Basic Telescope Design
Oldham Optical has produced an Excel Spreadsheet to assist in the basic optical design of telescopes. The spreadsheet may be downloaded from our website using the link supplied below. This version is believed compatible with any version of Excel from 95' onwards.
The spreadsheet has calculations for:-
2) Folded Newtonian
3) Cassegrain ("Classic" calculation with fixed primary mirror & "Alternate" calculation with fixed tube length)
4) Maximum Possible Field of View (restriction caused by focuser)
5) Airy Disk Angle and Size
From a few basic parameters, the spreadsheet calculates the various sizes, diameters, distances and other physical parameters of a telescope.
Note it is for physical measurements only and takes no account of the various aberrations that have a major effect on off-axis viewing. It is aimed at giving the prospective telescope designer, or just someone wanting to learn more about telescopes, a basic understanding of telescope size and resultant mirror sizes and positions.
Please take a few minutes to read the entire page throughout before attempting to use the spreadsheets. There is a discussion about fields of view and telescope tube diameter in the Newtonian section that is also of great interest to Cassegrain designers, and there is an item of interest to all about restrictions that may be caused by the telescope focuser.
In a Newtonian, another parameter is the position of the focal point (FP in our Newtonian diagram), outside the tube of the telescope.
This could be a minimum of around 50mm for a very simple eyepiece, but is more likely to be about 75mm and possibly a figure more than 100mm to mount a camera. The width of the camera must be less than this figure or it will protrude inside the tube of the telescope.
Note for simplicity, the spreadsheet assumes the telescope tube is the same diameter as the primary mirror. In practice the telescope tube inside diameter must always be some figure slightly larger than the mirror and you will need to allow for this in your (FP) figure. See further down this page for details of minimum telescope tube internal diameter.
A very important parameter is the field of view required, and this needs more explanation, because it involves a compromise in the design of the telescope.
A telescope having a large field of view is attractive - 35mm cameras (or even larger) may be attached, as well as simply using the telescope for direct viewing by eye but having a large field does have drawbacks.
Larger fields of view need bigger elliptical flats or secondary mirrors which in turn cause a larger obstruction to incoming light.
The "level of obstruction" is measured as the ratio of the obstruction diameter to the primary mirror diameter and expressed as a percentage, (D2/D1 in our Newtonian diagram). As an example, - a Newtonian with 500mm primary mirror and an elliptical flat of 100mm, (minor axis), would have an obstruction ratio of 20%. The drawback is that Obstruction ratios above say 20-25% begin to cause a progressive deterioration of the contrast ratio.
What this means to a telescope designer is that if the obstruction ratio is likely to be above say 25%, then he should aim for the smallest elliptical flat or secondary mirror that gives the field required.
So how big a field do you need? It depends on what you are going to do with the telescope.
If you are only going to use the telescope for direct viewing by eye, then the starting point is that the pupil of your eye is about 7mm diameter, so you can get away with a figure a bit more than 7mm. One recognised authority states that a 10mm field is quite sufficient while another suggests 14mm.
A 10 - 14mm field with a small Newtonian of 6 - 8" diameter is likely to give you a obstruction figure around 25%, so you may well decide to stick with that size of field if you are thinking about that size of telescope.
With larger telescopes above say 12" diameter, your options start opening out - the obstruction ratio for these same fields will usually be a lot lower - so you may consider going for a larger field with the object of possibly taking pictures through your telescope without too much compromise of direct viewing. The diagonal of a 35mm negative is about 43.2mm, so a field of say 44mm is needed to cover the full area of the negative.
If you do need a big field and cannot avoid an obstruction ratio above 25% - what does a poor contrast ratio actually mean?
It means that while you will be able to take very good views and good pictures of stars, which have a very high contrast ratio to start with, you will not do quite as well with the Moon or planets as these objects have poor contrast to start with.
As the obstruction ratio increases the fine detail on low contrast subjects like the Moon and planets will begin to fade. This fading increases as the obstruction ratio increases. The general view in the astronomical community is that it becomes noticeable about 20-25% (hence the figure of 25% suggested here), but some critical observers say they can notice a difference at 15%.
