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Kitchen table collimation of a Cassegrain-type reflector

Abstract
A method of daytime collimation of a Cassegrain-type reflector telescope is described which uses a circular target aligned on the optic axis of the primary mirror. Basic construction details are given for making a suitable target and a procedure is outlined for collimating both Schmidt-Cassegrain and Ritchey-Chrétien telescopes.

Introduction
The holy grail of collimation for any reflector telescope is the perfect alignment of the optic axes of the primary and secondary mirrors onto a single path, to minimise aberrations.  It goes without saying that with a properly collimated telescope, a suitable target placed squarely and accurately on the optic axis of the primary will appear centred and distortion-free when viewed through the eyepiece. Putting these two statements together raises the interesting prospect of being able to use an on-axis target as an alignment aid for daytime collimation of a Cassegrain-type telescope.

A precise position on the optic axis of the primary mirror can be determined easily by setting a point source of light at the centre of curvature of the mirror, defined as the point where a spot of light will reflect back to the same point. The fact that the mirror may be spherical, parabolic or hyperbolic is immaterial for this purpose, since any aberration of the returned beam is very small and in any case will be symmetrical about the optic axis and will not affect the ability to bring the image to an adequate focus overlying the point source. A target centred on this point is the basis of this approach to optical alignment.Figure 1 General arrangement of telescope with collimation target aligned on the optic axis of the primary mirror

Current daytime techniques
There is no accepted ‘standard’ daytime collimation routine for an SCT that I have been able to find. For the SCT, manufacturers’ instruction manuals and other respected sources invariably describe only star collimation1,2, typically adjusting firstly for symmetry of the shadow of the secondary mirror when off-focus at moderate magnification, followed by symmetry of on-focus Airy rings at high magnification. Several collimation aids exist in the market place that attempt to bridge the gap that exists between what can be achieved with daylight techniques and the need to make final adjustments using a suitable star, with examples ranging from the artificial star to complex (and expensive) laser-based products3.

For the Ritchey-Chrétien, the manufacturer-recommended collimation routine relies heavily on the coincidence of the optical and mechanical symmetry of the telescope design4. An internet search reveals a number of techniques devised to refine the adjustments to a near-perfect optical alignment using star collimation but are far from simple procedures. For both SCT and RC designs, viewing the ‘hall of mirrors’ effect of multiple primary/secondary reflections viewed from the front of the telescope is a useful check of symmetry but of limited use in making the adjustments necessary to achieving it.

The collimation target
Figure 2 The collimation target pattern; concentric target rings up to the maximum diameter of the primary mirror, with an accurately marked centre point. A suitable collimation target for this approach is a series of concentric rings drawn on a piece of card and arranged around a central spot of light. The maximum ring diameter needs to be the same as the diameter of the primary mirror. A typical pattern is shown in Figure 2 and is available to download as a pdf file along with this tutorial; when printed to the full width of an A4 sheet it is suitable for reflectors up to 200 mm. 

If you are downloading the target image, then for preference print it out on photo paper to maximise the contrast of the lines. If you want to make a target for a larger diameter primary mirror, then draw it directly onto thin card with a pair of compasses out of a school geometry set, using a felt tip pen to make good solid circles that are easily seen at a distance. The important rings, shown in red, are sized to be a few millimetres less than the diameter of the primary mirror and a few millimetres more than the diameter of the secondary mirror respectively. With an overall diameter of 8”, the red circles on Figure 2 are suitable for an 8” SCT and an 8” Ritchey-Chrétien. The other circles and the crosshairs are simply visual aids for assessing the symmetry of the image at the eyepiece.

Make a clean small hole in the exact centre - between half and one millimetre diameter is fine - then hold the card in front of and close up to a lamp and you will have a target of concentric rings about a pinpoint light source. If the card is not fully opaque, back it with a sheet of kitchen foil or similar and remake the pinhole.
Figure 3 The target image pasted onto a sheet of thin MDF board and mounted on a conventional photographic tripod makes the light spots much easier to align. Drill a 1mm hole through the exact centre of the cross-hairs and fix a light source as in Figure 4. Figure 4 An LED headtorch, bought from a local high street store for £1 makes a convenient light source. Modify it down to one LED, counterbore the MDF board to get the LED as close behind the pinhole as possible and fix it in place with double sided sticky pads.
Figure 5  Showing a Cheshire eyepiece alongside a 35mm film canister with a small hole drilled through the exact centre of the base, for use as a collimation eyepiece.Taping the target over the shade of an anglepoise-style desk lamp or small torch is the quick way of trying out this method, although it is a little awkward in practice because of the need to be able to move the target about with precision. A more permanent arrangement that is much easier to use is shown in Figures 3 and 4, where the target and light source are fixed to a sheet of thin ply or MDF board and mounted on a simple photographic tripod.

