NOTE: Words displayed in "Red" are changes to the original text either added or edited by J. Fly for clarification relative to the nature and use of the CATSEYETM Collimation System.
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Many articles have been written on how to collimate a Newtonian telescope, with little explanation about what is going on during the process. This article is a layman's examination of the Newtonian optical system, and how its components interact when properly collimated. Hopefully this 'behind the scenes' look will give telescope owners a deeper knowledge of the workings of their instruments.
Before continuing, some definitions are in order (see Figure 1):
Primary Mirror - The main optical element in a Newtonian telescope, usually having a parabolic reflecting surface. The useable area of the primary mirror excludes the bevel around the mirror's edge.
Light Column - Any circular column of incoming parallel light rays that can be reflected by the primary mirror.
Light Cone - The cone-shaped collection of converging light rays resulting from the reflection of a light column off a parabolic primary mirror.
Focal Point - The point where a light cone converges is called the primary mirror's focal point.
Optical Centerline - An imaginary line extending from the optical center of the primary mirror to the mirror's focal point. Geometrically speaking, it is also the parabolic axis of symmetry.
Central Light Cone - The light cone whose centerline falls along the optical centerline.
Focal Plane - The collection of focal points generated by all possible light cones defines a circular surface called the focal plane. The term 'focal plane' is a misnomer, as the surface is not planar. Instead, it is slightly cupped - more for short focal length telescopes and less for longer ones.
Collective Light Cone - The boundary defined by all useable light cones. It has the shape of a truncated cone (missing the pointed end) that is bounded on one end by the primary mirror and on the other end by the focal plane.
Secondary Mirror - The mirror used to reflect light coming from the primary mirror by an angle of 90 degrees so that it can be redirected into the focuser. The secondary mirror does this by intersecting the collective light cone at a 45-degree angle. By definition, the intersection of a plane and a cone is an ellipse, so the reflecting surface of the diagonal mirror is elliptical. Diagonal mirrors are usually referred to by the dimension of their minor axis (for example, a 2.6" diagonal has a minor axis dimension of 2.6" and a major axis dimension of 3.7"). The secondary mirror is usually attached to a mirror holder that allows minor adjustments for one axis of translation and three axes of rotation. As with primary mirrors, the useable area of the secondary mirror excludes the slight bevel around the mirror's edge (some mirror holder designs may obstruct even more of the outer edge of the secondary mirror). If the holder is larger than the mirror, it will also slightly increase the diameter of the secondary mirror's shadow on the primary mirror.
Spider Assembly - The spider assembly has a central hub and from one to four 'vanes' connecting the hub to the telescope tube. Its function is to provide a rigid support for the secondary mirror and its holder. Unfortunately, spider vanes also cause the contrast-robbing diffraction spikes seen when looking at a bright object. The brighter the object, the more distinct the spikes. Spikes are caused when light is diffracted as it grazes past a spider vane. These spikes are oriented perpendicular to the edge of the vane and each vane will produce an opposing pair of spikes. For example, a single vane will produce two spikes, each extending in opposite directions from the object. A three-vane spider produces six spikes, spaced 60 degrees apart. A four-vane spider produces eight spikes, but they are stacked in pairs and visibly appear as four brighter spikes spaced 90 degrees apart. A curved-vane spider does not produce diffraction spikes but instead smears the diffracted light across the image.
Focuser - The focuser is responsible for holding the eyepiece at the focal plane and keeping the eyepiece's centerline coincident with the optical centerline reflecting off the secondary mirror. It also allows the position of the eyepiece to be adjusted along the optical centerline as necessary to bring the eyepiece into focus. The sliding portion that secures the eyepiece is called the drawtube.
Focuser Centerline - An imaginary line extending along the geometric center of an eyepiece or collimating tool that is secured in the focuser drawtube. The focuser and eyepiece centerlines may be offset very slightly, and this offset varies between focusers. This offset is due to a necessary clearance between the inside diameter of the drawtube and the eyepiece barrel, and from the set screw(s) pushing the eyepiece or collimation tool to one side of the drawtube.
Telescope Tube - The physical housing for the Newtonian telescope's optical system, primarily responsible for holding the primary mirror, secondary mirror, and focuser in rigid alignment. Although it can be a rigid shell, open truss, or other design, it will be referred to here as a tube for simplicity.
Telescope Tube Centerline - An imaginary line along the geometric center of the telescope tube.
Collimation Screws - Adjustment hardware (screws, wing nuts, knobs, etc.) located behind the primary mirror cell that allow the primary mirror to be tilted during collimation.
Vignetting - A condition caused by any portion of an incoming light column (or the resulting light cone) failing to reach the focal plane. The primary causes of vignetting are obstructions blocking the light's path or light missing a reflecting surface.
Now that the main terms have been identified and defined, the effect that each item has on the telescope's overall performance can be investigated.
II. Why Collimate?
In the simplest terms, the reason a Newtonian telescope must be collimated is to optimize the optical performance of the telescope. This is accomplished by the proper alignment of the telescope's components and their centerlines. Slight misalignments can cause or increase star image flaring, rob images of contrast, or prevent images from being uniformly in focus. Severe misalignments can reduce the light gathering capability of the telescope or make it impossible to bring objects into focus at all. In general, collimation becomes more critical to the performance of the telescope as the focal ratio decreases (especially below about f/6). This is primarily due to the increased curvature of the focal plane in these telescopes (lower focal ratio = shorter focal length = deeper mirror paraboloid = steeper light cone = more focal plane curvature). The next section will look at the operation of a 'perfect' Newtonian telescope...