So if your main intent in producing the telescope is principally to view the Moon or planets and you are not as interested in viewing the stars, and you are definitely not interested in any photography, - then you should probably design for 10 - 14mm field to keep the obstruction ratio as low as possible.
Note Cassegrains with wide fields can have obstruction ratios of 40% or over, and no-one says they are bad telescopes. You just have to live with the obstruction ratio that goes with the field you require.
If you just want to view or to take pictures of stars then don't worry about obstruction ratio at all - an obstruction ratio of over 50% will still give good views and pictures on stars.
Although you really need a field of 44mm for full illumination of a 35mm film negative, there is room for compromise. The object you are aiming at is usually deliberately positioned in the centre of the picture and you are usually not as interested as to what is at the edges. One recognised authority suggests you can still achieve acceptable pictures with the lighting level at the edge down to 70% of the centre.
The light level does not drop off immediately to zero once out of the fully illuminated area. There can still be a considerable distance available before the light level drops to 70%. For an average Newtonian of say F/3 to F/8, a fully illuminated field of 32mm will still be giving 70% or better at 44mm.
If you are especially interested in photography and a more even light level over the entire negative is very important to you, then you should consider increasing the fully illuminated field from 32mm to some value closer to 44mm - 36mm will give about 85%, and 40mm about 95%.
It's really up to you what compromise between size of fully illuminated field and obstruction ratio you decide to go for. Remember that a field of 32-44 mm can be used for both 35mm Camera photography and direct viewing, but a field of 10 - 14mm, while excellent for direct viewing and possessing a low obstruction ratio cannot be used with a 35mm camera.
CCD & Digital Cameras
CCD stands for "Charge Coupled Device" and is the sensor at the heart of a modern digital camera. If you are considering the use of a CCD or Digital Camera, you must find out the diagonal size of the sensor used in the camera and use that as the field of view required.
Note that prior to 2004, most CCD's that an amateur astronomer could afford came from the CCTV surveillance and security camera markets. They were fairly small in size and a field of 14mm for direct viewing would probably have been more than adequate.
Around 2004, Digital SLR Cameras became more affordable and standardised around a CCD sensor of about 23mm x 15mm. This gives a diagonal or field size of about 28mm, but at this size a 2" focuser is just about ideal to give an unrestricted fully illuminated field with one of these SLR cameras.
By about 2007, this group of cameras was packing about 8 Mega Pixels in their sensor area. At this value and with a typical lens of say F/5, the individual pixels are becoming as small or even smaller than the Airy Disc. No doubt the numbers of pixels will continue to increase because that is a big selling point for a camera. Though in practice the Airy Disc size will now provide the main limit on resolution. So a camera with more than say 8M pixels in this sensor size is actually very little advantage. Cameras with larger sensor areas similar to 35mm film can have more pixels before the airy disk becomes dominant. About 20M pixels in this sensor size is equivalent to the Airy Disc for a F/5 system.
So if you are thinking of building a telescope for digital photography then please check and confirm the size of the sensor in your camera first.
A CCD sensor is said to be more critical than film about needing an even lighting level. The rule of thumb that the lighting level at the edge of the film may be down to 70% may not be as appropriate but is still workable. Especially as once the photograph is copied onto a computer, there are plenty of software packages to enhance the pictures.
If you are thinking of buying a camera to try digital astrophotography and you already have a telescope with a 2" focuser, - then perhaps a second hand digital SLR with 6-8 Mega pixels in the 23mm x 15mm format might be a good first investment? It would get 100% illumination over its entire field, and its going to be cheaper than a newer model with more pixels.
Telescope Tube Internal Diameter
Confirm after you have completed preliminary optical design that the internal diameter of your proposed telescope tube itself will not restrict the fully illuminated field of view.
For a Newtonian, a very simple rule is that the internal diameter of the tube needs to be greater than the mirror diameter plus the F.O.V (Field of View) wanted.
For example, a 300mm Mirror giving a field of view of 44mm, needs a telescope tube of 344mm internal diameter.
A more accurate rule takes into account the length of the telescope tube, applies for Newtonian, Folded Newtonian or Cassegrain and is slightly more complicated.
The minimum tube diameter is the primary mirror diameter, plus the field of view divided by the ratio of the focal length to tube length.
