Sensitometer Design Principles

An enlarger with a wedge under it and a sensitometer do the same thing in the same order: light through a graded mask onto film. What separates them is not quality of construction. It is that a sensitometer is designed so that every quantity in the exposure equation is either fixed or measured, and an enlarger is designed so that they can all be changed conveniently. Convenience is exactly the wrong property in an instrument.

This page settles the design before any of it is built: which kind of exposure the instrument gives, what may and may not be done to the lamp during it, what colour the light is, how the light is spread, how long it lasts, what the wedge contributes, and how big the resulting uncertainty is. Two earlier parts do the underlying work and are cited rather than repeated: Part IV owns reciprocity failure, and Part XIII owns the measurement conventions that every figure here is quoted under.

What a sensitometer was, before it was an instrument

Kodak’s description of one is four boxes: a light, a shutter, a filter, a holder for a step tablet, and the film. The exposure is illuminance times time, and the illuminance can be read with a lux meter — their worked example is 100,000 millilux for one-fifth of a second, which is 20,000 millilux-seconds and a log exposure of 4.3. That really is the whole idea.

Hurter and Driffield had no such box. Their unit was the candlemetre-second: a standard candle at one metre for one second. Read what that cost them. The flame could not be relied on until it had settled to nearly 45 mm measured from the top of the spermaceti; the candle had to be shielded from draughts inside a black box open on one side, which also stopped it lighting up the room and reflecting back onto the plate; time was taken on a chronograph watch or a metronome, and they judged their timing errors too great below ten seconds. When they wanted less exposure than ten candlemetre-seconds they did not shorten the time — they moved the candle to two metres, quartering its intensity by the inverse-square law, and then verified experimentally that a quarter candlemetre for 40 s and one candlemetre for 10 s gave the same result.

Their reproducibility is the number to keep. On three separate days, working carefully, they obtained densities of 0.750, 0.730 and 0.720 from the same batch of plates. Four different standard candles gave 0.490, 0.490, 0.500 and 0.480 on one plate. That is a spread of about 0.03 in density from the source and the timing together — in 1890, with a candle.

Sheppard and Mees, seventeen years later, catalogue what replaced it. The sector wheel — a disc with increasing angular apertures spun in front of the plate — they attribute to Claudet in 1840 and to W. B. Bolton, note that Hurter and Driffield adopted it with nine apertures each twice the preceding, and that Scheiner used a ratio of 1 to 1.27. They are scathing about it: the angles cannot be cut accurately enough without the precision of circle division, the errors fall hardest on the smallest angles, and any wheel should be calibrated after it is made. The form they call the best theoretical one is General Sebert’s, shown at the Paris Congress of 1900, in which clockwork draws the plate past a row of slots of different lengths at a constant rate.

!Two instruments this page names and does not describe

The Eder–Hecht wedge and Kodak’s own laboratory sensitometers (the Type Ib, IIb and 101 that the literature refers to) belong in this history. The course has not found a primary source for the construction or the dates of either, so it names them as things that exist and describes neither. A plausible paragraph assembled from secondary accounts would read exactly like the sourced paragraphs above and would be worth nothing.

Intensity scale against time scale

There are only two ways to give a strip of film a graded exposure.

Intensity-scale: every step gets the same time and a different amount of light, the difference produced by a step wedge laid over a uniform source.

Time-scale: every step gets the same light and a different length of time — a sector wheel, a moving slot, or in the modern version a strip re-exposed under a mask at ten different durations.

Time-scale is much easier to build. It needs a timer, which you have, rather than a calibrated wedge, which you must buy. It is also wrong, and Sheppard and Mees name the reason in the same breath as they name the objection to intensity scales: the Bunsen–Roscoe reciprocity law fails. Equal products of intensity and time do not give equal density, so the two methods cannot give the same curve, and the question is only which way each one is wrong.

They are wrong at opposite ends.

Intensity-scale loses at the toe. Every step is one second long, but the dense end of a 3.0 wedge delivers a thousandth of the illuminance of the clear end. ILFORD describe low-intensity reciprocity failure as a reduced efficiency in forming stable development centres at low light levels — so the faintly exposed steps are penalised, and the toe is depressed and stretched.