III. The 'Perfect' System
A typical Newtonian telescope can be illustrated as shown in Figure 1 below:
Figure 1: Typical Newtonian Diagram
(Click for Full Size) Here is a description of what is happening: Parallel rays of light enter the telescope tube, travelling parallel to the telescope's optical centerline. They reflect off the primary mirror, whose geometric centerline lies exactly on the telescope tube centerline. The centerline of the reflected 'light cone' also lies exactly on the telescope tube's centerline. The secondary mirror, tilted at 45 degrees so that it reflects the light cone by exactly 90 degrees, is located along the optical centerline and positioned laterally so that there is no light 'lost' unnecessarily past its edges. The reflected light cone now exits through a hole in the side of the telescope, through the focuser, and down the centerline of an eyepiece.
And Now for the Rest of the Story...
This is an adequate depiction of the process, but there are some subtle 'behind the scene' events not explained by this diagram. A more detailed description of each of these steps is warranted:
Parallel rays of light enter the telescope tube, travelling parallel to the telescope's optical centerline. - This is okay for show and tell, but in actuality, rays of light that aren't parallel to the telescope mirror's optical centerline are used by any given eyepiece. If not, then only one incoming light column would make it to the focal plane. The maximum angle of these 'off-axis' light rays is determined by each eyepiece's true field of view, which equates to the angular size of the circular disk of sky visible in the eyepiece. The diagram should therefore be modified slightly to identify 'incoming light' as any light ray that originates in that circular disk of sky. These light rays then travel to the primary mirror along innumerable light columns which are bounded by a truncated cone that can be drawn from the perimeter of the disk to the perimeter of the primary mirror (see Figure 2).
Figure 2: Additions to the Typical Newtonian Diagram
...Whose geometric centerline lies exactly on the telescope tube centerline - The telescope's mirror should be located near the center of the telescope tube. This step in the collimation process for a Newtonian telescope starts with the installation of the primary mirror. The importance of this centering is covered in the next paragraph.
The centerline of the reflected 'light cone' also lies exactly on the telescope tube's centerline - The optical centerline is tilted to an optimal position during collimation by adjusting the three collimating screws in the primary mirror cell. If the primary mirror isn't centered in the rear of the telescope to begin with, then there is an increased chance that the front edge of the telescope will vignette, or chop off, some of the incoming light. For this reason, steps should to be taken during the installation of the primary mirror and other components so that once collimated, the optical centerline will be roughly aligned with the centerline of the telescope tube.
The secondary mirror, tilted at 45 degrees so that it reflects the light cone by exactly 90 degrees, is located along the optical centerline and positioned laterally so that there is no light 'lost' unnecessarily past its edges. - The main function of the secondary mirror is to redirect light cones into an eyepiece that is physically positioned outside of the path of the incoming light columns. (An added benefit of having another mirror is reflecting the light a second time, therefore preventing the focal plane image from being 'mirror reversed'.) However, its size, shape, and position are critical to the performance of the telescope and it can be the most difficult component to position and collimate. The secondary mirror is supported by the spider assembly whose lateral position is fixed during installation. Once installed, slight adjustments can usually be made that will allow the secondary mirror to be rotated about the telescope tube axis, repositioned fore and aft along the tube axis, and/or tilted with respect to the tube axis.
Light reflected from the primary mirror in most Newtonian telescopes is intended to 'hit' the secondary mirror at a 45-degree angle (45 degrees from the mirror's surface) creating a 90-degree 'bend' in the light path. It will be pure chance if it precisely does. The angle of reflection is dependent on such things as the installed position and alignment of the focuser and of the primary and secondary mirrors. It is not critical for the light path to be reflected by exactly 90 degrees, and in fact, any angle could be made to work. However, the most efficient design employs a 90-degree bend as this angle minimizes both the height of the focuser/eyepiece and the size of the diagonal.
A widely misunderstood but extremely important optical effect caused by the secondary mirror is focal plane illumination (also known as field illumination). Focal plane illumination is the ratio (shown as a percentage) of how much light actually arrives at the focal plane compared to the amount that should have arrived. The ideal arrangement in any telescope is that every incoming light ray reaches the focal plane. However, this cannot happen with the classic Newtonian design for several reasons: 1) the size of the secondary mirror would have to be undesirably large; 2) the secondary mirror blocks some of the incoming light; and 3) reflecting surfaces aren't 100% reflective. Technically speaking, light losses from number 2 and 3 above do not 'count' when calculating focal plane illumination but will be discussed here anyway since they do reduce the amount of light delivered to the focal plane.
1) The size of the secondary mirror would have to be unnecessarily large - The size of the secondary mirror determines if a telescope's focal plane is fully illuminated at all points, fully illuminated in a circular area at the center and partially illuminated outside of this area, or only partially illuminated at any point. The position of the secondary mirror determines whether the distribution of focal plane illumination is centered on the focal plane. In calculating the minimum size of the secondary mirror, the maximum useable focal plane diameter must first be considered. This dimension is set by the diameter of the largest field stop of any eyepiece that will ever be used in the telescope. A field stop is typically a sharp edged ring positioned in front of the first eyepiece lens element in an eyepiece, and this ring sets the maximum focal plane diameter that can be used by that eyepiece. It also provides the sharp edged boundary of the image seen through the eyepiece itself. If there is no field stop, then the lens element holder itself attempts to perform this function and the boundary may appear slightly fuzzy.
