Kodak's own curves put modern colour negative at 0.6 to 4.9 percent quantum efficiency

Detective quantum efficiency asks how much of the information in arriving light a detector keeps, and it puts a film, a camera sensor and an eye on one scale. We derived it for the nine colour layers of three current Kodak motion-picture stocks, 5219 (500T), 7213 (200T) and 7203 (50D), from numbers Kodak prints on its data sheets, under a preregistered plan with planted checks. Peak detective quantum efficiency across the nine layers has a median of 2.1 percent and a range of 0.57 to 4.92 percent, an upper estimate because every photon is counted at the layer's most efficient wavelength.c1 In the green layer, 500T and 200T reach 4.5 and 4.9 percent although 200T needs about twice the photons; 50D needs 15.7 times the photons of 500T and reaches 1.5 percent.c2 Siedentopf's rule, that grain variance grows with density, lost on held-out points in 9 of 9 layers, and variance falls with density overall (median power slope -0.54); because our planted variance check failed, this is description only.c3 A straight hinge in log exposure was the best held-out response form in 9 of 9 layers.c4 A single Poisson hit-threshold model does not fit.

A film is a photon detector with a long history of measurement. The detective quantum efficiency (DQE)Definition: detective quantum efficiency (DQE) imaging science and detector physics The share of the information carried by the arriving photons that a detector's output keeps, measured as the square of its output signal-to-noise ratio divided by the square of the input's. 1 is a perfect photon counter. Excludes the plain share of photons absorbed, and the speed of a film. full definition of a detector compares the information in its output with the information in the light that arrived. Shaw introduced the photographic form of the idea in 1963 under the name equivalent quantum efficiency [2] and used it to compare the information capacity of photography with other detectors [3]. Dainty and Shaw's book on image science [4] treats DQE curves, granularity and the characteristic curve together. We found these works through searches run on 9 November 2026 and read the abstract of the second Shaw paper and the catalogue records of the others; the full texts were not read.

What a sheet gives is enough for a ceiling estimate. Kodak publishes, for each colour layer, the characteristic curveDefinition: characteristic curve photographic sensitometry; also called the H and D curve The developed optical density of a film plotted against the logarithm of the exposure it received. Excludes the film's spectral sensitivity and its grain. full definition, the rms granularityDefinition: rms granularity photographic sensitometry The standard deviation of density read through a small round aperture scanned across a uniformly exposed patch. Kodak's sheets use a 48 micrometre aperture. Excludes how grainy the image looks to a viewer, and noise measured at other apertures. full definition against density, and the spectral sensitivityDefinition: spectral sensitivity photographic sensitometry For each wavelength, the reciprocal of the exposure energy per unit area needed to reach a stated net density, here 0.2. Excludes sensitivity to white light or to a named illuminant. full definition. From the first two come the noise-equivalent quanta (NEQ)Definition: noise-equivalent quanta (NEQ) imaging science The number of photons a perfect detector would need to give the same signal-to-noise ratio as the real output. Excludes the number of photons that arrived. full definition; from the third comes the number of photons. Their ratio is the DQE. A search summary we could not trace to a primary source put the best older films near 1 percent. We found no published DQE for the VISION3 stocks; that is what our searches returned, and it does not show that none exists.

The same sheets bear on two working rules. Siedentopf's ruleDefinition: Siedentopf's rule photographic science The classic statement that the variance of density grows in proportion to the mean density, so that rms granularity grows as its square root. Excludes Selwyn's law, which concerns the size of the measuring aperture. full definition says the variance of density grows in proportion to mean density, and it is the basis of signal-dependent grain models used in film emulation; Stephenson's grain simulation states it together with Selwyn's aperture law [5]. And a Poisson threshold modelDefinition: Poisson threshold model photographic science and visual physiology A model in which each grain, or each rod cell, responds once it has absorbed at least n photons, with photon counts following Poisson statistics. N is the hit number. Excludes models in which response grows smoothly with every photon. full definition, in which a grain develops after it absorbs n photons, has been used for both grains and rod cells in the eye. The study asked whether one such model describes the response and the noise of layered colour film together.

