The Zip Dob, a Folding Telescope

Mel Bartels
Aperture Fever Newtonian Focal Ratios Over the Years Eyepieces Over the Years Early F3 Telescopes and Reports Widest Fields: Not All Focal Ratios are Created Equally A New Relationship: Maximum Aperture or Field of View Impact of Increased Aperture on Visibility
The Problem with Standard Mirror Blanks The Meniscus Shape to the Rescue Meniscus, the Superman Mirror Meniscus, the Lightweight Mirror Kilns to Slump Meniscus Shapes Does Slumping Reduce Effective Aperture? Is F3 Hard?
Cascading Telescope Changes Thanks to F3 A "Centered" Center of Gravity Origins of the Folding Design Towards Better Telescope Design Tube Integrity Wire Spider Focusing Range
Optimizing the F/3.0 Design Results Conclusion Notable F3 and Faster Scopes


A New Way to Look at Things Diagonal calculator Folding and sliding telescopes Richest Field Telescopes Amateur Telescope Making

Aperture Fever

 Aperture fever is one of those delightful afflictions. It can be triggered at any moment: while enjoying a star party, maybe when reading an observing report, or even perusing a telescope catalog. A particularly pernicious form is stuffing more aperture into a given size and weight. Who doesn’t want a bigger travel scope that still fits into a box and yet isn’t too heavy to cart around?

My 13.2 inch [34cm] f/3.0 is conceived to squeeze as much aperture as possible into a compact package that fits into a back seat of a car, yet can be carried as a single unit in my arms to an observing spot. It unfolds from its travel configuration to its observing configuration in about one minute. At a recent star party, a gentleman came by and asked if it was an eight inch or ten inch scope.  When I explained that it was a 13 inch, he apologized. No apologies needed – that was a compliment!

The first image is from the Oregon Star Party 2010 Telescope Walkabout. The second image is of me observing during the Oregon Star Party, August 2011. It's a 20 second exposure with red light illumination of foreground for a couple of seconds. Image by Craig Stott.


Newtonian Focal Ratios Over the Years

The evolution of Newtonian focal ratios closely mirrors eyepiece technology. In fact, it can be said without exaggeration that the ever increasing sophistication of eyepiece design is an enabling technology. As better corrected eyepieces yielded better views in fast Newtonians, even faster telescopes were built. This gave new opportunities to sell better corrected eyepieces of wider fields of view. Look at the following graph.

Perhaps surprisingly, the consensus fastest focal ratio has steadily decreased uniformly over the past 40 years. Most surprisingly, if the trend continues, we’ll be at f/2.5 by the end of the decade!

Eyepieces Over the Years

Look at the growth of corrections in the eyepieces and their apparent fields of view:
Year       Eyepiece Design
1960       Huygens, Ramsden
1970       Kellner, RKE
1980       Plossl, Erfle, Orthoscopic
1990       Coma corrector + Nagler
2000       Radians
2010       P2 coma corrector + Ethos
2020       ???

Early F3 Telescopes and Reports

F/3 telescopes are beginning to make their appearance, for instance, an f/3.3 telescope project is described in Miller and Wilson’s Making and Enjoying Telescopes, published 1995. The breakthrough for me came when the French group, ADIA, built a 40 inch f/3.0 several years ago (see notable F3 scopes below). The accomplished, expert French telescope maker and observer, Frederic Gea, reported marvelous views and pinpoint images to the edge of the field of view, as long as a coma corrector was in place. I determined that I had to see for myself, and set about designing and building a new f/3.0 telescope. Recently Mike Lockwood, Steve Swayze, Kai Kretzschmar, among others, have made f/3.0; Lockwood ventured down to f/2.6. The reports are uniformly positive and exciting.

Widest Fields: Not All Focal Ratios are Created Equally and Why F3 is the Ultimate Focal Ratio for Richest Field Observing

The old rule of thumb that telescopes with a range of focal ratios can achieve Richest Field performance as long as a suitably matched eyepiece is used is no longer valid. Eyepieces of extreme apparent field of view are now available, but only in shorter focal lengths.

Here's a table showing how eyepiece apparent field of view and focal length impact the RFT experience for varying focal ratios.

Table generated for aperture = 13 inches, exit pupil = 6mm.
Telescope focal ratios optimized for several popular eyepieces.

