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Reciprocity failure: the science

Lately I have been playing with the idea of trying some long exposures on film or direct-positive paper, but reciprocity law failure complicates shots that need much longer than a second of exposure. To explain why, answer the following question. When you close down the aperture by one stop, you can compensate for this by lengthening the exposure time by how much? … It probably didn’t take long to realize that you simply double the exposure time. However, chemical processes ongoing in the emulsion during exposure, makes the response deviate from the reciprocity law for very short or long(ish) exposures. In this article, I will introduce these processes and explain how to deal with their effect in practice.

Reciprocity failure explained

For most photographers, the concept of reciprocity will be second nature. It tells us that the product of the intensity of the light and the exposure time is constant for a given density on the negative. This means that if we reduce the intensity by a factor of two by means of a field stop, we have to compensate for this by doubling the exposure time to get the same total dose. Likewise, the opposite is also true. In practice, this relation holds very well when the exposure time is between 1/1000 s and 1 s, but breaks down for very short or relatively long exposures.

To explain why, we need a simplified model of the emulsion. For this I rely on the simplified latent image theory by Gurney and Mott [1], which I found in ‘A Textbook of Photographic Chemistry’ by D. John and G. Field [2]. Although this theory was established in 1938 and has long since evolved [3], it allows me to explain the underlying processes on a conceptual level without digressing too much in crystal theory and complex chemistry.

Consider a small section of the emulsion, which contains silver and bromide ions in a lattice, and a small speck of silver sulphide, which is contained in the gelatin support. This is depicted in Figure 1a. When light is absorbed by this emulsion, some electrons are liberated from the ions and are free to move through the crystal lattice. The silver sulphide traps these electrons, and becomes electrically charged (Figure 1b).

Figure
Figure 1: a grain in the emulsion contains a lattice of positively charged silver ions (gray) and negatively charged bromide (green) ions. Silver sulphide specks (orange) are present in the gelatin support and the emulsion. When light hits the grain, electrons are liberated and are absorbed by the silver sulphide speck (b). Defects in the lattice allows the silver ions, which are attracted by the negatively charged speck, to move and realize silver clusters to be formed near the speck (c).

The silver bromide lattice is not perfect and contains defects such as interstitial holes. These holes allow the atoms some freedom to move about within the lattice. The positively charged silver ions are attracted by the negatively charged silver sulphide. This makes the silver ions want to move towards it. When they have reached the silver sulphide speck, they absorb the excess electrons that were stored in the speck and metallic silver is formed. During the exposure, there is thus a build up of silver atoms in and around the silver sulphide. The migration of the positively charged silver ions is extremely fast and can take as short as 10-11 s (one hundredth of a billionth of a second). In normal photography, exposure times lie between 10-3 s (1/1000) to 10-2 s (1/100). Therefore, there is ample of time for silver nuclei to be created. When these nuclei or silver become large enough, a latent image is formed.

While the positively charged silver ions are attracted by the negatively charged silver sulphide, likewise the negatively charged bromide ions are repelled. This leaves two options: either the bromide can rebromate the metallic silver atoms, and so reduce the effect of the exposure, or be absorbed by the gelatin. For normal exposure times the latter is the dominant path.

The actual chemical process of forming these silver nuclei consists of multiple stages, in which sub-image specks are created first, before a stable silver nucleus can be formed. The high intensity illumination required for very short exposure times, can cause some of the intermediate steps to saturate. This renders that following steps cannot take place at their intended rate and thus slow down the formation of stable silver nuclei. This retardation of the process means a longer exposure is needed to develop the required density. We call this high intensity reciprocity failure, or HIRF.

With low intensity exposures, only a few electrons migrate toward the silver sulphide. Some of them may be absorbed on their way, while at the same time some of the unstable (sub image) silver nuclei may decompose or the bromide ions may rebromate the metallic silver. Effectively, the formation of silver specks becomes less efficient because of the smaller amount of freed electrons, and is partially counteracted by chemical processes that would otherwise be too inefficient to notice. The formation of a latent image, therefore, takes considerably longer. This is called low intensity reciprocity failure, or LIRF.

