Things to consider before starting

This page describes some aspects worth consideration before starting the actual telescope design. It does so by thinking about a virtual project of building a 10 inch Newton telescope on an equatorial mounting. In fact it is left over from my first attempt to the scope i'm building right now. So, the resulting design is not at all finished, and should be considered as an exercise. Hopefully, other beginning telescope makers can find anything useful on this page.

This page is cut in the following sections:

• Requirements, or: what do i want from a telescope?
• Considerations, some theoretical background for making design choices.
• Design, how it has worked out for the requirements above.

Requirements.

The telescope should have the following main characteristics:

• Transportable; it should be small enough to load it in a car, the backyard is way too much light-polluted to allow good performance.
• Low-cost; this is my first scope and it is built mostly to gain building and gazing experience.
• Equatorial mount; i want to use it also for CCD photography, and such a mount makes driving the hour axis easier.
• Simple construction; avoid exotic parts or advanced machining, so that it can be build with normal hardware-store components and a basic toolset.

Apart from these requirements i also made the following preliminary design choices:

• Primary mirror: is made of low cost 19mm plate glass. The largest closed tube size to fit in the car trunk limits the size to approximately f/6-7 at 250mm diameter. It also seems to be a nice to handle measure for a first mirror.
• Optical Tube Assembly: Closed octagonal wooden tube, which can be rotated to change eyepiece direction. Although a bit harder to make than for exame sonotube, i guess that with a closed design the chance on a good construction is larger than a truss-style.
• Mounting: the tube can be placed in an equatorial fork as well as a simple Dobson mount. The equatorial is meant for backyard and CCD purposes, the Dobson is more easily transportable.
• Focuser: I'd like to see how far you can get with a drill, handtools and stock aluminium, so i choose to make my own 32mm crayford-style focuser.

Theoretical foundations.

This section deals with the theoretical basis for some design choices, and has a somewhat generally applicable character. The design of my telescope, presented in the succeeding section, is based on this theoretical background. First some optical performance considerations are given, and subsequently some thoughts about mechanical issues.

Optical performance

The optical performance parameters addressed in this paragraph are:
Magnification,
Limiting magnitude,
Coma,
Vignetting,
Contrast.

Magnification

The range of useful magnifications is determined by the diameter of the eye pupil in dark and the diameter of the primary mirror. The bundle of light cut off by the primary mirror aperture is projected into a smaller bundle of light leaving the eyepiece, by ratio of the magnification. When the exit bundle is too large (i.e. magnification too small) the eye pupil will cut-off the exess, effectively causing vignetting. This vignetting is most visible when the exit and eye pupil are equal in size. In the case of a 250mm primary and 7mm pupil diameter, the ratio becomes approximately 35. Note that another factor playing a role in low magnification is vignetting at the eyepiece fieldlense. At such low magnification the true field of view my become larger than admitted by the combination primary focal length and field lense diameter. For example a plossl eyepiece used with 35 power will have a true field of view of 1.4°. For a focal length of 1600mm such eyepiece assumes a primary focal plane diameter of 40mm, which is impossible to obtain with a 32mm focuser! A remedy for this would be to shorten focal length, but this in turn makes high power harder to reach.
The upper magnification limit is determined by diffraction effects. The limited aperture size causes the image of a point source (like a star) to be spread out into an image that shows like a disk with a set of rings around it. The size of this disk is inversely proportional to the aperture size. As a rule of thumb, the maximum useful magnification is about 2 times the aperture in mm, which in my case results to 500. The associated dawes limit of resolution is approximately 0.45 arc seconds, which means that smaller details can not be observed.

In practise it can in some cases be useful to go beyond the upper magnification limit, for example to split a narrow double star. Also using magnification lower than the calculated minimum may be used when field of view is considered more important than light gain. Dropping too far below the lower limit, the telescope will eventually show vignetting at the focuser tube or the field-lens of the eyepiece. Also the secondary obstruction may become visible as a blind spot in the middle of the field.