To fully illuminate every point on this focal plane, the secondary mirror will have to reflect all available light from the primary mirror to each point. Take another look at Figure 2. The telescope pictured there has a secondary mirror that is appropriately sized to produce a moderate area of full illumination. However, it is still not large enough to intercept all of the light columns reflecting off the primary mirror. This is evidenced by the red and blue lines that are drawn as though they have been reflected, but don't actually touch the secondary mirror. To fully illuminate the focal plane shown the secondary mirror's size would have to be enlarged enough to reflect these lines.
Another way to look at this is that the secondary mirror must reflect an entire light cone to produce a fully illuminated focal point for that cone. If some of the light cone fails to be reflected, then the illumination at that cone's focal point will be less than 100%. Therefore, for 100% illumination across the focal plane, the secondary mirror must be sized large enough to fully reflect every light cone. This is undesirable, however, since increasing the secondary mirror size will decrease image contrast. The solution is to sacrifice some image brightness to keep the secondary mirror reasonably sized. This is done by creating a smaller fully illuminated area at the center of the focal plane and then allowing a visually acceptable drop-off in image brightness from this area to the edge of the field. For visual observing, it is usually difficult to notice this drop-off in illumination. However, it can be apparent in photographic images taken at prime focus, where the film is placed at the focal plane. A 'rule of thumb' suggested by many telescope makers is to be sure that there is a half-inch diameter or so of full illumination in the central area of the focal plane. A simple formula for calculating the secondary mirror's minimum size (minor axis) based on a specified diameter of 100% illumination is located in Appendix A.
To visualize full illumination, imagine looking at the reflection of the primary mirror seen in the secondary mirror from a 'vantage point' anywhere on the focal plane. If the entire perimeter of the primary mirror is visible with at least some space around it (see Figure 3, left image) then at least a portion of the focal plane will be fully illuminated. (Note that Figures 3, 5, and 6 only show the reflection of the primary mirror...all other reflections have been omitted for clarity.) A rough idea of the size of the fully illuminated area can be seen by keeping the edge of the primary mirror's reflection in contact with the physical edge of the secondary mirror as your eye is moved around the view (see Figure 3, right image).
Figure 3: Typical Reflections of the Primary Mirror
To center the distribution of focal plane illumination on the focal plane, the secondary mirror must be properly positioned. Since the secondary mirror is intersecting the converging light cones at an angle, the geometric center of the mirror will not fall on the center of the light cones. This creates a condition called 'secondary offset' where the secondary mirror, when properly placed, is shifted slightly away from the focuser and by the same amount towards the primary mirror. Figure 4 illustrates this effect.
Figure 4: Secondary Offset
Failure to offset the secondary mirror has some consequences. These consequences will be addressed separately for each offset direction:
Offset Towards the Primary Mirror - This offset is a 'no-brainer' provided the secondary mirror is visually sighted by aligning its perimeter so that it is concentric to the focuser during installation. If so, then it will be automatically offset in this direction. However, having the wrong offset or no offset at all will cause the illumination distribution at the focal plane to be shifted by the amount of the error. This means that the image in the eyepiece will not be the brightest at the center, and there may be a slight difference in brightness between one edge of the field and the directly opposite edge.
Offset Away from the Focuser - Unless the spider assembly or secondary mirror holder is specifically designed to include it, offsetting in this direction can be difficult. For a typical 4-vane spider the mounting holes may be drilled slightly shifted in the tube wall in order to accommodate the offset. It may also be possible to offset the spider using the spider leg mounting hardware by loosening the leg(s) nearest the focuser and tightening the farthest leg(s). This solution is less desirable as it may tend to increase the width of diffraction spikes seen around bright objects, or even make each existing spike 'branch' into two spikes. The primary reason for offsetting the diagonal away from the focuser is to keep the optical centerline and the telescope tube centerline coincident and prevent vignetting at the front entrance of the telescope. If this could be a problem, or if the most perfectly possible aligned system is desired, then include this offset dimension. When offset in this direction is not included, the optical centerline will be reflected by the secondary mirror by slightly more than 90 degrees. This will be compensated for by primary and secondary mirror tilt with no detriment to the telescope's performance.
As indicated earlier, a properly sized secondary mirror will not fully reflect every possible light cone, with the result being the image brightness at the focal plane diminishes as the radial distance increases away from the optical center. This reduction in illumination can be visualized by returning once more to the reflection of the primary mirror seen from the imaginary vantage point at the focal plane. That point can be shifted far enough off center that the reflection of the primary mirror 'disappears' off the physical edge of the secondary mirror (see Figure 5, left image). The amount of light still being reflected off the primary mirror to that point on the focal plane compared to the maximum amount of light possible equates to the percentage of illumination at that point. For example, if only 80% of the primary mirror is available to reflect light to a point on the focal plane, then that point is 80% illuminated. It is not unusual to see a 30% drop in illumination from the center to the edge of the focal plane in a 'healthy' system (which equates to less than a .5 magnitude drop).Figure 5: Visualizing Reductions in Illumination
(Click for Full Size)
2) The secondary mirror blocks some of the incoming light - Focal plane illumination is a function of how much of the light that is supposed to make it to the focal plane actually arrives there. Unfortunately, since the secondary mirror is positioned in the incoming light path, it will block, or vignette, some of the light. Imagine only one centered column of light entering the telescope. Since a shadow equal to the size of the secondary mirror is projected onto the primary mirror, that portion of the primary mirror does not contribute at all to illuminating the focal plane. However, since an infinite number of light columns are coming into the telescope and 'hitting' the primary mirror from various directions (refer again to Figure 2), they will all cast shadows of the secondary mirror onto the primary mirror. This results in a circular area smaller than the diameter of the secondary mirror where light is totally blocked, and an additional circular zone where light is partially blocked (see Figure 5, right image). This blocked area from the secondary mirror, or 'true secondary shadow', will not be perfectly round or perfectly centered on the primary mirror due to the angle of the secondary mirror and secondary offset (if present).