Either way, whether the exposure is extremely short or very long, the process that creates the required density on the negative is retarded and a longer exposure time is required to reach the expected density on the negative. Or in other words, the linear relation between dose and density no longer holds.

Low intensity reciprocity failure in several films

High intensity reciprocity failure is only of real interest to a select group of film users today and is relevant in high speed flash photography or scientific work. Low intensity reciprocity failure, on the other hand, can be encountered in a multitude of scenarios that are relevant to many photographers. The remainder of this article is therefore dedicated to the low intensity reciprocity law failure.

In Table 1, I have summarized the exposure times at which LIRF becomes apparent for commercially available films. It is obvious from the data that Fujifilm’s Provia and Neopan Acros are the apparent king and queen when it comes down to providing very good reciprocity. For these films even the required exposure corrections are very mild at +1/2 or +1 stop on top of the indicated exposure times (by your light meter) of up to 8 minutes and 1000 seconds (16 min 40 sec), respectively. In comparison, Kodak recommends a +3 stops correction for Tri-X when your light meter gives you an exposure time of just 100 seconds.

Table 1: Onset exposure time for low intensity reciprocity failure to occur for available film stocks.
Manufacture Stock Onset exposure time (s)
Ilford Pan F, FP4+, HP5+, Delta 100, Delta 400, Delta 3200, XP2 Super 1/2
Kodak Tri-X 320, Tri-X 400, T-Max 100, T-Max 400, Ektar 100, Portra 160, Porta 400, Portra 800 1
Fujifilm Superia 200, Superia X-tra 400, Superia X-tra 800, Superia X-tra 1600, Pro 160NS 2
Fujifilm Pro 400H, Velvia 50, Velvia 100 1
Fujifilm Provia 100f 128
Fujifilm Provia 400x 60
Fujifilm Neopan Acros 100 120

The question arises what makes the one film a much stronger performer in terms of LIRF than others? This question has, as many similar questions, no answer that can be given with absolute certainty. However, one may try to give an educated guess. Most manufacturers are very secretive about their processes, as this is what gives them a competitive edge over their competition. Likely, we will never know the true answer for sure, as this kind of information tends to disappear when the original researchers retire and companies close their doors for good. The patent libraries, however, reveal a few clues.

As a general rule-of-thumb it seems that so called ‘designer grains’ perform better then naturally formed grains in terms of reciprocity failure. The more regularly shaped grains have a larger average exposed area, making them more efficient in converting light into free electrons. This is supported by recent work by Hailstone and De Keyzer in 2004 [4]. From the results they obtained can be concluded that by designing the shape, size and thickness of the grains, the LIRF behaviour can be altered. However, patents filed by Eastman Kodak in the 1990s [5] mention chemical inclusions in the emulsion of substances other then silver bromide, such as iron hexacyanide, iridium or palladium, that substantially change the reciprocity behaviour. Especially iridium seems to be a popular inclusion for controlling LIRF behaviour, based on the mentioned patents of Kodak and some of Fujifilm. Given that the patents often mention the relationship between the chemical composition and LIRF, rather than the relationship between grain shape/size and LIRF, it is likely that this is a more dominant parameter. These inclusions were introduced at the same time when these ‘designer grains’ became more commonplace, so it cannot be ruled out that there is a combined action.

An additional option for improving LIRF behavior was found by Spencer and Shares of the Research Laboratories of Eastman Kodak Company and was published in 1967 [6]. It suggests that LIRF behavior is a combination of intergranular and intragranular processes. The latter is described adequately by the Gurney-Mott hypothesis that was discussed above. Intergranular reciprocity failure exists when the freed halides (bromide in the case of a silver bromide emulsion) can diffuse over macroscopic distances across the grain boundaries. As bromide has the effect of retarding the latent image forming process, diffusion of bromide from one grain to another can greatly affect LIRF. It was found, however, that the addition of a proper halogen acceptor to the emulsion before coating it onto the support practically eliminates this intergranular effect. The acceptor neutralizes the bromide before it crosses the grain boundary, so that no ill effects are possible. In the study, acetone semicarbazone, sodium nitrite and hydroquinone were used as halogen acceptors of which the first was found to be most effective. It is interesting to note here that hydroquinone is also used as a developing agent. Its inclusion into the emulsion could therefore influence the development process.

