BUILDING A GALILEAN TELESCOPE

It is quite possible, and not at all difficult, to build a good-quality, fully-functional Galilean telescope for under $50. The essential ingredients are two good quality singlet lenses and a convenient and stable focusing mechanism. If the completed telescope is to be used for astronomical observations, a stable means for pointing the telescope over a wide range of angles is also essential.

The authors of this website do not build telescopes for others. Building a Galilean telescope yourself is a very simple and rewarding project. Once the parts are at hand it should take you no more than an hour or two to assemble a working version.

On this page we give some suggestions for obtaining suitable lenses from well-known optical suppliers, and two suggestions for simple, if not beautiful, methods of assembling them into a telescope. The PVC version, as used for taking the pictures on this website, is lightweight, weather-resistant, and very durable, but may require internal baffles to suppress the reflections from the inside of the shiny tubes. The baffles slightly restrict the number of fields of view that can be seen by moving the eye around the eyepiece. The cardboard version is bulkier and less durable, but, owing to the larger diameter and less reflective surfaces of the tubes, should not require any baffles. Next, we give very limited suggestions for mounting and testing the finished telescope and, for those seeking historical authenticity, review the specifications of Galileo's lenses. We then compare the magnification, field of view, and resolution expected with Galileo's lenses to that obtainable with several possible combinations of commercial lenses and finally, point you to some additional internet resources and describe a couple of "Galilean" telescopes that can be purchased ready-made.

Selecting Your Lenses

Good quality singlet lenses can usually be obtained from such standard sources as Edmund Scientific, Melles Griot, or Newport Corporation. You can find many other sources of new and used singlet lenses on the internet. For example one recently recommended in Sky and Telescope is OptoSigma. Engineering directory services, such as GlobalSpec, or the Laser Focus World or Photonics Spectra Buyer's Guides, will give you links to more than a hundred other suppliers of both stock and custom spherical lenses. Although one expects modern glass lenses to be of generally good workmanship, in the absence of interferometric testing, it is impossible to tell if any particular lens ordered from these suppliers will be better or worse than those used by Galileo. Most suppliers are rather vague as to the expected quality of their lenses. Many give no specification at all. For those willing to pay a much higher price, CVI Laser (now part of Melles Griot), among the major suppliers, claims to provide surfaces good to one-tenth wave, far better than needed for diffraction-limited performance. At the other extreme, Rolyn Optics, one of the oldest industrial optics suppliers, offers a complete line of positive and negative meniscus-type ophthalmic quality lenses. These come in rather large diameters (52-65 mm) at a quite reasonable price, but they are manufactured from the cheaper B270 glass, which tends to be less homogeneous than the BK7 glass used for the other lenses suggested here. The surface figures are also likely to be less accurate. In addition, even if well made, for use as a telescope objective, a sharply curved eyeglass lens is not expected to perform as well as one of flatter shape; although, as shown below, the practical difference appears to be slight. The prices given in the following tables are for new lenses. Anchor Optics, among others, offers surplus lenses with diameters and focal lengths suitable for making a Galilean telescope for well under $10 each.

To build a Galilean telescope, you need to select a long positive focal length lens for the objective and a short negative focal length lens for the eyepiece. The magnifying power of your completed telescope will be the ratio of the two focal lengths and the separation of the lenses (when focused at infinity) will be their sum. For example, a +1000 mm FL objective with a -50 mm FL eyepiece will give 1000/50 = 20X power in a total tube length of 1000 - 50 = 950 mm when focused on a distant object. If you want to focus on nearby objects you need to be able to pull the drawtube out. All Galilean telescopes produce erect, non-inverted images; similar to what you are accustomed to seeing through binoculars but with greater magnifying power and a much smaller field of view.

A selection of possible lenses is given in the following tables. The lenses are ranked by price, but the choices are quite arbitrary. Check the suppliers' catalogs for many additional possibilities. None of the standard commercially-available lenses precisely match the surviving lenses attributed to Galileo, so feel free to experiment. In general, choosing a larger eyepiece will permit more fields of view to be seen as the eye is moved around, and larger objectives will give higher resolution. Higher magnification is achieved by choosing longer focal length objectives and/or shorter focal length eyepieces as explained in the previous paragraph. Simulations of the results to be expected with a number of combinations of lenses are given below.

The prices quoted are those given on the suppliers' US websites as of January, 2006, and are all for uncoated lenses. Edmund does not offer singlet lenses with focal lengths longer than 750 mm; and Newport has no singlets with focal lengths longer than 1000 mm. Melles Griot offers a line of 30 and 50 diameter lenses essentially identical in specifications to those listed here from OptoSigma, but priced about $2 more. Both series go to a maximum focal length of 5000 mm (16.4 feet). The pricing of lenses is a little strange and you can sometimes buy a larger diameter lens for less than a smaller diameter one of the same focal length. We would recommend doing this since the larger diameter lens can always be stopped down (as Galileo did). The telescope with which the pictures on this website were taken uses the Newport KPX124 as its objective and an Edmund's NT45-028 for the eyepiece, but we have no particular reason to think these lenses are any better than any of the others.

