Interpreting Characteristic Curves

Basic Introduction

The examination of exposure ranges we’ll be looking at below are derived from the manufacturer provided characteristic curves for each film. Before we dive into the comparison, lets first go over the terminology required to interpret these charts.

To start simply, opacity refers to the the ratio of light that is blocked by a sheet of film over the amount of light that passes through it. For those working in the sciences, you’ll be aware that when we deal with ratios we often prefer to work in the logarithmic scale. When we take the base 10 logarithm of the opacity, we refer to this as density.

If you’ve never worked on logarithmic scale before, it can be a bit tricky to wrap your head around. Increasing the density by 2 corresponds to a one hundred times increase in opacity ($$\text{Opacity} \times 10^2$$). On the other hand, a decreasing the density by 1 results in one-tenth the opacity ($$\text{Opacity} \times 10^{-1}$$).

Above are the characteristic curves for Kodak Portra 400 and Kodak Gold 200. I simply did a google search for the datasheets of these films and then digitized the plots holding the characteristic curves for each color.

You’ll notice the x-axis is also in logarithmic units. Here, $$H_v$$ represents luminous exposure (lux seconds).

As you’ve probably guessed, this graph shows us how the light exposure causes darkening of the film. Following the curves from left to right, they start horizontal (the base/fog zone) then quickly turn upwards into a relatively constant slope. This region of consistent slope is what we refer to as the film’s latitude. The distance this region spans along the x-axis can be interpreted as our exposure range. High quality film should have a more consistent slope within the latitude range.

Notice how Kodak Gold sees a drop in the curve slopes around $$\text{log}_{10}(H_v) = 0$$? In addition, you can see some inconsistencies in the slope of the blue curve within the mid region of the film’s latitude.

This won’t be surprising to those who aware of the price difference between these films… but from the curves we can infer that Kodak Portra has a larger exposure range and we’re expecting more consistent exposures within the film’s latitude.

Contrast Curves

Now we’ve covered the basics, you may be left wondering if there’s a more sensible manner to report this information in for amateur photographers. After all, your camera probably doesn’t provide you with expected exposure values in $$\text{log}_{10}(H_v)$$ units, right?

Lets focus on trying to answer a simple, practical question: How many stops above middle gray can I overexpose my film by?

When we talk about overexposure, we naturally think in terms of exposure value, $$E_v$$ (or more commonly presented as $$\text{EV}$$). When shooting a dark subject on a bright sunny background, you may want to set you’re exposure value to +2. This would tell your camera to overexpose by 2 steps, resulting in the mean brightness of the photo to be 4x ( $$2^2$$ ) brighter than middle gray. Ideally, overexposing your bright background will avoid underexposing the dark subject (we’re pretending you don’t have spot metering in this example).

Note that exposure value is also a logarithm, but in base 2 rather than base 10 like the metrics we were examining earlier.

The equation above was ripped from wikipedia and $$N$$ indicates the f-stop of the aperture and $$t$$ is the shutter speed in seconds. In practice (i.e. on your cameras’ exposure compensation dial), $$E_v$$ is usually adjusted so that a value of 0 indicates middle gray for your particular ISO speed. For a given ISO value (i.e. the film sensitivity), we can calculate the required exposure to achieve middle gray with the following equation:

With the above equations, we can now transform the x-axis of our characteristic curves into $$E_v$$ with respect to middle gray.

Applying this transformation results in the following plots:

Now we’re getting somewhere! Here we can see that Portra 400 gives us about 3 stops more exposure than Gold 200. We’re assuming that Gold 200’s latitude ends around an $$E_v$$ of 4, where the curve starts to dip. However, we’re not quite finished yet…

I wouldn’t be surprised, if based on these curves, you were to disagree with me that the latitude of Gold 200 ends at an $$E_v$$ of 4. The changes in slope are subtle, yet can have a large impact on the film quality.

The slope of the characteristic curve is termed the contrast of the film. If we were to directly plot the contrast, we’d get a more easily digestible representation of the film’s latitude.

Now you’re probably more convinced that the latitude of Gold 200 ends at an $$E_v$$ of 4, right? In addition, its also clear that Portra 400 has an extra stop of under exposure. For those who are familiar with the price difference between these films, these are unsurprising results.

For the rest of this post, I’ll be showing contrast curves I digitized by hand. Manufacturers typically only provide the characteristic curves in their datasheets so these contrast curves have to be created. I used the free tool WebPlotDigitizer for laboriously digitizing characteristic curves in datasheets I managed to find, followed by applying LOESS smoothing curves to the resulting datasets in R. The plots were done with ggplot2. Be aware that some fluctuations in contrast may be a result of my shaky mouse hands… so try to focus on the general latitude range and don’t take too much stock in minor contrast fluctuations.

Comparison of Exposure Ranges

Now, hopefully the following plots will now make sense to you.

TL;DR: The dynamic range (latitude) of a film with respect to exposure stops above and below middle gray (the x-axis) is represented by the flat plateau of the contrast curves below.

The above plot shows three brands of (very) cheap film. For those who are starting analog photography (myself included), you’ve probably spent time googling which of these are the best value for money. Based on these plots, we can see Fujifilm c200 has a notably different exposure latitude. Kodak Gold 200 ranges from -2 to +4 stops while Agfa Vista 200 has a similar range but the upper limits that peters out around +3. In contrast c200 ranges from -3 to +5.

For beginners who just want cheap film to burn through while honing their analog skills, c200 seems the best choice. The wider exposure latitude is more forgiving for bad metering, meaning you have more freedom to both over- and underexposure your shots while still preserving detail. That being said, we should also note that c200 keeps relatively more detail in the overexposures than under-, as seen by the slightly positive slope of the exposure latitude (higher contrast at + exposures as compared to - values).

In addition, you’ve probably heard other more experienced photographers mention that analog film is better at dealing with overexposure versus under-. The plots below show a larger collection of films I was able to find datasheets for which support this claim.

In the above plot, Kodak Portra 400 and Fijifilm Superia Xtra 400 dominate with large exposure ranges and distinctly flat latitudes. Another notable observation is the surprisingly poor underexposure tolerance of Fujifilm Superia 200. For this film, it would be high recommended to always overexpose by at least 1 stop (I’m led to believe this film was discontinued relatively recently).

Interestingly, I’ve also heard many people mention that Ektar has strong reds. If we examine the contrast curve, we can see that at optimal exposures, there is a notable peak in red contrast spanning at least a stop.

As a parting note, I’ll again mention to be cautious about interpreting small fluctuations in film contrast, as these datasets came from manually digitizing characteristic curves from datasheets. That being said, after creating these contrast plots I double checked the datasheets for Vista 200, Ektar 100, and Gold 200, and I can verify that these general inconsistencies in the blue color contrast are accurate representations of the trends in the supplied characteristic curves.

I was motivated to make these plots due to the overwhelming subjectivity in reviews of films. While a lot of film preference is inherently subjective (i.e. your preferred color balance), hopefully you now have the knowledge to make more quantitative comparisons between films for those questions which warrant it (such as determining exposure latitude).

P.S. If you find any issues in the math or representation of contrast curves… please let me know! I’m just a dude trying to wrap my head around the overwhelming load of information in the analog photography world.

References

• Film shooter collective: An excellent introduction to reading characteristic curves.

• Molecular expressions, Optical microscopy primer: I found this to have good details regarding terminology and the more technical aspects of reading film datasheets.

• sprawls: Another great resource for interpreting characteristic curves.

• imatest: Resources on how to calculate the relevant exposure resulting in middle gray from ISO values (i.e. light meter math).

Updated on: 2019-12-20