figures 1
and 2The Autocollimator
An analysis of principles and operation
revised version: April 5th, 2003
To collimate a Newtonian telescope, you need to make the optical axis of the
primary mirror (also known as the main mirror) and the optical axis of the eyepiece (or focuser) coincide, to very close
tolerances. They coincide if either of these (equivalent) criteria are met: 1) they are parallel and intersect at
one point or 2) they intersect at two separate points (the
90 degree reflection of the optical axes by the secondary is of no consequence
here). For further explanations and terminology, please refer to my
collimation page.
In practice, the most important criterion is that the optical axes intersect at the (common)
focal plane - in other words, the coma-free center of the primary mirror's focal plane is centered in the eyepiece field of view. If they are separated here (I call this a
1A error), there will be coma at the center of the field of view, and the tolerance for this error
can be decided from wave-optic criteria. If this tolerance is met, a residual angle (a 1B error) between the axes
means that the cone of light from the primary is slightly tilted with
respect to the axis of the eyepiece. For angles below a degree or so, this has little effect on the image (the tolerance for separation of the axes at the
primary mirror's surface is an order of magnitude wider than at the focal
plane). However, if the collimation is done to make the optical axes
intersect at a point away from the focal plane, a 1B error will cause an
1A error at the focal plane.
The alignment of the axes can be accomplished as outlined here (see my
collimation page for details):
The autocollimator
The autocollimator as used for collimating Newtonians (other devices of the same name exist) is fairly simple in design: it consists of a flat mirror, with a small peephole in the center (drilled, or with just the reflective surface removed), mounted in a cylindrical barrel to fit a focuser. A line perpendicular to the mirror and centered in the peephole defines the autocollimator axis. The mirror is critically adjusted to make this axis coincide with the center of the barreland thus the focuser/eyepiece axis of the telescope.
The proponents of the autocollimator (among them are Vic Menard and Tippy D'Auria, authors of the booklet "Perspectives on collimation" - I refer here to the 4th edition), claim it can be used to reach very high precision in collimation - even if not so simple to use, perhaps. But is such a claim reasonable and realistic? Does the autocollimator offer better collimation than other tools that are simpler to use - and how is it best used?
How the autocollimator works
If you mount the autocollimator in the focuser, aim the telescope at a bright background (avoiding the sun), and look into the peephole, you see the inside of the telescope much as you see it in a plain peephole, or Cheshire eyepiece: the primary mirror is lit up, with the shadow of the secondary (slightly offset), and inside this shadow you see (darkly) reflected the focuser and inside it the autocollimator mirror (its very center hidden by the primary mirror center spot). It is the reflections in the autocollimator mirror that are important, so let us study their significance.
While the geometry is essentially straightforward, the sheer number of reflections in the three mirrors tends to be rather overwhelming, so I'll simplify by omitting the secondary whenever appropriate. The primary mirror (paraboloid, but for this discussion, considering it spherical is accurate enough) and the flat secondary and autocollimator mirrors make together a system capable of forming real images. Note that the autocollimator mirror is assumed to be at the focal plane, even if this is not very critical in practice. Also, it is assumed that the system is nearly collimated already, so the reflections are not grossly displaced.
figures 1
and 2
In figure 1, you see outlined how an image of the primary mirror spot is formed after being reflected first in the autocollimator, then the primary mirror, then the autocollimator again (ignoring the 4 intervening reflections in the secondary!). Looking in the peephole, you see this real image reflected in the primary mirror (at least if the spot is bright enough - not if it is black), as a fainter version of the original spot, and possibly more or less hidden by the spot itself. This image is in turn reflected back near the original spot, and so on.
If the reflections are brought to converge, it means that the tangential plane of the primary at its center is accurately parallel to the autocollimator - or equivalently, the axes of the primary and the autocollimator are accurately parallel - but it does not mean that they coincide! In "Perspectives..", this condition is referred to as "converging" of the spots. As the primary mirror's axis may fall arbitrarily far from the peephole at focus, this does not indicate collimation unless you have first ensured that the optical axis is indeed centered! As shown in figure 4, if the offset of the primary mirror's axis at focus is R, the offset of the focuser axis at the primary mirror is also R (a 1A error, see my collimation page - in this case, the angular i.e.1B error is zero).
figures 3 and 4
In figure 2, you see how the peephole is imaged, after a similar chain of reflections, back to the autocollimator mirror, near the peephole itself. If the image is accurately centered on the peephole, all light that comes back into the hole is what went out of it in the first place - as you have your own eye pupil there, you see the whole autocollimator mirror quite dark. In "Perspectives..", this is called "to close the optical axis on itself".
If the primary mirror is tilted in such a way that a line perpendicular to the mirror, at the point where the autocollimator axis hits it, coincides with the autocollimator axis itself, "darkening" will occur - note that this can happen at any point where the focuser axis may fall. All lines perpendicular to the mirror will intersect at the center of curvature (COC), including the optical axis of the primary. Thus, the condition for darkening is that the optical axes intersect at the COC, but it does not mean that they intersect at the focal plane. If the image falls outside the peephole, the autocollimator will look successively brighter from (multiply) reflected background light. Figure 3 shows "darkening" with the secondary in place. If the autocollimator axis is offset from the center of the primary by a small distance P, the primary mirror axis will be offset by P/2 at focus (an 1A error. The angular error 1B is P/2F where F is the focal length).
