How to understand 18% gray?

Discussion in 'Digital Photography' started by Steven Woody, Nov 26, 2007.

  1. Steven Woody

    Steven Woody Guest

    why 18% gray is in the mid of the full scale of brightness from
    darkest to brightest? what's the math behind it?
     
    Steven Woody, Nov 26, 2007
    #1
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  2. Steven Woody

    EAL Guest

    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
     
    EAL, Nov 26, 2007
    #2
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  3. 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.
     
    Kevin McMurtrie, Nov 26, 2007
    #3
  4. Steven Woody

    cmyk Guest

    "Steven Woody" <> wrote in message news:...
    > 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
     
    cmyk, Nov 26, 2007
    #4
  5. Despite the science behind it, in reality it is the art that counts.
    For most situations 18% works well. However for some situations and for
    some expectations of a result some other gray will work better.

    In other words, don't worry so much about the science of photography
    that it gets in the way of the art. :)

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



    --
    Joseph Meehan

    Dia 's Muire duit
     
    Joseph Meehan, Nov 26, 2007
    #5
  6. "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, Nov 26, 2007
    #6
  7. Steven Woody

    Douglas Guest

    "David J. Littleboy" <> wrote in message
    news:...
    >
    > "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
     
    Douglas, Nov 26, 2007
    #7
  8. 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
     
    Dave Martindale, Nov 26, 2007
    #8
  9. Steven Woody

    Neil Ellwood Guest

    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
     
    Neil Ellwood, Nov 26, 2007
    #9
  10. Steven Woody

    Peter Irwin Guest

    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.
    --
     
    Peter Irwin, Nov 26, 2007
    #10
  11. "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
     
    David J. Littleboy, Nov 27, 2007
    #11
  12. Steven Woody

    Steven Woody Guest

    thanks for all your explains and that actually made me in the way of
    understanding. now, another question poped up in my mind: how to
    map a 18% point ( or a mid-tone point ) in a 1 to 255 scale in digital
    photo file? there are four possible answers i can guess,

    1, 255/2 = 128
    2, 255*0.18 = 45
    3, 0.18^(1/2.2)*255 = 117
    4, 0.5^(1/2.2)*255 = 186

    which one is right?
     
    Steven Woody, Nov 27, 2007
    #12
  13. On Nov 26, 1:21 pm, "Douglas" <> wrote:
    > "David J. Littleboy" <> wrote in messagenews:...
    >
    >
    >
    > > "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


    I'm too lazy to look it up now, but weren't the definitions for ASA
    and ISO speeds based on an exposure just above the toe of the
    characteristic curve? I always assumed the 18% value was related to
    that.

    On the other hand, didn't the ISO for digital speed try to stick as
    close to that for film speed as possible?
     
    Don Stauffer in Minnesota, Nov 27, 2007
    #13
  14. Don Stauffer in Minnesota <> wrote in
    news::

    > On Nov 26, 1:21 pm, "Douglas" <> wrote:
    >> "David J. Littleboy" <> wrote in
    >> messagenews:...
    >>
    >>
    >>
    >> > "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

    >>

    stuff sniped

    One other reason I've not seen mentioned yet is that it's the level all our
    exposure meters, even the ones in our digital cameras are set to "see".
    That is if you expose a white or black object with you built in meter, it
    tries to give you an expose that will make it 18% gray. So including a gray
    card will give you something to set your meter by.

    John Passaneau
     
    John Passaneau, Nov 27, 2007
    #14
  15. Steven Woody

    Steven Woody Guest

    On Nov 27, 11:16 pm, Don Stauffer in Minnesota <>
    wrote:
    > On Nov 26, 1:21 pm, "Douglas" <> wrote:
    >
    >
    >
    > > "David J. Littleboy" <> wrote in messagenews:...

    >
    > > > "Steven Woody" <> wrote:

    >
    > > >> why18% 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 at18%, 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

    >
    > I'm too lazy to look it up now, but weren't the definitions for ASA
    > and ISO speeds based on an exposure just above the toe of the
    > characteristic curve? I always assumed the18% value was related to
    > that.
    >


    what i can remember is the 0.1 plus filmbase + fog density on which
    the ISO speed was based.