As noted above, there is no guarantee that lenses, even ones purchased from the most reputable suppliers, will meet any particular standard of quality. If you encounter image quality significantly worse that that shown on this website, a defective objective lens is to be suspected. The clearest sign of a poorly made objective is a lack of symmetry in the image. For example, an object seen through the telescope should look the same if the telescope is pointed so the object appears at the top edge, bottom edge, left edge or right edge of the field. If you can see a difference in focus, color or size when imaging the same object in different, symmetrically placed, parts of the field, then there is something wrong with the objective. A common problem with commercial lenses is wedge: a lack of parallelism between the front and rear surfaces. If the objective lens suffers from wedging, then even though it appears to be mounted square to the tube, you may not be looking down its optical axis. This problem can be alleviated, to some extent, by mounting the lens at a slight angle, but finding the correct angle (needed to restore symmetry) can be very tedious. A really bad objective may even show obvious ripples and distortion when you look through it with the unaided eye (e.g., looking down the tube after removing the eyepiece).

Constructing Your Telescope

The purpose of the construction is to place the lenses at the appropriate distance from one another, to shield the observer's eye from unwanted light, and to provide a convenient means for adjusting the distance between the lenses so they can be focused on targets at different distances. These objectives can be achieved in any number of ways. In addition to the actual assembly directions for the present telescope, we offer two very simple basic designs. Feel free to experiment and invent your own. Incidentally, good optical design dictates that the curved surfaces of the lenses should face outward, as shown in the following diagrams (which are not at all to scale). However for these very slow systems the actual orientation of the lenses is not critical.

How the Present Telescope was Built

The mechanical parts of the telescope used to take the photos shown on this website were planned with some care and the assembly took a number of hours. The materials used include PVC pipe and plumbing fixtures, nylon bushings, masking tape, epoxy and RTV. Complete details are given on a separate page.

Basic Design Using PVC Pipe

PVC pipe, usually white in color, is commonly used in home and yard plumbing projects and is readily available in a wide variety of diameters in most hardware and home improvement stores.

1. After selecting your lenses, find a PVC tube that will accommodate the eyepiece. This will be used for the drawtube.
2. Find another PVC tube into which the drawtube can slide. The two PVC tubes are indicated by the tan color in the diagram above. The drawtube is normally much shorter than the main tube. If you wish, the drawtube could also be made larger and slide on the outside of the main tube.
3. Fabricate shims (green) to take up the slack between the two tubes. You want the drawtube to slide freely, but with enough friction that it won't fall out when the telescope is pointed vertically. Glue the shims to the outside of the drawtube. Alternatively, wrapping the drawtube with tape at several places should work. Because PVC tubes are often a little out of round you may be able to place lengthwise strips of tape in such a way that the drawtube will slide in one position yet lock when rotated.
4. Insert the lenses with appropriate bushings to hold them firmly in place. In our case, for our choice of lenses and tubes, we found rubber grommets intended for routing computer cables through holes in furniture worked very well. Optical alignment is not terribly critical, but try to check that your lenses are square to the axis of the tubes.
5. Insert the drawtube into the main tube and your telescope is ready for use!
6. Point the completed telescope at a distant point of light and check that you see a nice, round diffraction disk that changes symmetrically as you go in and out of focus. If necessary, adjust the tilt of the lenses.
7. The purpose of the baffles (the two black objects near the middle of the drawing) is to prevent light from the objective from striking the interior surface of the drawtube, and to prevent the eye from seeing the shiny interior of the main tube. The baffles are paper or foam disks with holes in their centers. They are glued to paper or plastic rings to hold them in place. You may not need baffles if you can successfully spray the inside of the tubes with flat black paint. To see whether you need baffles, check if you have a problem with glare when looking at a bright object, such as the Moon. If you need baffles, make a scale drawing of your setup and draw lines from the center of the eyepiece to the clear aperture of the objective. Plan your baffles so they stay outside of this cone. Push the baffles into the tubes to the desired positions.

Alternative Design Using Cardboard Shipping Tubes

Our second suggested design uses cardboard tubing. There is a particular kind of tube commonly used for storing and mailing maps and posters which we find ideal. These are typically about 3 feet long by 3 inches in diameter and come with plastic end-caps. One end-cap makes a convenient tiltable surface for mounting the objective lens. The 3-inch diameter shipping tube is indicated in red in the following drawing, with its end-cap in dark green. The remaining parts are usually easily fabricated from parts at hand.

