Pool-water filtration has been around since the Roman baths.
Today we have several ways to filter our pool-water. Residential pools use basically 3 types of water filtration;  DE Filter (Diatomaceous earth) , Cartridge filter (a replaceable paper cartridge), and Sand Filter (layers of particles of sand in a tank).
With DE Grid replacement and constant replenishment of DE powder, (which  is not safe to breathe), is the most costly to use. It’s said that DE filters down to approx. 2-5 microns size of particles. And with backwashing needed when the DE filter gets filled with dirt,etc., a lot of pool-water & DE powder is sent into the street. After cleaning the filter by backwashing, you need to replenish the DE powder through the pool skimmer to re-coat the DE Grids inside the filter tank.
It’s said that Cartridge filters down to approx. 10-20 microns size of particles.  Backwashing is not performed with a Cartridge filter. You take apart the filter, remove the cartridge and wash it off with a high pressure hose. And, you don’t need to constantly add replacement powder after each cleaning.
The easiest to use, and by far the least expensive over time, is the sand filter. It’s said that the sand filters down to approx. 15-30 microns. The sand stays in the tank when you backwash the filter to clean it. And sand is the least expensive to replace, in its tank, which you will do in about 4-5 years or so. You suck out the old sand with a shop vac, clean the tank off, and pour in new bags of special pool-filter sand, not play sand!
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Over the years, I have tried other filter media in a sand filter tank, such as expensive Zeolite. It filtered much finer than sand, but Later-on I found that the Zeolite mining process in the US, was not consistent. We had problems with caking & clogging at times.
The best media for a sand-tank filter, is “GLASS PACK”.  It’s much more expensive than sand,  but by far the easiest and best filtration; down to as low as  2-5 microns. It saves 75% on water, because of the short and less frequent backwashing, and saves up to 25% on lost chemicals too; and there is ZERO silica dust. It’s made from 100% post consumer waste- that’s crushed glass bottles-No Plastic!.
Crushed glass filtration media is less likely to block or channel than silica sand or Zeolite, and will not support moss or fungus growth in the filter media. And ECOsmarte Glasspack has been tested & certified to NSF61 for drinking water & NSF50 for commercial pools.  It contains no crystalline or silica; resulting in better lung protection and a far healthier environment. And no Problems with DE powder disposal, which in many areas is being banned, due to possibility of the DE getting into the ground-water,etc. There is too much more to discuss here; but my pools using glass are sparkling clear with superior filtration and less restriction to the water flow back to the pool. For more info go to: www.glasspackfilter.com.  Sincerely; Rich DeMarco;  www.paradisepoolandspa.com