For instance in the cut it will be observed that the rays e and a′ focus barely beyond C and by the time they reach D are well spread apart. The relative distance of the dots upon these corresponding plates, with the distance between the plates, shows exactly at what point between C and D these particular rays actually did cross and come to a focus.
Determining this is merely a matter of measuring up similar triangles, for the path of the rays is straight. Similarly inspection will show that the rays d and d′ meet a little short of B, and measurement of their respective records on the plates C and D would show the existence of a zone intermediate in focus between the focus of e,e′ and the general focus at B. The exact departure of this zone from correct focus can therefore be at once measured.
A little further examination discloses the fact that the outer zone represented by the rays a,b, and a′,b′ has not quite the same focus at the two extremities of the same diameter of the objective. In other words the lens is a little bit flatter at one end of this diameter than it is at the other, so that the rays here have considerably longer focus than they should, a fault by no means unknown although fortunately not very common.
It will be seen that the variations between the two screen patterns on C and D, together with the difference between them, give accurately the performance of each point of the objective represented by an aperture in the screen. And similar investigations by substantially the same method may be extended to the astigmatic variations, to the general color correction, and to the difference in the aberrations for the several colors. The original papers cited should be consulted for the details of applying this very precise and interesting test.
It gives an invaluable record of the detailed corrections of an objective, and while it is one with which the ordinary observer has little concern there are times when nothing else can give with equal precision the necessary record of performance. There are divers other tests used for one purpose or another in examining objectives and mirrors, but those here described are ample for nearly all practical purposes, and indeed the first two commonly disclose all that it is necessary to know.
Now and then one has to deal with an objective which is unmitigatedly dirty. It can be given a casual preliminary cleaning in the way already mentioned, but sometimes even this will not leave it in condition for testing. Then one must get down to the bottom of things and make a thorough job of it.
The chief point to remember in undertaking this is that the thing which one is cleaning is glass, and very easy to scratch if one rubs dust into it, but quite easy to clean if one is careful. The second thing to be remembered is that once cleaned it must be replaced as it was before and not in some other manner.
The possessor of a dirty objective is generally advised to take it to the maker or some reliable optician. If the maker is handy, or an optician of large experience in dealing with telescope objectives is available, the advice is good, but there is no difficulty whatever in cleaning an objective with the exercise of that ordinary care which the user of a telescope may be reasonably expected to possess.
It is a fussy job, but not difficult, and the best advice as to how to clean a telescope objective is to “tub” it, literally, if beyond the stage where the superficial wiping described is sufficient.