1. Cut a hole in the end-cap (dark green) almost as large as the diameter of your objective lens. Securely tape or glue your lens to the end-cap, taking care to get it well centered. If you have a suitable tube, but without an end-cap, fabricate a similar cardboard ring that can be pushed in the end of the tube to hold your objective.
2. If you are using a plastic end-cap and it is not opaque, make a cardboard ring that can be inserted, as shown, just behind the objective to prevent stray light (outside the lens) from entering the main tube.
3. Find a second tube suitable for holding your selected eyepiece. This will be your drawtube (indicated by light green in the drawing). After cutting the drawtube to the appropriate length, fabricate a cardboard ring of a diameter correct to slide firmly down the main tube and glue this to the end of the drawtube, as shown. Let the joint dry.
4. Fabricate a second identical cardboard ring, and after the drawtube has been inserted into the main tube, slide this second ring down the drawtube and glue it to the end of the main tube, as shown.
5. When the second joint has dried, the draw tube should slide easily and accurately in the main tube, as indicated, yet have enough friction not to fall out when the telescope is turned vertically.
6. Insert the lenses and test your new telescope on a distant point of light. Adjust the tilt of the objective to get the nicest possible diffraction spot, then tape or glue it firmly in place.

Mounting Your Telescope

Do not expect to be able to hand-hold a Galilean telescope of 10 power or more. The combination of its length, high magnification and small field of view will make pointing extremely frustrating, and once the target has been located hand tremor will make it impossible to fully appreciate the quality of the image.

For viewing terrestrial targets, laying the telescope on a solid horizontal surface and using shims for fine pointing is adequate; but for astronomical targets a more elaborate mounting is essential. For those with an existing telescope, we feel the piggyback arrangement shown on our Galilean Telescope Homepage is ideal. Not only does the ability to use the spotter scope for finding targets greatly relieve the pointing problem, but the drive motor (if present) allows one to track astronomical targets as they move across the sky with the same ease as in the main scope. For those without an existing telescope a sturdy camera tripod with pan and tilt controls can be adapted to the purpose, but will prove much more frustrating to use. Some sort of gun-sight type arrangement (or possibly a piggy-backed smaller and less powerful Galilean telescope) would have to be added for rough pointing.

For those seeking historical authenticity, we are unaware of any verifiable information as to how Galileo mounted or pointed his telescopes. However, this does not mean he held his telescope by hand as suggested by any number of romantic paintings. As pointed out by Galileo himself, the human hand is not steady enough for observations at 20X. Even in 1609 a variety of visual sighting devices were in use, and many had adjustable mounts. Galileo presumably adapted the technology of his day to the problem at hand. Prior to his involvement with the telescope, one of Galileo's main claims to fame was his development and marketing of a device he called the "military compass," a kind of ruled divider that had applications in surveying, drafting and pointing cannons. In a 1977 paper Galileo scholar Stillman Drake reproduced a sheet of drawings [1] of accessories sold for use with Galileo's military compass. Among the accessories is a universal joint which could be mounted atop a tripod. The joint consists of a spherical ball held captive in a hemispherical cup, with one screw for tensioning and another (on top of the ball) for holding the compass. It is similar to, but appears more robust than, the ball mount of Isaac Newton's first tiny reflecting telescope of 1668. We do not know if Galileo used such a mount with his telescope, but we do know he could not have observed Jupiter's moons holding his telescope by hand.

By 1613, in connection with his scheme to reckon longitudes at sea by timing eclipses of the moons of Jupiter, Galileo is said to have proposed, built and tested a helmet-like contraption for holding his telescope. He called it the celatone. To further counteract the motions of the ship, the observer wearing the celatone was supposed to sit in a special gimbaled chair. We know of no evidence that Galileo used a celatone for any of his own astronomical observations, but he obviously had the imagination to consider many possible schemes for mounting his telescopes.

As to the devices used by Galileo's contemporaries, in a 1971 article, the Smithsonian Institution's Silvio Bedini [2] shows several examples of telescope mountings dating from as early as 1613-1617 that survive either as actual artifacts, or are depicted in the art of the day. Typically, they appear to consist of a pedestal with some kind of universal joint at the top for adjusting the elevation angle of the telescope, and possibly a swivel below for adjusting its azimuth. But again, we have no idea of what kind of mounting Galileo actually used.

[1] See Plate 6 of Stillman Drake, "Tartaglia's Squadra and Galileo's Compasso," Annali dell'Istituto di storia della scienza di Firenzi 2, 35-54 (1977). This article is reprinted in Drake, Essays on Galileo and the History and Philosophy of Science (University of Toronto Press, 1999), Vol. 3, pp. 33-44. The original article is available online via Nuncius Online, a part of the IMSS's free digital library.

[2] Silvio Bedini, "The Tube of Long Vision: the physical characteristics of the early 17th century telescope," Physis 13: 147-204 (1971).