It is possible for the totally blocked area on the primary mirror to be reflected/projected back onto the secondary mirror. If the reflection/projection of the blocked area converges after it intercepts the secondary mirror, there will be a tiny unused spot on the secondary mirror similar to the one on the primary mirror. If it converges before it intercepts the secondary mirror, then the entire secondary mirror is being used. This effect should not be confused with the reflection of a single shadow of the secondary, which is projected all the way to the focal point. The presence of a 'dead spot' on the secondary mirror depends on the combination of the real field of view of the eyepiece used and the focal length of the primary mirror. For example, a short focal ratio telescope with an ultra-wide field eyepiece may not exhibit a dead spot, but may when using a narrow field eyepiece. The calculations for this are beyond the scope of this treatise.
3) Reflecting surfaces aren't 100% reflective - Focal plane illumination deals with how much of the light that is supposed to make it to the focal plane actually arrives there. Since it is factual that not all light is reflected by typical Newtonian mirror surfaces, that light was never expected to make it to the focal plane to begin with. However, this light loss can be significant - up to 15% or more lost at each reflection depending on the condition of the mirror surfaces. If both mirrors have a 90% reflectance (a reasonably good value), then only 81% of incoming light makes it to the focal plane (100% x 90% x 90% = 81%).
Let's recap/reword what has been said so far: First, the secondary mirror necessarily blocks some of each incoming light column, and reduces image contrast in the process. Second, the primary mirror reflects only a percentage of the light from each light column, and the secondary mirror reflects only a percentage of the light from each reflected light cone. Finally, when the secondary mirror reflects an entire light cone to the focal plane, then the focal plane for that cone is considered fully illuminated.
What happens when the secondary mirror is undersized? If it is sized so that it can fully reflect only the central light cone (the reflection of the primary mirror just fills the secondary mirror), then only the very center point in the focal plane will be fully illuminated by the primary mirror (see Figure 6, left image). Illumination will be 100% at the center and then diminish towards the edges.
Figure 6: Illumination Problems Seen from the Focal Plane
If the secondary mirror is so undersized that it is too small to fully reflect the central light cone, then the optical system will perform as though it has a smaller primary mirror (see Figure 6, right image). The aperture will be effectively limited to the portion of the primary mirror reflected by the secondary mirror, affecting both the telescope's light gathering and resolving capabilities.
So far, only the size of the secondary mirror has been addressed. However, a secondary mirror's performance will be greatly affected by its position, or distance, from the primary mirror. As mentioned earlier, as the size of the secondary mirror increases, the overall contrast of the optical system decreases. As the secondary mirror's size decreases, the area of full illumination at the focal plane decreases and finally disappears altogether, thereby reducing the effective aperture of the telescope. As the secondary mirror is moved towards the primary mirror, it must be made larger to reflect enough light cones to produce a fully illuminated area and the focused eyepiece height increases. As the secondary mirror is moved away from the primary mirror it can be made smaller and still produce the same fully illuminated area, but the height of the eyepiece will decrease until the focuser drawtube protrudes into the incoming light path. The goal then, is to choose the smallest secondary mirror possible while positioning that mirror as far as possible from the primary mirror. This will provide the largest illuminated field for any given secondary mirror size.
The reflected light cone now exits through a hole in the side of the telescope, ... - The hole made in the tube wall must be of sufficient size to not vignette any reflected light cone. This is usually not a concern since the hole is typically sized larger than the outer diameter of the focuser drawtube.
... through the focuser, and down the centerline of an eyepiece. - However, the focuser drawtube must also be large enough to not vignette any reflected light cone. As mentioned before, the focal plane diameter is usually set by the field stop diameter inside the eyepiece. Only the light cones converging within this circle will be used by the eyepiece. Since the focuser drawtube extends past the eyepiece, it is in a position where it could vignette the light if the drawtube diameter is too small and/or too long.
The location and alignment of the focuser is a critical step in the collimation process. Although the position of the secondary mirror drives the location of the focuser on the telescope's tube, it can be tricky to locate and extremely difficult to reposition once mounted. The location of the focuser and secondary mirror ultimately determines where the focal plane will fall outside the telescope tube. Since the focused position of each eyepiece can vary, it is important to locate the focuser so that all combinations of eyepieces and Barlow lenses can be brought into focus within the range of the focuser's drawtube movement. In addition, the perpendicularity of the centerline of the focuser to the telescope tube will determine how centered the optical centerline will be in the telescope tube and can complicate the collimation of the secondary mirror. As stated earlier, centering the light cones is important for preventing vignetting of the incoming light columns by the front edge of the telescope.
As stated in the definition of the focuser centerline, the exact centerline of an eyepiece and the centerline of the focuser aren't usually coincident. However, since collimation tools are secured in the same focuser drawtube as the eyepieces, this difference, even if large, is not usually a problem. What is generally more of a problem is repeatability of position when securing an eyepiece or collimation tool in the focuser drawtube. Eyepieces are typically inserted into the drawtube until the eyepiece shoulder contacts the drawtube's top edge. Tightening the set screws can 'cock' the eyepiece slightly if the contacting surfaces aren't all square to one another. Some collimation tools require tightening without shouldering the tool. Without the shoulder, and unless the set screw(s) are very tight, the tool may shift with surprisingly little force.
