How to make a 65 cm lens with a 20 cm hole in it for a Hamiltonian telescope?

How to make a 65 cm lens with a 20 cm hole in it for a Hamiltonian telescope?

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This answer to What (the heck) is a Hamiltonian telescope? Is this one? confirms that the telescope in the question linked there is indeed as described and that the first lens is a full 65 cm aperture lens, the second element is a full 65 cm negative meniscus back-silvered, and some corrector lenses are embedded= within a hole in the large primary lens.

Optically I can imagine that it might be possible to let the light transmit again through the primary and still compensate, and mechanically that seems more attractive than polishing a double-sided transmission lens with a hole through the center.

But apparently that's what's been done.

Question: How to make a 65 cm lens with a 20 cm hole in it for a Hamiltonian telescope? I'm thinking about issues including the following:

  • Is the blank cast with a hole already, or is it drilled?
  • If drilled, is that before the first side is polished, before one side and after the other, or after both sides?
  • After drilling does one need to anneal the glass again?

Glass can experience strain-induced birefringence among other things, so I am really interested in finding out how optical surface figures are applied to both sides of this lens with a big hole in it without causing optical problems within the bulk of the glass.

Image from this answer to What exactly is a Hamiltonian telescope? Is this one?

Drill or core the blank (anneal if needed… most likely not if annealed to begin with) use pitch to glue a plug of the same material in the hole grind, polish and figure as normal then remove the plug.

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  • 2 lenses with a focal length of 35 mm, each salvaged from a single-use disposable camera.
    Make sure the flash has been discharged and remove the battery before you open the camera. Use insulated tools (like screwdriver and pliers). The students might need help extracting the lenses from of the cameras.
  • 2 metal washers with an external diameter of 2 cm and an inner hole of approximately 1 cm diameter
  • 1 black cardboard or rubber disc with an external diameter slightly smaller than the washers (approximately 1.2 to 1.5 cm) and a small hole of approximately 2-3 mm diameter. This is the diaphragm: it ensures that the centre of the lens is used rather than the edges, as these can distort the image.
  • 4 plastic tubes, to form the microscope body and support, with the following dimensions:
    • Microscope body tube: 16.5 cm length of Ø18 (1.8 cm external diameter, internal diameter 1.6 cm)
    • Main support tube: approximately 17 cm length of Ø23 (2.3 cm external diameter, internal diameter 2 cm)
    • Two smaller support tubes: each an approximately 10 cm length of Ø16 (1.6 cm external diameter)

    An OTA’S Dust/Lens Cap HOLE – What does the telescope designer expect us to do with it?

    I have a 12” Meade SCT – No HOLE a Celestron NexStar 114mm GT Newtonian – w/Hole and a Sky-Watcher Pro ED 120 refractor – w/Hole. Those holes are about 2” in diameter.

    Based on my search for “Dust/Lens Cap hole” in in all CN forums, CN members offered the following:
    • Take advantage of the smaller opening on the lens cap for higher focal ratio for observing Venus.
    • Use the included centercap to watch the moon and sometimes the brightest planets.
    • If you check out the Moon, and it looks to bright, that is what the small hole in the cover is for. Take the small cover off the hole, and place the large cover on the telescope. It will cut down the brightness of the moon.
    • Removing the center cap of my front dust cover reduced chromatic aberration (CA,) but also dimmed the view of the Moon or planets, but with the reduced aperture there wasn't the high magnification detail I was wanting to get.

    And what did my owners manuals say? NOTHING – Two of the three OTAs manuals make absolutely no mention of the Dust/Lens cap. The Celestron has one mention of a lens cap (Remove the lens cap before your start your semi-automatic alignment.) And,of course, both Celestron and Sky-watcher manuals never mention the small hole.

    I can offer that this makes sense for the refactor – dimming the light and reducing visible CA, but on the Newtonian the secondary mirror and supports are visible in that hole and thus I would expect them to further reduce the incoming light to a “why even try?” level.

    So on 4/19/20 I emailed my question to Sky-Watcher Support: “What is the purpose of the

    2” hole in the lens/dust cap of my 120 ED?”
    Their next day reply: “Hello, The original use for this was to remove the 2" cap and make is easy to slide your fingers in to remove the cap. We have had people add Solar Film to the inside of the cap to use this as a solar filter as well or with no film to use it as a very small aperture mask.”

