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Correcting for film reciprocity failure


This page is a work in progress, reporting the results of my testing as it occurs. Please check back from time to time for further updates.

Introduction
Kodak Correction for Most Black and White Films
Other Published Correction Data
My Testing Method
Testing Provia 100F
Recommended Correction Factors for Provia 100F
Testing Kodak 160T
Testing Fuji Acros 100
References

Introduction

Photographic emulsions typically give the same results when two separate frames of a given film are exposed to the same total amount of light, meaning light intensity multiplied by exposure time. When the intensity of light falling on the film is reduced by half by choosing the next smaller lens aperture, the same film density can be obtained simply by doubling the exposure time. This ability to give equivalent results with one stop increase of exposure time for a one-stop smaller lens aperture is called the reciprocity effect, and films that follow it are said to follow the reciprocity law, or give good reciprocity results.

Most common films manufactured over the past several decades follow the reciprocity law over a range of exposure times from about 1/1000 second to about 1/10 second. Some more recent emulsions, such as those with T-grain technology, extend that range, sometimes substantially. Some of the best films available today are capable of giving good reciprocity results over a range of exposures from 1/2000 second or less to many tens of seconds, or in the case of Fuji Acros 100, to many minutes. This covers the range of exposure times most people are likely to use in general photography, and even covers most low-light and available-light applications.

However, there are times when photographers find the need to use exposure times that lie outside of the range where their film of choice gives good reciprocity results. This is especially true in night photography, where exposure times can range from several seconds to many minutes or hours. In this range of exposure times, selecting a smaller lens aperture in order to increase depth of field, or to choose the aperture of maximum sharpness for a given lens, leads to an underexposure of the image on the film if the reciprocity law is assumed to hold. This effect is called Reciprocity Failure, from the failure of the film to follow the reciprocity law in that regime. The amount that the response of a given film departs from the reciprocity law varies from one type of film to the next. This effect can also vary between the emulsion layers in color film, which leads to long-exposure color shift, as each layer responds differently to the increased exposure time.

Reciprocity failure is a non-linear decrease in light sensitivity (speed) that occurs at extremes of very short exposure times, very long exposure times, or both. It is also called "the Schwarzschild effect" for astronomer Karl Schwarzschild, who published an empirical formula describing it in the year 1900. Since the effect is repeatable, it can be characterized, understood, and corrected for. Film manufacturers often provide reciprocity failure correction information on their film data sheets, which are often available on their web sites. Most of the time, the recommended corrections are in terms of increased lens aperture, though some manufacturers give a correction factor that can be multiplied to the indicated exposure time (the time a light meter would give you) to yield a corrected exposure time. The problem is, especially for night photography, that the lens aperture chosen for a given image may be critical to the success of that image, meaning that reciprocity failure correction must be applied as a further increase in exposure time. I find the time correction factor to be far more useful in practical work.

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Kodak Reciprocity Correction Data for Black and White Films

Kodak provides a table of corrected exposure times for "Most Black and White Films" (provided in the table below), which gives good results for many older (pre-T-grain) emulsion types, such as Kodak's Tri-X and Plus-X films. It also gives reasonably good results for some of their older color negative films. I have used it as a guide for determining corrected exposures for some films made by other manufacturers, including color negative and slide films, obtaining good results in many cases.

Kodak Black and White Film Reciprocity Failure Correction Data
Indicated Exposure Time (Seconds) Correction Factor Corrected Exposure Time (Seconds) Remarks
1 1.5 1.5
2 2.0 4
3 2.67 8
4 3 12
8 4.5 36
10 5 50
15 6.33 95
20 6 120
30 7 210
40 7 280
60 (1 minute) 8 480 (8 minutes)
120 (2 minutes) 9 1080 (18 minutes)
180 (3 minutes) 9 1500 (25 minutes)
240 (4 minutes) 10 2400 (40 minutes)
360 (6 minutes) 10 3600 (1 hour)
600 (10 minutes) 12 7200 (2 hours)
900 (15 minutes) 13.33 12000 (3 1/3 hours)
1200 (20 minutes) 12 14400 (4 hours)
1800 (30 minutes) 12.67 22800 (6 1/3 hours)
3600 (1 hour) 12.5 45000 (12 1/2 hours)
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Other Published Reciprocity Correction Data

A table including Kodak data for Tri-X and T Max, as well as Illford data for HP, is available on The Nocturnes web site "Tips and Tricks" page.