One last problem concerning focusers is image shift. The focuser drawtube should track nearly perfectly in a straight line while travelling either inward or outward without shifting from the weight of the eyepiece or from frictional loads in the mechanism. If drawtube motion isn't repeatable, then collimation results will not be repeatable and image quality may suffer.
With all of the apparent difficulties in collimating a Newtonian telescope, owners may be tempted to throw up their hands and quit at this point. Fortunately, once a telescope is set up and collimated the first time, periodic collimation should be relatively easy. If handled carefully, many telescopes will stay reasonably collimated even when transported over great distances. In addition, even if the telescope is not perfectly collimated it may still perform satisfactorily. The best thing to do is to just jump in and try it, as a lot will be learned about the telescope's optical system along the way. It is, however, considerably helpful to have an experienced friend to help do it the first time. Here's how it is done...
IV. Collimation Tools
Collimation tools are secured in the focuser's drawtube and help in collimating, or aligning, the optical components of a telescope. The most common collimation tools used are the:
Sight Tube - This tool consists of a tube with a larger diameter shoulder on one closed end and cross hairs mounted across the inside diameter on the other end. The closed end has a peephole drilled through it on the tool's centerline. It is usually built 5" to 6" in length to improve its accuracy by increasing the distance between the peephole and the cross hairs. The primary use for this tool is to position and collimate the secondary mirror and to square the focuser, although it can also roughly collimate the primary mirror.
"Classic" Cheshire - Similar in appearance but shorter than the sight tube, this tool lacks cross hairs and has an internally mounted mirrored surface angled at 45 degrees from its centerline and visible through an opening along one side. It also has one closed end with a peephole drilled through both the end and the internal mirror along the tool's centerline. The mirrored surface takes light directed in through the side opening and reflects it down the tool's centerline. The light is then reflected off the secondary mirror, the primary mirror, the secondary mirror (again), and finally back through the peephole. Visible through the peephole are the reflection of the primary mirror's center mark and the reflection of the Cheshire's peephole. This tool's only function is to collimate the primary mirror, which is done by adjusting the collimation screws on the primary mirror cell so that the reflection of the center mark is coincident with the reflection of the Cheshire's peephole. When used in total darkness, a light must be directed into the opening in the side of the tool to provide the necessary illumination to see the reflections. A 'trick' to doing this is cupping a hand over the end of a red flashlight, while holding the illuminated portion of the palm over the opening in the tool. The flashlight can be shown directly into the opening provided it has a diffuse lens and can be dimmed sufficiently so that it will not significantly affect dark adaptation.
Autocollimator - This tool is a short, shouldered tube that has a peephole drilled through its one closed end on the tube's centerline and a mirrored surface perpendicular to the tool's centerline on the inside. If the optical system is 'closed', then light cannot enter and reflect between the primary, secondary, and autocollimator mirrors and the reflection of the autocollimator mirror seen through the peephole will be dark. (This "dark" view with the autocollimator is only the 1st step and indicates "close" secondary collimation; however, when the autocollimator image reference is the CATSEYETM reflective triangle placed on the primary, convergence of the multiple images of the center spot is the ultimate final step to "perfect" secondary collimation.) This tool requires plenty of illumination directed towards the primary mirror from the front of the telescope, so is generally only useful when checking the alignment of the system when dark adaptation doesn't need to be preserved. (Ruining "night" vision is not a concern when using a red LED light at night to illuminate the CATSEYETM reflective triangle). Note that improvements to the performance of the optical system using this tool will be very slight. (Visual performance sensitivity at this stage is dependent on the degree of secondary misalignment and the focal length of the telescope, and CAN be visually significant relative to "detail" resolution.)
Laser Collimator - A laser collimator uses a low-wattage battery-powered laser to project a red beam down its centerline which reflects off the secondary mirror, the primary mirror, the secondary mirror (again) and then back onto itself. The beam itself is invisible except on dewy nights or in extremely dusty scopes, but a red dot is visible at each reflected surface. On some models, a reticule mounted on the tool also projects cross hairs with reference tick marks. They are available with both 1-1/4" and dual 2"/1-1/4" barrels. This tool can be used in either bright daylight or total darkness to collimate the primary and secondary mirrors, and can be used to square the focuser.
Combination Sight Tube/Cheshire - This tool combines a Cheshire and a sight tube by lengthening a Cheshire and adding cross hairs. Its use isn't significantly different from using the individual tools separately and is more a matter of preference.
Modified Cheshire - (See the "CATSEYETM" below). This tool looks much like an autocollimator, having a short, shouldered tube that has a peephole drilled through the one closed end on the tube's centerline, but with a reflective surface perpendicular to the tool's centerline on the inside. To use it properly, a square or triangular piece of reflective material must also be affixed to the center of the primary mirror (for primary mirror center marking comments, see Collimation Steps below). A red flashlight is then aimed down the telescope tube to illuminate the two reflective surfaces. Functionally, it operates the same as a Cheshire during collimation, so it will not be addressed separately in the following collimation steps.