Time-scale loses at the shoulder. Every step gets the same illuminance, so the heavily exposed steps are the long ones. ILFORD’s own compensation table is written for exactly that case: a metered ten seconds needs 20.4 s of real exposure on HP5 Plus. The long steps therefore fall short of where their nominal exposure puts them, and the upper part of the curve is pulled down — which reads as lower contrast.

The same film, the same nominal exposures, by the two methods

• Intensity scale: one second, wedge grades the light
• Time scale: fixed light, ten different durations

Show the numbers behind this plot

Two characteristic curves plotted against the same relative log exposure axis running from -2.4 to 1.5. Both start together at a base density of 0.12 at the far left. The intensity-scale curve rises later out of the toe but then climbs more steeply, passing 1.54 at log exposure zero and flattening towards a maximum near 2.34. The time-scale curve leaves the toe slightly earlier, because its faint steps are given full illuminance for a short time rather than a thousandth of the illuminance for a full second, but from the middle onwards it climbs less steeply and flattens much lower, reaching only about 1.97. The two curves therefore cross in the lower third and diverge upward, so that the time-scale curve reports both a slightly higher speed and a distinctly lower contrast from the same material.

Series	Relative log exposure	Density
Intensity scale: one second, wedge grades the light	-2.40	0.12
Intensity scale: one second, wedge grades the light	-2.10	0.13
Intensity scale: one second, wedge grades the light	-1.80	0.16
Intensity scale: one second, wedge grades the light	-1.50	0.24
Intensity scale: one second, wedge grades the light	-1.20	0.42
Intensity scale: one second, wedge grades the light	-0.90	0.68
Intensity scale: one second, wedge grades the light	-0.60	0.96
Intensity scale: one second, wedge grades the light	-0.30	1.25
Intensity scale: one second, wedge grades the light	0.00	1.54
Intensity scale: one second, wedge grades the light	0.30	1.82
Intensity scale: one second, wedge grades the light	0.60	2.05
Intensity scale: one second, wedge grades the light	0.90	2.21
Intensity scale: one second, wedge grades the light	1.20	2.30
Intensity scale: one second, wedge grades the light	1.50	2.34
Time scale: fixed light, ten different durations	-2.40	0.12
Time scale: fixed light, ten different durations	-2.10	0.14
Time scale: fixed light, ten different durations	-1.80	0.19
Time scale: fixed light, ten different durations	-1.50	0.30
Time scale: fixed light, ten different durations	-1.20	0.50
Time scale: fixed light, ten different durations	-0.90	0.75
Time scale: fixed light, ten different durations	-0.60	1.00
Time scale: fixed light, ten different durations	-0.30	1.24
Time scale: fixed light, ten different durations	0.00	1.45
Time scale: fixed light, ten different durations	0.30	1.63
Time scale: fixed light, ten different durations	0.60	1.78
Time scale: fixed light, ten different durations	0.90	1.88
Time scale: fixed light, ten different durations	1.20	1.94
Time scale: fixed light, ten different durations	1.50	1.97

Both curves are drawn to teach the direction of each departure and were not measured. What is sourced is the direction: low-intensity failure penalises the faint steps of an intensity scale, and the long-time correction ILFORD publish penalises the bright steps of a time scale. 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.

Which should an instrument use? The one that matches how a photograph is actually made. A camera gives one exposure time across a subject of varying luminance, so an intensity scale is a model of the real event and a time scale is a model of nothing. That is also what the standard the course’s speed criterion is modelled on requires; ISO 6 is cited by number, as Part XIII established, and no part of it is reproduced here.

The design decision: intensity scale, one fixed exposure time, the wedge providing the whole ladder. This is also why the wedge is the one component that cannot be improvised.

The intermittency effect, and the one thing it forbids

Sheppard and Mees put the next constraint in place, and they measured it rather than asserting it.