For example, A 500mm F8 Cassegrain with a tube length of 1000mm and a field of view of 100mm would be 500 +(100/(4000/1000)) = 525mm internal diameter. In practice this allows a few mm more than this figure for tolerance in positioning the mirror and tube fittings.
You may now need to go back and check the focal point (FP) is sufficiently outside the new tube diameter.
We advise you to try to stick to standard sizes and standard focal ratios for the primary mirror if you can. While we can build to any diameter or focal ratio, please note that if you choose something unusual or exotic we may have to manufacture the special tooling required and that cost would have to be passed on to you in the purchase price! If you think you do want something unusual then please discuss your requirements with us. We may already have the tooling on the shelf or may be able to suggest another approach.
Elliptical flats do not present the same problem of tooling - we can supply virtually any size you might want with no significant price breaks.
Another thing to note when designing your telescope is to provide sufficient adjustment for slight differences in focal length. While a 500mm F/4 is supposed to be exactly 2000mm focal length, in practice there is tolerance on this figure. Achieving a surface accuracy of better than 1/4λ is the prime objective. So please design your telescope to cope with up to ±0.5% error on the focal length. See the manufacture page for details why the allowance is necessary.
If you want a long focal length for high magnification, you might consider a Folded Newtonian. The major advantage of this configuration is that it reduces the length of the telescope tube, which in turn reduces the size of any dome needed to house it.
It also lowers the height of the eyepiece which may prevent you needing to stand on something with the tube at high elevations.
The big disadvantage with the Folding Newtonian is the obstruction ratio. This can easily be over 40%, so they must be designed to keep the optical flat and elliptical flat as small as possible for the field required.
Folded Newtonians have an extra parameter - the distance between the primary mirror and the optical flat (L in our diagrams), but for any one combination of primary mirror, and Focal Point, (FP), there is only one optimum length for this parameter. Please be guided by the spreadsheet using the instructions and guidance therein. We could have made this operation fully automatic, but leaving the optimisation manual takes only a couple of minutes and allows the designer to try other dimensions. We can supply optical flats in any reasonable size.
The Folded Newtonian
If you need a powerful but compact telescope, or an especially wide field, then you will be considering a Cassegrain. For instance, our 500mm F/8.2 Cassegrain set provides a field of about 100mm for "serious" medium format photography. Our 500mm F/12 version is higher magnification, and is OK for 35mm photography.
We have provided two spreadsheets for calculating the telescope sizes. The "classic method" defines the primary mirror focal length and focal ratio as well as the system focal ratio, but an alternate calculation specifies the primary mirror diameter and the telescope tube length instead.
The focal point for a Cassegrain is behind the primary mirror, and the distance behind is called the "vertex back focal length", (d in our diagrams). It is usually between 100 and 350mm.
Note that if you specify or propose a primary mirror faster than say F/2.8 - you might not like the resulting cost! It starts getting very expensive going lower than this figure! Please follow the guidance in the spreadsheet. Obstruction ratio rises as L increases, so designing for a primary around F/2.8 is a good starting rule for an amateur.
Do not change the telescope design dimensions significantly after you have ordered a Cassegrain mirror set.
The curve on the mirrors will be optimised for that particular primary to secondary mirror spacing and vertex back focal length agreed at the time of the order.
While it is subsequently possible to achieve a focus and good viewing on-axis operating the mirror set with a different spacing and vertex back focal length; it will bring in off-axis aberrations which increase as the distances depart from the design figures.
Small movements are still perfectly acceptable such as allowing for different focal length eyepieces, - but all wide field or film applications should aim to operate at close to the mirror separation and vertex back focal length agreed. If in any doubt, please contact us and we can provide more guidance and some sensible tolerance limits.
If you are very ambitious, you could try the following figures in the calculation:-
Primary Mirror Diameter - 2400mm
Focal Ratio - 24
Distance between Primary and Secondary Mirror - 4890mm
Field Required - 300mm
Vertex Back Focal Length - 1500mm
They are of course from the Hubble, or as near as we can get to the real figures from the information readily available in the public domain.
Sorry! Oldham Optical do not keep these sizes of Mirrors in stock!!
