(Go back one page to three-color compensation,
or back to the introduction)

As we cram more and more colors on each laser, which are closer and closer
together, we have to compensate between every pair of channels. Furthermore,
we are starting to use fluorophores which can be excited by multiple lasers,
which generates the need for cross-laser compensation. (For instance, Cy5PE
can be efficiently excited not only by the 488 nm Argon laser line, but
also a 633 nm HeNe laser line--and emit very similarly to APC. APC, however,
is not excited by the 488 nm line. Therefore, we can compensate from the
first laser Cy5PE channel to the APC channel to remove the contribution
of Cy5PE fluorescence on the second laser, leaving only APC fluorescence).

Multi-color compensation is a simple extension of two-color compensation,
through the use of linear algebra. Let's assume that we are measuring **n**
different fluorescent molecules, all of which may contribute fluorescence
to each of the other channels. Therefore, the measured signal in any channel
is given by:

whereM(1) =A(11) xF(1) +A(21) xF(2) + ...A(n1) xF(n)

M(2) =A(12) xF(1) +A(22) xF(2) + ...A(n2) xF(n)

...

M(n) =A(1n) xF(1) +A(2n) xF(2) + ...A(nn) xF(n)

Thus, the coefficients

Once we have determined the coefficients

If we premultiply both sides by the inverse of the coefficent matrix (M = A x F

Computationally, therefore, we invert the coefficient matrixA' x M = A' x A x F = F

In the case of three-color compensation commonly done on today's flow cytometers (first laser), only two pairs of compensations are done (for a description, click here). In this case, the coefficients

Finally, it's time to deal with autofluorescence.