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Reciprocity law failure

Purpose

The purpose of this page is to look at the phenomenon of "reciprocity failure" from both somewhat scientific viewpoint and practical one, with an emphasis on characteristics of reciprocity failure of current photographic films.

Because of this practical relevance, the treatment of science part is greatly abbreviated. Readers wishing to further details are referred to references.

Reciprocity law failure

In ideal world, if the light intensity doubles, one can always halve the exposure time to obtain identical exposure on photographic materials. Or, when the light intensity halves, one can double the exposure time to compensate. This is the "reciprocity law" which usually but not always applies to real world materials; there are cases where real materials fail to obey this law. The failure is seen when light intensity is extremely low as in nightscape photography, or extremely high as in some flash exposures. Although the degree of this phenomenon is governed by the light intensity of the exposure, it is often described in terms of exposure duration for practical photography purposes. This simplification works as long as you are measuring incident light (or reflected metering off standard gray card) and aiming at normal exposure level. In this article, we use intensity for theoretical discussions and exposure duration for practical aspects.

Silver halides

Silver chloride and silver bromide crystals are one kind of solid state device called "indirect gap semiconductors." These photosensitive crystals react with photoelectron to form small silver specks on or in the crystals. These silver specks are amplified during development process to image-forming silver grains.

In typical silver halide materials for negative images, various chemical sensitizers are used to improve latent image formation and developability of latent silver specks. (A different kind of sensitizer, called sensitizing dye or spectral sensitizer is also used to achieve desired spectral sensitivity of photographic materials.)

When light is absorbed by silver halide crystals, photocarriers consisting of free electrons and free holes are generated. The desired photographic effect is obtained by allowing the free electrons to react with silver atom to form silver catalytic center or latent images (LI), and removing holes by reactions involving variety of non-silver species including dyes and gelatin. Silver halide crystals with a latent image are preferentially developed to image-forming silver grains during the development process (Figure 1). This is a chemical amplification of latent image specks.



Figure 1: A simplified depiction of principle of silver halide photosensitive material and the role of latent image.

The sequence of events from absorption of light to formation of latent image is discussed in the literature on latent image theory. A classic model proposed by Gurney and Mott (1938) survived through recent advancement in the field, and is still largely accepted today. Their model is simply shown in Figure 2.



Figure 2: Theoretical model for latent image formation proposed by Gurney and Mott 1938.

Upon absorption of light, electrons and holes are generated in the silver halide. Both of these can take one of three states, (1) free or mobile; (2) trapped; (3) atom. The actual distributions of electrons and holes in these states are considered to be at equilibrium, as indicated by arrows in Figure 2. Formation of latent image is a reaction between a free electron at a silver atom. However, some electrons are dissipated by the recombination process, which mainly occurs between free hole and trapped electrons. The recombination process is thus undesirable from photographic viewpoint. Based on the model in Figure 2, it is apparent that latent image formation is promoted by stabilizing atom state of the electron.

The model in Figure 2 also shows that absorption of two photons is necessary to nucleate or initiate latent image growth. The Ag1 state ("electron at atom") after absorption of the first photon is unstable, because its electron is at equilibrium among free, trapped and atom states until one more photon is absorbed to proceed to the Ag2 state ("two silver atoms"). At low intensities, too few photons are absorbed in a unit time, and this unstable Ag1 may disappear by returning the electron to one of the other states with a positive probability before the crystal receives the second photon necessary to nucleate the stable latent image. This unstable Ag1 state lasts for a few seconds (half life) in typical photographic films. This is one cause of low intensity reciprocity failure (LIRF), and this factor is controlled during designing and manufacturing through choosing suitable degrees and kinds of crystal defects, impurities (dopants), chemical sensitizers, dyes, core/shell structures, etc. Another source of LIRF is the loss of electrons to environment such as gelatin and dyes over a longer time scale. This occurs while silver atoms dissociate and reform inside the crystal in the process of forming stable latent image. This loss of electrons to environment is usually more slower than the former mechanism, typically taking about a minute (half life).

Note that Ag2 latent image formed after two photons are absorbed is only a minimum requirement for the stable latent image formation, and this does not guarantee that it will be amplified through development process. With typical continuous tone photographic developers, a few extra photons must be absorbed to make larger catalytic center in order to be developed. This is the threshold latent image size, and this depends on the particular developing conditions.

On the other hand, when the light intensity is very high, too many electrons are available within a unit time, and several latent image sites are nucleated within one crystal. This leads to inefficient growth to a size that can be detected through development. This is the major source of high intensity reciprocity failure (HIRF). This characteristics is governed by deep trap effectiveness and threshold latent image size.