"CATSEYETM" Cheshire - Similar in functionality to the Classic Cheshire, this augmented, compact tool provides its annular reference via a highly reflective surface on the front face of the device which is perpendicular to the drawtube axis. The light to illuminate it comes from daytime sky light or night time (LED) light illumination directed toward the "front" of the scope and it's bright image is seen through the peephole via reflection off the primary and secondary. As a companion component to the CATSEYETM, the center spot on the primary is a unique reflective triangle which is also illuminated by the front-end light and it's reflection is also visible through the peephole. As with the Classic Cheshire, this tool's only function is to collimate the primary mirror, which is done by adjusting the collimation screws on the primary mirror cell until the points of the triangular center spot are coincident with the inside diameter of the CATSEYETM's circular reflective surface reference image. Ideally, the orientation of the triangle on the primary has been specifically set to align the points of the triangle with the location of the collimation screws to facilitate intuitive adjustments. When used in total darkness, a red LED light is simply directed at the center of the primary mirror from the front of the scope to provide the necessary illumination to clearly see the reflections.
Film Canister - Although most people wouldn't consider this a serious collimation tool, a simple film canister can be used to aid in collimation when nothing else is available. This is done by drilling a peephole in center of the lid and cutting out the bottom of the canister. Its size will fit nearly perfectly in a 1-1/4" focuser drawtube. Its primary use is to provide a centered peephole for inspecting the optical components. As such, it performs similarly to a crude sight tube without the cross hairs.
V. Collimation Steps
Except for the autocollimator and film canister, all of the collimation tools listed above require that the primary mirror's center be marked, or 'spotted' as these tools indicate visual alignment with respect to a reference mark on the primary mirror. It is assumed, when center marking the primary mirror, that the optical and geometric centerlines are at the same spot on the mirror. Although this is improbable, the distance between the two is likely to be small. A way to verify this (after the fact, unfortunately) is by using the star collimation check (see the section titled Star Collimation Check below). The following collimation steps assume that they are coincident.
Center marks should be sized, shaped, and colored to provide an easy indication of alignment with the collimation tool used. The 'classic' center mark for use with a Cheshire is a square piece of white or black plastic tape, approximately 5/16" to 3/8" on a side (or an equilateral triangle 3/8" to 1/2" on a side). If the spot corners are not discernable ("black" or poorly illuminated), then the center mark may need to be larger to allow them to slightly protrude into the ring image. Avoid paper as it has a tendency to come off with subsequent mirror washings. The distances between opposing corners must be precisely the same. When collimated, the image seen in the Cheshire using either option will be a circle with the tips of the square or triangle slightly protruding around the perimeter. An advantage of the triangular center mark is that the three points of the triangle can be aligned with the three collimation screws on the primary mirror cell. (The CATSEYETM way) Note that the primary mirror must be prevented from rotating in the mirror cell for this method to work. With practice, it is easy to determine which collimation screw must be turned to 'move' the center mark in relation to the circle. (This is a significant additional visual queue and is a distinct advantage with the CATSEYETM System.)
Either of these center marks will work with the laser collimator when aligning the secondary mirror, but for collimating the primary mirror, a small circular hole should be punched through the center of the mark to allow the laser to reflect off the mirror underneath. An option that works well with a Cheshire (but not a laser for collimating the secondary mirror) is crossed lines made using a fine, felt-tipped permanent pen. This produces a 'bulls-eye' effect, where the Cheshire circle is bisected by the crossed lines when properly collimated. A white adhesive ring (the kind used to reinforce punched holes in notebook paper) can be used with a laser collimator since the central hole allows the laser to reflect off the mirror. Depending on the size of the laser's beam, a reinforcing ring's hole may be too large. Although the ring will produce concentric disks to align when using a Cheshire, the disks will be dark and may be difficult to see. (Neither a laser collimator nor additional "marks" are needed for complete collimation with the CATSEYETM system)
Since the center portion of the primary mirror is in the shadow of the secondary, the center mark will not usually vignette any light. However, the diameter of the area on the primary mirror totally blocked by the secondary mirror is smaller than the projected diameter of the secondary itself. Its size is a function of the true field of view of the eyepiece used and the distance between the primary and secondary mirrors (see Figure 5). An equation to calculate the secondary mirror's 'true' shadow diameter is located in Appendix A. Any mirror mark used should be small enough to fit comfortably inside this diameter.
The following steps can be used to collimate a Newtonian telescope (For purchased telescopes, there may not be anything the user can do about step 2. The focuser and spider assembly will already be mounted in steps 3 and 4, and any further alignment will depend on the adjustment capability of the components.):
Lay the mirror on a sheet of thin paper larger than the mirror and use a fine tipped pencil or pen to trace around the mirror (wrapping paper is excellent for this and can be used for larger mirrors). Remove the mirror and cut along the traced line, producing a paper disk the size of the primary mirror. Fold the paper in half, carefully aligning the edge, and then fold it in half again. The folded paper will now be a quarter of a circle, with one a square corner. Snip off a small piece at the corner so that when the paper is unfolded, there will be a small square cutout at the disk's center. Take the unfolded (and flattened) paper disk and carefully lay it straight down onto the mirror's surface.
If the mirror is permanently bonded to a mirror cell, or if you don't want to remove the mirror from its cell, then create a paper disk using a compass. For larger circles, a homemade compass is easily made to any diameter using a strip of cardboard cut a little longer than the radius of the desired circle. Punch two holes in the cardboard, one for a pivot point and one for a pencil tip. Draw the circle and enlarge the center hole slightly. Cut the circle out and lay it straight down onto the mirror's surface.