Finding the right exposure correction (in theory)

The processes described above retard the development of the latent image and render that longer exposure times are required to realize the required density in the negative. This was noticed by Schwarzschild in his low intensity astronomical work, which led him to propose an exponential modification to the reciprocity law in 1899 [7]. You will still find references to this work in many publications, and people still refer to it as the Schwarzschild law. The proposed correction is a generalization of the reciprocity law and reads: I tp = constant. When p = 1, the reciprocity law is produced, making this relation a generalization of the reciprocity law. To model the LIRF behaviour of his plates, Schwarzschild found p = 0.8 as the appropriate parameter value. Unfortunately, this turned out to be of only limited validity and the relation worked for other emulsions only when different values for p were used.

In the 20th century, both high intensity and low intensity reciprocity failure have been subject of theoretical analysis and experimentation to satisfy both the academic interest and the practical applications. Although a full discussion of the physical and mathematical underpinnings of these theories is outside the scope of this article, it is instructive to have a closer look at the underlying concepts and the resulting findings.

These models all consider the development of a latent image inside a single silver halide grain. As discussed before, the action of light on the grain allows specks of metallic silver to develop. You may remember from your physics classes, that light is quantized, meaning that the energy arrives in well defined packets called photons. The time between two photons arriving is random. Once a photon is absorbed, an electron is freed that could potentially contribute to forming a sub-speck of metallic silver. However, it will not be free to move long. Some of the freed electrons will travel great distances in the grain, while others are absorbed almost instantly again by adjacent atoms in the lattice. The probability of one freed electron being “free” at any moment decreases as time passes by. Luckily, many of these photons arrive at the short intervals and on average each electron is “free” for a time τ. When multiple electrons are free at the same time, a latent image can be rendered. By fitting the mathematical models that are part of the latent-image theory to experimental data on density-dose relations, it was found that two electrons have to be “free” at the same time to form a sub-image speck [8]. However, more electrons are required form a developable speck, which may depend on the grain size frequency distribution [9, 10].

It is obvious that when the intensity goes down less electrons are “free” at the same time and that the probability of forming a developable speck goes down as well. Using adequate probabilistic models, the reciprocity functions can be derived. Unfortunately, these models are very mathematically involved and only general characteristics can be obtained for real films. This is because the grain size is not uniform, intergranular effects are not taken into account and the amount of quanta required to render a speck developable may not be the same for all grains. Let us therefore consider only the asymptotic behavior for very low intensity and thus very long exposures.

In 1950, J.H. Webb concluded that in the limit of very low intensities, the measured exposure time must be increased by a factor as – 1 to obtain the right density [8], where the value of s is equal to the number of light quanta that strike the grain within the critical time τ. The parameter a is then emulsion specific. On a log-log plot of density versus dose (product of intensity and time), this translates to a constant slope of 1. Katz [11] and Anderson [10] both arrive at exponential behaviour for the LIRF reciprocity law failure. They arrive at similar slopes as Webb, but differ in the onset point.

Finding the right exposure correction in practice

Moving from the realms of science and mathematical models to photographic practice makes us wonder how to deal with LIRF in practice?

A first starting point is provided by the film manufacturers. They supply guidelines on how to use their films for long exposures, which may serve as a starting point for determining the right exposure time that fits your aesthetic and process. Patrick Gainer [12] took experimental data provided by Howard Bond [13] and fitted the exponential relation tc = a (tm)b to it, where a and b are fitting parameters, tm is the measured exposure time and tc is the corrected exposure time. He concluded that although the values of a differ from film to film, exponent b has a value of 1.62. This was found to be valid for all tested films (Ilford HP5+, Ilford Delta 100, Kodak T-Max 100 and 400 and Kodak Tri-X 400). This fitting function seems to agree with the theoretically predicted behavior for long exposures as described in the previous section.

