Fascinating article about how the origins of the telescope are not quite so clear after all. (Pun intended!)

(EDIT: Roger wanted me to emphasize that he doesn’t think he has the final word on this history. Later, I’m going to try to make his graphics more visible, too. Looks like WordPress has changed how you add photos again!)

More on the Origins of the “Telescope.” LONG!
From: Roger Ceragioli
Date: Mon, 25 Jul 2022 21:30:48 EDT

Greetings again.  The Galilean telescope is a peculiar beast optically.  Part of the reason it was the first form of telescope was that it gave an erect image, using only two lenses.  But because there is a particular third optical element (the human eye) involved, we need to consider the total sytem (convex objective, concave eyepiece, human eye) to understand what may have happened in 1608 as well as in the decades prior.

And so in this email, I want to review some aspects of this “bionic” system.  Part of what has, in my opinion, afflicted the debate over the origins of the telescope is lack of attention to the nature of this total bionic system.  

Now, it is, of course, hardly conceivable that if the first eyeglasses came into use around 1295 AD, using convex lenses to treat long-sightedness (presbyopia), and concave lenses came into use around 1450 to treat myopia, for 150 years no one bothered to experiment with placing different types of lenses together to find out what would happen.  As I mentioned previously, we read in Fracastoro’s book, Homocentrica (a book on planetary theory) about the marvelous effects of putting one convex lens on top of another.  Apparently this means directly on top of one another, and not at a distance.  Still it shows that people were putting lenses together in the 16th c.

Giovanni Battista della Porta in 1589 mentions combining a convex with a concave (ie. the essence of an early telescope), and that if you know how to do it right, both nearsighted and farsighted people can see clearly.  So I would propose, not that he “invented” the telescope, but that he took a step forward and invented a kind of variable focus low power two-lens eyeglass system.  It could have been constructed as follows:

Pay no attention to the title of the slide, when it says “Galilean-Type Refractor.”  Instead, notice the magnification: 1.25x (a VERY low power), and how the device is constructed.  You have on left a 4-diopter (10-inch focus) convex lens, good for old people to do close-up work.  And on left a 5-diopter concave, good for strongly myopic people.  You do the viewing from right to left through the eyepiece, placing your eye’s pupil as shown.

Now, part of the reason why eyeglass lenses can be optically quite terrible and work just fine, is that in daylight the eye’s pupil closes down to about 2 or 3 mm in diameter.  In the dark at night it opens to 5, 6, 7 or even 8 mm, depending on age, to let in more light.  The above diagram assumes 2 mm.  The blue, green, and red lines passing from left to right represent NOT colors of light, but different ray bundles coming from differing directions out of the graphic on left.  I.e. different field positions.  Blue is on-axis, green is 2 degrees off-axis, and red is 4 degrees off-axis.  The bundles all converge on the eye’s biological pupil and are focused onto the retina.

What’s important here is that in this sytem, the eye’s pupil becomes the delimiting factor in determining how much light enters the eye from each object point.  By one definition of magnification, 

Magnification = Diameter of Entering Bundles/Diameter of Exiting Bundles in a telescope.  

By measuring the bundle diameters we derive the magnification.   So, for example, if you have a 200 mm telescope mirror, then the entering bundle is 200 mm in diameter.  And if the exiting bundle is only 1 mm in diameter after it comes out of your eyepiece, then we can say that your telescope’s magnification is 200x.  In the diagram above, if the magnification is 1.25x and the bundles of rays passing out of this “telescope” and into your eye are each 2 mm in diameter, then by the equation the bundles entering the objective must by 2 x 1.25 = 2.5 mm.

So in the above system, the objective lens doesn’t need to be any better than a common eyeglass lens for the viewer to find the (barely magnified) scene perfectly sharp.  It would, therefore, have been easy for Della Porta to make the above device and have it work just as he says.  In 1609, when asked, he sent the following rough sketch: 

Crude, but it sure looks like a telescope.  The “c” tube “trombones” in and out to focus.  By this stage 20 years later, Porta was sneering at the device and calling it “crap.”  Crap in the sense that it was amusing, but had little effect on “making things nearer.”  With my 1.25x version above, the length of the device would be about 100 mm.