There is one third possible mode of operation: the autocollimator can be used as a Cheshire to collimate the primary, by making the dark peephole appear centered inside the donut center spot. When this happens, the 1A error is minimized, regardless of any remaining 1B error. However, when the collimation is getting close, the autocollimator mirror will be dark, and it may no longer be possible to see the reflection of the peephole. If so, you must use the Cheshire instead.
If both "darkening" and "converging" can be achieved simultaneously, it would mean that both the focuser and primary mirror axes are coincident (to unknown tolerances) - this, of course, indicates collimation. The errors of both conditions will add, however, and the accuracy will be determined by the sum of errors - making either error very small does not help, if the other error cannot also be made small.
In "Perspectives..>", M/D'A state that any correction using the autocollimator should be done by adjusting the secondary only, and that the first step is to close the optical axis on itself. This, i.e. darkening, could always be achieved by tilting/rotating the secondary, even if you would have to do it by trial and error. In the general case (figure 5), we start with the primary mirror axis offset by A/2 at the autocollimator, and the focuser axis by B at the primary. A and B, determined by previous coarse collimation, could be expected to be of the same order - and with reasonable care, typically one or a few millimeters.
figures 5 and 6
If the secondary were very close to the focuser, tilting it to achieve darkening would not move the primary mirror axis, so the miscollimation will still be A/2 at the focal plane, but at the primary, the error (fig. 6) will now be A instead of B! (This is not strictly true, there will be added some fraction of B at focus, but as the secondary is closer to focus than to the primary mirror, the addition is likely small unless B is excessive). M/D'A claim that the telescope "should now be collimated to a reasonable degree of accuracy". As stated above, the tolerance at the focal plane is an order of magnitude stricter than at the primary, so if the collimation was acceptable in the first place, it will also be acceptable after this step, even though it is generally not improved.
What if you now try tweaking the tilt of the secondary to line up the center spot and its reflection? You can reduce the error at the primary from A to A/2 (and since even A was acceptable, this reduction is not significant), but the error at the focal plane is not reduced (and the "darkening" is lost, to some extent). Repeating this sequence of will not reduce errors further.
Can there be another way to achieve better collimation with the autocollimator?
As outlined in fig. 3, if the axes all are in the same plane, you could change the position and tilt of the secondary (to the position outlined in grey), achieving collimation. However, in the general case of imperfect collimation, the axes are not in the same plane and can never be by adjusting the secondary only. You also have to tilt either the primary or the focuser - some modern ones are adjustable, and such focusers are highly recommended in "Perspectives..".
If you have brought them into the same plane, how do you proceed? Start with "conventional" collimation, as described above. At this stage, the primary's optical axis is centered in the collimator - possibly a bit away from the focal plane, and there may be some small residual misalignment of the focuser axis. The only thing that the autocollimator could achieve in this situation is to improve the alignment of the focuser axis - and after re-alignment with the Cheshire, the extra 1A error in the true focal plane can be reduced. This is simple to do, if you have an adjustable focuser - just make the spots converge (illuminate the spot with a flashlight if necessary) and check again with the Cheshire. If you adjust the secondary instead, it is more likely that you need to adjust the primary with the Cheshire, but after that, you are probably close enough not to need another repetition.
Is it worth the extra effort?
This is of course a matter of opinion. There was a debate over the YAHOO Bigdob group late in 2002, with Vic Menard, myself and others. Here, some other aspects not covered in "Perspectives" or this webpage came to light. The main aspect here is that once you have collimated the primary accurately, you can use the autocollimator to visualize and minimize any residual 1B error. /P>
Let's do some back-of-the-envelope calculations to see what to expect. I believe it is easy enough, even with a sight tube, to make the focuser axis hit within 1/300 focal length from the primary's center spot - this is about 0.2 degrees, and assuming a focal length of 60" (1500 mm), this is 0.2" (5 mm) off. With a laser, you can easily get to within 1/1000 f.l., or 0.06" (1.5 mm - note that this is by no means close enough if you intend to collimate your primary with the laser beam!). With a Cheshire, the plane of collimation is between the peephole and the shiny face - if you insert it as far as you can in the focuser without obstructing the light opening, it means the plane of collimation is no more than 1" (25 mm) off. Thus, the extra 1A error is no more than some 1/300" (0.08 mm) - totally insignificant. With a Barlowed laser, Barlow lens in "normal" position, the error is even less.
Real-life focusers have some significant slop. Watch the spots converge and rack the focuser a little in and out - do the spots stay converged? Remove the autocollimator, insert it again, and perhaps tighten the locking screw a little differently. Do the spots still stay converged? If not, the extra precision that the autocollimator could give is of no practical relevance anyway.
Still, if you think the improvement is worthwhile, go ahead and use the autocollimator. But I suggest you consider these pieces of advice:
Put away your copy of "Perspectives", and use the directions here - or wait for the next edition, #5.
Start with close collimation, using the sight tube + Cheshire, or perhaps laser + Barlow
Adjust the focuser, if at all possible, not the secondary, to make the spots converge.
Forget about making the autocollimator dark - disregard the Tectron webpage instructions.
Don't expect any visually significant improvement over what you get with the laser/Barlow combo or even the humble Cheshire/sight tube.
In "Perspectives of Collimation", M/D'A write: " before we decided to write this book, the autocollimator was without question the least understood of the collimation tools". I do not see that the authors have done the analysis of operation that would have contributed to such understanding, or to assess the tolerances involved.
Nils Olof Carlin