To see how this agrees with the data supplied by the manufacturers, I collected the data that is available from the datasheets and fitted it to the the same function. The corresponding model parameters are listed in Table 2. It is evident that none of the data result in a value for the exponential b equal to 1.62. Therefore, I recommend you use these only as a starting point for experimentation. Especially for very long exposure times that run into several minutes, data is very scarce and experimentation may be necessary. Also, it should be noted here that when you are shooting colour slide film, such as the infamous Fuji Velvia, it will require the use of colour correction filters on the lens to compensate for differential reciprocity failure in the different layers of the film. Although this may be partially remedied by extra corrections in the(digital) darkroom, a properly exposed slide will make life much easier.

Table 2: Fit parameters for specific films.
Manufacture Stock a b Remark
Ilford Pan F, FP4+, HP5+, Delta 100, Delta 400, Delta 3200, XP2 Super 0.9425 1.4995 Based on 13 data points obtained from a graph.
Kodak Tri-X 320, 400 2.0828 1.3803 Only 3 data points, obtained from table.
Kodak T-Max 100 1.1280 1.1244 Only 3 data points, obtained from table.
Kodak T-Max 400 0.5291 1.3768 Only 3 data points, obtained from table.
Fuji Superia 200, Superia X-tra 400 1.000 1.1667 Only 3 data points, obtained from table.
Fuji Superia X-tra 800, Superia X-tra 1600 1.3662 1.2584 Only 3 data points, obtained from table.
Fuji Pro 400H 1.000 1.2852 Only 2 data points, obtained from table.
Fuji Velvia 50 0.7422 1.2852 Only 4 data points, obtained from table.
Fuji Velvia 100 0.5673 1.1667 Only 3 data points, obtained from table.

It is also important to realize that most of this data is based on a mere 3 data points, which is barely sufficient to fit a two-parameter model. Also, the data provided by Ilford is the same for all their films, which makes me suspicious regarding its accuracy. Light of shorter wavelengths is more energetic and frees electrons more easily. As the spectral responses of the Ilford films differ, it is unlikely that their LIRF behaviour is very much comparable. An enquiry posted to Ilford by user silveror0 of APUG in the early 2000s, confirms this inaccuracy, as Ilford responded the following:

We do use the same curve for ALL our films and it is essentially an average curve designed to be a reasonable guide for all our films. We are conscious that this is a weakness in our current Technical Information and we intend to provide curves for individual films when time and resources permit. However, there will be some batch to batch variability in this characteristic and so careful workers will need to run their own tests.

The provided data has not changed since, and I doubt it ever will. Especially because the research and development departments of film manufacturers are very limited in size nowadays. The lack of reliable data renders offering accurate reference equations or tables impossible. For now, and probably till the end of film, you will have to test the reciprocity behavior of your film stock yourself.

Update, 12 May 2017: I have recently learned that Harman Technical Service is working on closing this gap. They have kindly provided me their preliminary data, which I have incorporated in Inverso. Ilford/Harman will release definitive data soon!

Making a calibration curve will involve careful testing under controlled lighting conditions, a reproducible development procedure and parameters, and densitometric measurements. Unfortunately calibrated transmission densitometers are hard to come by on the second hand market, and can cost between 500 – 1500 euro when bought new. Unless you are one of the lucky ones to already own one of these, a simpler, but coarser method can be used using step wedges. An example of how to do this is given by Howard Bond [13]. It should be noted here, that doing this properly is rather involved, takes a lot of time, but above all a lot of film. Bond reported that he spent over 30 days and 300 sheets of film to gather sufficient data to construct the curves that he presents in the cited article.

A more pragmatic, but less accurate method is described by Kit Courter [15]. In stead of a step wedge of known densities, Kit photographs a 18% gray card under lighting conditions that are similar to that of the intended scenes. A first roll of film is shot at a the metered exposure, assuming that reciprocity holds. The intensity is changed by closing down the aperture one stop for every next frame, while adjusting the shutter speed accordingly. A second roll is shot in the same way, but in stead at the guessed corrected shutter speeds. This can be based on the calibration curve provided by someone else or the manufacturer. The developed films are then both compared to a known standard, either by use of a densitometer or by visual inspection. Based on this comparison, a new estimate for the correction factors can be attained. If the wanted accuracy is not reached yet, a new set of rolls is exposed. In this iterative manner, one can close in on the the right correction factors. Note though that the obtained curves are dependent on the lighting conditions, as the spectral content of the light changes. For example, a moonlit scene will give different reciprocity behavior in comparison to a sun lit scene, and one may need to make several curves.