Limiting magnitude

Another limit set by the primary mirror is the amount of light gain, which determines the weakest stars that can be seen by eye vision. The naked eye can normally see stars of magnitude 6; the light amplification of the 250mm mirror will add almost 8 magnitudes to this.
The gain factor is determined by the ratio of aperture surface of the primary mirror and the eye pupil, being approximately 1250. In the logarithmic magnitude scale this yields a limiting magnitude of 13.8.
When the telescope is used with a CCD camera, the limiting magnitude will be much higher. The CCD array is very sensitive because it is capable of accumulating light energy during a period of time.

Coma

A telescope mirror can only make a perfect (diffraction limited) image on the optical axis. Off-axis the image suffers from coma, which shows as the stretching of a point into a "comet" shape. The amount of coma is proportional to the distance from the optical center, the value of the coma coefficient depends on the mirror curvature. For a parabolic mirror it is inversely proportional to the square of the focal ratio. In any case, slower mirrors (high f/ratio) have larger "coma free" area.

A formula for the amount of coma, is:

• Linear coma = r * 3/(4N)²
• Angular coma = r * 172/(f*(4N)²)

In case of a 250mm, f/6 parabolic mirror, angular coma at 5 mm off-axis is approximately 3.5 arc seconds. This is also the practical resolution limit that is reached under average seeing conditions. Therefore a prime image field of 10mm diameter can be considered coma-free, this corresponds with 23 arc minutes, or the full field of an 11 mm Plossl (50˚) eyepiece.
Note that this calculated figure is probably worse than perceived in reality. An other way used to calculate the coma-free field is to take the square of the focal ratio, which in this case gives 36mm coma free field.

Vignetting

Imagine the cone formed by the primary mirror and the focal point on the optical axis. If this is the full width of the light bundle the secondary will just fit into this cone (usually at a point some 20% down from the focal plane). Such a setup would give a 100% ilumination only on the optical axis; slanting the cone away from the axis will cause the secondary to cut-off part of the cone. Now imagine a secondary which is larger than this central cone; it would allow a whole set of cones that make an angle with the optical axis. The set of cone top points in the focal plane form the 100% illuminated field; moving away from the optical axis beyond this limit will cause cut-off again.

Vignetting is caused by a too narrow enclosure, cutting off the full width of the light path (i.e. the set of cones), so that it affects vision through the eyepiece. The elements that usually cause vignetting are: the secondary mirror, the focuser drawtube and the OTA front aperture.

Since the telescope will also be used with my CCD camera, the 100% illuminated field should at least cover the full CCD array, which in this case has a diagonal of 8 mm. Vignetting becomes noticeable to the eye when the light is reduced to approximately 70% of the full illumination. Therefore the 70% limit should be outside the largest field lense of the set of eyepieces used. In this case, operating a 1.25" focuser, it is not likely to exceed 25mm.

With a 50mm secondary mirror and 210mm distance between secondary and focal plane, the fully illuminated field has a diameter of 17mm. The 75% limit is at 34mm diameter, thus far enough outside the focuser tube to cause any degradation. In fact it is slightly oversized, and allows the secondary diameter to be brought back to 42 mm. In that case, the 100 and 75% limits will be 8 and 26 mm respectively.

Contrast

Contrast is a measure of the dynamic range of the image field, or the ratio between the high and low intensity parts of the image. Also the spatial rate of illumination variation, or the sharpness of details, is part of the contrast (this is related to the resolution). Therefore two types of contrast may be distinguished which i refer to as "local" and "global". If the illumination of the focal plane is set out graphically in a 3-D plot, there will be a sort of mountain landscape. The steepness of the slopes is the local contrast, while the maximum relative peak hight can be seen as global contrast.
Local contrast can thus be defined as the intensity variation on the scale of maximum resolution. Loss of local contrast is mostly affected by imaging faults.
Global contrast can be defined as the intensity difference between image and background. Loss of global contrast is caused by stray light reaching the image plane.

For maximization of local contrast, obstructions of the light-path should be limited as much as possible. Because of the limited aperture (the primary mirror diameter) a point is always imaged as a diffraction pattern of concentric rings. Obstructions in the light-path, such as the secondary mirror and the spider, cause further deterioration of this diffraction pattern.
In optimization of the secondary mirror size, changes required by other parameters affect the diameter only marginally. Therefore, maximization of local contrast is a relatively unimportant criterium for optimization.
Another obstruction is the spider, which is the cause of the "spikes" around star images, perpendicular to the spider arms. Thinner spider arms make the intensity of the spikes less. The layer of cold air forming around the arm material effectively makes them look thicker, thus intensifying the effect. A solution would be to use material with low thermal capacity, or wires. Also using a four- instead of a three-arm spider will improve contrast because it results in only four spikes instead of six. Also should be taken care that the focuser drawtube, when fully racked in, does not obstruct the light path.