Testing Your Telescope

Although testing a telescope with astronomical targets is fun and instructive, it is fraught with problems and uncertainties, including the frustrations of pointing and guiding, but much more importantly, the extreme variability of atmospheric conditions, which can, at times, blur the astronomical target beyond recognition. We find that tests using terrestrial targets (as were probably performed by Galileo) are usually both more informative and more quantitative, and give more repeatable results. This distinction was recognized already by the 1660's, when the ambiguous claims of Divini and Campani for the superior resolution of their optics on astronomical targets were resolved by looking, through telescopes of each, at the equivalent of a modern optometrist's eye chart. This interesting chapter in the history of telescope testing is told in an article by Righini-Bonelli and Van Helden available through the Nuncius Online service in the digital library of the IMSS. Their article includes examples of several of the original seventeenth century test charts(**).

From the historical record it appears that Galileo's best telescopes had a resolution of four or five arc seconds and operated at about 30 power. Through such a telescope it should be possible to read the 2 mm type in the average newspaper at a distance of 100 feet. If your objective lens is not capable of doing this, then it is not comparable to Galileo's best. It is either too small in diameter, too poorly figured, too inhomogeneous, and/or made of a too high dispersion material. In performing such a test, it may be helpful to use a higher power eyepiece than the one you actually plan to use in the final telescope (the resolution of the telescope is determined primarily by the quality of the objective, and for testing that, the eyepiece does not have to be historically authentic).

For a more accurate test, we provide, on our Galilean Optics Page, a modern test target and an example of how it looks through the website telescope at a distance of 214 feet. To test your own telescope, you can print a copy of this target, mount it at an appropriate distance and determine the finest line patterns you can resolve. There are many other equally suitable test targets available over the internet. Whichever one you use, your print will probably not match the original size of the target. You will have to measure the spacing between the centers of the dark lines in your print and then calculate the angle that they subtend when placed at your target distance. Please note that the website telescope has a clear aperture of 23 mm. If your telescope has a different diameter objective, its resolving power should be higher or lower in inverse proportion to the clear aperture.

** If you have trouble locating this article through the digital library, it may be possible to access individual pages directly by typing in addresses like: http://193.206.220.2:85/BD/324905/324905_00037z.jpg  This particular image, if the URL works, is page 33 of the original article, showing a chart printed by Paolo Falconieri. The URL indicates it is the zoomed (400 dpi) version of the 37th photo in the sequence for this article, which is digital library item #324905. Other test charts appear on pages 35, 37, 50, 52, 82, 84, 116, 126 and 128 of the original article. If the previous link works, then images of those pages can be accessed directly by altering the page number in the URL in the address bar of your web browser, keeping in mind that you have to add 4 to the page number to get the photo number. However, we recommend accessing the article through the normal interface so that you can see the whole article and better understand how the charts were used.

Galileo's Lenses and the Properties of their Glass

As described elsewhere on this website, Galileo's surviving optics consist of two complete telescopes and one broken objective lens preserved at the museum (IMSS) in Florence. Only the broken objective is known with certainty to have been used by Galileo, and even for that it is unclear to us if the present 38 mm stop with which it is displayed accurately represents the diameter used by Galileo. According to his own report Galileo used the broken objective to discover the moons of Jupiter, but the eyepiece he used with it has apparently not survived, so the power and tube length of that telescope is not known. Experts seem to agree that the double concave eyepiece of the short leather-covered 21-power telescope (designated here as GAL 2B) is a replacement from a later era, and NOT the original lens. The other, longer and more crudely-built, telescope preserved at the IMSS is of 14-power. In the opening paragraphs of Sidereus Nuncius Galileo refers to telescopes of 20 to 32 power. He also states that the wonders he is about to describe cannot be observed with lower power. Czech amateur Leos Ondra has uncovered evidence based on Galileo's notes about the Trapezium star system that the telescope Galileo was using at that time (1617) must have been about 27 power. An undated noted about the apparent diameter of the star Sirius suggests that Galileo was familiar with how it looked through a 32 power telescope, just as we would suspect from Sidereus Nuncius. Whether either of these observations involved the 38 mm objective is unknown. Given this evidence, it seems unlikely that the IMSS 14-power telescope was ever used for Galileo's astronomical observations. It also seems unlikely that the elaborately gilt 21-power telescope is the experimental instrument used for the earliest observations described in Sidereus Nuncius.

Experts seem to be divided as to whether Galileo ground his own lenses or purchased them from the opticians of the day. He certainly purchased and tested some as evidenced by the letter cited in the article by Giuseppe Molesini. The letter says that all but three from a lot of 300 lenses received from an eminent Venetian optician in 1616 had to be rejected.

The upshot of this is that in attempting to recreate Galileo's view of the heavens, a slavish copying of the five surviving lenses is probably pointless. Nonetheless their optical properties have twice been carefully studied (by Vasco Ronchi in 1923 and by the team of Vincenzo Greco, Giuseppe Molesini and Franco Quercioli in 1992-3) and their results are summarized here. The two studies gave slightly different values for the focal lengths and refractive indices of the various lenses. For purposes of identification, we will refer to the objective of Telescope I as GAL 1A and its eyepiece as GAL 1B. The objective and eyepiece of Telescope II are GAL 2A and GAL 2B, while the broken objective is GAL 3. We present here the average of the results from the two studies. Full details are given on a separate page. All focal lengths were measured at 5500 Angstroms.

