Filtering out green algae

   Your best bet, if you want to mechanically remove green algae, is to use a
filter designed to be used with diatomaceous earth.  They often claim to
"polish" the water.  I don't know about polishing the water, but the System
One unit I have used does an excellent job of removing very fine particulate
matter.  I have tried to use a columnar type cartridge that claimed to polish
the water, it had pore sizes smaller than your typicall micron cartridge and
even though it was installed inline after a regular micron cartridge, it
clogged very quickly and within a day the flow rate on my filter was nearly
zero.   Most filter pumps are not designed to handle the back pressure
created by a cartridge with pores small enough to capture green water algae.
 Even the diatomaceous earth filters are only designed to be operated for a
few hours at a time.