A good summary of manufacturers published reciprocity failure correction data for color films is available on the photo.net web site.

The results of some detailed testing of Fuji Velvia can be found here .

With the dramatic change in film technology over the past few years, the old Kodak table is no longer the best source for correction data. Many of today's films have expanded reciprocity response to one or several seconds. For example, Fuji's remarkable RDPIII Provia 100F slide film has full reciprocity response out to 128 seconds. Kodak's E100VS is reputed to have long reciprocity response as well, however I have no experience with that film and so can't comment on it. I get the impression that most T-grain emulsions adhere to the reciprocity law out to over a minute exposure duration, however that has yet to be completely confirmed to me by a reliable source.

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My Testing Method

For moonlight photographs, exposures over two minutes are usually required to give the desired effect, and there are not many films with reciprocity failure correction data published out to that range. Consequently, it is necessary to test films for reciprocity failure over the range of exposures required for moonlight work, in order to obtain the reciprocity correction factors needed.

The goal in performing this test is to obtain a series of correction factors that provide the same image optical density over a range of indicated exposure times. You know the correction factors are correct if all images in a series have identical density, just as they would be if you were photographing the gray card in daylight over the normal daylight range of exposures (i.e. selecting an EV that places the gray card brightness on Zone V, and then adjusting the exposures within that EV).

The following method works well for me. I make two series of exposures of a Kodak 18% gray card under moonlight conditions, with each series starting at a large lens aperture (small f-stop number) and progressing by half f-stops, increasing the exposure time with each increase in f/stop number. The first series assumes that the reciprocity law holds - in other words, the exposure time doubles with each whole increase in f/stop (or increases by 41% with each half-stop change). The second series assumes a "trial curve" that represents a guess at what the final corrected exposure will be. If I don't have anything else to go on, the first trial curve doubles the exposure time of the first series at the same f-stops. After the film is developed, the optical density of the images are measured and compared against a standard (I use 1.30 density units - a typical Zone V slide density). You can develop your own standard by photographing a gray card in sunlight at the exposure indicated by your camera meter (Zone V exposure), and then measuring the optical density of that image. I take the optical density of the images from each series at the same f-stop, and then interpolate between the given exposure times to figure what time would be needed to give the standard density. For example, if the image from the first series at f/5.6 is 4 minutes, and has a density of 1.10 units, while the image from the second series at the same f-stop at 8 minutes has a density of 1.5 density units, I would choose 6 minutes as a guess at the correct exposure to obtain a density of 1.30 units for an indicated time of 4 minutes, or a correction factor of 6/4, or 1.5. Repeat for the full range of f/stops used in the test, and you get a series of correction factors for a range of times. Now repeat the test with the new factors, and see how close you come, and adjust the trial curve as the results warrant. Repeat until you have the desired accuracy. I find that three rolls of film, each on a different night, usually does it. Given that I can get one test in per full moon, that's two months to go through the whole test for a given film.

One thing to note is that you have to have each image of the gray card of uniform density across the frame. I use a 135mm f/2.8 lens, and place the camera so that the lens is about eighteen inches from the gray card, so as to be sure the frame is filled with gray card and nothing else. You have to ensure that the camera shadow (as well as the shadow of the photographer!) does not fall on the gray card. You also have to be sure that the card faces the moon, and you may have to adjust the position of the card while doing the test to ensure the lighting on it is uniform over a period of several hours. This is necessary since the moon moves 15 degrees of arc across the sky each hour. I try to set up the card to lead the moon by 15 degrees, and then change the position two hours later. That way you are always within 15 degrees of directly facing the moon, which reduces the variation in the lighting due to cosine loss to less than 3.5 percent, or well below a level that will affect the results.