Some might think that the performance of a modern replica would differ from that of one of Galileo's day because of differences in the optical properties of the glass used. Those properties are defined by the refractive index and how it varies with wavelength. This variation is called the "dispersion" of the glass. Glasses with high dispersion will produce more chromatic aberration than those with low dispersion. As part of his 1923 evaluation Vasco Ronchi measured how the focal length of each of the surviving objective lenses associated with Galileo varied with wavelength. From these data, and his measured thicknesses and radii of curvature, the indices of refraction at each wavelength can be computed.

The modern commercially-available lenses suggested above are almost all fabricated from the common modern optical glass called "BK-7". As can be seen in the following graph, Galileo's large broken objective, used to discover the bright moon's of Jupiter, has optical properties very similar to BK-7. The other two objectives have significantly higher refractive indices.

The re-evaluation of the lenses by Greco, Molesini and Quercioli suggests that the indices for GAL 1A deduced from Ronchi's data may be systematically high due to a faulty measurement of the front radius of curvature. If this is the case, its dispersion curve may actually lie between GAL 2A and GAL 3, rather than above them.

The focal length of a thin glass lens operating in air is inversely proportional to the difference between the refractive index of the glass (n) and the refractive index of the air (≈ 1). The dispersion of glasses is usually described in terms of something called the Abbé factor, which compares the refractive index n_F in the blue F line (wavelength 4861 Å) and n_C in the red C line (wavelength 6563 Å) of hydrogen to either a yellow line of helium or a green line of mercury. For the present purposes, since the chromatic aberration comes primarily from the objective lens, it seems more useful to consider the simple ratio:

   R = (n_F - 1)/(n_C - 1)

This ratio gives the fractional difference in focal length of the objective for these two wavelengths. A ratio of R = 1.010 indicates that if the blue light comes to a focus at 1000 mm, the red light will come to a focus at 1010 mm. The following table is arranged in order of decreasing refractive ratio (dispersion)

In addition to the glasses shown in the preceding graph, we give the refractive ratio for B270, a cheap optical crown glass commonly used for eyeglasses and other low precision optics; the crystal calcium fluoride (known as fluorite), used in some very expensive modern astronomical refractors; SF11, a common "flint" glass; and PMMA, a clear acrylic material used for making molded plastic lenses (and compact discs). Although lenses made of B270 or PMMA have very similar dispersion to BK7 (and Galileo's large broken objective), they are best avoided because of their frequently low homogeneity (ripples). A fluorite objective, or one made with a similar low dispersion optical glass such as Schott N-FK51A, would give a modest reduction in chromatic aberration compared to the lenses used by Galileo. At the other extreme, inadvertently using a singlet objective made from a modern flint glass would give a large increase in chromatic aberration, and the images obtained would be significantly fuzzier (lower contrast) than those shown below for a comparable f/ratio (ratio of focal length of objective to diameter).

William Wragg, a visitor to this website, inquired whether the chromatic aberration might be reduced by using a negative (concave) eyepiece made from flint glass in combination with a (convex) BK7 objective. The answer is yes, although for the f/numbers illustrated below the improvement in image quality is barely noticeable. If a positive (convex = Keplerian) eyepiece is used, using a flint glass eyepiece will actually increase the chromatic aberration compared to an all BK7 telescope; although, again, for the present f/numbers the difference is very slight.

Expected Results

In the following table we compare the results expected with various combinations of lenses. As a point of reference the present telescope (Example 5) and the two complete surviving Galilean telescopes are shown (Examples 1 & 2). We also show the hypothetical combinations of Galileo's large broken objective with the two surviving eyepieces (Examples 3 & 4). Galileo's lenses are referred to by the codes given in the previous section, while modern commercial lenses are designated by their manufacturer's catalog numbers, as listed in the two tables at the start of this webpage.

