How to understand 18% gray?

why 18% gray is in the mid of the full scale of brightness from
darkest to brightest? what's the math behind it?

On Sun, 25 Nov 2007 21:37:51 -0800 (PST), Steven Woody
wrote:

why 18% gray is in the mid of the full scale of brightness from
darkest to brightest? what's the math behind it?

It really means that 18% of incident light is reflected.

Human perception of brightness is logarithmic, though, and not linear.
Basically, logarithmic means we are multiplying instead of adding.
Compound interest is logarithmic. So is the frequency of the notes on
a piano. So is the decibel scale for measuring sound pressure.
Likewise with the light plotted on a typical histogram.

You can make (or imagine) a set of brightness patches by starting with
100% reflection and halving each time. The next is 50%, then 25%,
12.5%, 6%, 3%, and 1.5%. That's 7 patches. It is a logarithmic
sequence; the factor is 1/2. The first patch is white, the last very
dark gray, virtually black. In the middle it will be middle gray,
12.5% actually, a bit darker than 18% gray.

You can fiddle with sequences like this to make as many patches as you
like, with different gradations of brightness between them. Using a
factor of 0.75, we get 13 steps, with the middle being 18%:
100 75 56 42 32 24 18 13 10 7.5 5.6 4.2 3.2.

Ed

In article
,
Steven Woody wrote:

why 18% gray is in the mid of the full scale of brightness from
darkest to brightest? what's the math behind it?

It can be mid-way for exponential gamma.

The exponential gamma has its origins in old tube TV circuits but it
remains in use because it models visual perception reasonably well. It
shifts more digital levels into areas where the eye is most sensitive.
Few things in the natural world are linear.

"Steven Woody" wrote in message ...
why 18% gray is in the mid of the full scale of brightness from
darkest to brightest? what's the math behind it?

See:
doug.kerr.home.att.net/pumpkin/Scene_Reflectance.pdf
and
doug.kerr.home.att.net/pumpkin/Exposure_metering_18.pdf

Cheers
--
cmyk

"Steven Woody" wrote:

why 18% gray is in the mid of the full scale of brightness from
darkest to brightest? what's the math behind it?

While the "logarithmic" answer people have given is correct, it's easier to
see if you remember that a one stop difference means a twice the brightness.

So if you have mid-gray at 18%, you get five (that's all, folks) useful
tones on a print: 4.5%, 9%, 18%, 36%, and 72%. If you toss in 0% and 100%,
that makes 7 (although you probably won't be able to see the difference
between 4.5% and 0).

David J. Littleboy
Tokyo, Japan

"David J. Littleboy" wrote in message
...

"Steven Woody" wrote:

why 18% gray is in the mid of the full scale of brightness from
darkest to brightest? what's the math behind it?

While the "logarithmic" answer people have given is correct, it's easier
to see if you remember that a one stop difference means a twice the
brightness.

So if you have mid-gray at 18%, you get five (that's all, folks) useful
tones on a print: 4.5%, 9%, 18%, 36%, and 72%. If you toss in 0% and 100%,
that makes 7 (although you probably won't be able to see the difference
between 4.5% and 0).

David J. Littleboy
Tokyo, Japan



Perhaps a usefulness not yet explained or stated is for matching colour. I
use a white, black and grey card (home made) in the first shot of a scene. I
use it with the "levels" function of Photoshop and so far (maybe 1000
frames) it works better than nearly any other post shoot white balance.

I don't believe digital photography has the same use for a grey card as film
shooters have.

Douglas

Steven Woody writes:
why 18% gray is in the mid of the full scale of brightness from
darkest to brightest? what's the math behind it?

It isn't exactly in the middle, really. Any given scene has a darkest
tone you want to record and a brightest tone you want to record, and the
middle tone for that particular scene is halfway in between.

Now, it's not halfway between in linear-light space, because the eye
responds logarithmically. Suppose you have a scene whose brightness
ranges from 1 to 100 on some arbitrary (but linear) light meter scale.
To the eye, a brightness of 50 is "one step" darker than 100, and 25 is
an equal-sized step darker than 50, 12 is another step darker again, and
so on. So the midtone for this particular scene is actually a
brightness of 10, in the sense that it is just as much brighter than the
minimum (10X) as the maximum is brighter than the midtone (10X).

One general way to calculate this is:

midtone = sqrt(min_bright * max_bright)

This value is called the "geometric mean" of min and max brightness.
You can also average logarithms:

midtone = exp( (log(min_bright) + log(max_bright)) / 2)

The magic value of 18% comes from somewhere else. Someone did a study
and found that the average reflectance of a large number of
photographic scenes was 18%. So if they set their incident light meter
to assume that light from the scene was 18% of the light falling on the
meter, they would (on average) get a good exposure. Similarly, if they
had an 18% reflectance grey card, and measured the light on it with a
reflected light meter, that would also be a good exposure.

It happens that, in many scenes, the average scene brightness is
actually pretty close to the middle tone (halfway between darkest and
lightest areas of interest), so it's also useful to expose as if it was
the middle tone, giving equal range above and below it. But that's not
necessarily true, and spotmeters and the zone system are tools for more
accurately figuring out what the tonal range of your scene is, and how
to place that relative to what your film (or sensor) can capture.

Dave

Steven Woody wrote:

why 18% gray is in the mid of the full scale of brightness from
darkest to brightest? what's the math behind it?
Go back 100 years or so and ask.


--
Neil
reverse ra and delete l
Linux user 335851

Steven Woody wrote:
why 18% gray is in the mid of the full scale of brightness from
darkest to brightest? what's the math behind it?

The gray card is a development of the "artificial highlight"
method of exposure metering. Before the gray card was invented,
Kodak recommended using a 90% white card and setting your light
meter at 1/5 of the normal film speed rating. The gray card
simplifies this because you don't need to change your meter setting.

90/5 = 18

Peter.
--

"Douglas" wrote:
"David J. Littleboy" wrote:
"Steven Woody" wrote:

why 18% gray is in the mid of the full scale of brightness from
darkest to brightest? what's the math behind it?

While the "logarithmic" answer people have given is correct, it's easier
to see if you remember that a one stop difference means a twice the
brightness.

So if you have mid-gray at 18%, you get five (that's all, folks) useful
tones on a print: 4.5%, 9%, 18%, 36%, and 72%. If you toss in 0% and
100%, that makes 7 (although you probably won't be able to see the
difference between 4.5% and 0).

Note that Dave M. has provided a much better discussion of this issue than
the above.

Perhaps a usefulness not yet explained or stated is for matching colour. I
use a white, black and grey card (home made) in the first shot of a scene.
I use it with the "levels" function of Photoshop and so far (maybe 1000
frames) it works better than nearly any other post shoot white balance.

I don't recommend this. I have two Kodak gray cards here that have radically
different color compositions: one is somewhat blue, the other quite warm.

David J. Littleboy
Tokyo, Japan