The plan was written and hash-locked in a preregistrationDefinition: preregistration research method (metascience) A dated written plan for a study, fixed and hash-locked before any result is seen: the question, the data, the statistic, the controls, the forecasts and the kill conditions. Excludes a plan revised after looking at the outcome, and a protocol written only for the record after the run. full definition on 31 October 2026 at 06:12:46 UTC, and the run followed at 06:12:48. It names the data, the measures, the planted checksDefinition: planted check research method; called a positive control in experimental science Data built so that the right answer is known, run through the same analysis before the real data, to show that the analysis can see the effect when it is there. Excludes any check made on the real data, which cannot show what the analysis misses. full definition, two controlsDefinition: control statistics and experimental design A version of the data with the structure under test removed (for example shuffled or pooled), scored the same way as the real data, so the real score has something to beat. Excludes a comparison with a different dataset or with a published number. full definition, the forecasts and the kill conditionsDefinition: kill condition research method (our usage, after Popper's falsification) A rule written in the preregistration that, when met, decides against the claim with no room for judgement after the run. Excludes reasons found after the run for setting a result aside. full definition. The decision it informs is what the grain and response parts of our film renderer should use.

One disclosure comes from the file itself. Before the lock, the 5219 stored curves had been looked at and one hand calculation had been made for the 5219 green layer, giving a DQE of about 0.11 with assumed values of gamma and sigma. So the forecasts for 5219 were not blind. The stocks 7203 and 7213 had been looked at only for calibration.

The rules that decide each verdictDefinition: verdict research method (our usage) The pass or fail of one preregistered rule set against the run's numbers, read off by code. Excludes an interpretation written after reading the numbers. full definition were written into the run's plan before the run. Any failed planted check voids its block. The full list is in Appendix A.

The data are the Kodak VISION3 technical data sheets for 5219 (500T), 7213 (200T) and 7203 (50D) [1]. The curves were digitised from the published vector sheets: for each of the blue, green and red layers, the characteristic curve, the diffuse rms granularity curve measured with a 48 micrometre aperture, and the spectral sensitivity curve at a net densityDefinition: net density photographic sensitometry Optical density above the film's base and fog, so that unexposed film reads zero. Excludes the density of the base and the fog themselves. full definition of 0.2. The curves were resampled to a grid of 0.05 in log exposure. The sheets are Kodak's copyright. This paper reports only values derived from them and redraws none of their curves.

Kodak notes that its granularity figures use a modified measuring technique. We did not correct for it.

For each layer, let $S$ be the sheet's spectral sensitivity at the layer's peak wavelength ${\lambda }_p$, in reciprocal erg per square centimetre, at net density 0.2. The exposure that reaches net density 0.2 is $1/S$, and dividing by the energy of one photon at ${\lambda }_p$ gives the photon count per unit area there:

with $h$ Planck's constant and $c$ the speed of light, converted to photons per square micrometre. Counting every photon at the most efficient wavelength makes $q_{02}$ the fewest photons that could give net density 0.2, and so makes the DQE below an upper estimate.

At log exposure $x$, the photons inside the 48 micrometre aperture, of area $A$, are

where $x_{02}$ is the log exposure at which the curve reaches net density 0.2.

Let $\gamma$ be the gammaDefinition: gamma photographic sensitometry The local slope of the characteristic curve: the change in density per unit change in log exposure. Excludes the display gamma of video and computer screens. full definition of the curve at $x$, taken from a smoothed derivative, and $\sigma$ the rms granularity at the same point. Then

Each layer's peak DQE is the largest value of eq. 4 over points with net density and gamma both above 0.05.

For points with net density $D$ above 0.1, four laws for the variance ${\sigma }^2$ were compared: Siedentopf's ${\sigma }^2=aD$, a constant, an affine law $c+aD$ and a quadratic. Each was scored by BICDefinition: BIC statistics; the Bayesian information criterion A model score that adds a penalty for each fitted parameter to the misfit, lower being better, so that a more flexible model must earn its extra parameters. Excludes a test on held-out data. full definition on all points and by its hold-out scoreDefinition: hold-out score statistics and machine learning The error of a model fitted on one part of the data and scored on a part it never saw. Here fitted on the lowest 70 percent of the axis and scored on the top 30 percent. Excludes an error computed on the points used to fit. full definition in log variance on the top 30 percent of density after fitting on the rest. A power slope $b$ was fitted as

so that Siedentopf's rule corresponds to $b=1$.

Eight forms for net density against log exposure were fitted on the lowest 70 percent of the exposure axis and scored on the top 30 percent: Hill, Naka-Rushton with exponent 1, single hit, Erlang with real n, lognormal, Weibull, hingeDefinition: hinge curve fitting A response that is zero below a threshold exposure and rises in a straight line above it, here in log exposure. Excludes any form that saturates at high exposure. full definition and soft hinge. The hinge has two parameters, a threshold and a slope. BIC was reported beside the hold-out score, though the forms have different numbers of parameters.

The threshold model fits net density and log variance together, with hit number $n$ in 1, 2, 3, 4 and 6 and a lognormal spread of grain area with free width, and picks $n$ by BIC.

