Digital BW, The Print

Austin writes:

> I have all the information I need, the frequency
> and the intensity.

"The" frequency?  But for every pixel in the original scene, there are
multiple frequencies of light, each with its own intensity.  Indeed, in most
cases, there is an _infinite number_ of different frequencies, each with its
own intensity.  You can plot this on a graph, with the x axis set to
frequency and the y axis set to intensity.  The graph produces a continuous,
wiggly line.  And this line is different for every pixel in the original
scene.

Now, when you take a color picture, this line is collapsed into just three
numbers: red, green, and blue.  To do this, a one-way function is applied to
the original spectrum.  The red, green, and blue values are determined by
integrating the areas under three separate curves superimposed on the
original spectrum.  However, there are many different distributions of
energy under these curves that will produce any given red, green, or blue
value.  The conversion is many-to-one.  As a result it is irreversible.
Once you've recorded your three numbers, you can never reproduce the
spectral distribution that is responsible for creating those numbers,
because there exists an infinite number of different distributions that will
produce any given set of numbers.

In other words, once you've captured the image in color with an RGB capture
method, you can never again recreate the original spectral distribution of
the scene.

And this is where the problem arises.  Because, in order to accurately
duplicate the results that would be obtained in photographing the scene with
a _different_ capture device (color or black and white, it doesn't matter),
you _must_ have the original spectral information for the scene.  But you
can't get that now, because you lost it when you performed your one-way
conversion to RGB.  So the duplication is impossible.  In fact, even a
decent simulation may be impossible.  You'll never be able to simulate the
effects of a narrow-band color filter, for example; you can't even come
close.

Just think of the color yellow.  Yellow in RGB is represented by roughly
equal R and G values, and a low B value.  But for any given triplet of RGB
values perceived as yellow, there exists an _infinity_ of original spectral
distributions that can produce that triplet--and you have no way of knowing
which one of these distributions produced it in the original image.  And
even though all these distributions produce an identical result in your RGB
capture, to another device with a different spectral sensitivity (such as
B&W film behind a narrow-band color filter, or even B&W film by itself),
they may _not_ produce identical results; they may, in fact, produce
dramatically different results.  And there is no way for you to know which
results they might have produced with other capture methods.  As a result,
you cannot duplicate or simulate the results that would be obtained with
those other methods using only your RGB information.

> The converse is, of course, not true, you can't
> go from B&W to color.

Actually, that is only a specific and obvious instance of a much more
general problem.  You can't go from color to color, either (which is why you
cannot accurately simulate Velvia with a scan of Provia).  You can't
simulate the results from anything that would normally be a function of the
original spectral distribution, because you no longer have that
distribution, and you can't recreate it from a simple trio of numbers.