Figure 3: A hypothetical reciprocity failure derived from the model shown in Figure 2.

Figure 3 shows a reciprocity failure curve thus derived from the model shown in Figure 2. The horizontal axis is logarithm of intensity, the vertical logarithm of intensity-exposure time product. The curve is an isoresponse curve, which can be thought of as levels of exposures needed to make just detectable latent images, or equal density after development. At low and high intensity regions, upward deflections are seen, indicating loss of effective speed in these regions. An ideal material fully obeying the reciprocity law would exhibit horizontal straight line in this plot.

Experimental data of reciprocity failure of various silver halide materials are available, but many experiments focused on low intensity side for practical and technical reasons. One such example is shown in Figure 4. Although the figure is differently annotated, the axes are in the same quantities as in Figure 3. Added slanted lines indicate constant exposure time lines.



Figure 4: An example of reciprocity failure of real photographic materials. Several silver halide crystals with different chemical sensitizers are shown in the same axes as Figure 3.

This figure is due to A. P. Marchetti et al. (1984), and it came from the context of comparing the effect of sulfur dopants. It is included here as a case example only. Different silver halide crystals are shown with different low intensity reciprocity failure (LIRF) and speed. It can also be read that AgBr octahedral crystals give faster speed, but they exhibit poorer LIRF compared to slow AgCl crystals or AgBr cubic crystals, with minor differences depending on the selection of sensitizer.



Figure 5: An example of reciprocity failure of real photographic materials. Polaroid Type 55 positive/negative instant film, rated speed of ISO 50/18° is shown in the same axes as Figure 3. A unit change in log exposure is about 3.3 stops equivalent.

Reciprocity characteristics of photographic films

As discussed above, films lose some of their speed as the light incident on it becomes very dim. In practical photography, it is often described by the metered standard exposure time, and the corrected exposure time. With an ideal reciprocity law, there is no correction necessary for all exposure durations, but as the light gets dimmer, real photographic materials require increasingly larger correction factor is necessary to ensure same amount of shadow density registered on the film. These data are usually published by the film manufacturers, but the details and accuracy of published data varies. Examples of representative film categories are shown in Figure 6 below.

Plus-X, Tri-X and AGFA APX 100 and 400 exhibit very comparable reciprocity failure (at least based on their published data), and these conventional technology films usually require 1 stop increment at 1 second, and progressively larger correction factor as the metered exposure time prolongs. (Now greatly regrettably discontinued AGFA APX 25 exhibits slightly improved reciprocity failure than Plus-X.)

Tabular grain films use advanced control on silver halide dopants, crystallization processes, dyes and gelatin materials, which contribute to improved reciprocity law characteristics. T-MAX 400 exhibits superior property than slower Plus-X or APX 100, and T-MAX 100 is even better at longer exposure region. T-MAX 100 and 400 exhibit almost same characteristics in modestly long exposure range, up to about 10 seconds. Furthermore, more recent member in the industry, Fujifilm Acros 100 is probably the best pictorial b&w film on the market today in terms of reciprocity law failure. The curve for Acros 100 is very near ideal law curve, requiring very small correction for long exposures.

Low intensity reciprocity law failure expands contrast because the film loses sensitivity selectively in shadow region of the image while maintaining the normal speed in highlights. Therefore, development time is usually contracted to compensate for the increased contrast registered on the film. Films with superior reciprocity characteristics such as T-MAX 100 and Acros 100 minimize or eliminate this undesirable problem.

Because of this LIRF, a film rated at lower speed may paradoxically be faster in effect than a film rated at a faster speed. For example, T-MAX 100 is faster than Tri-X if the metered exposure time is longer than a few seconds. Fujifilm Acros is faster than T-MAX 400 if the exposure is longer than a couple of minutes. Because of the contrast-expanding nature of reciprocity failure, T-MAX 100 and Acros 100 are the preferred choices in these cases, respectively.



Figure 6: Reciprocity law failure of Plus-X, T-MAX 400, T-MAX 100, and Acros 100 compared against ideal characteristics.

The curves for Acros was made by using Michael Covington's formula,

exposure time = (metered time + 1)1/p - 1

fit to the published data. However, this formula does not fit well with published data for conventional technology films. Fitting for longer end (e.g. 100 seconds) of exposure will undershoot the correction for moderately long (e.g. 10 seconds) exposures. Therefore, I made a similar exponential model of three free parameters by letting the exponent to be a polynomial of the metered time, and this model was fit to published data by minimum square error criterion in log-log scale. This model was used for Plus-X, TMX and TMY curves in Figure 6.

High intensity reciprocity failure is much less significant in usual pictorial photography conditions, especially with tabular grain technology films. Therefore, this issue is not discussed here.

