Friday, February 19, 2010

Newtonian Reflecting Telescope

This instrument is mentioned several times by Stephenson, probably because Isaac Newton, who invented it, is a central character throughout The Baroque Cycle. The first appearance is at pages 171 ff in Quicksilver. Daniel Waterhouse has the presentation telescope out in public in 1670, before it was donated to the Royal Society. According to my Encyclopaedia Britannica, that donation actually happened in January 1672, not in August 1670. Stephenson's description matches fairly well to photographs of the real thing (as in Wikipedia), except for another, more serious, anachronism.

The concave mirror (“dish”) at the closed end of the tube is said to be made of silvered glass. The process of chemical deposition of silver onto glass was not invented until 1835. (See e.g., Wikipedia.) Newton actually used speculum metal, an alloy mostly of copper and tin. It had long been used for making hand mirrors. The major deficiencies of speculum metal are, that it reflects only a fraction of the incident light when newly polished, and that it tarnishes rapidly, with degradation of the reflectivity. Such a mirror must be repolished frequently, with the danger of damaging the desired shape ('figure') of the surface. A silver-on-glass mirror is far superior, firstly because the silver has a higher initial reflectivity, and tarnishes more slowly. Secondly, a tarnished silver coating can be dissolved off the glass, and replaced by a fresh coat, without any effect on the figure of the glass.

The use of speculum metal for telescope mirrors extended beyond the discovery of chemical silvering, such as in Lord Rosse's six-foot diameter "Leviathan", finished in 1845. (See e.g., Wikipedia.) If Newton had made a silver-on-glass mirror in 1670, the switch-over would have happened many decades earlier.

At this first appearance, and in two other places, there are descriptions of the use of a Newtonian reflector for observing events on the surface of the Earth. There are several things to be considered in evaluating the utility of a Newtonian reflector as a terrestrial telescope.

The first of these is the nature of the image formed by the mirrors, which is to be examined with the ocular lens. I first looked through a Newtonian telescope in 1946, but this is the first time I have fully analyzed the image. The concave primary mirror forms a real image, which is both inverted across the axis of the mirror, and 'flipped' by the reflection. This could be verified by examination of the primary image in an 'off axis' (Herschelian) telescope. In that configuration, the primary mirror is tipped to one side, so that the observer’s head does not block the passage of light from the object to the mirror. The flipping of the image is revealed, for example, in that the sweep-second hand of a clock would seem to be moving counterclockwise, and lettering would be reversed.

In a Newtonian telescope, a plane diagonal mirror is inserted between the primary mirror and its focal point, thereby directing the light across the tube and out its side. This second reflection flips the image again. This real image is thus direct, in that lettering would appear normal, and a sweep-second hand would move clockwise. However, the orientation of this image must be evaluated by careful ray tracing through a telescope, as it is likely to be used.

The small presentation telescope, on its ball-and-socket mount, could indeed be used on a tabletop, especially if one wished to be as discrete as possible out in public. (That is how Waterhouse set it up, in Stephenson’s description, although there are few details given.) With the tube nearly horizontal and pointed at the object of interest, the most convenient orientation of the ocular (eyepiece) would be upward. For a person seated behind the telescope, bending forward to look down into it, the real image would be inverted, or equivalently, rotated through 180 degrees. For a person seated on either side of the telescope, bending forward to look down into it without moving it, the real image would seem to be rotated through 90 degrees. Any horizontal line, such as the edge of a step, would appear to be vertical. For a person seated at the open end of the tube, bending forward to look down into it, the real image would appear to be erect. The problem, of course, is that the person would have to contort his body awkwardly, in order not to block the light from entering the tube.

Lord Bolingbroke’s telescope [pages 539 ff in The System of the World] appears to have been essentially the same as Newton’s presentation telescope, but perhaps resting on a somewhat higher surface. He was apparently standing, “hunched over the eyepiece, twiddling the tube ... this way and that.” The ball-and-socket mount would require exerting enough force to overcome the friction, in order to adjust the angle of the tube below the horizontal. Lord Ravenscar noticed “the tiny lens of the eyepiece” as he stepped up to the telescope. That description certainly applies to Newton’s telescope.

