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    Well ... I've only seen research type spectrophotometers, but
I'll have a try.

1)    A colorimeter, I would expect, would have photocells measuring
    the amount of light through three fairly broad filters,
    typically red, green, and blue.  All three are measured (and
    displayed) at the same time.  This can give an approximation of
    what is being produced by a screen (or other light source), but
    lacks a lot of the details.  It's advantages would be that it is
    quick to use and inexpensive.

2)    A spectrophotometer, however, has a very narrow band filter,
    which color is continuously adjustable.  A "monochromator" is an
    example -- though you don't usually see these outside of R&D
    labs, either. You feed light in one end, and take light out the
    other end.  There is a big knob calibrated in wavelength, and
    the wavelength (color) allowed through is selected by internal
    diffraction gratings or prisms.  (I never got a chance to dig
    into one at the lab. :-)

    The filter is slowly adjusted through its range, and the amount
    of light getting through at each wavelength is either stored for
    later display (in a computerized model), or is plotted on a
    graph with a drum plotter (in the older examples which I have
    observed being used).  Note that this must be done slowly,
    because the narrow bandwidth of the filter allows very little
    light through to the sensor, so it takes time to accumulate
    enough information (clear of the noise).

    This gives you very fine detail about what is happening to the
    light.  You will see bright lines from certain emission sources,
    or dark lines from absorption by certain things in the optical
    path.

    They are available in various spectral ranges.  I've seen some
    which work in the far infrared and in the ultraviolet (both of
    those need to have the optical path pumped down to a good vacuum
    before running the test, as air absorbs some wavelengths of far
    IR and of UV, and may also glow under irradiation with some UV
    wavelengths, giving false readings.

    The ones for the standard visible range don't have to be run in
    a vacuum.

    I'm not at all sure how one would build a spectrophotometer to
    monitor the output from a CRT or a LCD display.

    I would be interested in seeing the spectrum from each of the
    "colors" on my LCD display.

    As both of these are at least an order of magnitude less
expensive than the spectrophotometers which I have seen, I'll not
attempt to answer here.  IIRC, they were made by Nicolet.

    Enjoy,
        DoN.