(Go back to Why we need compensation?, or back
to the introduction)

If a fluorescent dye emission is collected through two different filters,
then we can always estimate how much emission is in the second filter based
on how much is in the first. This is because the two will also vary proportionately.
Consider the example below: on the left is the spectrum of fluorescein at
some concentration "X". On the FACS, we measure fluorescein, PE,
and Cy5PE through the three filters shown (typically, in the channels FL1,
FL2, and FL3). On the right is the spectrum of fluorescein at a concentration
equal to twice "X".

Notice that every part of the spectrum in the more concentrated solution
has increased by the same amount (two-fold). The amount of signal that we
measure in each channel is proportional to the area under the emission curve
that is covered by the filter (in this example, the darkest portions). The
area under the curve in the FL1 band on the right is twice the area under
the curve in the FL1 band on the left.

Why is this important? Because it means we can exactly determine the area
under the curve in the FL2 channel based on the area under the curve in
the FL1 channel!

We do this by collecting a sample that has no fluorescent molecules *except*
fluorescein. Therefore, the amount of signal in each channel (FL1, FL2,
and FL3) will be due only to fluorescein. (This is not strictly true, because
of cellular autofluorescence--however, let's ignore autofluorescence for
now! It turns out that it does not affect the compensation process.) From
this "compensation sample", we can compute the ratio of the area
under the FL2 curve to the area under the FL1 curve for fluorescein. For
typical FACS machines, this ratio is something like 15%--i.e., the area
under the FL2 curve is 15% of the area under the FL1 curve.

Now, because this ratio (15%) does not change when there is more or less
fluorescein around, we can always know exactly how much fluorescein is in
the FL2 channel based on measuring the FL1 channel (it is always 15% of
the FL1 channel). Therefore, if we subtract 15% of the FL1 signal from FL2,
then no matter how much fluorescein is present, the "corrected"
FL2 measurement will always be zero.

That means that we can now add PE to the measurement: and the amount of
fluorescence in the FL2 channel (after we subtract 15% of the FL1 signal)
will be the "true" PE fluorescence--we have now measured the contribution
of PE exactly, whether or not there is fluorescein present. This is what
we call "one-way" compensation: we have corrected for the fluorescein
signal in the PE channel.

But... PE also emits in the FL1 (fluorescein) channel! Now what? We have
to perform two-way compensation.