    Well, I like the “make it easy to slide your fingers in to remove the cap!” design intent. Though the ridge on the Celestron lens cap and the tabs on the S-W cap make it really easy to pull them off the OTAs. But the metal cover on my 12” SCT is really tight and I put a handle on the cover to assist with it removal – finger hole(s) would have been more appreciated on the SCT.

    Also I had previously determined that my Orion Glass Solar filter for my Nikon 10X50 binoculars will completely cover these holes (albeit with some means added to prevent it falling off!) No need to buy a full size aperture filter (at least not until I test it and determine if the sun looks just fine in that 2+” aperature.)

    Well, to conclude my essay, I really want to believe the OTA designer DID intend to provide a finger hole to aid in the Dust/Lens cap removal, but I’m not sure about it, Any one wish to help me understand the need for a Dust/Lens cap hole?

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    Horn Antenna for the 21cm Neutral-Hydrogen Line

    Abstract : Van de Hulst predicted the existence of the radio emission of neutral hydrogen at 21 cm and in 1951 Ewen and Purcell succeeded in detecting this emission with the horn antenna shown above. In this post we want to describe the design and the construction of a low cost horn antenna with the aim to detect and measure this emission coming from our milky way.


    The hydrogen 21-centimeter line is the electromagnetic radiation spectral line that is created by a change in the energy state of neutral hydrogen atoms. This electromagnetic radiation is at the precise frequency of 1420.4 Hz , which is equivalent to the vacuum wavelength of 21.1 cm in free space. This wavelength falls within the microwave region of the electromagnetic spectrum, and it is observed frequently in radio astronomy, since those radio waves can penetrate the large clouds of interstellar cosmic dust that are opaque to visible light. The study of this radio emission can help us to evaluate the presence of hydrogen in interstellar clouds and to understand the structure of our milky way.


    Neutral hydrogen radiates at 1420.4 MHz, and studies have shown that red and blue shifts of up to 2 MHz may be observed. Therefore our goal is to design a horn antenna to receive signals in the range of 1420.4 ± 2 MHz. The antenna is just a length of copper wire cut to l =5.25 cm, about a quarter of the wavelength λ =21.1 cm corresponding to 1420.4 MHz. With these numbers in mind, we have to design a waveguide and horn to efficiently direct desired frequencies toward the antenna (the copper wire).
    An open waveguide is not an effective energy radiator (and similarly an effective receiver) due to the impedance mismatch at the mouth. Things improve by widening the walls of the trumpet-shaped guide, thus coupling the impedance between the waveguide and the intrinsic one of free space.


    The first component of the system is the waveguide. As we know waveguide is a hollow metal pipe used to carry radio waves. The electromagnetic waves in a (metal-pipe) waveguide may be imagined as travelling down the guide in a zig-zag path, being repeatedly reflected between opposite walls of the guide. For the particular case of rectangular waveguide, it is possible to base an exact analysis on this view and derive the propagation modes and cutoff frequency.
    The drawings below shows a rectangular waveguide with the electrical and magnetic field of the main propagation mode (TE10). The direction of the antenna determines the polarization direction of the wave that is picked up, the electrical field is polarized vertically, parallel to the antenna, the intensity is zero on the surface of the metal waveguide and the maximum intensity is reached inside the waveguide in a position depending on the wavelength of the radiation. The pattern of the propagation mode is also characterized by a waveguide wavelength λG .

    The cutoff wavelength – the maximum wavelength that can propagate in the waveguide in the direction of the side “a” – is λ = 2a. This is equivalent to saying the waveguide acts as a high pass filter with cutoff frequency of ν = c/λ. The following drawing can help to understand this behavior of the waveguide. In order to minimize dispersion in velocity down the waveguide in the range of interest, a waveguide should be used for frequencies greater than 1.25*ν . Additionally, in order to suppress higher order modes they should be used for frequencies less than 1.9*ν.

    Now we have all the data to design our waveguide. Fortunately we can use for this purpose a normal 5lt can (for example a can for oil). The measures of this rectangular container are the following : a = 146 mm, b = 117 mm. We check, referring to the following drawing, that all conditions are verified and we proceed to the calculations for positioning the antenna.