Maximization of global contrast can be achieved by minimizing stray light that enters the OTA, and somehow may reach the focal plane. The stray light can be originated from earthly sources, but also bright celestial objects (such as the moon) are a cause. This background illumination can only be minimized by taking care of proper absorption of non tangential light. Methods to achieve this are flat black paint, baffles at strategic places, interior surface roughening and forward extension of the telescope tube.

Mechanical issues

Cooling of the primary mirror

When the telescope is moved outside, it needs to reach thermal equilibrium before maximum performance can be expected. While the equilibrium is not reached, the lightpath is disturbed by convective air currents, which is noticeable even at 1° temperature difference. These currents mix air of different temperature (and different index of refraction), comparable with the "trembling" of the air over a hot surface.
Another reason to let the telescope cool is because the mirror is deformed while there are still temperature gradients inside the material. Plate glass has a quite large expansion coefficient, and therefore such mirrors used to be made slightly undercorrected, in order to compensate for the deformation effect during the slow cool-down process. When the mirror no longer has internal temperature gradients, the original shape is regained.
For my telescope i took a more deterministic approach; the mirror is fairly thin and can be brought to thermal equilibrium quickly by means of a fan. Therefore the mirror is figured as a complete paraboloid, and fast cooling is provided by means of a fan. The question to be answered rightnow is: how long does it take to cool?

Some mathematics for estimation of the cooling time

The mirror is assumed to be an infinite flat plate with thickness 2L. Symmetry of the problem allows to look at one half of this thickness only. It is furthermore assumed that the mirror surface is always at the same temperature as the environment, i.e. the final temperature to be reached. The initial homogeneous mirror temperature is T₀ and the environment is at temperature T₁.

For window glass, the properties have the following values:
 l = 0.81 W/m.K
 r = 2500 kg/m³
 C = 760 J/kg.K

For a 19mm thick plate, these parameters yield a time of approximately 8 minutes to let the center reach 1% of the original temperature difference.

In reality it is very hard to keep the glass surface on ambient temperature level, because the heat capacity of the glass is much higher than that of air. The derived result may for example be achieved when the mirror is submerged in flowing water, but in the real situation cooling times will be much higher.

Concluding, the mirror surface temperature must be kept as close as possible to T₁, to approach the shortest possible cooling time of 8 min. To achieve this , the boundary layer must be kept as thin as possible, which may be achieved by a high-speed air flow. Therefore, the telescope must be equipped with a fan.

To calculate a realistic time estimate the heatflow differential equation can be modeled with a PDE solver, such as FlexPDE. When solved with the already known mirror parameters, and a sound assumption of heat-loss due to forced convection, this should yield realistic values for cooling times.
In the model i used a heatloss of 50, 20, and 10 [W/m².K], for back, side and face respectively. These values are taken from literature, where free convection yields a 5-10 and forced air cooling yields a 10-100 [W/m².K] heatflow. Since the front cooling is not totally free convection, 10 is chosen, and the other valuess are also reasoable estimates.
The temperature profile resulting from the simulation with FlexPDE has a maximum in the mirror center, somewhat offset to the front. After half an hour the temperature difference has fallen from the initial 20K to below 1K. After an hour the differences are less than 0.15K over the whole mirror, which may be considered negligible. The deformation due to the mentioned temperature profile will (as expected) appear as undercorrection.
You can download the FlexPDE data file from the resources page somewhere else on this site.