An intermittent exposure — light delivered as a train of flashes — does not give the same result as a continuous exposure of the same total. They credit A. and L. Lumière with first showing this in 1881 and Abney with the first complete investigation. Because their own sensitometry used a sector wheel, they tested whether it mattered: two Wratten ordinary plates exposed together for five minutes, one with the wheel at 1520 revolutions per minute and one at 9.5. At the bright end the two plates agreed closely. At the faint end they did not: at log E 0.80 the fast wheel gave 0.105 and the slow wheel 0.245, and at log E 1.10, 0.307 against 0.470. Their conclusion was practical: keep a sector wheel below 100 revolutions per minute and the intermittency error is negligible even for slow plates.

Read the direction carefully, because it decides a modern design question. Faster chopping was worse. Fast enough, the material stops resolving the individual flashes and responds as though to a continuous exposure at the average intensity — which, being a lower intensity, suffers low-intensity reciprocity failure. Slow enough, each flash acts on its own at full intensity, which is what a time-scale exposure is trying to deliver. The intermittency effect is low-intensity reciprocity failure wearing a different hat, which is why the glossary files them together.

!The design rule this produces: no PWM during an exposure

A microcontroller dims an LED with pulse-width modulation, typically at hundreds of hertz to tens of kilohertz. A 1 kHz PWM signal is a train of flashes at most a millisecond long with gaps between them — far into the regime Sheppard and Mees found worst, and thousands of times faster than the 100 rpm below which they were prepared to call the error negligible.

So the instrument’s LED is driven at a fixed direct current for the whole exposure, switched cleanly on and cleanly off, and the microcontroller’s PWM peripheral is not used to set its brightness at any point. Brightness is set by the driver’s current, which is a knob you turn once and then measure.

This is a rule the course adopts on the evidence it has, and it is deliberately conservative. The critical frequency above which a modern emulsion stops resolving flashes is not published in any source the course has read, and the course will not assume a number for it. If you want to know, the experiment is at the foot of this page — and it is a good one.

The illuminant, and why the answer here is “relative”

ISO 6 refers the sensitometric illuminant to a separate standard, ISO 7589, which defines the daylight and incandescent tungsten sources a standard speed rating assumes. This course does not purchase either standard and quotes neither. What matters for the design is that a standard speed is tied to a standard spectrum, and an LED is not one.

A phosphor white LED is a blue emitter with a phosphor over it. Cree’s relative spectral power distribution for the white XP-E2 is exactly that shape: a narrow peak at the blue pump and a broad hump across the greens, yellows and reds. It is not a black body and it is not daylight.

A phosphor white LED against a panchromatic film's sensitivity

• Phosphor white LED, relative emission
• Panchromatic film, relative sensitivity

Both curves are drawn to show shape and were not measured or traced. The LED shape follows the blue-pump-plus-phosphor structure Cree's own distribution chart shows; the film shape follows the general form of a dye-sensitised panchromatic emulsion with a red cut-off. ILFORD publish HP5 Plus's spectral sensitivity as a wedge spectrogram to tungsten at 2850 K rather than as numbers, so no numbers are traced here. The coloured strip approximates where the visible spectrum falls and is a reading aid only; the wavelengths in the labels carry the information. The bands and curves are drawn to show the relationship, not measured.

Three consequences, and the third is the one that matters.

A lux meter will not translate this into an exposure. Lux is photopically weighted — it counts green heavily and blue and red lightly. The film’s weighting is different, and the LED’s output is concentrated exactly where the two disagree most. A lux reading of a white LED is a perfectly good measure of whether the lamp has changed, and a poor measure of how much the film received.

A monitor photodiode is worse still, and is not trying to be a photometer. The BPW34’s sensitivity peaks at 920 nm, deep in the infrared where no black-and-white film responds at all, and runs from 420 to 1120 nm. It is a constancy sensor: it answers “is the lamp doing now what it did an hour ago”, which is precisely the question the instrument needs answered during an exposure.

So the speed this instrument measures is relative, and the course already ruled on how to say so. Every figure is quoted as the course’s own measurement under the course’s own criterion, never as an ISO speed. That is not a limitation this design introduces; ILFORD themselves rate HP5 Plus on a practical evaluation and say plainly that it is not the foot speed the ISO standard uses.