The image quality (assuming decent glass) would be perfect all over the field:

Here the colored dots do represent colors of light.  The black circles represent the size of the Airy disks.  Since the dots for the three sample colors (486, 546, and 656 nm representing the visual spectrum) all fall well within the black circles, we can surmise that a viewer using the system will see everything sharp.  The device is only of interest in showing the basic geometry of a Galilean-style refractor, and in that it can focus to varying distances, from infinity to about 2 meters.  Anyone can use it, since like a telescope no matter what the state of your eyes (nearsighted or farsighted) you can refocus.  But the magnification is hardly noticeable.

Now, if you try to increase the magnification, then the difficulties arise.  Let’s say we replace the eyepiece with one that magnifies to 6x:

Here I have stretched the drawing vertically by 5x versus reality to make the paths of the rays for different field positions clearer.  The first thing that’s happened is that because of the 6x magnification, now the entering bundles are 2 x 6 = 12 mm in diameter!  For each field position, the entering rays cover much more of the objective lenses surface now, just as in a real telescope.  But, indeed, this IS now a real telescope! 

The result is that any appreciable defects in the objective lens WILL degrade the image.  If the glass is of low quality in transmission, or if the lens surfaces are not very spherical, they will blur the images, just as the objective in your childhood “Trashco” telescope used to do.  It is these problems that Rolf Willach rightly pointed to in his book, The Long Route to the Invention of the Telescope.  But there are still more that he did not discuss.

Because in this type of optical system the “pupil” (ie. where all the ray bundles intersect) as at the eye, and there is a lot of refraction far away at the objective lens, you will inevitably get “lateral color” in the images:

Here we have a spot diagram for the 6x system.  On-axis we’re ok.  But off-axis at 0.125 and 0.25 degree (the true field of view is now much smaller than before), the red, green and blue bundles are decentered from one another.  That means that stars will be seen stretched and smeared, ie. very unsharp.  Also, on-axis we now see longitudinal chromatic aberration, although not bad.  This system won’t work well as a telescope, because most of the field of view will be smeared.  It is this effect (as well as any smearing from surface figure error or glass inhomogeneity) that Lipperhey needed to correct.

He did so, it appears to me, probably by imposing a diaphragm on his objective lens.  We don’t know this for certain, but it is very likely, as Willach first suggested.  Now, the important part to understand is that if the objective diaphragm makes the bundles of rays exiting the eyepiece smaller than the eye’s own pupil, then what Lipperhey really did was to transfer the pupil of the bionic system from the human eye to the objective lens (where it should be for a telescope).  This transference instantly sharpens images in the outer field:

The system layout and raypaths now look like so:

The entering bundles all intersect at the objective and diverge where the eye pupil goes.  So we get much sharper images, with much reduced chromatic effects, but at the cost of a narrow, very narrow field of view.  Galilean telescopes are infamous for their narrow fields of view.  You have to “scrunch” your eyeball up against the eyepiece glass and move it side to side to see as much field as possible.  This is inevitable given the optics.  And it all gets worse in general as the magnification increases.

If you want to reach even 20x or 30x, it’s necessary to make the telescope longer and longer, to mitigate the chromatic effects.  My 6x system above is only about 400 mm long, similar to terrestrial telescopes seen in early images.  But for an astronomical telescope, magnifying 20 or 30x, you might need triple or quadruple of that.  With triple or quadruple of the objective size.  That is 24 or 32 mm.  Galileo’s famous 1610 telescope with which he found Jupiter’s largerst moons, seems to have had an aperture of 38 mm.  It required a mounting (as Galileo advised) to hold it steady.

To conclude, we have a number of other people aside from Lipperhey who claimed to have used a device similar to his before him.  Certainly, Della Porta did in 1589.  And perhaps also, Jacob Metius of Alkmaar, as well as an unidentified “young man” in Holland.  It may be that Raffaello Gualterotti had something like this in Italy, and Joan Roget in Spain, as well as others.  Likely, if these devices really existed, they were of very low power.  Metius admitted that his didn’t work too well.  But the point here is that I think these claims should not all be dismissed as fraud or sour grapes.