To complete the 'kit of parts' needed for this procedure you will also need a collimation eyepiece, available commercially as a Cheshire eyepiece or homemade from an eyepiece cap, 35mm film canister or similar (see Figure 5).
 
The Method
Arrange the telescope horizontally on a flat surface facing the collimation target such that the distance between the two can be varied easily by sliding the telescope backwards and forwards. The kitchen table is ideal, hence the title of this article. Roughly determine the centre of curvature of the primary mirror by looking into the telescope and moving closer or further away until you find the point at which your eye appears enormous. Place the collimation target at this range with its pinpoint light source squarely in front of the telescope and then slide the target and telescope closer or further apart until the returned spot of light is sharp on the target surface. Figure 1 shows the general arrangement. If the reflected spot is too dim, cautiously open up the pinhole source a little.

Now very carefully adjust the target position until the returned spot of light overlays the pinpoint source. This can be made easier and more accurate if you slightly increase the distance between telescope and target to defocus the image to a doughnut ring three or four millimetres diameter; the rather dim ring is much easier to get symmetrically over the much brighter light source than simply aligning two sharp spots when one is so much brighter than the other (Figure 6). Accurate alignment to well within one millimetre is the aim and is easily achieved. Check that the target is still reasonably square to the telescope; it is now accurately on the optic axis of the primary mirror. Figure 7 illustrates the requirement.
Figure 6 The defocused returned doughnut ring alongside the point source........ Figure 7......and accurately aligned over it
Figure 8 The view through the focusing tube of a collimated SCTWith a collimation eyepiece (figure 5) in place in the eyepiece holder look into the telescope, remembering that what you are looking at is a symmetrical, on-axis target as seen by its reflection in both the primary and the secondary mirror. If the telescope is accurately set up, the outer ring of the target should lie neatly and evenly spaced around the rim of the field of view (usually the exit aperture of the telescope housing) and the inner ring of the target should be seen symmetrically around the rim of the secondary mirror holder (as in Figure 8). Any misalignment is immediately obvious and can be adjusted out as appropriate to the type of telescope being set up.
For an SCT it is simply a matter of adjusting the tilt of the secondary until the outer red ring on the target is symmetrical with the outer rim of the FOV, taking care as you do so that you don’t knock the telescope out of alignment with the target in the process. The inner red ring of the target should simultaneously sit around the rim of the secondary.

RC collimation is less straightforward because of the separate tilt adjustment of both mirrors. The first step is to adjust the tilt of the primary to get the outer target ring into the FOV. This obviously throws out the alignment of the primary with the on-axis collimation target, which needs to be continually corrected as you progress. Then adjust the secondary to align the reflected centre spot from the collimation eyepiece with the ring on the centre of the secondary mirror, at which point it will be necessary to repeat the whole process to converge rapidly to a satisfactory symmetry of both outer and inner target rings in the viewed image. ‘Before’ and ‘after’ photos, Figures 9 and 10, show the performance of a Ritchey Chrétien set up to the manufacturer’s conventional collimation instructions (Figure 9) and then re-aligned to this method (Figure 10). 
Figure 9 The target as viewed from the centre of the focusing tube with the telescope carefully set up according to conventional manufacturer’s instructions. Misalignment of the target rings is obvious. Figure 10 The same setup as Figure 9, but with the primary tilt adjusted to the method described in this article
Further refinement of the Ritchey-Chrétien collimation
The Ritchey-Chrétien mirror collimation as described makes the implicit assumption that the axis of the focusing mechanism is accurately aligned along the primary mirror axis, which may not be the case even in the smaller 6” and 8” designs where no independent adjustment is provided. A technique for achieving alignment of the focusing mechanism (or at least checking its accuracy) is given here but should only be undertaken with great care by someone confident in dismantling the telescope. It will also need a collimation laser of the sort designed to fit the eyepiece holder and should precede collimation of the primary and secondary mirrors as described in the previous text.

Remove the mounting bar(s) from the bottom (and top, if fitted) of the tube assembly. Remove the fixings that attach the primary mirror casting to the telescope tube and separate the complete primary mirror/focusing mechanism assembly from the rest of the telescope. Support it horizontally, preferably on simple v-blocks or similar. Using figure 11 as a guide, set up the collimation target to achieve coincidence of the light source and the primary mirror reflection as before (figure 7). Under ideal circumstances, a laser collimator inserted into the focusing mechanism will now throw an exactly coincident spot onto the centre of the collimation target.
Figure 11 Coincidence of the primary mirror and focusing mechanism axes.
Chances are that the laser spot will appear several millimetres off-centre. It now remains to find the source of the error and if possible correct it, noting of course that as already stated the focuser tilt is not independently adjustable on the smaller RC telescopes. Check firstly that the primary mirror is not loose; the central clamp ring needs to be just tight enough to prevent any tendency for the mirror to rotate or slide in its mount. Rotate the laser in the focuser and the focuser on the extension tube to both check how accurately the laser has been set up and for any sense that the focuser is off-square. Rack the focuser in and out and check for any looseness or droop. Consider rotating the mirror on its mount to see if the mirror itself has an off-centre component. Correct any problems that are found; the objective is to find a repeatable and stable arrangement that gets as near the ideal of figure 11 as possible.

