I've read in many places that one of the canonical uses of iris diaphragms is to align a laser beam, but I'm having trouble understanding how this works, since I can always setup a set of arbitrarily many iris diaphragms such that a laser beam passes through them at any angle. Therefore if I take, say, two iris diaphragms and adjust their position such that the laser passes through both of them, it doesn't seem to tell me anything about whether the beam is aligned or not. What am I missing? Does their utility require carefully measuring their positions with a ruler? In that case couldn't you achieve the same result without the diaphragms (ie a piece of paper and a ruler)?
It's a back-and-forth process where the irises, laser, and external references are aligned to each other. For example, after setting up a laser, you want the laser to be level with the optical table. To do this, take a single iris on a post and adjust the post until the laser hits the center. Then, slide the iris towards and away from the laser. If the spot moves vertically, the laser is tilted up or down. Adjust the laser and the iris and repeat until the laser spot doesn't move when the iris is moved. Now the laser beam is horizontal. Get a second iris on a post at adjust it so that the laser hits the center. Now you have two irises at the same height to use for further alignment of the optical system.
In this example, the external reference was the surface of the optical table. In other cases, if the irises are mounted on rails, they can be used in conjunction with steering mirrors to align the laser beam along a path towards other optical elements. With both irises from the previous paragraph mounted on the same rail, the laser will be aligned to the rail when it passes through both iris apertures.