    > On the other hand, didn't the ISO for digital speed try to stick as
    > close to that for film speed as possible?
     
    Steven Woody, Nov 28, 2007
    #15
  16. Steven Woody

    Steven Woody Guest

    On Nov 27, 12:13 pm, Steven Woody <> wrote:
    > thanks for all your explains and that actually made me in the way of
    > understanding. now, another question poped up in my mind: how to
    > map a18% point ( or a mid-tone point ) in a 1 to 255 scale in digital
    > photo file? there are four possible answers i can guess,
    >
    > 1, 255/2 = 128
    > 2, 255*0.18 = 45
    > 3, 0.18^(1/2.2)*255 = 117
    > 4, 0.5^(1/2.2)*255 = 186
    >
    > which one is right?


    any clue?
     
    Steven Woody, Nov 28, 2007
    #16
  17. Steven Woody

    EAL Guest

    On Tue, 27 Nov 2007 19:20:58 -0800 (PST), Steven Woody
    <> wrote:

    >On Nov 27, 12:13 pm, Steven Woody <> wrote:
    >> thanks for all your explains and that actually made me in the way of
    >> understanding. now, another question poped up in my mind: how to
    >> map a18% point ( or a mid-tone point ) in a 1 to 255 scale in digital
    >> photo file? there are four possible answers i can guess,
    >>
    >> 1, 255/2 = 128
    >> 2, 255*0.18 = 45
    >> 3, 0.18^(1/2.2)*255 = 117
    >> 4, 0.5^(1/2.2)*255 = 186
    >>
    >> which one is right?

    >
    >any clue?


    I don't understand the question. I know "poped" means to make holier,
    but what does "in digital photo file" mean? And how is 255 supposed to
    relate to a percent?

    Ed
     
    EAL, Nov 28, 2007
    #17
  18. Steven Woody <> wrote:
    >On Nov 27, 12:13 pm, Steven Woody <> wrote:
    >> thanks for all your explains and that actually made me in the way of
    >> understanding. now, another question poped up in my mind: how to
    >> map a18% point ( or a mid-tone point ) in a 1 to 255 scale in digital
    >> photo file? there are four possible answers i can guess,
    >>
    >> 1, 255/2 = 128
    >> 2, 255*0.18 = 45
    >> 3, 0.18^(1/2.2)*255 = 117
    >> 4, 0.5^(1/2.2)*255 = 186
    >>
    >> which one is right?

    >
    >any clue?


    Here's a table that might interest you. The two columns
    marked "Levels" list the number of levels that fstop
    range is divided into; hence, in the brightest zone an
    image from 12-bit linear data can have 2048 distinctly
    different values for brightness, while in an 8-bit gamma
    corrected image there are 69 possible distinct levels in
    that zone.

    Fstop | Linear Linear Gam.Cor. Gam.Cor. Gam.Cor.
    | 12 bit Analog Analog 8 bit 8 bit
    Range | Levels Value Value Value Levels
    ------|-----------------------------------------------
    1 | 2048 1.0 1.0 255 69
    2 | 1024 0.5 0.72974 186 50
    3 | 512 0.25 0.53252 136 37
    4 | 256 0.125 0.38860 99 27
    5 | 128 0.0625 0.28358 72 20
    6 | 64 0.03125 0.20694 53 14
    7 | 32 0.015625 0.15101 38 10
    8 | 16 0.007812 0.11020 28 8
    9 | 8 0.003906 0.08042 21 6
    10 | 4 0.001953 0.05868 15 4
    11 | 2 0.0009765 0.04282 11 3
    12 | 1 0.0004883 0.03125 8 2


    The useful dynamic range basically ends when one full
    fstop is divided into fewer than 8 values. Hence a
    12-bit linear data set has about a 9 stop useful dynamic
    range, while an 8-bit gamma corrected data set has about
    an 8 stop range. (With fewer than 8 levels the
    quantization distortion becomes too apparent, and the
    results are referred to as "posterized".)