All in all, the process is rather involved and will take perseverance to complete. If you are really into night shots or long exposures (anyone here that wants to use that 10 stop neutral density filter?), you will unfortunately have to endure the suffering of meticulously testing and comparing.

Pull processing to keep the contrast in check

Beside the odd occasion in which we are photographing a plain wall or the inside of the lens cap, regular photography results in an image that contains both shadows and highlights. Areas that receive little light even with normal exposure times, i.e., the shadows, are more affected by low intensity reciprocity failure then the highlights, which may receive sufficient light already in a short exposure. This means that the contrast changes for long exposure. Beside correcting the exposure time, a correction of development time may thus be necessary as well. Because the shadows are much more affected by LIRF than the highlights, normal development would result in an image of higher contrast. When this is not desired, the development time has to be shortened to keep the highlights in check, while allowing sufficient time for the shadows to develop detail and catch up.

Kodak is the only manufacturer of the big three (Kodak, Ilford and Fujifilm) to recommend changes in development times. These are typically changes in the development time between 10% to 30%, which correspond to half a stop to a full stop of under-development (pull processing). I could not find other sources that give guidance on this, so again, you will have to find this out by trial-and-error if you find that contrast needs to be tempered.

Reciprocity failure in paper

The silver bromide process is nowadays by far the most popular wet print process in use. It relies on chemistry that is very similar to that used in film, and it is then not surprising that paper emulsions also suffer from reciprocity failure. However, in practice this is more of academic interest, than it is of practical concern. In contrast to the photographer, the printer has the advantage of being able to make test strips. In doing so, the effect of reciprocity failure is already taken into account and no correction factors are required in determining the right exposure time.

Lambrecht and Woodhouse discuss reciprocity failure of paper emulsions in their book  “Beyond Monochrome, 2nd edition” [14]. Unfortunately, I do not own this book, so I had to satisfy myself with the online preview on Google books. They note that if you are using a more advanced system for determining the print exposure time, for example an easle metering system, or if you calculate the right exposure time for an enlargement of an existing print (for which you know the right time) by scaling relations, you may find that the print is lighter then expected. Lambrecht and Woodhouse found from measurements, that the reciprocity failure in prints is very mild though. While for film corrections of many stops may be required, paper may only need corrections in the order of 1/6th to 1/3rd of a stop. They further show that the characteristic curve (density versus exposure dose) is only shifted, which means that a change in exposure time is sufficient to correct for the reciprocity failure. The contrast of the print is not much affected and does not require adjustments.

When you are using paper outside the darkroom, for example for paper negatives, it pays off to do your own testing. Here we are again back in the realm of the photographer, who cannot make test strips on location. As the spectral response of paper can differ greatly from manufacturer to manufacturer, you will have to do this anyway to determine the effective speed for the type of lighting conditions you want to shoot in.

Conclusion

The science of reciprocity law failure is much vaster than I can reasonably explain and summarize in a single blog post. It contains many subtleties that are far beyond the scope one would ever need for non-scientific photography. This, however, also means that practical aspects are discussed in large numbers in terms of anecdotes and popular scientific publications but are scarce in the scientific literature. Reproducible results are therefore hard to come by. It seems that there has been no conclusive study of correction functions that apply to modern films and that can be of use to modern day analog photographers. We will have to rely on data obtained through meticulous testing either done by ourselves, or those provided by others. Either way, if you are an enthusiast night time shooter, or want to work with very long exposures like Alexey Titarenko, you may need to invest (a lot of) time and money in characterizing film to get corrections that work for you.

Seeing that one print on the wall, however, may all be very much worth it. Happy shooting and printing!

References

[1] R.W. Gurney and N.F. Mott, “The theory of the Photolysis of Silver Bromide and the Photographic Latent Image”, Proceedings of the Royal Society, 164A, 151-67 (1938).

[2] D.H.O. John and G.T.J. Field, “The Emulsion Exposed”, A Textbook of Photographic Chemistry, Londen, UK: Chapman and Hall Ltd, 1963.