    Radio Emission Data
    f = 1420,4 MHz – Neutral Hydrogen Emission Frequency
    Δf = 2 MHz
    f = 1420,4 ± 2 MHz
    λ = 21,1 cm – Wavelength
    l = λ/4 = 5,25 cm – Quarter Wave Antenna

    Waveguide Dimensions
    a = 146 mm
    b = 117 mm

    Waveguide Cutoff Frequency
    λc = 2*a = 29,2 cm
    fc = c / λc = 1027,4 MHz
    f > 1,25*fc = 1283,7 MHz – OK
    f < 1,9*fc = 1951,3 MHz – OK

    Antenna Positioning
    λG = 30,57 cm – Waveguide Wavelength
    d = λG/4 = 7,64 cm – Quarter Wave
    l = λG*3/4 = 22,92 cm – Waveguide Lenght

    A horn antenna or microwave horn is an antenna that consists of a flaring metal waveguide shaped like a horn to direct radio waves in a beam. Horns are widely used as antennas at UHF and microwave frequencies, above 300 MHz. An advantage of horn antennas is that since they have no resonant elements, they can operate over a wide range of frequencies, a wide bandwidth. Our antenna is a “Pyramidal horn” : a horn antenna with the horn in the shape of a four-sided pyramid, with a rectangular cross section.
    By adopting the measures of similar projects, where a compromise was made between gain and size, we chose the following measures. In addition, our horn antenna will have to connect with the rectangular waveguide described above.

    A = 750 mm
    B = 600 mm
    RE = 700 mm
    RH = 700 mm

    a = 146 mm
    b = 117 mm

    With an online application we have determined the antenna gain that turns out to be Gain = 18.16 dB ≈ 18 dB

    The beam width can be calculated from the geometry of the antenna. We limit ourselves to reporting the values ​​we obtained from antennas built with similar geometries.

    ● Gain : 18 dB
    ● Half Power Beam Width : 20° H-plane, 24° E-plane

    These data are however in accordance with the general theory that assigns an angular resolution to an antenna given by the relation:

    Δθ ≅ λ/D = 21/75 = 0.28 rad = 16°

    The horn antenna is a rather directive antenna, however the dimensions of our antenna are limited and this makes the angle covered rather large. The spatial resolution of our antenna will therefore be about 16° and will not allow us to resolve structures with a spacing of less than 16°. The extension of the radio sources obtained with the antenna will be the convolution of the real extension with the radiation pattern of the antenna : in practice this means an enlargement of the detected dimensions. We report below as an example the radiation pattern of a similar pyramidal horn antenna.


    For the construction of our antenna we used a 5lt can as a basis for the waveguide and then we had the 1.2 mm thick raw aluminum sheet cut and bent by a workshop for the construction of the horn.


    The upper part was cut from the can, then we cut the edges to leave an integral part of the calculated length of 23 cm. We left the side flaps that will be used for fixing on the aluminum sheet. In the calculated position, a hole was made for a type N panel connector, on which a piece of a thin brass tube was welded which constitutes the actual antenna. An N-SMA adapter is connected to the panel connector, fixed with four screws. The images below show the waveguide.

    The horn was assembled from sheet metal cut and folded according to the following drawing.

    The waveguide was then fixed to the horn using the edges of the can itself fixed with screws and aluminum adhesive tape. The aluminum adhesive tape was also used to cover the joints between the sheets and with the can so that the inside of the horn is as flat and homogeneous as possible. To increase the rigidity of the structure it may be useful to glue aluminum profiles, for example square shaped, on the four major sides of the horn: in this way the sheets are prevented from deforming due to their own weight.

    Antenna Stand

    For the mechanical support of our horn antenna, we used a simple wooden bench on which we hinged a wooden base on which the waveguide and the pyramidal horn rest. The inclination is adjusted simply, by raising or lowering the antenna and inserting an adequate support under the base.


    The Intenet contains numerous examples of antennas and receivers for the emission of neutral hydrogen at 21 cm. At the following link there is the description of an excellent similar project : probe-the-galaxy-on-a-shoestring-with-this-diy-hydrogen-line-telescope, and this is the related documentation : Hydrogen Line Project Documentation.
    A site very rich in information (I would say indispensable ..) is the following DSPIRA

    Next Step

    This project continues with the construction of the receiver : Low-Noise SDR-Based Receiver for the 21cm Neutral-Hydrogen Line

    If you liked this post you can share it on the “social” Facebook, Twitter or LinkedIn with the buttons below. This way you can help us! Thank you !


    If you like this site and if you want to contribute to the development of the activities you can make a donation, thank you !

    Two lens system – Image distance and magnification

    To determine the image distance, the lens equation can be used.

    Apply lens equation to first lens

    di1 = 12 cm First image located 12 cm behind the first lens

    Image generated from first lens going to be object for the second lens

    Lets apply lens equation to second lens

    Final image located at 32.31 cm behind second lens.