The mirror cell

Any glass disk will show deformation when mounted. For a telescope mirror this mounting induced deformation has to be kept within bounds. Figuring errors are typically in the order of λ/10, and the goal is to keep additional deformation well below this. The way to achieve that is by suspending the disk on strategically placed points, that distribute the weight. The set of points can not be fixed in height if there are more than 3, because then the supports will not transfer deterministc forces; i.e. the system is physically overdetermined. Therefore the supports have to be grouped in groups of maximum 3, which in turn may be grouped again until 3 points are left over, which can be connected to the collimation bolts.
The support requirements for a specific mirror can be easily found with the PLOP program. Just fill in the material properties (in my case for plate glass) and mirror size, and then auto-generate a cell of choice. According to my simulations, a six point mirror cell is plenty sufficient to support my mirror. The six points should be placed at 59% of the mirror radius. The resulting RMS error due to sagging is less than λ/200. The resulting error is actually less than achieved with a 9 point cell. This is due to the fact that the deformation with supports organized in a ring may cause more absolute deformation, but the resulting shape approaches a paraboloid better than other formations. This deformation can be compensated by refocusing, which can be taken into account in PLOP simulations.
The support points need to be connected to the three cell supports, or collimation bolts. In case of a six-point cell, pairs of points are conected by cantilevers, which in turn can be supported by a plane or by collimation bolts directly.
You can download the PLOP data file from the resources page somewhere else on this site.

The tube assembly

One of the preliminary design choices is to have an octagonal closed wooden tube. It may be more difficult to make than a square tube, but an advantage is that the focuser can be put on one of the 45° planes. This makes access to the eyepiece a bit easier, especially at low altitudes.
Such an octagonal tube can be made quite simple, by glue/screw 8 strips of thinnish plywood onto a set of ribs. The the tube is given its rigidity by the box construction, so it is important to have good contact of all parts. The central hole in the ribs can be calculated from the mirror diameter and the widest field of view possible. This field of view is determined by the focuser tube and the focal length: arctan(30/1750). This means that the aperture at the front of the tube must be approximately 30mm wider than the mirror diameter (i.e. 280mm). This is the mechanical minimum, optically there should be more play, because of air currents along the tube-walls.
Another consideration is that a closed tube shields the lightpath from convection caused by the environment, such as your body. Also it is easier to shield off stray-light that may deteriorate global contrast. Also the mounting point of the declination axis can be anywhere along the tube length, which is not very obvious whith an open construction.
The backside can be made with some play, so the mirror can be moved up and down giving some more focuser play (possibly needed for the CCD camera).

Access to the eyepiece without having to use a step determines the focal length of the primary mirror, and hence also the length of the tube. My eyes are at 1700mm height, so that should be the maximum height of the eyepiece when looking at the zenith. Considering that in this case the primary face is about 200mm above the ground, and for a 250mm mirror about the same distance is needed from tube axis to focal plane, the focal length can be maximum 1700mm. For the 250mm mirror this means a focal ratio of approximately 6.5.

The mounting

The length of the tube is pretty much fixed by the primary mirror and focuser characteristics. As a rule of thumb, the tube length is approximately equal to the focal length. The bit you gain by folding the light-path is compensated by the mirror cell and the neccessary extension of the tube beyond the focuser.

The choice of mounting is determined by ease of implementation and access to the eyepiece. For an equatorial type of mount i pre-selected a few options; German, Split-ring and Fork.
The idea of making a German equatorial mount i discarded quickly, because it is too hard for me to build one that is rigid enough to support the weight of the tube assembly.
The split-ring and fork mount can be made from wood, and may be heavy because of the low center of mass.
Because i chose a closed-tube design, the mass center of the OTA, and therefore also the declination axis, will be further away from the primary than with the lighter open designs. Therefore the ring of a split-ring design needs to be pretty large to allow for the tube to cross the equator plane. Adding weight to the back side can solve this, but then there is also the issue of near-horizon observation: it will be neccessary to kneel to be able to use the eyepiece.
The following sketch gives the approximate dimensions of both types of mount for the telescope. From this it is clear that near-horizon observation is much more comfortable with the fork mount, for near-zenit there is not much difference.

Care must be taken in design of the fork, it must be extremely rigid as to minimize vibrations and sagging. Like with the split-ring it is also beneficial for the fork length (and thus rigidity) to keep the center of mass as close as possible to the primary mirror.

Finally: the design.

This section is about the design in which everything finally came together. The drawings are quite poor, but at least give an idea. More accurate CadStd drawings can be downloaded from the resources page elsewhere on this site.
The following topics are addressed:
primary mirror,
mirror cell,
crayford focuser,
tube assembly,
mounting.