Telescope Focal Ratio Eyepiece Coma corrector X Eyepiece Focal Length mm Apparent FOV deg Telescope Focal Length inches Eyepiece Field Stop mm Actual FOV from Field Stop deg Actual FOV from Field Stop with Coma Corrector X deg FOV area deg^2 Magnification
2.5
 Ethos
 1.15
 17
 100
 32
 29.6
 2.1
 1.8
 2.5
 55
3.0 Ethos 1.15 21 100 40 36.2 2.1 1.8 2.5 55
3.8 Nagler 1.15 26 82.0 49 35.0 1.6 1.4 1.5 55
5.2 Nagler 1 31 82.0 67 42.0 1.4 1.4 1.6 55
6.3 Orion Q70 1 38 70.0 82 44.0 1.2 1.2 1.1 55

Notes on derivation:
Most columns are published values from the manufacturer.
The "Coma corrector X" is the magnification factor built into the coma corrector.
The exit pupil is the eyepiece's focal length divided by the focal ratio, further divided by the coma corrector magnification factor.
The "Actual FOV from Field Stop deg" is given by the formula: field stop in inches / focal length in inches * 57.3

There are three keys that work in concert:
1. Shorter eyepieces allow faster scopes to maintain 6mm exit pupil.
2. Wider apparent fields of eyepieces allow shorter eyepieces to achieve the same field stop as longer focal length eyepieces.
3. Since the field stops are essentially the same, the faster focal ratio results in a shorter telescope focal length which results in a larger field.

Here are the widest fields possible (each at 6mm exit pupil) for the above focal ratios through 13 inches aperture observing M31 (image from Stellarium):
F/2.5 or F/3 - 2.5 square deg field
100 deg Ethos
 F/3.8 or F/5.2 - 1.5 square deg field
82 deg Nagler


 F/6.3 - 1.1 square deg field
70 deg wide field

Another interesting way to look at it is to calculate the maximum aperture possible for different focal ratios given a field of view. The focal ratios are optimized for widest angle eyepieces.
field of view = 1.8 deg, exit pupil = 6mm

Telescope Focal Ratio Eyepiece Eyepiece Focal Length mm Apparent FOV deg Eyepiece Field Stop mm Coma corrector X Mirror Diameter
2.5 Ethos 17 100.0 29.6 1.15 13.1
3.0 Ethos 21 100.0 36.2 1.15 13.0
3.8 Nagler 26 82.0 35.0 1.15 10.1
5.2 Nagler 31 82.0 42.0 1 10.2
6.3 Orion Q70 38 70.0 44.0 1 8.7

Going down to f/3.0 or f/2.5 means jumping up in aperture from 10 inches to 13 inches. In other words, what we could see previously with 8 inch scopes and wide angle Erfle eyepieces in the 1960's to 1990's and with 10 inch scopes with Naglers in the 1990's and 2000's is now seen with 13 inches aperture. This increase in aperture increases the limiting magnitude by a whole number.

Formula is: mirror diameter = eyepiece field stop * exit pupil * 57.3 / (field of view * eyepiece focal length * 25.4) (from: field of view = eyepiece field stop / telescope focal length; focal length = focal ratio * mirror diameter; eyepiece focal length / exit pupil = focal ratio)

For more on Richest Field Telescopes, see my web page http://www.bbastrodesigns.com/rft.html

A New Relationship: Maximum Aperture or Field of View Based on Varying Focal Ratio While Holding Exit Pupil Constant
 

Impact of Increased Aperture on Visibility

Recalculating Blackwell's visual detection data as presented in Clark's Visual Astronomy shows that the increased aperture for the same field of view results in significantly brighter views. The first chart is for the difficult small Horsehead Nebula and the second chart is for the somewhat difficult very large California Nebula. They are arranged so that matching exit pupils yield the same field of view (which means that magnification is greater for the larger aperture). The larger aperture for the same field of view that F/3 with the 21mm Ethos yields results in a consistent 0.15 log contrast gain. That’s an increase in apparent brightness roughly equivalent to the ratio of the apertures.



The Problem with Standard Mirror Blanks

However, for large thin mirrors to be made at f/3, something has to be done about the shrinking center thickness. A 40 inch diameter mirror at f/3 has a sagitta or central depth approaching an inch. That leaves precious little thickness at the center of the mirror. I determined to try a meniscus mirror, where the entire blank is curved to the appropriate shape by softening in a kiln, resulting in a mirror of constant thickness.

