point is not 0.1 of the rise above the base
• Yes, because both points lie on the curve
• It cannot be decided without knowing the development time

Show the answer and why

Answer: No, because the chord length is 2.06 rather than 2.00 and the lower point is not 0.1 of the rise above the base

Two conditions have to hold, and this chord fails both narrowly. Its length is the hypotenuse of 1.75 and 1.10, which is the square root of 3.0625 plus 1.21, or 2.066, where the convention requires exactly 2.00. And the lower point should sit at base plus 0.1 times the density difference, which would be 0.10 plus 0.110 equals 0.21, not 0.20. Neither error is large, and the resulting slope of 0.63 would not be far wrong, but the reason the convention is arithmetic rather than approximate is so that two people working from the same table get the same number rather than two numbers a couple of hundredths apart.

Question 2. From a tabulated curve with base-plus-fog 0.15, you find that ΔD = 1.20 satisfies the convention. What is the contrast index, and what are the densities of the two chord points?

• CI = 0.60; points at 0.27 and 1.47
• CI = 0.75; points at 0.27 and 1.47
• CI = 0.75; points at 0.15 and 1.35
• CI = 1.20; points at 0.15 and 1.35

Show the answer and why

Answer: CI = 0.75; points at 0.27 and 1.47

The points are D0 plus 0.1 times 1.20 = 0.15 plus 0.12 = 0.27, and D0 plus 1.1 times 1.20 = 0.15 plus 1.32 = 1.47. The run is the square root of 4 minus 1.44, which is the square root of 2.56, exactly 1.60. So CI = 1.20 divided by 1.60 = 0.75. Notice that the closed form CI = ΔD over the square root of 4 minus ΔD squared means you never have to read the run off the graph: once ΔD is found, the contrast index follows by arithmetic alone, which is what makes this convention usable in a spreadsheet.

Question 3. Why does the average gradient over a whole step-wedge strip almost always come out lower than the gamma of the same strip?

• Because average gradient is measured with a different densitometer geometry
• Because the chord for the average gradient includes the flat foot of the toe, where the curve contributes run but almost no density rise
• Because average gradient uses natural logarithms
• Because the strip was underdeveloped

Show the answer and why

Answer: Because the chord for the average gradient includes the flat foot of the toe, where the curve contributes run but almost no density rise

A chord from the lowest measured density to the highest spans the whole exposure axis, including the region below the toe where the curve is nearly horizontal. That region adds to the denominator of the slope and almost nothing to the numerator, so the average is pulled down. Gamma excludes it by construction, and contrast index includes only a defined slice of the toe, which is why contrast index usually sits between the two. On the Kodak sample curve the three come out at 0.51, 0.62 and 0.63, and the ordering is not a coincidence.

Question 4. You develop for twice as long and gamma rises from 0.55 to 0.70 rather than to 1.10. Which statement best explains it?

• The developer became exhausted, which is the only cause
• Gamma approaches a ceiling exponentially, as gamma infinity times one minus e to the minus kt, so equal increments of time buy less and less contrast
• The film has a maximum contrast index of 0.70
• The temperature must have dropped during the second half

Show the answer and why

Answer: Gamma approaches a ceiling exponentially, as gamma infinity times one minus e to the minus kt, so equal increments of time buy less and less contrast

Sheppard and Mees established the form in 1907 from their work on the dynamics of development: gamma rises towards gamma infinity, the ultimate development factor the plate can reach, along an exponential approach whose rate constant k depends on the plate, the temperature and the developer. Contrast per minute is therefore largest at the start and falls away, which is exactly what the published contrast-index against time curves show as their flattening. It also explains why chasing a very high contrast index by time alone is a poor trade: you are working on the flat part of the curve while fog, which has no such ceiling, keeps rising.

Question 5. A datasheet says its starting-point times are intended for printing with a diffusion enlarger. You print with a condenser. What should you do, and why?

• Develop longer, because a condenser needs more contrast in the negative
• Develop less, because a condenser raises the effective contrast of the negative through the Callier effect
• Nothing, because enlarger type affects only exposure time
• Change paper grade only, because development cannot be adjusted after the fact

Show the answer and why

Answer: Develop less, because a condenser raises the effective contrast of the negative through the Callier effect

A condenser sends a directional beam through the negative, so light scattered by the silver is lost to the projected image and the effective density rises. Scattering increases with density, so the dense parts rise more than the thin parts and the projected contrast increases: ILFORD quantifies it as about an extra grade, and notes it depends on how much silver is left in the negative, which is the signature of a scattering rather than a lamp effect. Kodak’s own instruction is to shift one column to the left in its development table for a condenser, which is a shorter time and so a lower contrast index. Develop for the enlarger you own.

Question 6. A page in a later part wants to report a contrast figure it measured itself. Which wording does this course permit?

• The ISO contrast index of this film in D-76 is 0.62
• Contrast index 0.62, measured under the criterion defined in Part XIII, which is modelled on ISO 6
• ISO 6 gives a contrast index of 0.62 for this development
• CI 0.62

Show the answer and why

Answer: Contrast index 0.62, measured under the criterion defined in Part XIII, which is modelled on ISO 6

The course does not purchase the standards and quotes no part of them, so it cannot attribute a figure to one; and there is no such quantity as an ISO contrast index in any case, since the standard the criterion is modelled on is about speed. The last option fails for a different reason: a bare CI figure does not say which of three constructions produced it, and the three disagree by up to a fifth on the same curve. Naming the criterion, and naming the standard it is modelled on, is both the honest form and the useful one, because a reader can reproduce it from the definition on this page.

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