We see above why such devices could easily have existed and probably did before 1608.  And yet we also see why they would in general have failed, if their authors tried to increase the magnification.  It required that the system pupil be transferred from the eye to the objective lens, before you could get a functioning telescope of notable magnification.  The reason is not only what Rolf Willach has rightly pointed too (glass quality and surface/wavefront figure), but also because of the underlying optics of chromatic aberration.

The same thing happened in the 1630s, when the Keplerian telescope was adapted for terrestrial viewing.  Its output image had to be inverted and reversed.  Kepler himself had suggested a method already in 1611.  But in practice this led to terrible results, due to lateral color error, smearing off-axis stars.  Let us remember that chromatic aberration as such was not recognized until Isaac Newton in the 1670s.  Before then people had no idea that light is not intrinsically white.  They thought colors were some kind of modification of white light.  But what kind of modification, and how it all worked utterly flummoxed them.  So there was no meand to intentionally correcting color error.  No theory or solutions could exist until much later.  

And so, just as I suspect Lipperhey may have hit upon a solution to his problem through the use of a diaphragm, possibly under the influence of a false (then widespread) theory of how the eye works, so too when Anton Maria Schyrleus de Rheita, and later Giuseppe Campani found the first effective 3-lens terrestrial eyepieces, which completely corrected the lateral chromatic aberration plaguing Kepler’s 2-lens eyepiece, they couldn’t know the true reasons why their systems worked.  Yet work they did. 

Cheers,

Roger

Here are some pix of the progress Alan Tarica, Michael Chesnes, Bill Rohrer and I have made so far on our conversion project for the university-grade Ealing telescope mount’s motor drive at The Hopewell Observatory, with moral support from other Hopewell members.

The project has gone through quite a few different very-low-budget but very-labor-intensive phases.

(We are a low budget organization, and being a retired school teacher, I for one have more time than I have money.)

The first phase involved me trying to re-install the clutches on the original gear and synchronous motor system from the 1970s.

This required careful disassembly and re-assembly of a very complex gear train, which I did accomplish, but I was unable to fine-tune the exact amount of friction needed, so I gave up on that approach and decided to try an electronic conversion that many other folks had been using on their own telescopes.

Namely, an Arduino-based system called OnStep that grew out of the modern CNC industry that powers modern 3-D printers and most modern fabricating machinery of all types.

Our version has MaXESP3 boards made and sold or generously given to us by Ken Hunter and George Cushing. We have also had considerable help from OnStep’s Howard Dutton, Robert Benward, and NCA’s own Prasad Agrahar.

The MaxEsp board (about the size of my hand) powered two little stepper motors (roughly cubical, 5 cm on a side) donated by Prasad. We were given by Ken, and also purchased, some tiny LVL and TMC stepper drivers about the size of a postage stamp that fit into rails on the MaxEsp board. The motors were connected to the wonderful original Byers gears inside the mount by ingenious little direct-drive couplings donated by Prasad.

This rebuild required me to remove all the original motors and gears and clutches in the scope mount’s motor box and carefully line up the new motors with the telescope shaft, which required some careful machining and filing.

We discovered that those stepper motors didn’t have enough torque to drive the mount, even with all of the optical tubes removed.

(Btw, connecting all these electrical components was a huge learning curve for me! There are SOOOO MANY different types of connectors, and we have now discarded several types as unsuitable. Wiring up and soldering some of those connectors require the skills and steady hands of a seasoned watchmaker or Heathkit veteran — which I am not. My hands shake terribly!! One small slip of one of my hands, one time, was enough to fry two of those tiny drivers and blow a tiny fuse… I had to adjust a tiny potentiometer screw while the circuit was live… I didn’t realize there was a better place to connect my grounding lead to… fortunately those drivers only cost a few dollars…)

It was suggested to add a belt and put pulleys of different sizes onto the stepper motor and the mount shaft. That required moving the stepper motors and hence a bit more machining.

But that didn’t work either.

So I ordered bigger stepper motors.

But the first ones I ordered also didn’t have enough torque either! I found I could stop their rotation with my bare hand!

So I ordered some more powerful stepper motors. And got rid of the belts and pulleys. (We have extras if anybody’s interested!)

But they needed more current (amperes) and voltage than the Tiny postage-stamp sized stepper drivers could produce.