White or green: the decision, and the evidence for it

A green LED would be better photometry. Its output sits near the photopic peak, so a lux meter reads it with far less weighting error, and a single-die emitter’s spectrum is more stable than a two-component mixture — Cree publish a chart of relative chromaticity against current and temperature for the white parts, which is evidence that the blue-to-phosphor ratio moves with both.

The course chooses white, for one reason that outweighs those: the instrument’s job is to produce curves that can be compared with manufacturers’ published curves, and those are made under broadband illuminants. A green exposure measures a green speed of a panchromatic film, which is a real number about a different question. The prices of that choice are stated rather than hidden: a spectrum that moves a little with drive current and temperature, controlled by the same fixed-current and warm-up discipline that controls the flux; and a lux figure that is a constancy check rather than a photometric conversion.

Anyone who wants the better photometry should build the green variant — the green XP-E2 has a typical forward voltage of 2.7 V at 350 mA and a thermal resistance of 9 °C/W, so it needs a slightly better heatsink — and write “green, dominant wavelength as the maker gives it” on the instrument certificate, where it belongs.

Uniformity: the geometry that decides everything

A Stouffer T2115 is half an inch by five inches: the illuminated field must cover 127 mm of length. If the light falls off along that length, the fall-off adds itself to the wedge’s densities and is read as film behaviour. Part XIII already measured this under an enlarger and expressed it in wedge steps.

For a small source facing the film plane, three effects compound. The inverse-square law reduces the illuminance with the square of the slant distance. The cosine law at the film reduces it again, because the light arrives obliquely and spreads over more area. And a Lambertian emitter sends less light sideways than forward, by another cosine. With θ the angle from the axis:

E(θ) ÷ E(0) = cos⁴θ, where tan θ = r ÷ d

Off-axis fall-off from a small Lambertian source

E is illuminance, r the distance from the axis in the film plane, and d the axial distance from source to film. The three cosines are elementary geometry rather than a citation: one from the longer slant path squared, one from the oblique arrival at the film, one from the source’s own fall-off with angle. Expressed as the course’s working unit — log exposure — the fall-off at the end of the wedge is −4 log₁₀(cos θ), and the target is 0.02 log H, which is an eighth of one nominal wedge step.

🧮How far away the lamp has to be

Half the wedge’s length is r = 63.5 mm. Work the fall-off at the end of the wedge for a range of distances:

Source-to-film distance d	cos θ	cos⁴θ	Fall-off, log H
100 mm	0.844	0.508	0.294
150 mm	0.921	0.719	0.143
200 mm	0.953	0.825	0.083
300 mm	0.978	0.916	0.038
400 mm	0.988	0.951	0.022
500 mm	0.992	0.969	0.014

At 150 mm the ends of the wedge are 0.143 log H darker than the middle — very nearly a whole nominal wedge step, which would be an outright fraud dressed as a measurement. To reach 0.02 log H from a small source you need about 420 mm of throw, and a box 450 mm deep.

Across the wedge’s width the same arithmetic is trivial: r = 6.35 mm at d = 200 mm gives 0.0009 log H. The long axis is the entire problem.

This is why the design has an opal diffuser and a chamber rather than a bare LED at the far end of a tube. The table above is the worst case, for a source small compared with the distance. An opal panel comparable in size to the wedge is not a small source: each element of it obeys cos⁴, but the film sees the whole panel, and in the limit of a very large uniform panel the illuminance becomes uniform. The flattening is real and large, and it depends on the panel’s size, the chamber depth and how white the walls are — which is why the course measures it on the enclosure page with a uniformity map instead of predicting it here.

The diffuser is also the reason the lamp needs headroom. Much of what the LED emits is absorbed in the chamber walls or scattered backwards. ISO 5-2, cited by number, is the standard that specifies the geometric conditions for transmittance density, and its publisher’s preview records that the 1985 edition replaced the integrating-sphere method with a diffuser, typically opal glass — the same component, doing the same job, at the reading end of the chain.