    Lens magnification can be find using

    First lens has magnification of – 0.2
    Image magnification in terms of object and image height can be write

    First lens has magnification of – 0.2, the image is inverted and is 0.2 times of original height.

    Lets apply image magnification equation to second lens

    Second lens has magnification of – 1.15
    Image magnification in terms of object/image height is

    Image generated from first lens going to be object for the second lens

    From this equation we see that total magnification is the product of m1 and m2.

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    Glue weight can be a major weight factor, but it doesn't have to be. You can easily use 0.1-0.5 grams of glue (or less) on a 10-gram boomilever. The two most common, and probably best suited glues for building would be CA glue and Gorilla Glue.

    CA glue is super glue. There are many different brands such as Krazy-Glue, Loctite Super Glues, Zap-a-Gap, along with many many others. The best CA glues are probably industrial CA glues, such as products from Hobby Lobby or BSI industries. CA glue is divided into two main categories.

    The first is medium viscosity (thickness) CA. This is an all purpose glue. It dries in about 10-15 seconds and reaches maximum strength in an hour or less. It is ALMOST ALWAYS found in a purple label.

    The second is Blue CA. This is very thin viscosity CA glue. It is thinner than water, and soaks into balsa very quickly. It is better for balsa than bass. This dries in 2-5 seconds or quicker. This is VERY strong, but is hard to use. A single drop is good for very strong bonds.

    The other widely popular glue is Gorilla Glue. It is VERY strong, and expands LIKE CRAZY. One drop will expand into about 2/3 of a centimeter. Be careful when using this. This is best for the distal end, and the base. If using this for other bonds, and you want the gorilla glue to dry or set faster, a simple solution is to simply drop a few drops of blue CA onto the Gorilla Glue. It will cause the glue to set very fast. Use with caution as it may even lower strength by a little.

    Another popular glue is epoxy. Epoxy is made by using two different compounds and mixing them together creating a very strong bond. It is very heavy. Some other glues used are Weldabond, Titebond III, and Ambroid. Ambroid is in the same class as CA glue.

    The two varieties most heavily favored are basswood and balsa wood, both which can likely be purchased at a hobby store. You should proudly march into your favorite hobby store that stocks balsa and basswood armed with a hundredth gram precision scale and weight all the size sticks you desire.

    Lightest balsa sticks by the yard: 1/16 * 1/16 sticks are around .3 grams. 1/8 * 1/8 sticks are around .7 to .8 grams. 1/4 * 1/4 sticks are around 3 grams

    Please EXPERIMENT with using different weights for compression. The most important aspect of wood is not size, but density. The more dense (i.e the more relatively heavy compared to other wood of the same size), the stronger the members are. Experiment with different densities to find the right density for your boom.

    I do not have the lightest basswood stats on hand. Using the lightest 1/16 * 1/16 basswood sticks for the tension sticks may result in premature failure. Please experiment.

    It is often a good idea to buy sheets of balsa/bass and cut strips/sticks to a size using a balsa stripper instead of buying sticks of sizes because it gives greater flexibility with sizes, its also generally cheaper than buying sticks and sheets are more consistent in terms of density than sticks unless the sticks are carefully sorted.

    Basically, everything should be made of balsa except for the tension sticks which should be basswood. This shouldn't imply that this is the only way to do things. We don't intend to stifle creativity. However, the main idea to remember is that balsa wood is better at compression then tension.


    converging lens: a convex lens in which light rays that enter it parallel to its axis converge at a single point on the opposite side

    diverging lens: a concave lens in which light rays that enter it parallel to its axis bend away (diverge) from its axis

    focal point: for a converging lens or mirror, the point at which converging light rays cross for a diverging lens or mirror, the point from which diverging light rays appear to originate

    focal length: distance from the center of a lens or curved mirror to its focal point

    magnification: ratio of image height to object height

    power: inverse of focal length

    real image: image that can be projected

    virtual image: image that cannot be projected

    Selected Solutions to Problems & Exercises

    6. (a) 3.43 m (b) 0.800 by 1.20 m

    7. (a) −1.35 m (on the object side of the lens) (b) +10.0 (c) 5.00 cm

    12. (a) +7.50 cm (b) 13.3 D (c) Much greater

    14. (a) +6.67 (b) +20.0 (c) The magnification increases without limit (to infinity) as the object distance increases to the limit of the focal distance.