The Meniscus Shape to the Rescue

Unexpectedly, meniscus mirrors are quite strong. The nine point support I was envisioning wasn’t needed; instead a simple three point back support and two point edge support supports the mirror without observable distortion. The analogy goes like this: pick up a piece of paper and wave it. See how it bends over? Now cut a pie section out of the paper and tape the remaining paper into a cone shape. Waving it around doesn’t bend it at all: the cone is a stronger shape.

Meniscus, the Superman Mirror

A full thickness 12 inch or a thinner 13 inch mirror require a 9 pt support.  Deformation is clearly seen in the star test if a 3 pt support is used.  And high power images are heavily compromised in very thin 12 inch mirrors made from flat glass.  Not a trace of deformation can be seen at highest powers in the star test with the 13 inch meniscus mirror on a 3 pt support.  The meniscus mirror has an equivalent thickness of a mirror made from a flat piece of glass 1.4 inch thick where the concave curve is not only ground into the face but also a convex curve is ground into the back side of the mirror.  The weight reduction is key: less weight means less deflection.  Taking into account the weight reduction and the equivalent thickness means that this meniscus mirror is twice as stiff as a full thickness blank. For example, one cannot use PLOP to calculate deflection using a thickness equal to the sagitta plus edge thickness because the weight reduction is missing as a factor: PLOP's deflection estimate is too severe (remember that PLOP is designed for flat backed mirrors; for more go to David Lewis' PLOP) . A simpler support is fine; how much simpler needs to be determined empircally.


Meniscus, the Lightweight Mirror

Meniscus mirrors are lightweight because the curved glass is relatively thin. Consequently the glass cools quickly. As long as a light breeze is blowing, I don’t need a fan while observing. Taking the scope outside requires about a 15 minute cool down period with the fan running, after which the star images are very stable. Since I use a fan, I can substitute inexpensive plate glass. Plate glass further cools 25% faster than Pyrex.  So the plate glass reaches equilibrium a few minutes quicker than Pyrex.  Plate glass runs 20x cheaper than Pyrex. The downside is that when making your own mirrors, plate glass is a a pain during figuring because care must be taken to ensure that the glass is in equilibrium with its ambient surroundings. It's necessary to take active steps to equilibriate the mirror.  I use fans blowing air in an insulated room on the mirror during the indoor star test. Thanks to active mirror cooling, I can do a half dozen figuring sessions each evening.

Kilns to Slump Meniscus Shapes

In a sense, computer controlled kilns promise to be an enabling technology, allowing thin mirrors to be slumped to very large diameters, no longer being limited to sheet Pyrex’s width of 40 inches or so. Instead of grinding a curve into the mirror’s face, the mirror is placed upside over a convex mold and heated until the glass softens and folds down over the mold. The kiln is then directed by computer control through the annealing cycle, cooling the glass over a period of several days. The cost of a kiln plus plate glass is competitive with a Pyrex sheet glass blank, with the bonus that the kiln can be used again.

Does Slumping Reduce Effective Aperture?

No, not at F/3. See my derivation of a formula to calculate at Slumping Mirror Reduces Effective Aperture.html

Is F3 Hard?

Part of my interest in the 13 inch f/3 was to see how difficult grinding an f/3 mirror truly is. Well, I can report that it is fundamentally no different than grinding any other mirror, except that more parabolization is pushed into a smaller aperture. I used standard mirror making techniques with excellent results. I gauge the difficulty of the 13 inch f/3 to be roughly equal to the difficulty of grinding a 20 inch f/5. Curiously, the 13 inch f/3 has about the same degree of parabolization as the 20 inch f/5. So if you can make a somewhat larger mirror, then you can confident in attempting a somewhat smaller f/3 mirror.

Cascading Telescope Changes Thanks to F3

I quickly realized that such a short telescope called for a new telescope mounting design: the incredibly stubby truss tubes as commonly built begged to be replaced. It’s important when considering the patterns of telescope design to allow the design to grow organically. If one component varies from tradition, then it is likely that surrounding components will also.

A "Centered" Center of Gravity

An f/3 with a lightweight mirror places the center of gravity farther up the tube than what is customary. This results in benefits such as balance insensitivity, small footprint, and a smaller eyepiece swing from horizon to vertical.