One wonders where Bolingbroke got this telescope, so that he had it in July 1714. Newtonian telescopes were apparently not commercially available in that era, probably because Newton’s original model was not a good instrument. It had a spherical surface on the concave mirror, because Newton was unable to produce a paraboloidal surface, which would focus parallel rays to a point. Especially with the small f-ratio of about 3.1, spherical aberration would produce large fuzzy images of stars, or of each point in an extended object.

In 1721, John Hadley presented a Newtonian telescope of his own construction to the Royal Society. He had developed a method of producing and testing a paraboloidal surface on the primary mirror. His telescope had image quality comparable to the best refracting telescopes of the time. The renewed interest in the reflecting telescope led a London optical firm to start making them thereafter. (See e.g., .)

The “big Newtonian reflector” on Huygens’s roof in December 1687 [pages 755 ff in Quicksilver], would have been too long for someone to bend over its closed end and see into the eyepiece. Huygens could have made it himself; he had already made refracting telescopes. It was in some form of alt-azimuth mount, on a pedestal or tripod. At any rate, it was easy to “sweep ... the instrument back and forth.” The altitude axis might have been at about shoulder height. With the tube nearly horizontal, the most convenient orientation of the ocular would be horizontal, to one side or the other. For a person standing on either side, looking horizontally into the telescope, the real image would be inverted. Thus, the Newtonian reflector typically presents an inverted, direct, real image to the person using it conveniently, just as the objective lens of a refracting telescope does.

The ocular lens, to produce a virtual image from that real image, can be chosen using the same criteria, irrespective of the nature of the device which formed the real image. A true natural philosopher (Newton, Waterhouse, or Huygens) would use a positive (Keplerian) ocular lens for looking at astronomical objects. It is placed beyond the real image, and gives a magnified virtual image of it, without changing its orientation. Such a user would simply ignore the fact that the final virtual image is inverted. This is no problem with astronomical objects, because there is no preconception as to 'which way is up', for an enlarged image of a planet, nebula, or star cluster.

That is not the case for a useful terrestrial telescope, with which one expects to see people, things, and activities 'right side up'. In the present era, there are three ways to produce an erect final virtual image. The simplest is to use a negative (Galilean) ocular lens, placed between the real image and the device which formed it. The main disadvantage is a restricted field of view, plus the impossibility of superimposing cross-hairs onto the image.

Another way is to put a prism system into the path of the light converging toward the real image, to erect it by multiple reflections. This is fine for prism binoculars, but in a reflecting telescope it would block and/or scatter some of the light enroute between the object and the primary mirror. The first such prism system was invented in 1851 ( ), and so was unavailable for Stephenson's characters.

The third way is to insert a positive lens between the primary real image and the positive ocular lens. This 'erecting lens' produces an erect real image, which in turn produces an erect virtual image. This can have about the same width of field as the simpler Keplerian telescope, but it has several disadvantages for astronomical use. It increases the light path by at least four times the focal length of the erecting lens, which must be accomodated by additional tubing. For a Newtonian telescope, the additional tubing would 'stick out' from the side of the main tube. The brightness of the virtual image would be decreased, by reflection of some of the light at the added surfaces, and by absorbtion of light in the added glass.

Even worse, in the era of these stories, the only available lenses were single pieces of glass. Each lens would contribute its own chromatic aberration to the final virtual image. Newton's main reason for developing the reflecting telescope was to eliminate chromatic aberration in the primary image. Achromatic lenses, which reduce or eliminate chromatic aberration by using two different types of glass, were not invented until 1729 (Encyclopaedia Britannica).

Thus, the only reasonable way to produce an erect virtual image in a Newtonian telescope, available to Stephenson's characters, was to replace the usual positive ocular lens with a negative lens. It is intriguing that Newton's method of adjusting the focus, by changing the length of the main tube, would make this relatively easy. A person who regularly spied on his neighbors (Bolingbroke), might keep the negative lens installed at all times.