Aperture is the clear diameter of the objective. Tube Length is the distance in millimeters from the objective to the eyepiece when the telescope gives the best simulated resolution for a target at infinity. This point was generally found to lie a few millimeters short of the point calculated by summing the nominal (paraxial) focal lengths of the two lenses. Power is the angular magnification of the telescope. It is dimensionless. Single Field gives the angular extent visible with the eye in a fixed position. This has been calculated using North's formula assuming a 4 mm diameter pupil, 4 mm back from the last surface of the eyepiece lens. The formula requires the diameter of the objective. For Galileo's lenses, the stated clear aperture was used. For the modern commercial lenses, a diameter 2 mm less than the catalog diameter was assumed. The field is expressed in arc-minutes in target space. A value of 10, for example, means that the telescope's field will cover a target that appears 10 arc-minutes in diameter to the unaided eye. The two diameters given represent the start and end of the ring of vignetting. The brightness of the image will start to fall off at smaller diameter of the two. Light from the target can be seen to the outer diameter, but it will appear very dim there. To convert these diameters to values in image space (the apparent angles as seen through the telescope), multiply these values by the telescope's power. For example, if the field of view in target space is 14 arc-minutes and the telescope power is 20, to the eye, the apparent diameter of the field seen looking through the telescope will be 14x20 = 280 arc-minutes or 4.7 degrees. Total Field is an estimate of the total angular range in target space that can be observed by moving the eye around the eyepiece. It is expressed in degrees, and was estimated by dividing the eyepiece clear aperture by the tube length. As with the objective, for the modern commercial lenses a diameter 2 mm less than the catalog diameter has been assumed. Visibility will not be very good at the extreme ends of this range, and the image quality will also be degraded. The angular diameter of the Sun and Moon is close to one-half degree; a Total Field greater than one-half degree means those objects can be seen in their entirety through a fixed telescope by moving the eye. Central Image shows a thumbnail of a geometric ray tracing simulation of the image size and quality expected in the central 1 degree of image space (i.e., the central 1 degree of the view as seen magnified through the eyepiece). The assumed target is a 2 arc-minute square white card at infinity with three black bars having a separation (between centers) of 10 arc-seconds (i.e., these are the angles it would subtend as seen by the unaided eye). Click on the thumbnails to see full-sized simulations. The expected resolution of Galileo's telescopes has been calculated using Ronchi's dispersion data for Galileo's objectives (see below). All other simulations have been calculated using the dispersion curve for BK7. All lenses are assumed to have perfectly spherical surfaces over the diameters used, and the distance from the front surface of the objective to the front surface of the eye lens has been set equal to the specified Tube Length. At other lens spacings, the images would be expected to look a little different. For further details of how the simulations were created, and to see how the images are expected to change as the tube length (focus) is varied, see our Focus Page. Based on test photos of a similar target pattern taken with the website telescope, the present simulations systematically underestimate the actual resolution and make the images seem considerably more colorful than they actually appear to either the camera or the eye. That is, the actual images at best focus will likely look both crisper and less colorful. Nonetheless, the present simulations should be useful for comparing the relative performance of the various configurations. That is, if the simulations show that the resolution of one configuration is better than another, then it will likely be so in reality. More accurate, and less ambiguous, estimates of the likely resolution achievable with any given configuration can be made using a slightly different software that predicts the appearance of closely spaced point sources (results not shown here).

Some Possible Lens Combinations

#	Objective	Eyepiece	Aperture (mm)	Tube Length (mm)	Power	Single Field/ Vignetting (arc-min)	Total Field (deg)	Central Image	Cost
1	GAL 1A	GAL 1B	26	1223	14.0	5.7 to 15.6	0.51		-
2	GAL 2A	GAL 2B	16	906	20.2	11.0 to 16.5	1.00		-
3	GAL 3	GAL 1B	38	1593	17.9	3.8 to 12.6	0.39		-
4	GAL 3	GAL 2B	38	1652	35.4	5.6 to 9.7	0.55		-
5	KPX124	NT45-028	23	949	20.0	9.5 to 17.2	1.39		$38.80
6	NT45-282	NT45-022	23	707	18.75	12.1 to 22.9	1.45		$45.30
7	011-2370	NT45-022	28	959	25.0	9.3 to 16.6	1.07		$41.80
8	011-3380	NT45-022	48	959	25.0	6.7 to 19.2	1.07		$46.80
9	011-3384	NT45-028	48	1449	30.0	5.3 to 12.3	0.91		$47.80
10	011-3386	NT45-026	48	1899	20.0	2.8 to 11.1	0.69		$47.80
11	011-3392	01 LPK 058	48	3850	26.7	1.9 to 5.0	0.42		$44.00
12	15.015	15.07	63	1200	13.3	14.5 to 23.3	2.93		$33.12