An example of the exposures needed for this come from a test I performed on Kodak 160T slide film on December 8, 2003, a night when the illumination provided a gray card surface brightness of about -3.0 EV. The first series consisted of exposures of 1 minute at f/2.8, 2 minutes at f/4, etc up to 16 minutes at f/11 (using half-stop increments between f/4 and f/11). The second series consisted of exposures with twice the time of the first, meaning 2 minutes at f/2.8, 4 minutes at f/4, etc up to 32 minutes at f/11. The total time for running the test, including setup time and exposures, was about three and one-half hours. The next morning, I made three exposures of the same 18% gray card, positioned facing the sun, at the camera settings indicated by the in-camera meter (Zone V), in order to obtain a reference standard.

You could have the film optical density measured by your lab, however I find that you can easily measure film optical density using a spot meter and a light table. I have a jig that locates the film in the same position on the light table each time, and that also positions the spot meter directly on top of the frame being measured, so that measurement conditions are the same from frame to frame. (The jig is no more than the slide holder that came with my flatbed scanner, positioned with one corner aligned with one corner of the light table.) If the jig allows the light meter lens barrel to see beyond the edge of the film, use a cardboard slide frame with the film cut out of it as a baffle between the test film and the meter lens barrel. Be sure you make "tare" readings of the base light table brightness several times during the time you are measuring the film density, to ensure the brightness does not change over time. You must have a stable "base" brightness for this to work!

Film optical density is measured in "density units", where an increase in density of 0.3 units gives a stop less light passing through the film. (0.3 is the base-ten logarithm of the number 2.) It turns out that my Pentax spot meter has an analog scale with scale lines every 1/3 stop, and a needle width just about 1/5 as wide as the spacing between the 1/3 stop lines. Thus by carefully estimating the location of the needle on the scale, I can reliably measure film density differences to 1/15 stop, or 0.02 density units. That is pretty good, about half the accuracy as many commercial densitometers used by professional photo labs, but certainly accurate enough for the purposes at hand.

By making the test exposure series discussed above, and measuring the density of each film frame, you get a set of data that can be plotted to show the trend of film density over the range of exposure given. (Plot density vs uncorrected exposure time.) From the curve, you can judge what adjustments have to be made while performing the next test. Once you have a density curve that is flat over the full range of exposures, you are done. In a practical sense, your curve does not have to be perfectly flat, since even the most discerning eye has a hard time detecting a 1/10 stop change in exposure. I strive for and often achieve a curve that has less than 5% variation in density, so as to ensure the results are well below that 1/10 stop threshold.

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Test Data for Fuji Provia 100F (RDP III)

Fuji Provia 100F is a modern T-grain emulsion that has astounding reciprocity response with long exposures. Compared against older emulsion types, it has better low-light sensitivity than an 800-speed pre-T-grain emulsion, making it very suitable for extremely low-light work. It is substantially faster in low light than the older Provia 400F emulsion, which (including its earlier formulation called Fujichrome Professional 400D) has been my standard moonlight slide film for many years. This remarkable state of affairs has lead me to embark on calibrating the reciprocity failure correction needed to make full use of this film. It is incredible to think that such a film exists, providing low-light speed, fine grain, high accutancy, and rich but not overdone color saturation all in one emulsion. The color shift with long exposures is just a bit toward the blue-green, but is barely noticeable. This stuff is gold, and I hope Fuji keeps it around for a very long time.