But first some general parameters, based on a quick model made with NEWT2.5 and the application of above theory:

Primary diameter	250 mm
Focal length	1600 mm
Secondary diameter	40 mm
Primary face to focuser axis	1389 mm
Focal plane to tube axis	211 mm
Focuser axis to tube front	200 mm
Primary face to tube back	100 mm
Tube length	1689 mm
Tube outer diameter	312 mm
Tube wall thickness	6 mm
Required diagonal offset	1.6 mm
100% illuminated area	8 mm ( 0.3 °)
75% illuminated area	25 mm ( 0.9 °)
Useful magnification	35 - 500 x
Useful eyepieces	45 - 3.2 mm
Dawes resolution limit	0.5 "
Angular coma coefficient	0.6 "/mm

For the Newt data file, see the resources page.

The primary mirror

The primary mirror is made of 19mm float glass (i.e. modern plate) which can be bought in almost every glass-shop. Some shops even have 25mm in stock, but this i much more expensive. The mirror has a diameter of 250mm, and will be cut out of a piece of 280mm square. The focal length is targeted to be 1600mm, which yields a sagitta of approximately 2.2mm.
To save the considerable cost for circle cutting (~50 Euro), this is done by myself. The expected total cost of the mirror will be under 150 Euro.

Cutting a disk out of the glass

The glass slab is a rough-cut square, so a circular disk of 250mm diameter has to be cut out of it. The idea is to trepan the circle from the square, much like the way it has been done by for example Jeff Baldwin or Ken Hunter.
A variable rpm drill is used on half the mains voltage, to obtain lower speed. The cutter disk is made of 25mm plywood, with three copper strips pointing down to the glass. The disk must be thick enough to counter the high torsion of the copper strips, induced by the drag during grinding. To avoid excessive drag, the strips are pre-shaped with a roc of 125 mm. The source of the copper is a 22mm gaspipe, which is heat-softened, split lengthwise and flattened.
For the first mirror blank, the disk was connected directly to the drill via a loosely coupled axis. This gives the drill and the disk some motional independence, and let the strips find their own way down through the glass. The drill shaft drives the disk with a pair of off-center pins. The whole assembly is mounted in a drill-press, which does not need to be exactly perpedicular because of the loose coupling.

The drill could barely handle the torque with such low rpm, because its' cooling depends on the rotation too. Burnt PVC fumes and smoke were the result, so for the following blanks i made a 1:10 set of pulleys. The drill can rotate 10 times as fast, and doesn't need to produce so much torque. The large pulley is made from three layers of appropriate thickness wood. The small pulley is made from a stack of M6 rings, 25mm diameter in the middle with a 30mm ring on top and bottom. The rings are glued together with cyanoacrylate.

To do: drawing of trepan installation

Grinding

For grinding the primary mirror the well trodden path of plaster and tile tool is chosen. If i cannot find any water-proof plaster type, i will use the normal modelling plaster (Plaster of Paris). This type of plaster has to be sealed with for example a polyurethane coating. Another way worth consideration is to use a basis of thick plywood, at least for the stage of rough grinding.

The sagitta of the mirror will be around 2.5 mm, so it is likely that after rough grinding the 3 mm thick tiles have to be renewed.

Polishing

The float glass has a relatively high coefficient of expansion, and also the 19mm is relatively thin. Local heating of the glass must therefore be avoided to prevent deformation, especially in the polishing and figuring stages. The idea is to use a wooden backing device to hold the mirror, preventing hand-mirror contact. Special care must be taken to avoid slip between mirror and holder. I don't yet know how to do this. Alternatively thick gloves can be used, but these may collect grit and also decrease control over the mirror and lap.

The mirror cell

The cell design is somewhat based on that of Albert Highe and Bruce Sayre, in that it consists of three lever beams on horizontal pivots 120° apart. These pivots are not mounted on an aluminium triangle, but mounted on a plate of plywood. The lever material is aluminium U-profile, 20 and 15 mm, which can be found in a hardware store. The support points are made of M4 T-nuts, screwed on the lever beam 74mm apart. The mirror is glued to these nuts with silicone caulk.