1. Galileo's Telescope #1.
2. Galileo's Telescope #2. Expected resolution significantly poorer than #1 due to smaller aperture.
3. Galileo's Broken Objective with Eyepiece from Telescope #1. Expected resolution very similar to Example #1.
4. Galileo's Broken Objective with Eyepiece from Telescope #2. Shorter focal length eyepiece increases power, but has very little effect on resolution.
5. The replica telescope used to take all photos shown on this website. Expected resolution similar to #1.
6. Longest focal length Galilean refractor possible with Edmund lenses. Resolution not as good as present telescope.
7. This was formerly the cheapest configuration, using Melles Griot lenses since increased in price. Resolution similar to website telescope
8. Increasing aperture without increasing tube length increases light grasp, but degrades contrast.
9. Contrast improved by lengthening tube. Still better if stopped slightly. May be a closer approximation to Galileo's "Discover" telescope.
10. Still longer focal length. Same power as present telescope; slightly better resolution due to larger aperture and longer tube length, but smaller field.
11. Extremely long tube (12-1/2 feet -- more than twice the length of any telescope known to have been used by Galileo) comes still closer to achieving the theoretical resolution of a 2-inch objective, but with a very small field of view. The aperture and focal length of the objective are similar to the one used by Christian Huygens (but with a positive eyepiece) to discover Saturn's moon Titan in 1655. For those interested in such very long refractors, there is interesting article by NASA planetary scientist Alan Binder in the April 1992 issue of Sky and Telescope (pp. 444-450). Inspired by the late-17th century telescope makers, Binder made a 3-inch singlet objective of 17 foot focal length from a piece of window glass, and mounted it in a long square wooden tube suspended from a pole by rope and pulleys a la the famous engraving of Hevelius' 150 foot aerial refractor. He made his own eyepiece as well, and has had great fun observing the planets through this instrument.
12. This example, using two Rolyn ophthalmic lenses, is very similar optically to Galileo's telescope #1, albeit with a larger aperture. The Rolyn catalog does not give a clear specification as to the shape of the meniscus. We have assumed a fairly extreme front surface radius of curvature of 75 mm, to illustrate the greatest likely image degradation caused by the meniscus shape. At the present f/ratio this degradation appears to be quite slight, although the best focus is farther inside the nominal position than in any of the other examples. Compared to Example 1, this telescope appears to have slightly better resolution and slightly poorer contrast; effects which may result solely from the larger aperture. Stopping the objective to a diameter of 23 mm gives a predicted image very similar to that of Example 1.

Additional Web Resources

An example of a student-built Galilean telescope and mountings are given on the Rice University's Galileo Project website. There are two pages showing pictures of their projects: one showing the telescope and its original mounting and another showing the same telescope on a new mounting. Since the lenses are specified in diopters, it would appear this telescope may have been constructed from eyeglass lenses cut to the desired circular diameter. Eyeglass lenses have two problems. The first problem is that, since the 1800's, at the suggestion of William Wollaston, eyeglass lenses have been built to a curved "meniscus" shape. They typically have a radius of curvature of about 75-100 mm, with the power of the lens coming from a small difference between the radii of the front and rear surfaces. As the wearer gazes in different directions, his eye rotates in its socket, but due to the curved shape, the visual path is always more or less normal (perpendicular) to the glass. This was found to reduce distortion. However when used as a telescope objective, the rays are all nearly parallel, and a much flatter configuration, such as the plano- or bi-convex lens is more appropriate. The second, and more serious, problem is that eyeglass lenses are only intended to be used over the 4 mm or so diameter of the observer's pupil, and the quality for that application does not have to be very high. When used as a telescope objective, the whole lens is being used at once, and its different parts may not work well together. Although Galileo may indeed have used the eyeglass lenses of his day (which seem to have been plano- or bi-convex in shape), he is believed to have sorted through hundreds of hand-made lenses to find a very few suitable for use as telescope objectives. His extreme care in the selection of the lenses is one of the keys to the success of his telescopes compared to those attempted by his contemporaries.

For those seeking historic authenticity, the readily-available article by Edison Pettit gives complete details, including cutaway drawings, of a replica of Galileo's long paper-covered 14-power telescope commissioned by George Ellery Hale in 1923. Scientific replica builders Jim and Rhoda Morris explain how they created an authentic-looking Renaissance covering for a replica of the shorter leather-covered 20-power telescope, used as a prop in a television documentary about Galileo. More recently, the Morrises visited the History Museum (IMSS) in Florence in connection with a commission to make an even more exact replica of the 20-power telescope for Griffith Observatory in Los Angeles. Their new webpage gives viewers a unique chance to see how the two telescopes attributed to Galileo are currently displayed at the IMSS. They also reproduce IMSS photos showing details of how the tube of the 20-power telescope was constructed from a series of thin wooden slats bound together with a resinous glue. Although the Morris' attention to detail is certainly commendable, it is, as mentioned earlier, unlikely that either of the IMSS telescopes was actually used by Galileo for his astronomical observations.

Ready-made "Galilean" Telescopes

The ProjectStar Telescope

For educators seeking a cheap solution for very young students, Project STAR offers a complete kit for constructing a 16-power refracting telescope of 400 mm focal length with a 43 mm diameter objective lens. The lenses are made of plastic, and probably molded. This kit, designed by the Harvard-Smithsonian Center for Astrophysics, was reviewed by Alan M. MacRobert in the April 1990 issue of Sky and Telescope (pp. 384-7), two years before the results of the interferometric tests of Galileo's lenses were known. MacRobert evidently subscribed to the commonly held view (in 1990) that Galileo's telescopes were of very poor quality; for although he says the Project STAR telescope is "a telescope that Galileo would have envied," he also says that the quality of the lenses in the seven kits he examined varied from "bad to wretched." It should also be noted that, at the time of the review, the eyepiece lens supplied with the kit was plano-convex; meaning that this is a Keplerian refractor, producing, as MacRobert points out, an inverted image with a much wider field of view than a true Galilean telescope. The contents of the Project STAR kit appear to have changed a little since 1990 (they now include the cardboard tubes and additional fittings), but the current on-line description does not specify if the eyepiece lens is convex or concave, it only says this telescope "is similar to Galileo's" and permits students to "see how the moon looked to Galileo." A complete Project STAR telescope kit currently sells for $9 plus shipping. In bulk, the kits can be purchased for $5 each.