The light path, with the two fall-off terms marked

1. 1LED on star board and heatsink — a small source; the cos⁴ table applies to this alone
2. 2Chamber, white walls — what is not absorbed here comes back out through the diffuser
3. 3Opal diffuser — turns the point into an extended source and flattens the field
4. 4Film, wedge, glass — emulsion to emulsion, contact held by the weight of the glass
5. 5d, source to film plane — 420 mm from a small source for 0.02 log H; far less with the diffuser, but measure it
6. 6r, axis to end of wedge — 63.5 mm for a 127 mm T2115

Two of the four cosines are the inverse-square law along the slant path; one is the obliquity at the film; one is the source's own fall-off with angle.

How much light, and for how long

The two questions are one question, because exposure is their product.

🧮The illuminance the film plane actually needs

Use the course’s speed criterion: S = 0.80 ÷ H, with H in lux-seconds. For a film rated 400 that puts the criterion exposure at H = 0.80 ÷ 400 = 0.002 lux-seconds.

The criterion point should sit near the dense end of the wedge so the whole curve fits on the strip — say step 16, density 2.30. The clear end of the wedge must therefore deliver

0.002 × 10^2.30 = 0.002 × 200 = 0.4 lux-seconds

which, in a one-second exposure, is 0.4 lux at the film plane. Kodak’s worked example checks out against this: 20,000 millilux-seconds behind a 0.95 filter is 2.24 lux-seconds reaching the wedge, and an ISO 100 criterion exposure of 0.0079 lux-seconds then lands at wedge density 2.45 — step 17.

Now the other end of the range. ILFORD note that Multigrade RC papers are roughly equivalent to a film ISO of 3 to 6. At 3, the criterion exposure is 0.27 lux-seconds and the clear step must deliver 53 lux-seconds.

So the instrument must be adjustable over a factor of about 130, or 2.1 log units, between fast film and paper. That is the specification the drive current and any fixed neutral filter have to meet between them — and it is the number that stops a builder buying a lamp for brightness. The problem is not getting enough light out. It is getting little enough, evenly.

The exposure time. The manifest for this part suggested one to four seconds. The manufacturers’ own statements will not support the upper half of that range. ILFORD state that exposure times of one second or less need no reciprocity compensation, and give the correction above that as metered time raised to a film-specific power — 1.26 for FP4 Plus, 1.31 for HP5 Plus. Four seconds on HP5 Plus is 4^1.31 = 6.2 s of effective exposure, which is a 0.19 log H error, larger than every other term in the budget put together. Foma are stricter still: their Fomapan 100 table gives a factor of 1× only up to half a second and already 2× at one second.

So the course’s design target is 0.5 s, with 1.0 s as the outer limit and only for ILFORD films, and any exposure longer than that is a documented departure whose cost is computed from the maker’s own factor and written on the strip. It is a real constraint on the design: a shorter exposure needs a brighter lamp, and a brighter lamp is harder to make uniform.

Why there is no mechanical shutter. In an LED instrument the lamp is the shutter. The switch’s own speed is set by the MOSFET gate charging through its resistor — 330 Ω into 1700 pF is 0.56 µs, as the electronics page works out — which against half a second is a part in a million. Note what the course does not claim: Cree’s XP-E2 datasheet publishes no switching or rise time at all, so the course quotes none for the LED itself, and the driver module’s own turn-on is measured on the build page rather than assumed.

A mechanical shutter would add three problems the design does not otherwise have: a shutter efficiency curve, since the blades take time to open and close and the film is partly exposed throughout; wear, so that the calibration decays; and vibration, in an assembly whose entire premise is that the wedge and the film do not move relative to one another.

The wedge is the ruler, and rulers are calibrated

Everything above controls one exposure. The wedge divides it into twenty-one, and its errors go straight into the log exposure axis.

Nominal is not calibrated. Stouffer are unusually clear about what the money buys: calibrated and uncalibrated guides come from the same production batches and are made with the same control, and what calibration adds is that each step is read on a densitometer and the readings recorded. The calibrated parts, the T2120CC and T1530CC, are read against NIST Standard Reference Material 38120C on a densitometer conforming to ANSI PH2.19-1986. An ordinary T2115 is manufactured to a 0.15 increment, not certified to it — which Part IX established and Part XIII inherited, and which this part does not revisit except to say that here is where buying the calibrated part finally pays.

