Medically I can't even imagine needing a sample unless it is to check for success post surgery
So far as I am aware, there is nothing per se
immoral about taking a sperm count or doing a sperm motility test, as long as the specimen is collected in a manner that does not run counter to Catholic moral principles.
It should be a very Catholic thing to want to increase one's ability to bring about the conception of a child. I can tell you (never mind how I know this, I just know) that large doses of Robitussin (guaifenesin) increase the amounts of all
kinds of mucus that the body produces (it will also give you the runs, but everything in life is a trade-off of one kind of another
), and not to add a TMI factor, but relations every other
day, as opposed to every day, during the fertile period, can also increase the sperm count, for obvious reasons.
Not medical advice, just anecdotes about low-tech, low-cost potential fertility optimizing methods based on common sense, and let's just say that my son turned 14 yesterday, so something
must have gone right.