As should be obvious from the rest of this website, we do not subscribe to the view that Galileo's telescopes must have been of poor quality. The Project STAR telescope may indeed provide some insight into how stopping down an imperfect lens can improve its performance; and, as MacRobert suggests, it is even likely that some of Galileo's contemporaries attempted to construct telescopes using lenses as bad as he suggests these are, but we do not feel that encouraging older students to look through a poor quality Keplerian telescope will give them any true sense of what Galileo actually saw. However, the dual myth that singlet refractors (even with good lenses) produce terrible images, and that the lenses available to Galileo must have been worse than the poorest of modern lenses has been repeated for so many years that it has assumed an aura of truth quite independent of reality.

The Telescope1609 Kit

Telescope1609.com is a new web-based company that offers a ready-made kit, including glass lenses, for assembling a 50 mm aperture 13-power Galilean telescope (1000 mm focal length double convex objective with -75 mm focal length double concave eyelens). The basic kit, sold for $29.95 plus shipping, provides the lenses and telescoping cardboard tubes. The tubes need to be cut to length and assembled. In the deluxe kit ($34.95), the tubes have been pre-cut, requiring only assembly and gluing. The tubes are not sprayed inside, or baffled, to suppress reflections. The 50 mm diameter eyepiece lens is stopped down to 5/8-inch (16 mm). The manufacturer informs us this is done because the lenses are poorly figured around the edges. The website provides full directions for assembly and may be helpful to those building cardboard telescopes of other powers with their own lenses. This particular telescope's power, although it exceeds that of most binoculars, is, unfortunately, marginal for reproducing Galileo's astronomical observations. The manufacturer's claim that this telescope has a 1-degree field of view (twice the diameter of the Full Moon) seems exaggerated. Possibly this refers to the total field that can be seen moving one's eye around the eyepiece stop when the telescope is pointed in a fixed direction (this value would increase to about 3 degrees if the eyelens were left at its full 50 mm diameter).

The Telescope1609 manufacturer kindly sent us one of their Deluxe Kits for evaluation. We found it to be as essentially as advertised. The lenses are indeed glass, the kit required only a few minutes to assemble and it performed reasonably well, but not as well as the website telescope. There was a noticeable asymmetry in the appearance of images formed in different parts of the field, and this seems to arise in the objective rather than the eyepiece. When examined with a higher power eyepiece the image shows the classic signature of astimatism: that is, a star appears as a line rather than a round dot, and the orientation of the line shifts by 90 degrees as one goes from inside to outside the best focus. This is undoubtedly due, at least in part, to the quite substantial wedging of the objective. The edge thickness of the sample lens varied by more than 0.5 millimeters over its 50 mm diameter. The field of view visible at any one time is a little under one-half degree (about 27 arc-minutes). As expected, the visual power is not really adequate for reliving Galileo's observations (Galileo himself said a minimum of 20 power was required to reproduce even his earliest observations). As a consequence of the low power and imperfect image we were unable (visually) to detect any of Jupiter's moons from our urban site. We may eventually post a photograph of a test target taken through the Telescope1609 unit. As with all commercial products mentioned on this webpage, our description of it does not constitute an endorsement.

The Galileo GR-1 Replica Telescope

The Galileo Visions Telescope Company, a manufacturer of binoculars, telescopes and accessories for amateur astronomers, sells a brass 20-power refractor. It can be purchased on-line from its manufacturer. The price is quoted as anywhere from $100 to $150. It is claimed to be an exact replica of the telescope that Galileo demonstrated at a banquet held in his honor in Rome in March, 1611 (this is the banquet at which the word "telescope" is supposed to have been proposed as a new name for describing devices like Galileo's), and to duplicate one of the telescopes at the IMSS. We do not know exactly what telescope Galileo may have demonstrated in Rome, but (although there is some resemblance in shape) neither the polished brass tubing nor the helical focuser of the GR-1 seem to match either telescope at the IMSS.

In response to an e-mail, the manufacturer tells us that the GR-1 is intended primarily for its decorative appeal. It appears to consist of a modern small-aperture refractor in an antique-looking housing. The objective is a 50 mm achromat (doublet) of 700 mm focal length. The manufacturer says the GR-1 produces an upright image, but we are not sure if this is accomplished with a singlet eyepiece (small Galilean field of view), or a modern multi-lens erector system (much larger field of view). They also point out that the GR-1 is quite heavy compared to their other refractors of similar size. Even though Galileo's first telescope consisted of lenses placed at the ends of a lead tube, his later astronomical telescopes are believed to have been quite light weight.

Images © Tom Pope and Jim Mosher
Last modified: February 27, 2008