If the focuser tilt is independently adjustable on your telescope it can now be set to place the laser spot precisely onto the centre of the collimation target, but no further adjustment can be made on the 6 inch or 8 inch RC designs.

Replace the primary mirror assembly back into the telescope tube, first making sure (by careful measurement) that the secondary mirror is held centrally in the tube. With the laser still in the focuser, use the primary tilt screws to align the laser beam with the centre of the ring on the secondary mirror (as viewed by reflection from the front of the telescope) and use the secondary collimation screws to tilt the secondary mirror such that the laser is reflected back on itself from the mirror centre. Several iterations may be necessary. The laser should now be removed and the primary and secondary mirrors can be collimated with the collimation eyepiece as described in the earlier text. By now, only the smallest adjustment of the set screws should be necessary. The objective is to try to achieve both a symmetrical target pattern when the centre spot of the collimation eyepiece is in the middle of the ring on the secondary and then be able to replace the collimation eyepiece with the laser and see that the laser beam is both centred on the secondary ring and reflected back on itself.

Summary
I own a conventional SCT and an 8” Ritchey-Chrétien and find that both can be easily collimated to a good standard with the method described here. How good a standard is a little subjective, but in my experience it certainly equates to, and is probably better than both the use of an artificial star and the common ‘off-focus’ star test. In this method, the target image is stable whilst adjusting the secondary mirror, whereas the traditional approach requires the star to be continually re-centred in the FOV, in itself making this collimation process much easier and quicker to perform.  It is particularly effective at setting the primary mirror alignment on a Ritchey-Chrétien to a much better state of collimation than the conventional ‘mechanical’ alignment process and is the only daytime method that I am aware of that will do so. Overall, the visual symmetry of the target image at the eyepiece brings considerable confidence about the general state of collimation of the telescope. Along the way there are also the side benefits of having a direct visual indication of the extent to which the smallest of adjustments affects the image, and all the convenience of working indoors when trying to achieve an equal torque on adjustment screws.

It cannot be perfect of course, since any visual alignment of this type must be subject to error and the symmetry has still relied on several mechanical references such the telescope front rim and the secondary mirror holder. Second order, more subtle effects like temperature, mirror flop and tube flex will also still exist when outdoors pointing at the sky, so the ‘on-focus’ Airy ring star test will always be necessary for peak performance. In my experience, however, this procedure gets closer to perfect collimation that any other of the several ‘daytime’ methods that I know of for the Cassegrain-type of telescope and does it with ease and a high level of confidence.

As a final comment, it is worth noting that the procedure is not easily adapted for collimation of the Newtonian design. In the Cassegrain telescope, the only adjustment readily available is mirror tilt, whereas in the Newtonian design the secondary mirror has not only tilt but also rotation and axial movements to set, neither of which can be easily achieved simply by pointing the telescope at a collimation target. Well established daytime collimation routines exist for the Newtonian that take this into account and achieve a high standard of accuracy that any variation of this procedure is unlikely to improve upon. Thus although the principles upon which this technique is based must hold for any reflector, its value for designs other than the Cassegrain-type may be limited to that of a useful confidence check.

Acknowledgements
My thanks are due to the management of The South Downs Planetarium for allowing me free access to their extensive collection of telescopes and in particular to Dr John Mason for his encouragement and help in writing this article.

Russ Slater October 2018
References
  1. How do I collimate my CPC Schmidt-Cassegrain telescope (SCT)?    Celestron Support Centre/Knowledgebase at http://www.celestron.com 
  2. Suiter HR. (2009) The Schmidt-Cassegrain, para 6.5.3 of Harold Richard Suiter’s Star Testing Astronomical Telescopes: A Manual for Optical Evaluation and Adjustment, 2nd ed. (Richmond VA, Willman-Bell Inc).
  3. Advanced SCT Laser Collimator. http://www.hotechusa.com/category-s/23.htm
  4. Astro-Tech AT8RC Instruction Manual:  https://www.astronomics.com/wp/wp-content/uploads/2017/04/astro-techastro-tech-at8rc-manual-pdf.pdf



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