By: Arjan te Marvelde
This page describes the design of a 250mm Newton telescope, and a fork mount. The page nor the design are finished, and the lot should be read as a collection of things you might consider when building a scope.
As parts of the design become reality, the gained experience will be added to the original of this page at my atm site.
The telescope should be:
All in all, these requirements lead to a design with the following characteristics:
|Primary diameter||250 mm|
|Focal length||1500 mm|
|Secondary diameter||50 mm|
|Focal plane to tube axis||210 mm|
|Tube outer diameter||318 mm|
|Primary face to focuser axis||1290 mm|
|Focuser axis to front||150 mm|
|Tube length||1540 mm|
|Required diagonal offset||2.08 mm|
|100% illuminated area||17.4 mm (0.67 °)|
|75% illuminated area||34.8 mm (1.34 °)|
|Useful magnification||35.7 - 492 x|
|Useful eyepieces||42 - 3 mm|
|FoV (50 deg eyepiece)||1.4 – 0.1 deg|
|Coma coefficient||5.2 µ/mm|
Independent of focal length, the primary diameter of 250mm theoretically gives useful magnifications in the range of 35 – 500, a diffraction induced resolution limit of 0.45 arcsec and a limiting magnitude of 13.8.
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 depends on the type of curvature, but for parabolic mirrors it is proportional to the distance from the optical axis, and inversely to the square focal ratio. In other words, the slower the mirror (the higher the f/ratio), the larger the "coma free" area.
A formula for the amount of coma, is:
|where:||r is the off-axis distance in the image plane,|
|N is the focal ratio,|
|f is the focal length.|
With the chosen primary mirror dimensions (250mm, f/6), coma at 5 mm off-axis is approximately 3.5 arc seconds, which 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 well known way to calculate the coma-free field is to take the square of the focal ratio, which in this case gives 36mm coma free field.
Imagine the cone formed by the primary mirror and the focal point on the optical axis. If this is the full width of the ligt path, the secondary will just fit into this cone, at a point some 20% down from the focal plane. Such a setup would give a 100% ilumination only on the optical axis; moving away from there 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 form the 100% illuminated field; moving further away from the optical axis will again cause cut-off.
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 decrease of illumination becomes visible in the eyepiece. The usual things that may 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 eyepiece field lense 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 may be defined as 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 it (which is related to the resolution). Two types of contrast may be distinguished: referred tyo as "local" and "global". Local contrast can be defined as the intensity variation on the scale of maximum resolution. 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, while loss of local contrast is caused by imaging faults.
For maximization of local contrast, obstructions of the light-path should be kept as small as possible. Because of the limited aperture (the primary mirror diameter) a point is always projected 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.
Minimization of secondary size is a relatively unimportant criterium for optimization. The variations in secondary size that are needed for optimization of other parameters (focuser height, illuminated field) are so small that it makes no noticeable difference with respect to contrast. An other obstruction is formed by the spider, which should be as thin as possible. Also using a four-blade spider instead of a three-blade will improve contrast because it results in four spikes around stars instead of six. Also should be taken care that the focuser, when fully racked in, does not reach 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, surface roughening or more likely a combination of these.
Plate glass mirrors used to be made slightly undercorrected, in order to compensate for the overcorrection caused by temperature gradients during the slow cool-down process. When the mirror has no temperature gradients however, the original form is regained. Therefore, for this telescope a more deterministic approach is taken; the glass 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 the OTA is provided with a fan below the mirror cell. The cell design must take this into account.
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 at the same temperature as the environment. The initial 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 specific heat 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 as thin as possible, which may be achieved by a high-speed air flow. Therefore, the telescope will be equipped with a fan.
Temperature gradient in and outside mirror.
The heatflow differential equation can be modeled wth a PDE solver, such as FlexPDE. When solved with the already known mirror parameters, and a sound assumption of heat-loss due to convection, this should yield realistic values for cooling times.
In the model i used a heatloss of 50, 20, and 20 W/m2, for back, front and sides respectively. The resulting temperature profile has a maximum in the mirror center, somewhat offset to the front. After 30 min. the temperature difference had fallen from the initial 20K to below 1K. After an hour the difference is negligible. The deformation due to the mentioned temperature profile will (as expected) appear as undercorrection.
The primary mirror has a diameter of 250mm, which just enables a speed of f/6 to f/7 with a reasonable tube length. With these dimensions it is still possible to reach the eyepiece without stairs, while observing the zenith. The mirror material is float-glass (or plate) which can be obtained easily in any glass shop in thicknesses up to 19mm. Also 25mm and possibly 32 mm glass is available, but on special order only and very expensive. To save the considerable cost for circle cutting, this is done in-house.
Estimated cost for the primary mirror:
|Float glass, 280 x 280 x 19 mm||27,00|
|Grit and powder (250mm kit)||34,00|
|Pitch (1.2 kg)||16,00|
|Plaster (10 kg)||10,00|
|Disposable anti-slip mat||2,00|
The glass sheet is a rough-cut square, so a circular disk of 250mm diameter has to be shaped 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 sticking down to the glass. The disk must be thick enough to counter the high torsion, induced by the drag on the metal strips during grinding. To avoid excessive drag, the strips are pre-bent with a roc of 125 mm. The disk is connected 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 is coupled to the disk with a pair of pins. The whole assembly is mounted in a drill-press, which does not need to be exactly perpedicular because of the loose coupling.
To do: drawing of trepan installation
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.
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 hinder cotrol over the mirror and lap.
The telescope can either be mounted on an equatorial or an azimuth mounting. For the equatorial there are two realistic options, a fork or a split-ring type (or a combination). The following sketch gives the approximate dimensions of both types of mount for the telescope. It clear that near horizon observation is much more comfortable with the fork mount. For zenit there is not much difference.
Fork versus split-ring 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.
Rough fork design.
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.
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.
Focuser, side view
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.
Focuser, top view.
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 baffles according to this list, position measured from back of the tube:
According to simulations with PLOP, a six point mirror cell is plenty sufficient to support the mirror. The six points should be placed at about 60% of the mirror radius (actually 59, but the silicone pads are large enough to mask some deviation). The resulting RMS error due to sagging is less than λ/200.
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 screwed to a plate of plywood. The lever material is aluminium U-profile, 20 and 15 mm, which can be found in any hardware store. The support points are made of M4 T-nuts, screwed on the lever beam 75mm apart. The mirror is glued to these poits with silicone caulk.
Mirror cell, top view.
Mirror outline and 60% mirror radius are dashed.
Mirror cell, cross section.
The cross section shows the central hole, which is made of 100mm 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 least contamination of the reflecting surface is best.
The cell should to some extent be adjustable along tube, to compensate for mismeasurements.