(Go back one page to two-way compensation,
or back to the introduction)
The common three-color compensation system compensates for spill-over between fluorescein and PE (FL1 and FL2), and between PE and Cy5PE (FL2 and FL3). This is performed as a simple extension of the two-color compensation; i.e., it is two sets of two-color compensations.
After doing the FITC-PE compensations, we turn to PE-Cy5PE. This is performed exactly the same as the FITC-PE: in other words, the PE-only compensation sample is run to compute the contribution of PE to the Cy5PE channel, and the Cy5PE-only compensation sample is run to compute the commensurate spillover.
This process results in 4 coefficients for compensation, two for each pair of channels.
You may have noticed that this process does not directly correct for the amount of FITC fluorescence in the Cy5PE channel (nor vice versa). Is this a problem? In general, the answer is no; but this can crop up. The way to know if it is occurring is to display the FITC vs. Cy5PE channels, after compensation, for the FITC-only, or Cy5PE-only samples. Because commercial cytometers do not allow for compensation between FITC and Cy5PE (i.e., between FL1 and FL3), if you observe spillover between these channels, you are basically out of luck.
It turns out that the problem is not very large, for the following reason: the ratio of fluorescein signal in the FL3 channel to fluorescein signal in the FL2 channel is very similar to the same ratio for PE (purely coincidence). The serendipitous result of this similarity is that by properly compensating for FITC between FL1 and FL2, and for PE between FL2 and FL3, you are essentially doing proper compensation for FITC between FL1 and FL3! (Remember, the PE compensation subtracts a fraction of the FL2 signal from FL3. This means that the uncompensated FITC signal in FL2 will also be used to correct FL3. Again, since the ratio of PE signal in FL2 to FL3 is close to that for FITC, proper PE compensation results in the right amount of fluorescein signal subtracted from FL3 based on the amount of fluorescein signal in FL2).
By the way, the reason this works is that all of the compensations happen simultaneously: the machine does not use the fluorescein-compensated FL2 signal when performing the PE compensation into FL3.
Notice, however, that if you were to use a different set of three fluors in these three channels, which require different compensation, then the FL1-FL3 compensation may not turn out correct. In this case, you would have no choice but to use software compensation techniques to correct the data post hoc.
Go on to the generalized approach to compensation.