TL;DR

**Relative** log(exposure) means that the numbers on the x-axis have no absolute meaning, but the

**difference** between two numbers is meaningful. The horizontal axis of the characteristic curve linked by the OP is expressed in "units" of log

10(exposure). These aren't really units, just like per cent (%) isn't really a unit, it's just a different way of expressing a value. If you take the difference between two x-axis numbers, and want to convert this difference into "units" of "stops of light", simply take the difference in units of relative log(exposure) and divide by 0.3.

There's a lot of fantastic answers above, but I thought I'd throw my hat into the ring as well. First off, if you are at all interested in learning more about sensitometry, I highly suggest the

Kodak Sensitometry Workbook. It is very tractable, and it gives lots of examples.

First, I understand the vertical axis - that is simply what the densitometer sees, but what about the horizontal? It is labelled "relative log exposure" but is in whole numbers, rather than stops (i.e., 0.3, 0.6, etc.).

Good question. When I have done film testing and produced my own "Hurter-Driffield curve" aka "H-D curve" aka "D - log(E) curve" aka "D - log(H)" aka "characteristic curve", I always express the x-axis in terms of relative exposure. Why do I do this? Because I don't know what the absolute exposure is!

Consider a

Stouffer step wedge: a piece of film with 21 steps of different opacities, where each step is progressively denser by 0.15 "density units". Since you know that each step is 0.15 denser than the previous step

†, you can simply place this wedge atop the film I want to test, and expose the film under the enlarger. What you have done is provide 21 different exposures to the film, in increments of 0.15 log(H) "units". You don't actually need to know the exact exposure that you gave the film in lux*sec (i.e the illuminance produced by the enlarger bulb in lux multiplied by the exposure time in seconds) to produce a D - log(H) curve. You can simply plot "relative log(H)" on the x-axis and arbitrarily choose the exposure received by the film under the densest portion of the step wedge as "zero relative log(H)". This is how I suspect the Bergger Pancro 400 curve you linked to was produced.

† Note: you can measure the density of the step wedge with a densitometer and plot that density on the x-axis.

But I don't know what those integers on the x axis mean. 1.5 what? 1 to 7 of what? That's my main problem.

Density is a unitless quantity. Density is log

10(opacity) and opacity is the ratio of incident illuminance to transmitted illuminance. Opacity is unitless since it is a ratio of two quantities having the same units (the units cancel.)

Absolute exposure has units. Exposure is illuminance (often expressed in lux or millilux) multiplied by time (expressed in seconds), so the typical dimensions of exposure are lux*sec.

A number given in "relative exposure" has no absolute meaning. If you take a number given in relative exposure and add some constant, you will obtain absolute exposure. But if the people presenting the D - log(H) curve did not measure the absolute exposure they gave the film, this constant is not known! Even so, a D - log(H) curve expressed in terms of relative log(H) still has all the useful information contained in a characteristic curve, except for information regarding the speed of the film (ISO/ASA). So, a number on the x-axis in such a curve is not meaningful by itself, but the

**difference** between two numbers on the x-axis

**is **meaningful! For example, the

**difference **between two points on the curve can give information about exposure latitude. The ratio of a difference in density to a

**difference** in relative exposure for two data points on the curve (i.e. the slope between two points) can give information about the gamma, contrast index (CI), and average gradient.

You can think of the relative log(exposure) axis as meaning that we don't know where to "fix" the curve along the x-axis. You can slide the entire curve left and right along the x-axis (i.e. horizontal translation), the curve shape doesn't change, so most of the useful information is retained. Note the sliding the curve along the x-axis doesn't involve scaling the x-axis. This is what I mean when I say that the absolute x-value at some point along the curve has no meaning, but the difference between two points is meaningful.

As stated in a few posts above, if you are more comfortable in stops (more accurately "steps"), a change of 0.3 relative log(H) is equivalent to 1 stop. Once again, a "stop" of light has no absolute meaning, it is a relative term. If you measure a scene with a light meter, and then the sun comes out from behind a cloud and the scene is suddenly illuminated by twice the number of photons, your meter will indicate a decrease in EV by 1 stop, thus ensuring the film receives the same exposure as before the change in amount of light in the scene. A doubling of the illuminance is equal to a increase of illuminance of 1 stop. Now consider a light meter that reads in units of log(H). A doubling of the illuminance would show an illuminance increase of 0.3 "log(H) units" on such a meter.

______________________________

~A brief aside~

Here's a question: why does a "stop" equal 0.3 of a log(H)? It seems a bit arbitrary. I tried to make this as clear as possible, but there's probably a better way to explain this.

First of all define exposure:

(1) H = E*t

where H is exposure, E is illuminance, and t is time.

The exposure (in lux) can be related to EV at ISO 100 by the following formula:

(2a) E = 2.5*2

EV
It can be shown that the change in illuminance in units of EV, or "stops", is related to the change in illuminance by the expression (2b). This is the mathematical representation of what I described in words in the paragraph immediately preceding this aside.

(2b) ΔE = 2

ΔEV
or, alternatively

(2c) ΔEV = log

2(ΔE)

where ΔE is the change in illuminance and ΔEV is the change in illuminance in "units" of exposure value.

The relative log(exposure) axis refers to log

10(H). Substitute the expression (1) for H:

(3) log

10(H) = log

10(E*t)

By the product rule of logarithms, we can write:

(4) log

10(H) = log

10(E) + log

10(t)

Now substitute expression (2a) for E into the first term on the right-hand side of (4):

(5) log

10(H) = log

10(2.5*2

EV) + log

10(t)

Simplify:

(6) log

10(H) = (EV)*log

10(2) +log

10(2.5)+ log

10(t)

Now, log

10(2) is approximately 0.3, and the remaining terms on the right hand are just constants (let's add the constants together call the sum C.) So we can write our final expression:

(7) log

10(H) = (EV)*0.3 + C

So, you can convert an exposure measured in EV at ISO 100 to a log

10(H) by multiplying by 0.3 and adding some constant.

So that's where the 0.3 comes from! A change of base from log

10 to log

2 involves multiplying by a factor of log

10(2).

______________________________

~An example of a practical piece of information that you can glean from such a curve~

So, as Bill said, if you consider that the straight line portion of the curve goes from 2 to 5 relative log(H), this represents a range of 5 - 2 =

**3** relative log(H). Convert to stops if that's more convenient:

(3 relative log(H))*(1 stop / 0.3 relative log(H)) = 10 stops.

Now consider that you have measured your scene with a spot meter. The brightest spot in the scene measures as having 7 stops light more than the darkest spot in the scene. Thus, your exposure latitude is:

10 stops - 7 stops = 3 stops

I hope all of this clarifies rather than confuses. I also hope this can give you a better intuition of sensitometry and maybe even helps you make better photos!