With this background established, we are ready to analyze Stephenson’s descriptions. Initially, Waterhouse was using Newton’s presentation telescope, which almost certainly contained a Keplerian ocular lens. (I have not found any reference which states that, but every diagram I have seen for the instrument shows a biconvex ocular lens.) It obviously did not have an erecting system between the eyepiece and the diagonal mirror. Thus every thing or person Waterhouse saw would have been inverted, making it difficult to identify persons or activities. There is also the fact that Newton’s telescope had an angular magnification of about 38x (Wikipedia). That is suitable for looking at astronomical objects, but it is ridiculously large for looking at things only a hundred yards away.

When Waterhouse, Fatio and Huygens were looking at Saturn with the big Newtonian reflector, they were almost certainly using a Keplerian lens. A short time later, with no mention of changing the ocular lens, Eliza was looking at a ship on the horizon. In a brief glance, Waterhouse was able to identify its sail plan, which would be difficult for an inverted virtual image.

Thus, in his mentions of a Newtonian telescope, Stephenson has apparently ignored the problem of the orientation of the image.

The final consideration, about using a Newtonian telescope for terrestrial observations, has operational and physiological aspects, which do not apply to astronomical observations. Almost every interesting (e.g., dangerous) terrestrial object can appear unexpectedly, and thereafter move unpredictably. In contrast, every astronomical object (except meteors and near-earth artificial satellites) is both predictable and very simple in its motion across the sky. Even the 'wanderers' (Sun, Moon, planets, and comets) come very close to sharing the motion of the 'fixed' stars over an observation period of several hours. Everything moves in a circle around the celestial axis, at about 15 degrees per hour.

Even if one idealizes the reflecting telescope by providing an erecting system, a suitable angular magnification, and low-maintenance mirrors (e.g., silvered or aluminized), it has a severe disadvantage compared to a refracting terrestrial telescope. (Stephenson typically calls such a thing a perspective glass, prospective glass, or spyglass. These names do not specify the exact nature of the instrument. It was most likely to be a Galilean telescope in that era.)

It is easy to acquire the enlarged image in a spyglass, because the axis of the observer's eye is parallel to the axis of the telescope. While continuing to look directly at the object of interest with both eyes, the observer interposes the spyglass before one eye, checking its alignment with the other eye. With a few minutes of practice, it becomes almost second nature. It is similarly easy to follow a moving object: move the head and the telescope together.

It is much more difficult to acquire the enlarged image in a Newtonian reflector, because the axis of the observer's eye is necessarily 90 degrees from the axis of the telescope. If the telescope is no larger or heavier than a spyglass, it could be held freehand. If the observer decided to hold it with the ocular upward, she could face the object of interest at all times. She would hold the telescope under an armpit, guessing which way to point it. Then she would bend her head forward, to look nearly straight down into the ocular. She would have to shift the alignment, either by guesswork, or with the help of someone crouching behind her to sight along the tube, until the image of the desired object appeared in the field of view. Thereafter, it would be fairly easy to follow a moving object. If it moved to the right, she would turn to the right. If it moved upward, she would straighten up somewhat. At some point, she might develop a 'crick in the neck', by keeping her head bent down.

Alternatively, the observer could decide to hold it with the ocular horizontal. The main tube would be horizontal in front of her, with one hand under the primary mirror, and the other hand under the open end. After spotting an object of interest by naked eye, she would then turn her whole body 90 degrees to one side, while raising the ocular to her eye. There would almost have to be an assistant alongside her, to sight along the tube, in order to acquire the image. To follow horizontal motion thereafter might not be too difficult, but it would surely take lots of practice, in order to learn how to tip the tube sideways in following vertical motion.

A mount for the telescope would not solve all these problems. The user herself could sight along the tube of the telescope at the object of interest. Then she must look 90 degrees away from the object of interest, into the eyepiece. With luck, the image would be somewhere in the field of view, but if the object had moved meantime, she must guess which way to move the tube to pick it up. The other eye is of no help. In trying to follow a moving object, the telescope tube is constrained by the mount. The user’s head must move to accommodate the motion allowed by the mount.

Altogether, birdwatching with a Newtonian telescope is almost too horrible to contemplate.

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