[3] J.W. Mitchell and N.F. Mott, “The Nature and Formation of the Photographic Latent Image”, Philosopical Magazine, 2 (21), 1149-1170 (1957). Online: http://dx.doi.org/10.1080/14786435708242745

[4] K. Hailstone and R. De Keyzer, “Latent-image formation in tabular AgBr grains: simulation studies”, The Imaging Science Journal52 (3), 164-175 (2004). Online: http://dx.doi.org/10.1179/136821904225011645

[5] W.G. McDugle, A.D. Gingello, J.A. Haefner, J.E. Keevert Jr., and A.P. Marchetti, “Photographic emulsions containing internally modified silver halide grains”, US4933272, 1990.

also: 

S.H. Kim, “Silver halide emulsions having improved low intensity reciprocity characteristics and processes of preparing them”, US4997751, 1991.

G.L. House, T.B. Brust, D.L. Hartsell, D.L. Black, M.G. Antoniades, J.A. Budz, Y.C. Chang, R. Lok, S.A. Puckett and A.K. Tsaur, “High chloride tabular grain emulsions and processes for their preparation”, US5320938, 1994.

R.L. Daubendiek, D.L. Black, J.C. Deaton, T.R. Gersey, J.G. Lighthouse, M.T. Olm, X. Wen and R.D. Wilson, “Epitaxially sensitized ultrathin tabular grain emulsions”, US5494789, 1996.

R.D. Wilson, M.T. Olm, R.L. Daubendiek, D.L. Black, J.C. Deaton, T.R. Gersey, J.G. Lighthouse and X. Wen, “Ultrathin tabular grain emulsions with reduced reciprocity failure”, US5614358, 1997.

[6] H.E. Spencer and D.H. Shares, “Low-Intensity Reciprocity Failure of a AgBr Emulsion: Effect of Halogen Acceptors”, Journal of the Optical Society of America57 (4), 508-512 (1967). Online: http://dx.doi.org/10.1364/JOSA.57.000508

[7] K. Schwarzschild, “On the Deviations from the Law of Reciprocity for Bromide and Silver Gelatine”, Astrophysical Journal 11, p. 89 (1900). Online: http://dx.doi.org/10.1086/140669

[8] J.H. Webb, “Low Intensity Reciprocity-Law Failure in Photographic Exposure: Energy Depth of Electron Traps in Latent-Image Formation; Number of Quanta Required to Form a Stable Sublatent Image”, Journal of the Optical Society of America, 40 (1), 3-13 (1950).

[9] L. Silberstein, “A theoretical Treatment of the Two Quanta Hypothesis as Applied to the Photographic Reciprocity Law Failure”, Journal of the Optical Society of America 29, 432-447 (1939).

[10] W.J. Anderson, “A model for reciprocity failure in photographic materials and its asymptotic behavior at low and high intensities”, Journal of the Optical Society of America 68 (7), 972-978 (1978).

also:

W.J. Anderson, “A probabilistic model for reciprocity failure at an n-atom developable silver speck in a photographic emulsion”, Communications in Statistics. Stochastic Models. (1), 31-42 (1989).

[11] E. Katz, “On the Photographic Reciprocity Law Failure and Related Effects. I. The Low Intensity Failure”, The Journal of Chemical Physics 17 (11), 1132-1141 (1949).

[12] P.A. Gainer, “LIRF is Lurking at Your F-Stop”, Unblinking Eye, Available online via http://unblinkingeye.com/Articles/LIRF/lirf.html, Accessed on 5 June 2016.

[13] H. Bond, “Black and White Reciprocity Departure Revisited”, PHOTO Techniques, July/August 2003, Available online via http://phototechmag.com/black-and-white-reciprocity-departure-revisited-by-howard-bond/, Accessed on 5 June 2016.

[14] R. Lambrecht and C. Woodhouse, “Paper Reciprocity Failure”, Way Beyond Monochrome, Oxford, UK: Focal Press, (2011). ISBN: 978-0-240-81625-8

[15] K. Courter, “Correcting for film reciprocity failure”, LunarLight, Available online via http://home.earthlink.net/~kitathome/LunarLight/moonlight_gallery/technique/reciprocity.htm, Accessed on 1 July 2016.

Published in In the Lab