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[filmscanners] Re: Density vs Dynamic range

This all seems to be a lot of vast overcomplication.  Dynamic range is the
highest signal divided by the lowest signal.  Density range is the highest
density divided by the lowest density.  The only difference between the two
is that dynamic range is additive, like primary colors in a CRT display, and
density is subtractive, like the subtractive primaries in a slide (cyan,
yellow, magenta).

So what is the dynamic range of a slide?  It doesn't have one; it has a
density range.  It only has a dynamic range if you shine light through it,
and then the dynamic range depends on the light source.  With no light
shining through the slide, its dynamic range is zero.  With light shining
through it, the dynamic range is equal to the luminosity of the brightest
part of the slide divided by the luminosity of the darkest part of the
slide; in theory, that would always be the same, but in practice, due to
other factors like stray light, it may vary depending on the situation.

So when you scan, what is the dynamic range and density range?  They end up
being the same thing.  Both are the ratio of the brightest possible spot on
your display (when displaying a given image) divided by the darkest possible
spot.  In most cases, this range will be _smaller_ than the range covered by
the data in the digital image you are displaying, because of device
limitations.  This is more true on CRTs than in projectors, and more true on
paper than on CRTs.

The maximum density/dynamic range of a scanned image is equal to the
luminosity represented by the highest pixel value divided by the luminosity
represented by the lowest pixel value.  If the image uses a linear space for
representation of the image--that is, if luminosity increases by exactly the
same amount between any two adjacent levels in the representation of the
image--then this range is simply equal to the highest pixel value plus one
divided by the lowest pixel value plus one, e.g., 256/1 for an 8-bit
representation (eight stops of range).  However, it's perfectly possible to
define a rendering space in which the steps between pixel values are unequal
(this is the notion of gamma, or other curve adjustments); in this case,
_any_ dynamic range is possible.  When you play with the steps between
pixels to increase or decrease dynamic range, though, you must accept that
the number of individually distinguishable tones in some areas of the image
will be diminshed, while the number of tones in other areas will increase.

For example, a typical positive gamma adjustment greatly increases the
increment of brightness in the steps betwen levels in the dark portion of an
image, and diminishes the differences between steps in the bright portion of
an image; so you lose resolution of tones in the shadows with a positive
gamma.  But since a typical CRT has poor resolution in the shadows to begin
with, by shifting the gamma to match the display, you get an image that
looks a lot more natural (a lot more like the original scene).  If you had a
device that could display any range of luminosities in perfectly linear
fashion, of course, you wouldn't want to apply any sort of gamma adjustment
at all.

Note also that film emulsions themselves impose a non-linear response to
light into their behavior.  The luminosity of the original image may have
increased by 5:1 in some part of the scene when it was photographed, but
slide film might boost that to 20:1 in that same location, if it was in the
midtones, or 2:1, if it was in shadows or highlights.  Essentially film has
a built-in gamma adjustment that accounts for the limitations of the display
devices with which it will ultimately be used; it records scenes very
unrealistically in an absolute sense, but since it matches the way they will
be display, the end result is a very realistic depiction.

CCDs have a linear response to light.  This is good in a strict sense, but
it doesn't match any kind of display device (paper, CRT, or anything) and so
digital cameras will routinely tweak the outgoing signal to make it look
more like that of film.

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