-My very basic knowledge that all ponds benefit from aeration. -I have copious amounts of Algae on the surface and black sludge on the bottom. -Unless you calculate aeration by sticking you finger in the air there must be X amount of air(O2) required per X volume of water.
I see I should have asked what you mean by "keep it clear"
To most (and me) that means the water should not be coloured in any way. The best way to do this is to have a biomechanical filter and a UV.
Duckweed is a real pain, but the easiest way to get rid of it is to over fill the pond / pool and let the duckweed float away with the excess water.
Sludge being dead / decaying matter should really be removed by mechanical extraction. There are some "chemicals" that claim to remove it, but it has to be some where, so if you want rid of it, you are going to have to "shovel" it out (all be it using a backhoe digger if you have to.
Air will only add oxygen feeding the plants you don't want.
Good quality costs. Bear this in mind before you start.
Sorry if my reply is NOT want you want to hear, but what I have said is true.