The testing described in this section has as a goal determining correction factors for indicated exposures up to 15 minutes duration under moonlight conditions. All test exposures are made of a Kodak 18% gray card placed facing the full moon, with the camera placed just far enough off to the side to avoid both specular reflections from the card and shadowing of the card by the photographer's big head. I am careful to ensure the gray card is within 15 degrees of directly facing the moon to ensure the card has the same illumination level during the entire test.

The graphs presented below give the results of tests performed to date.

Reciprocity Test Results



Test #1 consisted of a series of trials assuming no reciprocity failure correction was needed, as well as a couple of simple "guessed-at" trial correction curves. The results of the no-correction test indicate that this film gives good reciprocity results out to about 100 seconds, beyond which the film looses sensitivity rather slowly. Based on the results of Test #1, a "Best" trial correction curve was estimated by interpolation. This was then used to determine corrected exposure times in a second test.

Test #2 consisted of a series of exposures made without reciprocity failure correction, as well as a series of exposures using "Trial Curve #1", the "Best" trial correction curve arrived at after completing Test #1. The results of this test, plotted in the graph above, indicate two things. First of all, the overall density of the film was greater, which was to be expected since Test #2 was performed under a moon several days past full, while Test #1 was performed under a very full moon. The second result showed that Trial Curve #1, while better than anything used during Test #1, was still short of the mark. To reiterate, the goal is to arrive at a correction curve that gives uniform film density over the range of exposures from one seconds to approximately fifteen minutes. The results of Test #2 showed that exposures using Trial Curve #1 achieved pretty good results out to about 250 seconds, but beyond that the film density changed slowly with increasing exposure. Based on these results, a second trial curve, Trial Curve #2, was produced. A further test was then planned to see what results Trial Curve #2 would provide.

Test #3 compared the densities obtained using exposure correction factors in Trial Curve #2 with uncorrected exposures. In addition, care was taken to ensure the exposures were made for a Zone V placement of the card surface brightness, in order to avoid the miss-matched curves I had in Test #2. The resulting densities over the range of exposures are provided in the following graph:

Reciprocity Test 3 Results

The data curves from the two series of exposures are plotted against a "baseline" curve, which shows what the film response would look like with the correct reciprocity failure correction curve. Such a curve would provide a constant film density over the full range of exposures.
As expected, the curve for the uncorrected exposures departs from the "baseline" around 130 seconds or so. The good news is that the results with "Trial Curve #2" stay pretty much right with the baseline out to around 500 seconds, before they begin to gently deviate from the desired goal. This was an improvement over "Trial Curve #1", which resulted in deviation beginning around 250 seconds. We were getting there! However, more work was needed if the goal of reciprocity correction out to 15 minutes (900 seconds) were to be achieved.

The next step was to estimate what the correct exposures should be for these indicated times, given the test results. That was done by comparing the densities of the film resulting from exposures with and without the correction applied. By scaling the time values over the densities to the point where the desired density is reached, a better estimate of the correct factor is obtained. This method worked fairly well in Test #2. Once I had the new estimated values, I fit a curve to the new data points, and used that to interpolate new data points at convenient intervals of indicated exposure.

curve_3

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Courter's Recommended Provia 100F Reciprocity Correction Factors

The following table presents the correction factors I recommend for this film, based on testing performed to date. The data presented have been obtained using the interpolation curve, although the table also provides the actual data points from Test #3 for comparison purposes. Note that the maximum error in the values obtained from the interpolation curve is 2.4% compared to the test data. This magnitude of error is quite negligible, considering that a 1/3-stop change in exposure is around a 25% change in exposure time. Thus the maximum error in the curve is about 1/20 stop in exposure, or well below what I can measure with my film density measurement setup, as well as well below what anyone would notice in a photograph.