Contact and orientation. Emulsion to emulsion, wedge face down on the film. Turned over, the wedge’s polyester base sits between the two emulsions and light spreads in it before reaching the film, softening every step boundary. Part XIII’s lab page draws the sandwich; the enclosure build turns that drawing into registration stops so it happens the same way in the dark every time.

Spectral neutrality. A wedge for sensitometry must attenuate all visible wavelengths nearly equally, or its “0.15 step” is a different step for the blue peak of an LED than for the phosphor hump. A silver wedge made for graphic arts is close to neutral; a dyed or printed grey scale is not, and is not a sensitometric instrument whatever it costs. The standards set a numerical tolerance on this, which the course does not reproduce.

The error budget

Part II’s rule governs how these combine: for a quantity built by multiplying, the relative uncertainties add in the worst case, and the course teaches that bound rather than a statistical combination because the bound is arithmetic anyone can check. In log exposure, where multiplying becomes adding, that means the terms simply add.

Where the log exposure uncertainty comes from

1. 1Uniformity, 0.020 log H — the design target across the wedge; measured, not assumed
2. 2Lamp drift, 0.004 log H — one per cent of flux, held by constant current and a warm-up rule
3. 3Timing, 0.0002 log H — a few hundred microseconds in half a second
4. 4Wedge steps, unknown — systematic and common to every strip, so it cancels in a comparison and dominates any absolute claim
5. 5Illuminance and spectrum, unknown — absolute scale only; the course has verified no lux-meter accuracy specification

Attack the first bar. It is five times the second, a hundred times the third, and it is the only one that geometry alone can fix.

Read the bars in order and the conclusions are forced.

The relative scale is dominated by uniformity, and uniformity is geometry, which means it is the one term a builder can fix with a longer box and a bigger diffuser. Everything else is already smaller than it.

The absolute scale is dominated by things the course cannot measure well, and it says so. The wedge’s step errors are unknown unless the calibrated part is bought. The illuminance measurement rests on a consumer lux meter whose accuracy specification the course has not verified against any manufacturer or standard, so the calibration experiment states the method and leaves the number blank until a specification is in hand. And the spectral mismatch between a photopic meter and a panchromatic film has no correction the course can apply.

Processing is not in this budget at all, and that is deliberate: it is a density error rather than an exposure error, and the control strip is what separates it. Which is the whole subject of the second experiment in this part.

What Part XIII’s method could and could not support

Most readers of this course will keep exposing step wedges under an enlarger, and they should know exactly what that gives them, said plainly and without apology on either side.

What it supported, and still does. A characteristic curve of the right shape. A contrast index, computed under the course’s convention, good enough to compare one developer with another and this month with last, because the wedge’s errors are common to both sides of a comparison and cancel. A speed relative to the reader’s own other strips. And a working discipline — the control strip, the measured uniformity, the recorded head height — that is most of what sensitometry actually is.

What it could not support. An exposure inside the reciprocity-valid region: Part XIII’s own lab brackets at 4, 8 and 16 seconds, and its page says so in a callout rather than hiding it, but that is already a 0.19 to 0.4 log H departure and it falls unequally along the wedge, because the dense end is receiving a thousandth of the illuminance of the clear end for the same duration. A stable source: a tungsten lamp drifts as it warms, ages over its life, and changes colour as it does both. A uniformity better than the enlarger’s field, measured at 0.2 of a step in Part XIII’s own procedure. And a geometry that repeats, since the head height must be re-set and the wedge re-placed every session.

What the box buys is therefore not accuracy in the abstract. It is a shorter exposure, a source that does not move, a field that has been mapped once, and a geometry that is the same next month — and those four together are what turn a set of curves into a time series you can trust.