    To answer your question above requires knowing where you
    are going to set the white and the black points of the
    "display" (paper or monitor). For example, when
    printing on paper with a 5 fstop dynamic range, the
    printer would normally be adjusted to make 255 be
    "white" and 52 black. The middle zone, 3, would have
    values ranging from 100 to 136.

    Does "3, 0.18^(1/2.2)*255 = 117" look grey to you?

    --
    Floyd L. Davidson <http://www.apaflo.com/floyd_davidson>
    Ukpeagvik (Barrow, Alaska)
     
    Floyd L. Davidson, Nov 28, 2007
    #18
  19. Steven Woody <> writes:
    >thanks for all your explains and that actually made me in the way of
    >understanding. now, another question poped up in my mind: how to
    >map a 18% point ( or a mid-tone point ) in a 1 to 255 scale in digital
    >photo file? there are four possible answers i can guess,


    >1, 255/2 = 128
    >2, 255*0.18 = 45
    >3, 0.18^(1/2.2)*255 = 117
    >4, 0.5^(1/2.2)*255 = 186


    #1 would be correct if the file used 8-bit linear coding, but nobody
    does that because 8 bits simply doesn't give enough dynamic range or
    intensity resolution in the shadow areas. On the other hand, 16-bit
    linear coding is sometimes used.

    #2 makes no sense to me.

    #3 is close to correct assuming a particular exposure (see below). The
    nonlinear function y = x^(1/2.2) is how intensity is encoded in video,
    in JPEG files, and lots of other places. This is generally not
    adjustable, nor not adjustable very much.

    #4 tells you what you'd expect to find in the image file for a scene
    brightness of 50% of peak (e.g. one stop down), not 18%.

    Now more about exposure:
    You or the camera has a choice of what brightness in the image gets
    considered "1.0" and mapped to 255 in the file. Since images have
    areas of widely varying reflectance illuminated by different amounts of
    light, 255 doesn't necessarily represent "100% reflectance"; it's just
    the brightest tone that the camera has decided to handle. So the
    "0.18" in this expression is best regarded as "0.18 times peak white in
    this photo", not any absolute reflectance.

    It's actually more complex, too, because cameras may depart from this
    power function in the highlight and/or shadow areas in order to capture
    more brightness range at lower contrast in those areas. The "shoulder"
    and "toe" in film response does the same thing in chemical photography.

    Since the response tends to be more predictable in the midtones, one
    good way to expose images in the first place is to adjust the exposure
    so that something you have decided is of average brightness (e.g. an 18%
    grey card) ends up in the middle of the tonal scale where you've decided
    it should be (theoretically 117, but 115 or 120 or even 128 work too).
    Exposing so a grey card ends up in the middle of the code value range,
    or the middle of the film density range as measured by a densitometer,
    is very common.

    In the electronic world, it's sometimes more convenient to expose so
    that the brightest thing in the scene that you want to preserve
    information from ends up near, but not beyond, 255. You can do this
    approximately using any digital camera that has a histogram display.
    Some cameras also flash or put zebra stripes in areas that were
    overexposed in the preview image, which gives better visualization of
    what will be recorded correctly and what will be clipped.

    Dave
     
    Dave Martindale, Nov 28, 2007
    #19
  20. Steven Woody

    mirafiori Guest

    if you look at a photographic grayscale of 11 steps, the centre mid-gray
    (the sixth step) is indicated as 0.7. this is sensitometric density value, a
    log value of opacity.
    opacity = 100% of illumination upon X% reflected or transmitted light.
    if X=18%, then opacity = 100/18=5.5
    therefore sensitometric density = log5.5 = 0.74...-round off to 0.7.
    hence 18% reflection gray is 0.7 sensitometric density value and is the
    mid-gray between the white and black of a grayscale.


    "Steven Woody" <> wrote in message
    news:...
    > why 18% gray is in the mid of the full scale of brightness from
    > darkest to brightest? what's the math behind it?
     
    mirafiori, Nov 29, 2007
    #20
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