In published data, Eastman Kodak mentions exposures up to 100 seconds for their films, while Fujifilm mentions up to 1000 seconds for Acros 100. These limits are also reflected in Figure 6.

The deperture of the curve from the straight line can also be viewed as a loss of speed at that intensity. This can be better represented as in the next figure.



Figure 7: Reciprocity law failure of Plus-X, T-MAX 400, T-MAX 100, and Acros 100 compared as relative speed loss.

Steep line of Plus-X (and other conventional technology films) indicates that this film progressively loses speed in shadow areas, increasing contrast. This is commonly dealt with a large boost in exposure and reduction of development time.

On the other hand, relatively flat curves of TMX and Acros indicate that the relative speed loss is flat across the image's intensity range, and contrast increase due to reciprocity failure with these films is minimal. Therefore, only 1/2 to 1 stop increase of exposure is needed, with no adjustment in development process. Polaroid type 55 is expected to be very similar to the curves for TMX. Type 665 (ISO 75/20°) is slightly worse than type 55.

It may be convenient to print out Figure 6 and 7 for nightscape photography or other jobs requiring routine correction of reciprocity law failure. Download Figure 6 and 7 in PDF format (16kB.)

Note: the curve of Acros indicates slight speed loss at 1/10 second but this is due to the inaccuracy of Michael Covington's model formula. I wouldn't give any meaning to it; the real data for Acros should asymptotically tend to zero below a few seconds. Also, I would consider green (TMY) and red (TMX) are practically identical curve below 10 seconds. Slight deviation seen in Figure 7 is also due to model limitation.

Concluding remarks

In this article, we briefly reviewed physics of photolytic reactions of silver halide crystals, and mechanisms of departure from the reciprocity law based on a classic model which is still accepted today. For these topics, relevant chapters in Mees and James are highly recommended, as well as Sturmer and Marchetti's chapter in the book.

Low intensity reciprocity failure was also compared for four representative films available on market today. It is apparent that conventional technology films such as Plus-X, as well as Tri-X, APX 100 and 400 are inferior to T-MAX 400 in terms of reciprocity failure. It is also apparent that recently introduced Fujifilm Acros 100 has excellent reciprocity property, making it particularly well suited for low light photography.

The minimum "take home" message is that, if you are doing very low light pictorial photography of normal contrast, the best way is to choose films like Acros 100 (the next best is T-MAX 100), and overexpose by 1/2 to 1 stop, and process normally, preferrably in a carefully formulated phenidone developer. From the data presented in Figure 6 and 7, it is obvious that these films are very advantageous. In less challanging low light situation, T-MAX 400 may also find useful if the exposure can be managed within 10 seconds, because in this region TMY still has 1.5 to 2 stop speed advantage above TMX.

Acknowledgment

This article was a consolidation of my previous postings on this topic at pure-silver mailing list and a few other places. In pure-silver, Michael Gudzinowicz contributed detailed postings and Tim Daneliuk brought up the formula published in "Astrophotography for the amateur" by Michael Covington. Andrey Vorobyov also contributed to very stimulating discussions.

References

Gurney, R. W. and Mott, N. F. 1938. "The theory of the photolysis of silver bromide and the photographic latent image." Proc. Roy. Soc. London, A164, 151-167.

Hamilton, J. F. 1983. "A modified proposal for the mechanism of sulfur sensitization in terms of capture cross section." Photogr. Sci. Eng., 27, 225-230.

Mees and James. 1966. "The theory of the photographic process," 3rd ed. Macmillan.

Sturmer, D. M. and Marchetti, A. P. 1989. "Silver halide imaging" In Imaging processes and materials, Neblette's eighth ed., Ed. Sturge, J., Walworth, V. and Shepp, A., New York: Van Nostrand Reinhold.

AGFA technical data for AGFAPAN APX 25, APX 100 and APX 400 (Aug 1995).

Fujifilm Data Sheet Neopan 100 Acros (120).

Eastman Kodak Company, 1994. Publication F-8, Kodak Plus-X Pan and Kodak Plus-X Pan Professional.

Note: Publication F-7 for Verichrome Pan and F-12 for Ektagraphic HC, as well many other conventional technology films also suggest same reciprocity failure as Plus-X.

Eastman Kodak Company, 1995. Publication F-32, Kodak T-MAX Professional films.

Note: Ilford data suggest that their conventional technology films and Delta films have identical reciprocity failuer. This is hardly believable, especially when considering lack of specific details that are available from AGFA and Kodak data. Therefore, I did not include any Ilford product in this analysis. Kodak updated their product line in 2003 but they claim that their newly packaged products are essentially the same as their older products. Published data did not change materially, except for suggested processing time.