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