Design alternatives, and what each costs

A filtered tungsten source. Closest in spirit to the illuminant standards, since ISO 7589 defines its illuminants in terms of a tungsten source and filters. It also brings back everything the LED removed: a thermal source needs a mechanical shutter because it cannot be switched cleanly, it drifts as it warms and ages over its life, it draws far more power than a USB supply provides, and the conversion filter is one more component the course would have to source and verify. It is the right answer for a laboratory and the wrong one for this build.

A monochromatic green LED. Discussed above: better photometry, a more stable spectrum, a green speed rather than a panchromatic one. A defensible variant, and the certificate must say so.

A time-scale mode, deliberately, as an experiment. The same hardware can expose ten strips at ten durations without a wedge at all, with the drive current scaled so that each strip’s nominal exposure matches. Overlay the resulting curve on the intensity-scale one and the divergence drawn at the top of this page becomes your own measurement of your own film’s reciprocity behaviour — which is exactly the comparison Sheppard and Mees called desirable and difficult in 1907.

Recap

A sensitometer differs from an enlarger with a wedge under it in that every quantity in the exposure is fixed or measured. The exposure is intensity-scale — one time, the wedge grading the light — because that is how a photograph is made, and because reciprocity failure makes the time-scale alternative wrong at the shoulder while the intensity scale is only wrong at the toe. Sheppard and Mees measured the intermittency effect and found faster chopping worse, which forbids PWM dimming during an exposure and leaves fixed direct current as the only drive. The illuminant is a phosphor white LED, chosen for comparability with published curves rather than for photometric convenience, and it is why every speed this instrument yields is relative and is quoted under the course’s own criterion. Uniformity is the dominant error and is pure geometry: cos⁴θ puts a bare source 420 mm from a 127 mm wedge for 0.02 log H, and the diffuser is what makes a shorter box possible — by an amount that must be measured. The exposure is half a second, not the four seconds first proposed, because the manufacturers’ own reciprocity statements will not support longer. The wedge is the ruler, and only the calibrated part is a ruler rather than a rule of thumb. And the error budget adds, on Part II’s bound: 0.024 log H relative, and an honest blank for absolute.

Check your understanding

Question 1. The wedge is 127 mm long and you want the illumination at its ends to be within 0.02 log H of the centre. Working from a small source with the cos⁴ fall-off, roughly how far must the source be from the film plane?

• About 150 mm
• About 250 mm
• About 420 mm
• About 1200 mm

Show the answer and why

Answer: About 420 mm

Half the length is r = 63.5 mm. You need cos⁴θ ≥ 10^(−0.02) = 0.955, so cos θ ≥ 0.9886 and tan θ ≈ 0.152, giving d = 63.5 ÷ 0.152 ≈ 420 mm. Check the neighbours: 150 mm gives cos θ = 0.921 and a fall-off of 0.143 log H, very nearly a whole wedge step, and 250 mm still gives 0.054. The diffuser is what lets a real box be shorter than 420 mm, because it stops the source being small — but by how much is a measurement, not a calculation.

Question 2. You expose a strip for 4 s on HP5 Plus rather than the 0.5 s the design calls for. Using ILFORD's published factor of 1.31, how much exposure error does that introduce, and where does it fall?

• About 0.02 log H, spread evenly along the wedge
• About 0.19 log H, and unequally, because the dense end of the wedge receives a far lower illuminance for the same time
• None, because reciprocity failure depends on total exposure rather than on time
• About 0.19 log H, but it cancels because every step is exposed for the same 4 s

Show the answer and why

Answer: About 0.19 log H, and unequally, because the dense end of the wedge receives a far lower illuminance for the same time

The corrected time is 4^1.31 = 6.2 s, so the film behaves as though it had received 6.2 s of the nominal illuminance: log(6.2 ÷ 4) = 0.19 log H of lost speed. It does not cancel, because low-intensity failure is worse at lower illuminance and the dense end of a 3.0 wedge is receiving a thousandth of what the clear end gets. So the loss varies along the strip and changes the curve's shape as well as its position — which is exactly why the design targets half a second.

Question 3. Sheppard and Mees exposed two plates for five minutes through a sector wheel, one at 1520 rpm and one at 9.5 rpm, and found the fast wheel gave 0.105 where the slow wheel gave 0.245 at the same nominal exposure. What design rule follows for a microcontroller-driven LED?