Larger stepper drivers won’t fit directly on the MaxEsp board, and also need more voltage than the board can tolerate.

So Ken Hunter figured out a way to bypass that: he changed (for free!) some of the wiring on the back of two of our MaxEsp boards, and suggested some much larger stepper drivers about the size of a small deck of cards, and a regulated switching power supply that puts out a steady, adjustable direct voltage from 0 to 42 volts that is the size of a medium-length hardback novel.

But the MaxEsp board can’t take that many volts, so we needed something called a buck step-down power supply to reduce the 0-42vdc power down to a steady 10 or 12 volts – just for the MaxEsp board.

We wired all that up and re-adjusted the stepper motors and got the worm gear from the stepper motors to mate properly with the Byers gears on the scope mount — not an easy task! Physically screwing in the gearbox was insanely difficult until We figured out an easier way. We only fried two of the buck power supplies via short-circuits, but this was no great loss since five of them had cost about $15.

Everything worked great when we had all the components wired up **outside** the cavities built into the mount itself. But when we carefully slid the five separate components into those cavities, some of the many, many tiny little colored and numbered and labeled leads broke off that connected all those components, broke off.

Yes, we made wiring diagrams — I think we are on version eight or nine now! (Mine are done in pencil on large sheets of thick art paper. Bob Benward has generously made electronic versions for us; I’ll have to send him the revisions.)

We took it all back out, and did some trouble shooting. I tried using an old Heathkit oscilloscope made by the late Bob Bolster (one of the principal founders of Hopewell) but made little progress until Ken explained **where** to connect the o-scope leads (hint: at the output from the MaxEsp board and not at the output from the drivers), and Alan brought in a brand-new solid-state o-scope.

Using that info, and using Alan’s new, more sensitive and easier-to-use o-scope, and taking careful notes, and examining those outputs on the o-scope screen when we try to slew or track with the scope controls, I finally figured out that one of our OnStep boards had some defects, but the other two were ok.

It also became obvious that trying to shoehorn all these components inside the original compartments inside the Ealing mount wouldn’t work. We needed a nice sturdy electrical project box. I didn’t see any at local hardware stores that were large enough, so I ordered a sturdy steel one online. It ended up still being too small, so I exchanged it, and with Alan’s assistance, built standoffs to isolate and secure all the components, and I was able to mount and wire them all up correctly onto a removable steel plate that fits inside the box. It’s all modular, and swapping out components is pretty straightforward. (See the photos below.)

Michael, Alan and I decided to place the box against the north side of the masonry pier supporting the telescope. (Drilling the mounting holes into the concrete ended up being harder than I expected, but we got it done.) We also had to drill holes for the “Liquidtight” flexible electrical conduit that connects the OnStep/Arduino circuitry inside the box to the mount where the motors and gears reside. And holes for the fan and vent. And for the Wi-Fi / Bluetooth antenna. And the USB port.

When I finished wiring up everything, I turned on the power… and…

Nothing.

It turned out that I had done something to the 0-42VDC power supply so that it received 110VAC but put out nothing at all. I was too hot and tired to figure out and fix whatever I did on-site that Memorial Day, so I ordered another one, which should arrive this afternoon.

I’ll connect the new power supply on Sunday.

Here are some pix.

The fan and USB jack are on the left. Some of those dangly wires need shortening.

I had to stop up a number of the holes I had previously drilled in those panel covers on the mount, to keep insects out. If you don’t, marmorated stink bugs and lady bugs enter in droves and many die.

Very persuasive article explains why space travel is impossible. The main reason is gravity. Written by Allan Milne Lees; I found it on Medium.

Allan Milne Lees5 days ago·7 min read

===============================

Despite the populist hype of billionaire Sci-Fi fanboys and a perpetual stream of Hollywood entertainments to the contrary, humans will never explore the galaxy in person. In fact, we won’t even explore our own solar system up close and personal. This is not merely because robotic missions can do the job 1,000% better for 1/1000th the cost. It’s because of two fundamental biological reasons.

The first is gravity. Everything about our bodies is evolved to function under a gravitational acceleration at sea level of approximately 9.8 meters per second squared (9.8m²). Our hearts pump blood up to our heads, fighting gravity every centimeter of the way. Our muscles and bones are as strong as they are because every part of our bodies is fighting gravity every moment of our lives. Our sense of balance, which orients us spatially, depends on gravity being constant in one direction only: straight down.