Balance insensitivity means the telescope can move smoothly in altitude despite today’s heavy eyepieces: no counter-weighting need apply here. Small footprint means that the scope rotates in azimuth within the smallest possible circle. This has particular impact on observatories, which can be horrendously large with Dobs that balance close to the rear.  For instance, a 16 inch Dob might need a roll-off roof observatory 12 feet x 12 feet. By moving the center of gravity to the mid-point of the optical tube assembly, the building size can be greatly reduced. Roll off roof observatories are so much easier to build when the roof size is small. Minimizing eyepiece swing means that I can observe with the 13 inch sitting in a chair regardless of whether the scope is pointed at the horizon or is pointed vertical.

Origins of the Folding Design

It’s my observation that assembly time and difficulty has a large impact on how often the scope is used. It’s not so much how fast a scope could be assembled. Instead, it’s more of, “Do I have the energy tonight to drive somewhere and set it up?” The key is to avoid assembling the scope at all.

I studied a number of folding arrangements, which basically squeeze air out of the telescope as it folds up. Folding is much quicker and most importantly, easier than assembling. In the end I chose a three-fold arrangement that squeezes the telescope into a small cube, easily picked up and carried by hand (total weight is about 25 pounds). From the bottom up, the folds are 30 degrees, 42 degrees, and 108 degrees. Note that the folds add up to 180 degrees, which results in the upper end folded down against the primary mirror, about as compact as possible.

Google Sketchup model is available from the online repository at http://sketchup.google.com/3dwarehouse/details?mid=447e8896bc0fb328b47a4848f4241ae0

More on folding and sliding telescopes can be found on my web page, http://www.bbastrodesigns.com/FoldingScopes/FoldingTelescopes.html



Unfolding the telescope at the Oregon Star Party Telescope Walkabout, 2010

Towards Better Telescope Design: Multipurpose Parts

I always look for ways to create telescope components that serve multiple purposes. With the center of gravity in the middle calling for sweeping altitude bearings, it occurred to me that the reinforced altitude bearings can take the place of most of the truss tubes, and provide folding pivots to boot. This works quite nicely in practice – the telescope is rock solid with no hint of any vibration.

Tube Integrity

I use two tests to determine the design integrity of the optical tube assembly. First is the optical alignment test: can alignment be maintained exactly as the scope swings between horizontal and vertical? Finally, can I grab the upper end and twist the mirror end out of the rocker? This design passes both tests with flying colors.

Wire Spider

You might note the wire spider. I've been using wire spiders for many years. They work wonderfully in that there's no diffraction except short spikes around the brightest stars and the diagonal stays rock solid and unmoved, allowing perfect optical alignment from horizon to zenith. Curiously and counter intuitively, I discovered that the tension in the wires is irrelevant to supporting the diagonal properly. Mathematical analysis reveals that tension drops from the picture. Further, wire spiders have less springiness than tradional spiders, particularly when rotating the diagonal holder back and forth. On very large scopes, wind blowing through the upper end can create a never-ending vibration of the diagonal, visible as astigmatism at high power. Properly designed, both traditional and wire spiders need not suffer this ailment. The key is to break apart the spider at the hub into two separate sections like '>-<', separated by a hub that holds the diagonal holder. Consequently, stability and resistance to flexure and twist is determined by the geometry of the wires. Hence my wires cross in broad 'X's with the two 'V's on either side of the hub. The wire spider is a single piece of wire, wired into position by supporting the hub on a removable jig. You can see the drilled holes that hold the jig in position at the top of the upper end. Once the wire is strung into position, I tighten the eye bolts until there is no slop in the wire then remove the jig.
 

Focusing Range

Focusing range is a little discussed topic amongst amateurs. However, it is a primary factor determining how sharp is the image. Focusing range is the distance that the focuser can be moved on either side of the theoretically perfect focus yet not change the image sharpness.
The formula for focus range where the optical path difference is limited to quarter wave is: focus range = wavelength of light / index of refraction times the sin squared of the angle of the edge ray (focus range = λ /N' sin^2 U'). This simplies to 0.0001 * focal ratio squared. See Conrady's Applied Optics and Optical Design, volume 1, pages 136-7.
While a F5 scope has a focus range of 0.002, a F3 scope has a much tighter focus range of 0.001.
Best procedure is to obtain the ultra finest focuser, then carefully focus back and forth, stopping in the middle. If disatisfied, repeat. The difference at F3 is between a so-so Saturn and a great Saturn.