• Dim the LED with PWM at a low frequency, below about 100 Hz
• Dim the LED with PWM at a high frequency, above about 10 kHz, so the film cannot resolve the flashes
• Do not use PWM during an exposure at all; drive the LED at a fixed direct current
• Use PWM freely, since the intermittency effect applies only to sector wheels

Show the answer and why

Answer: Do not use PWM during an exposure at all; drive the LED at a fixed direct current

Their result says faster chopping is worse: at high frequency the material stops resolving individual flashes and responds as though to a continuous exposure at the lower average intensity, which then suffers low-intensity reciprocity failure. PWM at hundreds of hertz upwards is far into that regime — thousands of times faster than the 100 rpm below which they were willing to call the error negligible. The second option has the physics backwards, and the low-frequency option would put a visible flicker structure into a half-second exposure. Fixed current, cleanly switched, is the only drive that avoids the question, and the course adopts it rather than assume a critical frequency no source it has read publishes.

Question 4. A lux meter reads 3.0 lux at the film plane and the exposure is 0.5 s. For an ISO 400 film with the criterion point placed at wedge step 16 (density 2.30), is the lamp about right, too bright or too dim?

• About right
• Roughly four times too bright
• Roughly four times too dim
• Roughly a hundred times too bright

Show the answer and why

Answer: Roughly four times too bright

The criterion exposure is H = 0.80 ÷ 400 = 0.002 lux-seconds, and at wedge density 2.30 the clear step must therefore deliver 0.002 × 10^2.30 = 0.4 lux-seconds. In 0.5 s that calls for 0.8 lux at the film plane. Three lux gives 1.5 lux-seconds, which is 3.75 times too much — the criterion point would land near step 19 and the toe would fall off the end of the wedge. Turn the drive current down or add a fixed neutral filter. The surprise on this page is that a sensitometer's problem is getting little enough light, evenly, not enough of it.

Question 5. Why does the course choose a phosphor white LED over a green one, given that green sits near the photopic peak and a single-die emitter has the more stable spectrum?

• Because white LEDs are brighter for the same current
• Because a green exposure would measure a green speed of a panchromatic film, and the instrument's purpose is curves comparable with published ones made under broadband illuminants
• Because ISO 7589 specifies a white illuminant
• Because a lux meter cannot read a green source

Show the answer and why

Answer: Because a green exposure would measure a green speed of a panchromatic film, and the instrument's purpose is curves comparable with published ones made under broadband illuminants

The green case is real and the page concedes it: a lux meter weights green most heavily, so the photometry is better, and Cree publish a chromaticity-against-current-and-temperature chart for the white parts which is direct evidence that the blue-to-phosphor mixture moves. What outweighs it is comparability. A panchromatic film exposed only to green returns a true number about a different question. The prices of choosing white are named rather than hidden: a spectrum that shifts slightly with current and temperature, and a lux reading that is a constancy check rather than a photometric conversion.

Question 6. Your finished instrument has a mapped uniformity of 0.02 log H, a measured lamp drift of one per cent, and a timing repeatability of 300 µs in half a second. What relative uncertainty do you quote, and which term do you attack first?

• About 0.005 log H; attack the drift
• About 0.024 log H; attack the uniformity
• About 0.15 log H; attack the wedge
• About 0.024 log H; attack the timing

Show the answer and why

Answer: About 0.024 log H; attack the uniformity

One per cent of flux is log(1.01) = 0.0043 log H, and 300 µs in 500 000 µs is 0.0006 of the exposure, or 0.00026 log H. Part II's rule is that relative uncertainties add in the worst case, which in log exposure means the terms add directly: 0.020 + 0.004 + 0.0003 ≈ 0.024 log H. Uniformity is five times the next term and a hundred times the one after, and it is the only one geometry alone can fix — a longer chamber or a larger diffuser. The wedge does not appear in the relative figure at all, because its step errors are systematic and common to every strip, so they cancel in a comparison; they dominate any absolute claim instead.

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