The table will continue to be updated whenever I get around to performing more tests. I have used Curve #3 in the field under moonlight conditions, and the results have been very good indeed. In practice, it is best to test for the exact correction curve for a single batch of emulsion, since there are sometimes slight differences from batch to batch. I recently bought a case of this film, emulsion number RDP-III 033-628, which is now living in my freezer. I intend to use a couple of rolls from this case to update the correction curve. I will then have a good year's supply of moonlight film fully calibrated, so that I can anticipate exactly what it will do in the field.



Fuji Provia 100F (RDP III) Reciprocity Failure Correction Data
Updated June 6, 2003
Results from Test #3 and Trial Curve #3
factor = 1.00 for indicated exposure times up to 128 seconds
for indicated exposure times above 128 seconds:
factor = 1 + 1.0165E-06 * (t-128)^2 where t = indicated exposure time in seconds.
Indicated Exposure Time (Seconds) Correction Factor Corrected Exposure Time (Seconds) Remarks
0.10 1.00 0.10  
128 1.00 128 Fuji's published data says reciprocity holds to 128 seconds. My tests have shown this to be true.
160 1.00 160 From the interpolation curve
169 1.00 169 Data at this indicated exposure time from Test #3 gave a factor of 1.024 and a required exposure time of 173 seconds. Thus the interpolation curve at this point is low by 4 seconds, or 2.2%.
200 1.01 202 From the interpolation curve
239 1.01 242 Data at this indicated exposure time from Test #3 gave a factor of 1.026 and a required exposure time of 245 seconds. Thus the interpolation curve at this point is low by 3 seconds, or 1.3%.
250 1.02 254 From the interpolation curve
320 1.04 332 From the interpolation curve
338 1.04 353 Data at this indicated exposure time from Test #3 gave a factor of 1.063 and a required exposure time of 359 seconds. Thus the interpolation curve at this point is low by 6 seconds, or 1.7%.
400 1.08 430 From the interpolation curve
479 1.13 539 Data at this indicated exposure time from Test #3 gave a factor of 1.116 and a required exposure time of 535 seconds. Thus the interpolation curve at this point is high by 4 seconds, or 0.8%.
500 1.14 570 From the interpolation curve
640 1.27 811 From the interpolation curve
667 1.30 864 Data at this indicated exposure time from Test #3 gave a factor of 1.327 and a required exposure time of 885 seconds. Thus the interpolation curve at this point is low by 21 seconds, or 2.4%.
800 1.46 1167 From the interpolation curve
957 1.70 1626 Data at this indicated exposure time from Test #3 gave a factor of 1.670 and a required exposure time of 1598 seconds. Thus the interpolation curve at this point is high by 28 seconds, or 1.7%.
1000 1.77 1773 From the fit curve - extrapolation beyond last test data point
1280 2.35 3007 This point is a serious extrapolation of the data. It should not be relied upon without further testing.





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Testing Kodak 160T

I'm interested in this film as it's color shifts to a rich blue with long exposures, besides rendering incandescent light in more natural hues. It is a favorite of many night photographers.

After testing three rolls of Kodak 160T, the following preliminary reciprocity correction factors have been worked out. Note that no attempt to has been made to correct for any reciprocity failure-related color shift; I'm letting the color go wherever it will. Also note that this is a significant change from results presented here prior to Test #3 - I found an error in the data reduction of Test #2 that led me to erroneous results. That has now been corrected.



Kodak 160T Correction

Kodak 160T Reciprocity Failure Correction Data
for Daylight and Moonlight (NOT Tungsten Light!)
Updated January 22, 2004.
Results from Test #3       (roll number 2004-01-02)
factor = 1.00 for indicated exposure times up to 1 second.
For indicated exposure times from 1 to 4 seconds:     factor = 1.00 + 0.0881 * ( t - 1.00 )
For indicated exposure times above 4 seconds:     factor = 1.3473 - 0.1912 * Log(t) + 0.3443 * Log(t)^2
where t = indicated exposure time in seconds.
Maximum departure between curve fit and test data points is 9.5%, or approximately 1/20th stop
Indicated Exposure Time (Seconds) Correction Factor Corrected Exposure Time (Seconds) Remarks
0.1 1.00 0.1  
0.25 1.00 0.3  
0.5 1.00 0.5  
1 1.00 1.0  
2 1.09 2.2  
4 1.26 5.1  
8 1.45 12  
16 1.61 26  
30 1.81 54  
60 2.09 126  
90 2.28 206  
120 2.43 293  
150 2.56 384  
180 2.66 480  
240 2.84 682  
360 3.10 1119  
480 3.31 1589  
720 3.61 2601  
960 3.84 3686  