Optimizing the F/3.0 Design

Here are (unexpected) lessons learned from designing and building a very short focal ratio telescope. Results

Views through the telescope are wonderful. Incredibly wide fields at low power with pinpoint stars to the edge give way to high power views with excellent resolution and contrast. Dark nebulae have never looked better, showcase objects are wonderfully framed and globular clusters are resolved into tiny pinpoints of starlight at magnification. Here are early observations, images representing the field of view through the 13 inch from Microsoft's WWT. Keep in mind that these fields of view are with a 13 inch telescope!

 M31: spectacular aggregate view: entire galaxy along with companions fit into the field of view; striking multiple dust lanes; details in galaxy arms at the extensions and in the companions
Horsehead, Flame nebulae: in one view the Horsehead is faintly visible (no filter) with good detail in the Flame nebula; NGC 2023 and IC 435 are bright; all this despite a very bright Zeta Orionis
Pleiades: all of the extremely bright stars fit into a single view; extensive nebulosity everywhere, particularly detailed next to Alcyone with extensive sweeping from Merope to edge of view, along with some of the general nebulosity that surrounds the Pleiades M42 region: entire loop of M42 seen with lots of detail with some color; the green nebulosity embedding the Trapezium is quite striking, field of view extends from the open cluster NGC 1981 through NGC 1973/5/7 up past NGC 1980.
Markarian's Chain, the Virgo Cluster, M84-M86 area. The image is a good match to the view through the eyepiece (though the stars are missing)


Other interesting observations:
See my online visual detection calculator.

Consequently, I have changed how I describe my telescope: old style: 13” telescope at 55x; new style: 1.8 degree actual field, 100 degree apparent field, 6mm exit pupil, use the visual detection calculator for limiting star magnitude and to ascertain detection for extended objects. See my article, A New Way to Look at Things.


Observing at Oregon Star Party, 2010 (note the reflection of stars in the mirror)

For more on f/3 observing experiences, check out Frederic Gae et al large f/3 telescopes along with Lockwood's observations. Run, don’t walk to your nearest f/3 telescope, clear your mind of preconceptions and find out for yourself!

Conclusion

Design Aspect Advantages Disadvantages
F3 Wider field at lowest magnification (Richest Field) compared to f/4 and slower: excels at very low contrast difficult objects, excellent at high power - pinpoint images. Coma corrector required (with TeleVue P2 coma corrector, the coma is equivalent to that of an F/12, so better than standard Dob)

"No ladder" eyepiece height Primary mirror takes extra skill to produce

Telescope weighs less Not every eyepiece may perform well

Shorter stiffer tube assembly holds optical alignment (collimation) better Purchase additional eyepieces

Diagonal size same as f/4.5 scopes due to flatter field illumination profile Optical alignment (collimation) tolerance is 0.2 mm

Ultimate star hopping telescope with its extra wide field of view
 Focusing is very touchy at small exit pupils/high magnifications: need a precision focuser that resolves to better than 1/1000 inch. Focusing is probably the greatest practical disadvantage in the field.
Shorter tube with Center of Gravity mid-range Much smaller observatory footprint

Less eyepiece swing from horizontal to vertical

No need to counterweight heavy eyepieces
Meniscus mirror shape Stiffer glass because of meniscus shape and less weight means simpler mirror cell

Thinner meniscus shape equilibrates quicker
Folding design
 Compact travel profile
 Difficult to design folds so that there are no collisions

Setup time in seconds Precision construction required

Lighter weight
Wire spider Less diffraction than standard spiders Need jig for initial assembly

Inexpensive: a few dollars for the wire

Stronger than standard spiders because of the wider geometry

Notable F3 and Faster Scopes

Mike Lockwood's 14 inch f/2.5

 Steve Swayze's 8 inch f/3.0
 Mark Christensen's 6 inch f/2.7
AIDA 40 inch f/3.0
 Frederic Gea's 40inch f/3.0

Mark Christensen sent this image of the Small Sagittarius Star Cloud taken with his 6 inch f/2.7. It illustrates the stunning tack sharp field possible with super fast scopes.


last updated Feb 4, 2011