Without gravity, very bad things happen: the heart pumps too much blood to the head and too little to the lower extremities, leading to ocular distortions, crushing headaches, and nausea as the inner ear loses all sense of up and down. Our bones and muscles atrophy dramatically, even when hours each day are dedicated to exercises specifically designed with the intention of slowing down this decay. Put simply, our bodies are incapable of handling microgravity and despite the pictures of smiling astronauts merrily enjoying microgravity on the ISS, the harsh reality is that every single one of those astronauts pays a price very few of us would wish to incur.

The Sci-Fi fanboy response to this fundamental problem is either (a) to ignore it entirely, as per Musk and Bezos, or (b) claim that artificial gravity is the answer.

As Musk and Bezos are ignoring the problem we can likewise ignore them. So what about artificial gravity?

There are only two ways to create artificial gravity. The first is called “constant-g” which means that we accelerate our hypothetical space ship at a constant 9.8m² for the first half of the trip and then flip it around and decelerate it at a constant 9.8m² for the second half of the trip. Einstein’s insight that over areas too small to experience tidal effects such acceleration would be indistinguishable from regular gravity means that in theory Earth-style gravity could be induced in such a manner. Better yet, because the acceleration is constant, relativistic speeds will eventually be attained. In just 12 years (in the reference frame of the spacecraft) we could travel across our Milky Way galaxy. In a single human lifetime (in the reference frame of the spacecraft), under constant acceleration, we could reach the edge of the universe that’s observable from Earth. An Earth upon which, in that frame of reference, billions of years would have passed.

So with constant acceleration we get a “twofer.” Earth-identical gravity and the ability to traverse vast distances within a human lifetime. Problem solved!

Except that there is no way, theoretical or otherwise, to achieve constant acceleration of this magnitude. No propulsion mechanism, theoretical or otherwise, can overcome the problem of mass. In order to power the continual acceleration, our imaginary space ship is constrained by Newton’s observation that any action in a vacuum requires an equal and opposite reaction. In other words, to accelerate a mass of X by some amount of velocity we will need to discharge an equivalent amount of energy in the opposite direction. And that energy can only come from fuel. Which adds to the mass of our space ship. So now we need to expend more energy, which means we need more fuel, which means we’re now carrying even more mass, which means we need to expend even more energy, which means…

In other words, even with some imaginary technology that could convert matter into energy with 100% efficiency, there’s simply no way to get to 9.8m² constant acceleration for any meaningful amount of time. Sure, we can talk about things like an Alcubierre drive but then we’re just as entitled to say that Hogwarts will invent the Spaciamus drive to solve our problem instead. In other words, running off to hide inside imaginary “solutions” is no solution at all.

If constant acceleration can’t provide artificial gravity, what about centrifugal force? We all remember the rotating space station in 2001 A Space Odyssey and everyone knows that this was the only Sci-Fi movie ever to have utilized a science-based series of technologies. Plus, it’s easy to find on the Internet lots of schemes to create artificial gravity in this way, from tethering ships together and spinning them around a central axis to building enormous hollow rotating cylinders on the inside of which humans will experience Earth-like gravity. So, problem solved!

Except the movies and the Sci-Fi books mislead us, as is the way of popular entertainments.

First, the good news: if a person stood perfectly still and did not move in any way whatsoever, then centrifugal force could seem to mimic Earth-style gravity. Unfortunately, here’s the bad news: if they made any movement whatsoever, they would instantly be overcome by nausea and be disoriented.

Why is this? Imagine throwing a ball up into the air here on Earth. If you throw it straight up, it will come straight down, pulled by gravity toward the center of the Earth we’re standing on. But under conditions of “gravity” induced by centrifugal force, a ball thrown straight up will arc and fall away from the person who threw it because unlike here on Earth there’s a second force acting on the ball: centripetal force. As our inner ear orients us by means of reference to the constant downward force of gravity, this means that any movement at all — even something as minor as turning one’s head — would result in signals from the inner ear (responding to the centripetal force) jarring dramatically with the signals from our eyes. At best this would lead to our hypothetical human vomiting in a majestic arc; at worst it could render them incapable of any controlled movement whatsoever.