A further test should be made using these correction factors to be sure they provide a uniform film optical density. I stopped testing at this point, though, and started using the film in the field with good results.

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Testing Fuji Acros 100

This is my current favorite black and white film, with exceedingly fine grain, high acutance, and a nice smooth gray scale without much shoulder when developed in Agfa Rodinal. I use a dilution of 1:50, and soup the film for 11 minutes at 20 degrees C, with agitation of three inversions of the tank every minute. I am currently using a 4-roll Patterson tank, and find that volume of working material tends to hold temperature within one degree in my darkroom without the need of a temperature-control water bath.

Fuji's data sheet for this film says that there is no reciprocity failure out to two minutes exposure time, and recommends a one-half stop correction for times beyond two minutes. I have set out to test these claims. After testing three rolls of Acros 100, the following preliminary reciprocity correction factors have been worked out. I have had to look hard to find any appreciable reciprocity failure out to around 80 seconds, and the reciprocity failure I observed beyond that is incredibly small, with a correction factor of 1.2 needed at 15 minutes. That makes the response better even than that of Fuji Provia 100, and indicates that a one-half stop correction (factor of 1.5) for long exposures may in fact be too much! This is incredible stuff, to say the least. I have not yet run a roll through the whole range of exposures using these new factors, but plan to do so at the first opportunity. If all is well, there should be no variation in film optical density between a quarter second and 15 minutes indicated exposure time.



Fuji Acros Correction

Fuji Acros 100 Reciprocity Failure Correction Data
for Daylight and Moonlight
Updated January 25, 2004.
Results from Test #1       (rolls number 2004-01-03, -04, -05)
factor = 1.00 for indicated exposure times up to 80 seconds.
For indicated exposure times above 80 seconds:     factor = 1.000 + 0.000168 * t + -3.823E-08 * t^2
where t = indicated exposure time in seconds.
Indicated Exposure Time (Seconds) Correction Factor Corrected Exposure Time (Seconds) Remarks
0.1 1.00 0.1  
0.25 1.00 0.25  
0.5 1.00 0.5  
1 1.00 1  
2 1.00 2  
4 1.00 4  
10 1.00 10  
20 1.00 20  
40 1.01 40  
80 1.02 82  
160 1.04 166  
240 1.05 252  
480 1.08 519  
960 1.14 1090  
1920 1.19 2288  

A further should be made using these correction factors to be sure they provide a uniform film optical density. I stopped testing at this point, though, and started using the film in the field with good results.


Note to readers: As with many people, I have switched to digital photography for most things, including much of my night photography. I don't plan on doing much further testing of film at this point beyond what is shown here. I am using Tri-X and Provia 100F in 4x5 format, and find they have similar reciprocity characteristics to the 35mm format materials previously tested. I'd like to perform tests on this material to make sure of the similarity when I get the time, but have no idea when that may be!

I can try to answer questions sent to me at this email address.


C. D. "Kit" Courter
LunarLight Photography
Torrance, California, USA.


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References

Kodak Publications on Black and White Films can be found here.

Fuji film data sheets can be found here.

Ansel Adams, "The Negative", New York Graphic Society, Boston, 1981

There is also a lot of practical information on reciprocity failure than can be found by using the search engine at www.photo.net.



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Reciprocity Failure Correction
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Updated August 8, 2007