Mirror cell, top view.

The cross section shows the central hole, which is made of PVC pipe. This pipe guides the air from the fan to the space between the back of the mirror and the cell plate, where it flows sideways along the rear mirror surface. At the edge of the mirror the final baffle on the front side redirects the airflow somewhat over the mirror front, to further enhance the cooling.
The air flow may also be reversed, whichever direction gives best cooling and/or least contamination of the reflecting surface. Cooling is probably more efficient when blowing towards the mirror, because airflow tends to be more turbulent on the outlet side of the fan. Usually dust piles up on locations where the airflow decelerates below a cerin threshold, corners and shielded areas close to the flow.

The cell should to some extent be adjustable along tube, to compensate for mismeasurements.

The crayford focuser

As a focuser i chose to build my own 32mm crayford. This type of focuser is relatively easy to build from aluminium parts that can be bought in a hardware shop.

The length of the drawtube is 65mm, which is twice the inside diameter. This is important for the calculation of the distance from focuser axis to the front of the tube: to avoid stray light from entering the eyepiece it should be minimum half the aperture diameter. So this ditance must be set to 150mm, to be on the safe side.

The focuser drawtube is aluminium 32mm inside, 2 or 3 millimeter wall thickness. In the sideview two of the miniature bearings (e.g. from RC-car) are shown to show the heights. Focuser height ranges from 36 to 66 mm measured from outside tube surface, so the focal plane should be located about 50 mm outside the tube.

The tube assembly

The inner diameter of the tube assembly is 310mm. The crayford focuser, described elsewhere on this page, has a travel ranging from 36 to 66 mm above the tube surface. The focal plane is therefore assumed to be projected approximately 50mm outside the scope tube. Including the 4mm wall thickness, this gives a distance from primary mirror face to focuser axis, of 1500 – 310/2 – 4 – 50 = 1291mm.

To calculate the full tube length from this, the extra lengths at front and backside need to be added. To the back side this length is determined by the thickness of the mirror and the supporting cell, estimated to be 100mm. At the front the length is determined by the focuser tube dimensions, and has been calculated to be 150mm.

Overall length of the OTA then is 1541mm, but the exact measure is determined by the exact focal length of the primary mirror. To allow for deviations, the cell mounting is made so that some adjustment is possible in order to get the focal plane at the right position.

The tube has an orthogonal cross section. The focuser can then be mounted at one of the 45 deg sides. When the OTA has two pairs of bearings, or when it is mounted in a cradle, the eyepiece can be directed to the left or the right at convenience. Wall material is 4mm meranti triplex, the baffle rings are made of 6 or 9mm MDF or plywood (whichever is lightest).

The support of the tube walls is formed by the

The fork mount

It has an equator disk of 600mm across, and a fork with a length of around 500mm, which is considered to be the maximum for sufficient rigidity. The balance point is estimated on 400mm from the tube bottom, the tube being of 1540mm length. Since the mirror is relatively light (2kg), it is very likely that the tube needs some counterweights, which becomes more evident when the fork is made shorter.

If the fork is made shorter, a gap in the equator disk is needed to allow observation near the southern horizon. Ultimately there is no fork at all, and the mounting changes into a split-ring type.

With the split-ring variant, the ring needs to be bigger, to allow the complete tube to cut-through and still be strong enough. Clearly, the balance point needs to be very low, because the ring would have to be extremely large otherwise. This adds to the total weight, and also makes the total setup less stable.

All in all, the fork type is the mount of choice: more comfortable observation height for near-horizon, and less counterweight needed. However, care must be taken in the design of the fork construction. It suspends the total OTA weight over a long arm, and is therefore susceptible to vibration or sagging.

By using a relatively large equator wheel, the rotation can be easily automated by means of a friction drive. The length of the fork is determined by the place of the balance point of the OTA, but should be as short as possible.

An alternate mount for mobile use is a dobson, which can then use the same bearing principle as the fork mount. Instead of using a fork mount for photography, the dobson may also be put on an equatorial platform, which provides rotation about the polar axis.

NOTE: The fork must have no sagging when the scope is pointed east or west. How can i calculate this for a certain construction? I guess i have to dig up my books on construction mechanics.