The diagrams below show the difference between gravity (or constant acceleration at 9.8m²) and a rotating object. On Earth there’s only one force acting on us: gravity. On our imaginary rotating artificial gravity environment there are two forces: centrifugal, and centripetal. And that makes all the difference in the world.

Perhaps this is why Bezos prefers to ignore the problem; it can’t be solved just by throwing money at it. As for Musk, he makes people with ADHD look like paragons of sustained concentration so he probably doesn’t even know the problem exists. But even if you don’t know a brick wall exists, it still kills you if you slam into it at 1,000 kilometers per hour.

Gravity, therefore, is one reason why human beings will never be a space-faring species. It’s also the reason why it’s highly unlikely any other species capable of developing suitable technologies would ever become space-faring either. All organisms are highly adapted to the environments in which they evolve and it is extremely difficult to sustain organisms outside of their natural environments for any significant period of time. Add it the problems of solar radiation, the deleterious effects of microgravity, and everything else associated with space travel and it’s apparent that Sci-Fi fanboy dreams are a very poor guide to the future.

There is a second major reason why we humans will never be a space-faring species: psychology.

Our brains are as much the result of selection pressures as our bodies. Like our bodies, our brains are highly adapted to life on Earth. As a primate group species adapted to foraging, we’re not well-suited to being cooped up in tiny cages. We become obese and we develop all manner of mental problems. Without access to natural cues like water and grass and trees, we become stressed. When forced to interact with the same small group of people for years without respite, we become irrational and angry, or conversely withdrawn and depressed. Worse still, our emotional hardwiring makes us competitive even when cooperation is the optimal strategy, and our intellectual limitations lead us to acquiring and then strongly defending irrational and harmful beliefs.

Imagine, therefore, a space ship upon which 200 hapless humans attempt to exist for years or even decades. Instead of looking to Star Trek as our inspiration, a more probable vision is depicted in One Flew Over The Cuckoo’s Nest or perhaps the concluding episodes of some trash reality TV show.

It is difficult to imagine any species capable of making spacecraft not having equivalent psychological limitations, albeit likely somewhat different from those that control our own behaviors.

There are many other reasons why humans will never spread across the galaxy, but these two should suffice to prove the contention. This does not mean, however, that there won’t be money to be made in enabling space tourism. A few days in microgravity, ensconced in a modestly comfortable environment with a small number of others, could be a very congenial way for the wealthy to break up the monotony of holidaying in the Hamptons or on a private island in the Bahamas. Sheltered in low orbit by the Earth’s magnetic field, the dangers of solar radiation are reduced to a perfectly acceptable level and likely no worse than a dozen trips in a private jet. Microgravity sex will no doubt become this century’s equivalent of the Mile High Club that was so popular among the early jet-setters of the 1960s and 1970s.

But beyond a few amusing days spent orbiting the Earth while watching one’s champagne bubble around one’s head, and after the inevitable disaster of Mars Colony One, we will accept the fact that robotic missions are the real future. And then we will expand our knowledge of the universe exponentially instead of wasting hundreds of billions of dollars on futile dead-end fanboy dreams.

A few days ago, we silvered an 8” diameter 43” FL mirror that had previously been aluminized, and applied the Angel Guard coating.

We did a Ronchi test and some Foucault-Couder knife edge tests before stripping the aluminum and after the silver was applied.

To my amazement, we found that the mirror’s figure was about the same in both cases. How that works, especially how the Angel Guard coating is laid down so even and smooth over the entire mirror, is beyond me. But it DOES work.

Prior figure (aluminized mirror), seen with Ronchi grating of 100 lines per inch: https://share.icloud.com/photos/0LyqGC35cx0QfWKcd08aI0vzw…

Final figure (silvered mirror), with same Ronchi grating:

https://share.icloud.com/photos/03mdTeZD3dZ-bqGNoDZXSqpjw…

This is a video of us washing off the Angel Guard coating.

Here is a video of the finished mirror after drying. Notice that the very edge of this mirror did not take the silver coating, but the area uncoated is probably on the order of one or two percent of the total area.