Minimize sliding the paper as much as possible to prevent scratching the mirror's surface. Take an ultra-fine tipped, permanent marker pen and place a small dot in the middle of the opening in the disk. Carefully remove the paper disk. Now verify that the dot is in the center by taking several measurements from the dot to the mirror's beveled edge. If the dot is off-centered, it can be re-drawn in the appropriate location, or the old dot can be removed using a small amount of isopropyl alcohol. Note that isopropyl alcohol will leave a residue if allowed to evaporate and not immediately rinsed using distilled water. Stick the center mark on the end of a toothpick using a bit of tape or rubber cement on the end and position the mark so that the ink dot is visible through the hole in the mark. You generally only get one shot at this, since the mark will stick firmly at first contact, so take your time. Once located, firmly press the mark onto the mirror using a new pencil eraser.
When using a reinforcement ring for the center mark, just center the dot inside the inner diameter of the ring. The tiny ink dot(s) can be left in place since the laser's dot is much larger in comparison and because the ink will still reflect the laser's light.
While the primary mirror cell is accessible, make sure that all of the collimation screws are properly loaded. Do this either by snugging them all down and then loosening them two or three turns each, or by taking some measurements to make sure they are well within in their range of adjustment.
For solid tube telescopes, the following method can be used for squaring the focuser and provides a permanent feature for future collimation checks:
Take a wide paper strip and wrap it around the tube so that one edge bisects the focuser hole and there are a couple of inches of overlap at the ends. Dot matrix printer or banner paper is ideal, as the wider the paper, the more squarely it will wrap around the tube. Where the paper overlaps, make two fine marks along one edge (one mark on each of the two overlapping edges of the paper - one will be underneath the other). Remove the paper, align the two marks, fold the paper strip in half, and make a mark at the crease. Now wrap the paper back around the tube so that the crease mark is approximately at the center of the focuser hole. The two original marks should realign on the side opposite the focuser. Tape the paper strip where it overlaps to hold it snugly in place (do not tape the paper to the tube). Install a sight tube in the focuser drawtube, then temporarily mount the focuser in its mounted position using the two mounting holes not covered by the paper. The end of the sight tube should just touch the paper strip. If the cross hairs do not line up on the paper's crease mark, then reposition the paper as necessary. Once alignment is achieved, use a small drill bit to drill through the tube wall at the location of the two original overlapping edge marks opposite the focuser. A small, shortened brad or nail can then be inserted in the hole from the inside. Install the focuser and adjust/shim as necessary so that the nail head is centered in the cross hairs.
For truss-tube telescopes, a similar process can be performed using a poster board strip on the inside diameter of the cage assembly provided the inside of the cage is circular and rigid. Measure from the front or rear of the cage to the focuser centerline, and then make sure the strip is the same distance from the front or rear of the cage on the opposite side of the focuser. Mark the inside of the cage opposite the focuser. Adjust/shim the focuser as required using a sight tube.
Figure 8: Secondary Mirror Adjustments using the Sight Tube (continued)
Tilting adjustments should only tip the mirror towards or away from the focuser, and care should be taken to not lean the mirror to either side. The reflection of the primary mirror should be centered in the face of the secondary mirror, and the cross hairs on the sight tube should intersect over the center mark on the primary mirror. The drawtube may need to be racked in or out or the sight tube repositioned to be able to see the full reflection of the primary mirror. Verify that the alignment performed in step 5 is still good and then repeat these two steps if necessary until the best alignment is achieved. The primary mirror can now be roughly collimated by centering the cross hairs on the sight tube with the very small reflection of the sight tube cross-hairs seen in the secondary mirror (see Figure 8, right view). To prevent the possibility of loosening all of the collimation screws and having the primary mirror cell come loose, always adjust the same two screws during collimation.
Figure 9: Primary Mirror Adjustments using the Cheshire
Figure 10: Primary Mirror Adjustments using the CATSEYE Cheshire
VI. Laser Collimation
Before a laser collimator can be used, basic alignment of the optical system outlined in steps one through six above must already have been performed. The sight tube, or at least the film canister, should be employed to align the secondary mirror to the focuser drawtube's centerline. Due to the slanted secondary mirror, either tool will be slightly more accurate than when using a laser collimator equipped with a cross-hair reticule. Any laser collimator can be used if the secondary mirror is 'center spotted', but since there isn't always an unused spot in the center of the secondary mirror, this spot would have to be removed after the secondary mirror's installation. When using a laser collimator to collimate the primary mirror, the end of the collimator where the light exits the housing must be visible while looking in the front of the telescope. Some focuser/laser arrangements will not allow this, and may require the use of a small pocket mirror to be visible (an idea for 1-1/4" focusers is to use a film canister with a small hole punched in the center of the lid, snugly fitted in the bottom of the focuser drawtube. You can then check that the laser's beam reenters this opening). For the record:
WARNING: DO NOT ALLOW THE LASER COLLIMATOR'S BEAM TO SHINE DIRECTLY INTO YOUR EYE OR BE REFLECTED INTO YOUR EYE BY ANY OF THE MIRRORS!
A badly collimated scope may direct the laser's beam out the front of the telescope. If there is any doubt, hold your hand, not your eyes, in front of the scope to see if the dot is being properly reflected. The lasers used by most collimators are low power and not likely to cause damage unless you stare into the beam, but 'better safe than sorry' as the old adage goes. However, it is safe to look at the laser 'dot', which is only scattered light where the laser beam hits a surface.
Substitute Steps 7 and 8 above with the following steps when using a laser collimator without the cross-hair reticule.
Substitute Steps 7 and 8 above with the following steps when using a laser collimator with the cross-hair/tick mark reticule. Note that Step 1 above is optional using this tool.