It is suggested that you try the Newtonian spreadsheet first - it is the simplest and has less parameters to alter so will give you a better idea of how the calculations work, before moving onto the more complex sheets.
Basically fill in the parameters in red and the rest will be worked out automatically. Alter the values as necessary to optimise your design taking note of any instructions in green on the sheets.
All dimensions are nominally in millimetres but you can use other units, like inches, providing all measurements are in the same units.
The resulting summaries give the Telescope Tube Minimum Length, Optics Physical Sizes, Main Optical Dimensions, Obstruction Ratio and Angular Field of View. The Cassegrain sheet also gives Field Curvature for those of you considering very wide fields.
Using the Spreadsheets
Maximum Possible Field of View
This section is probably not necessary for telescopes designed solely for direct viewing with small fields of less than 14mm.
However, amateur telescope builders who intend to use their telescope for astrophotography with a 35mm or medium format camera require a larger field of view may be very interested. They have already been warned that the telescope tube must be big enough for their field of view, but they may not be conscious that the focuser fitted to their telescope may well impose a restriction on the maximum possible fully illuminated field.
As an example, a 2" focuser (50mm), will often limit the maximum field of view to less than the 44mm field necessary to fully illuminate a 35mm negative. Please refer to the Astrophotography page for more details. This sheet calculates the maximum field of view available from the focuser dimensions.
To use this sheet, measure the dimension at the neck of your focuser (L2), and the distance of the neck from the focal plane (L1).
Enter L1 & L2 and the primary mirror or system figures as per the other sheets and the spreadsheet will calculate the maximum possible fully illuminated field allowed by the focuser.
If this figure is going to be a restriction, then to optimise the situation the user may use this field value in the other sheets to find the size of elliptical flat or secondary mirror that gives this field. Using this size flat or secondary mirror will minimise the obstruction ratio of the completed telescope to give that field.
If you are considering using a Coma Corrector or a Field Flattener, then this sheet will also be useful for you. Enter the diameter of the Field Flattener or Coma Corrector as L2, and the distance from the film as L1, to calculate the approximate field of view. Note it is approximate because the spreadsheet does not correct for any change in the focal length caused by the corrector, which will make a small difference.
Illumination Outside Fully Illuminated Field
Most of the sheets have the facility to show the falloff of illumination outside the fully illuminated field. Enter the field of view required, and the percentage of illumination remaining at that distance will be calculated. Note that an restriction close to the focus, - (like the focuser itself) - causes a quicker falloff than a restriction at a greater distance.
We were asked to add a spreadsheet to calculate the angle and size of the Airy Disc for different sized mirrors. The angle of the Airy Disc is useful for astronomers trying to split double stars that are close together. If the angle in Arc Seconds between two stars is less than the angle in Arc Seconds of the Airy Disc, the telescope will never be able to split the stars. Increasing the diameter of the mirror will reduce the Airy Disc Angle.
The size of the Airy Disc has suddenly become more significant because the pixels used in the CCD sensors of digital cameras are now reducing past the size of the Airy Disc. An astronomer may want to consider matching the telescope to the pixel size of the camera sensor as there are diminishing returns in resolution from using pixel sizes smaller than the Airy Disc. Increasing the diameter of the primary mirror or reducing the focal length are methods of reducing the size of the Airy Disc for instance.
Oldham Optical hope you find this page and the spreadsheet useful and perhaps learn something about the optical design of telescopes (or just have fun playing with the figures!) The spreadsheet is protected from accidental alteration of the formulas by password, but if you consider yourself an expert with Excel and want to see or play with the formulas - the password is "oldham". Note some of the intermediate cell workings have the font colour changed to white so they are normally hidden from view.
If you feel a need to investigate Telescope Optics further, then we recommend one of the best books on the subject; "Telescope Optics", by Harrie Rutten and Martin van Venrooij. It can be bought second hand on the internet for about £35, or your local library can arrange the loan of a copy for a few weeks. For a lot cheaper, - providing you return it on time!
Airy Disc Size
There are only a few parameters that have to be taken into account in designing the main optical parts of a telescope: The two easy ones that apply to all types of telescope are the Primary Mirror Diameter, (D1 in our diagrams), and the Focal Ratio of the system. Both are self explanatory.