Each block had a planted check with a known answer, run through the same code.

Two controls built a null distributionDefinition: null distribution statistics The spread of scores a control gives over many random draws. Its 95th percentile is the bar a real score must clear. Excludes a theoretical distribution assumed rather than drawn from the data. full definition for a statistic. Shuffling density against exposure 25 times gave a top-form share of 0.36 on average with a 95th percentile of 0.44; the real share of 1.0 is above all of them, a p value from drawsDefinition: p value (from draws) statistics The share of control draws scoring at or above the real score, with one added to the count and to the number of draws, so it is never zero. Excludes a p value from a textbook formula that assumes a distribution. full definition of 0.038, which is the smallest value 25 draws can give. Pairing one layer's slope with another layer's noise 200 times gave a mean correlation of 0.66 with a 95th percentile of 0.76; the real 0.61 sits inside it, p 0.74, so that test could not separate the layers.

The preregistration called for a Benjamini-Hochberg correctionDefinition: Benjamini-Hochberg correction statistics A rule for many tests at once: rank the p values from smallest, and reject the k smallest when the kth is no larger than k over the number of tests times the chosen false discovery rate, here 0.05. Excludes a correction for one test, and the stricter Bonferroni rule. full definition at 0.05 over the control p values. The result file does not report it. With two p values, 0.038 and 0.74, the smaller would have to be at or below 0.025 to pass, and it is not, so after the correction neither control rejects. The hinge result rests on its hold-out errors, which Figure 3 shows, more than on the shuffle.

Peak detective quantum efficiency across the nine layers has a median of 2.1 percent and a range of 0.57 to 4.92 percent, an upper estimate because every photon is counted at the layer's most efficient wavelength.c1 Table 1 gives each layer and Figure 1 draws them. The peak falls low on the curve, at net density 0.06 to 0.31, in the toe.

In the green layer, 500T and 200T reach 4.5 and 4.9 percent although 200T needs about twice the photons; 50D needs 15.7 times the photons of 500T and reaches 1.5 percent.c2 The preregistered rule for "same efficiency at every speed" asked for a DQE spread of at most 3 across the three green layers while photon counts spread by 5 or more. The photon spread was 15.7 and the DQE spread 3.24, so the rule failed narrowly. Figure 2 shows the three points.

Siedentopf's rule, that grain variance grows with density, lost on held-out points in 9 of 9 layers, and variance falls with density overall (median power slope -0.54); because our planted variance check failed, this is description only.c3 The forecast slope was +0.15. The variance curves also show a hump in the toe. Our guess at a cause, untested, is the hand-off between fast and slow emulsions in a layered coating together with the colour masking couplers.

A straight hinge in log exposure was the best held-out response form in 9 of 9 layers.c4 Its median hold-out error was 0.112 in net density, and every form that saturates did worse, as Figure 3 shows. Negative stock shows no shoulder within the range a sheet covers, so a form that bends over at high exposure loses when it extrapolates. Hill's exponent, fitted anyway, had a median of 0.615, which here is the gamma in another guise.

The Poisson threshold model does not fit. On the channel the run used, the median error was 0.134 in log variance and 0.043 in density, against limits of 0.05 and 0.04. A later study of ours found that this fit passed the logarithm of the standard deviation where the model expected the logarithm of the variance. On the corrected channel the errors are 0.186 and 0.068, and the best hit number per layer changes from 1, 1, 1, 6, 6, 6, 6, 6, 6 to 1, 1, 1, 1, 6, 1, 6, 1, 1. The verdict stands either way, and no hit number is read as a measurement.

The DQE figures sit above the roughly 1 percent we saw quoted for older films, and the planted grains show the pipeline itself is good to about 11 percent. Counting photons at the peak wavelength pushes every value up. Two other choices move them by an amount and in a direction we did not measure: the single aperture with Kodak's modified technique, and the toe, where gamma is small, so that a small error in the digitised slope is a large share of it, and NEQ goes as the square of gamma. The order of magnitude, a few percent, is the safer reading than any one figure.

The green layers carry the clearest pattern. 500T and 200T keep the same share of the information while one needs half the light of the other. A faster film here buys speed by needing fewer photons for the same density, and it does not lose efficiency doing so. 50D breaks the pattern at 1.5 percent. One stock is not enough to say why.

For a film renderer the decision is plain. Grain should come from each layer's measured granularity against exposure, with no square-root-of-density rule, and the response of negative stock within the sheet's range needs no saturating shoulder.

The threshold result connects to a later study of ours on rod cells, which found that rods and film grain do not share one threshold model on the data available. Nothing in this paper bears on rods.