A laser collimator with the reticule can be used to evaluate how centered the light cone is in the telescope tube. To do this, point the open end of the telescope towards a flat surface and count the number of tick marks projected onto the surface along each cross-hair leg. There should be an equal numbers of tick marks on all four legs if the optical axis is centered.
The accuracy of both the visual tools and the laser collimator is only as good as their construction and the user's ability to judge the position of the reflections or laser dots and tick marks. As mentioned earlier, it is also assumed that the optical centerline is coincident with the geometric center of the primary mirror. For this reason, the biggest 'pitfall' of using collimation tools is that they will tell you that your telescope is collimated based solely on what is indicated at the point that you've chosen as the center of the primary mirror. These tools cannot factor in reflections contributed from all parts of the optical system. To do this you will need to check out the 'overall' collimation of the telescope by performing a star collimation check.
VII. Star Collimation Check
When a star is slightly de-focused on the inside or outside of focus, the star displays a bright disk surrounded by a series of rings. If the optics are well aligned, then the disk and rings will be concentric. Since a star check uses light reflected from all of the mirror surfaces, it can potentially detect a flawed collimation technique. This would be evident if, after performing a star test and making adjustments as necessary, the telescope's alignment was off as indicated using collimation tools. For example, if star checking consistently misaligns the primary mirror's center mark seen through a Cheshire, then this would be an indication that the optical axis of the primary mirror is not geometrically centered on the primary mirror. In future collimation checks, this misalignment could intentionally be introduced (or the center mark could be repositioned). Unfortunately, star tests are difficult to perform, as they require a night of good seeing, relatively high power, and a good quality eyepiece. Another difficulty is that adjustments made to the optical system will cause the star's image to leave the field of view, necessitating reacquisition of the target star. It is also important to keep the star's image centered in the field of view to minimize any field curvature effects. If the telescope is undriven, a moderately bright star like Polaris will allow the star's image to stay centered in the field during collimation.
VIII. Appendix A - Calculations
D = diameter of the primary mirror.
DF = the diameter of the desired 100% illuminated field.
DV = the diameter needed at the front end of the telescope tube or dew shield to prevent vignetting.
FL = focal length (approximately equal to D times the focal ratio).
FR = focal ratio, equal to the focal length divided by the diameter of the primary mirror (typically shown as f/4.8, f/6, f/10, etc.).
FS = the distance from the centerline of the telescope tube to the focal plane (you can determine the height of the focal plane by taping a piece of waxed paper across the drawtube and then racking the drawtube in or out until the star images seen projected onto the wax paper are as pin-pointed as possible).
Magnification = the number of times an object, as viewed with the naked eye, will be magnified with any given eyepiece, equal to FL (primary mirror) / (focal length of eyepiece).
Offset = the distance the secondary mirror must be shifted both towards the primary and away from the focuser to properly intercept all desired light cones.
PS = the distance from the primary mirror to the secondary mirror, equal to FL - FS.
PT = the distance from the front edge of the primary mirror to the front edge of the telescope tube or dew shield.
RFOV = the real field of view (in degrees) of an eyepiece. This value can be approximated by taking the eyepiece's advertised apparent field of view and dividing by the eyepiece's magnification.
Sact = the actual minor axis dimension of the secondary mirror.
Sreq = the minor axis dimension of a secondary mirror that will provide a required 100% illuminated area.
Smin = the minor axis dimension of the smallest useable secondary mirror (one that will utilize all of the primary mirror but will provide 100% illumination only at the center of the focal plane).
SD = shadow diameter of the secondary mirror on the primary mirror.
For the sake of commonality, examples worked in the following formulas will use dimensions taken from the author's Meade 12.5", f/4.8 Dobsonian Starfinder using a Panoptic 35mm eyepiece.
D = 12.5"
FR = 4.8
FL = 12.5" * 4.8 = 60"
FS = 12.4"
PS = 60" - 12.4" = 47.6"
PT (measured) = 53.5"
Sact = 2.6"
Eyepiece focal length = 35mm
Apparent FOV = 68 degrees
B. Secondary Mirror Size
Smin = D * FS / FL
Sreq = Smin + (DF * PS / FL)
Smin = 12.5" * 12.4" / 60" = 2.58"
Assuming a desired DF = .5" diameter,
Sreq = 2.58" + (.50" * 47.6" / 60") = 2.97"
(Note in the example above that the secondary mirror's actual size is just barely above the minimum calculated size and therefore will not produce the desired 100% illuminated field.)
C. Secondary Shadow Diameter
SD = Sact - (2 * PS * TAN(RFOV/2))
FL = 12.5" * 4.8 * 25.4 mm/inch = 1524 mm
Magnification = 1524mm divided by 35mm = 43.5X
RFOV = 68 degrees divided by 43.5 = 1.56 degrees
Shadow Diameter = 2.6" - (2 * (47.6") * TAN(1.56/2)) = 1.3" diameter
(note that this is half the actual diameter of the secondary mirror.)
D. Secondary Mirror Offset
Offset = Sact * (D - Sact) / 4 * (FL - FS)
E. Vignetting by Front of Telescope or Dew Shield
A good rule of thumb is for the front end of the telescope or dew shield to be larger than the incoming light cone by .5" or more. This will account for a slightly uncentered primary mirror, out-of-round tube or dew shield, and other small errors of construction. The largest possible RFOV of any potential eyepiece should be used for this calculation.
DV = 2 * PT * TAN (RFOV / 2) + D + .5
DV= 2* 53.5 * TAN (1.56 / 2) + 12.5 + .5 = 14.5"