Digital BW, The Print

Peter writes:

> Why should this be so hard?

I've explained this several times.  Apparently I lack the necessary talent
to make the explanation understandable.

> Every black and white film has a characteristic
> response curve, and that curve can be characterized
> for R, G, and B ...

No, it cannot.  The curve is just that: a curve.  The RGB values are just
three numbers--equivalent to three straight lines of different heights in
the spectrum.  All the rest of the curve between those three lines is lost
when a picture is taken in color.  Because of this, the original curve of
the original scene CANNOT be recreated from the RGB values.  And since the
original curve of the original scene MUST be recreated in order to proper
render a scene in B&W based on the sensitivity curves of a black and white
film, it is impossible to recreate the look of a scene capture in one way
with the look of a scene captured in another way.

The rule is much more general than this, in fact.  It is impossible to
translate any scene represented as a single set of monochrome values or as a
set of R,G,B values into any other scene represented in the same way,
because you MUST HAVE the original curves of the original scene in order to
effect the transformation, and you cannot get these from just one number, or
even from just three numbers.

Additionally, the rule applies indifferently to color film and B&W film, and
to color electronic sensors and B&W electronic sensors.

> So if you start off with a wide-latitude
> color film, like Portra, what limitations
> do you bump up against trying to simulate
> a given B+W film?

See above.  Portra produces a triplet of RGB values based on its own unique
sensitivity curve.  Once the film has done this, the original spectral
characteristics of the original scene are lost.  To create a rendering that
matches what some other film would have produced, you must have the original
spectrum of the original scene; three numbers won't do.

> It seems like all you have to do is compute
> a scalar from your source (color film) response
> curve to your target (B+W) response curve for
> each intensity level.

But you no longer have each intensity level.  You have only three levels.
Everything else in between is lost.

I've already provided an example.  Let me try again.

You have a special film (or a special filtered CCD) that is sensitive only
to the yellow light of low-pressure sodium-vapor lamps.  You take a picture
of a scene lit with these lamps in some areas, and lit with a blend of red
and green light in other areas.  You then take the same picture using an
ordinary color film or color CCD.

What will you get?  On the special yellow-sensitive film, the areas lit by
LPS lamps will appear bright, and all other areas will appear dark.  On the
color film, however, all areas will appear equally bright.

There is _no way_ to convert the RGB image from the color film in a way that
will duplicate the results you got from the yellow-sensitive film, because
the important information on the spectral distribution of the original light
is gone.

> What would NOT be described by that curve?

See above.

This rule applies even to color-to-color transformations.  You cannot
convert Portra to make it look just like Velvia, because part of the
spectral information on the original scene is lost and cannot be
reconstructed to make the transformation.