PROBABLY HALF OF THE TELESCOPES built by amateurs are of necessity made portable because their owners lack a suitable place to erect them permanently. And of these more than half are designed for limited portability within only 100 feet or so of the house. The means for moving such instruments need not be elaborate; the simpler the better. All manner of contrivances have been devised for this purpose, and one more example is shown in the illustration below. The carrier and the telescope base and mounting were built by C. W. Flohr of Denver, Col. The telescope proper, that is, the tube and the optics, was built by C. S. Walton of Wheatridge, a Denver suburb.

The base of this telescope is a light, hollow plywood structure open at the bottom. "It seems to squat down solidly almost, anywhere you put it," Walton writes. When the telescope is set up for use, the light wheelbarrow on which it has been trundled is detached like a sulky from a race horse and temporarily pushed into a corner. Roger Hayward's drawing shows the wheelbarrow and the manner in which it is temporarily attached to the telescope.

"The telescope is restrained from flip-flops by the handles and by a hinged latch," Walton says. A pushed conveyance such as a wheelbarrow in which the weight hangs from the arms of the pusher is inherently under better control and less accident-prone than the pulled four-wheel truck that is sometimes used, the stability of which is wholly dependent on the bumpiness of the ground.

Flohr's telescope is neither rough nor uncommonly elegant, but it is a type that many could build as, perhaps, their second instrument. It embodies a few relatively inexpensive machining and welding jobs that most amateurs are not equipped to perform at home, but there is plenty of evidence that in the average case the expenditure of about $10 for outside work is not a consideration that blocks the construction of an instrument.

The polar axis is a length of two-inch pipe that has been turned smooth in a lathe and rotates on simple bearings of wood, an excellent material for bearing-boxes. The declination axis is also a piece of two-inch pipe turned smooth. It rotates within an open-topped box of bent sheet-metal welded at the ends and without special bearings. "We didn't think such bearings would get hot," Walton comments.

The counterweight is a large, heavy, solid rubber ball.

The tube is free to rotate to place the eyepiece at the most comfortable observing position. "I wouldn't have anything else," Walton writes, after much experience with telescopes, including a 17-inch reflector that he made. This feature is being included in telescopes more and more often, by providing for either rotation of the whole tube by loosening its clamping bands or for rotation of the head alone.

A number of interesting comments on this proposal have been received. There is also evidence that the optical manufacturers have been at work on the problem.

James E. Lipp of Santa Monica, Calif., comments: "If we substitute the word 'uncoated' in place of Webb's word 'blackened' most of the result he desires could be obtained, since an uncoated area of glass reflects but a small percentage of the light that falls upon it. The method is to use a specially arranged set of masks and source of material to be deposited during the aluminization of the primary mirror by the evaporation method.

"The drawing [Figure 2 ] shows an arrangement to take care of the central and edge zones. The molten aluminum is in a small round crucible. A disk-shaped central mask is placed between the crucible and mirror and is supported from the center of the mirror. An annular mask with an opening larger than the disk is supported from the bell jar or another structure. Because of the finite size of the crucible each mask will cast a shadow on the mirror having an umbra (completely uncoated) and a penumbra with a smoothly tapered density of coating. With a given size of crucible the sizes of these two zones can be governed by the diameters of the masks and their distances from the mirror.

"Strips connecting the disk and annulus can be used as masks to offset spider diffraction. A better idea," Lipp continues, "contributed by James S. Thompson of Santa Monica, would seem to be to support the diagonal by means of a plane-parallel glass plate covering the entire aperture of the telescope, thus getting rid of the spider itself. The pane should have a nonreflective coating. It may be possible to apply a nonreflective coat just prior to aluminizing. This would further decrease the returned light from the unaluminized area without (I hope) affecting the reflectivity of the useful area."

Lyle T. Johnson of La Plata, Md., makes a proposal that is similar but different in detail. "Webb's anti-diffraction idea," he writes, "is very interesting. The result could be accomplished by aluminizing. The equipment could be set up as in John Strong's method for figuring mirrors by aluminization, described in his Procedures in Experimental Physics, pages 180-185; that is, by adding 'nonuniform films with the thickness of the film varying in just the manner required to parabolize a spherical mirror.' A diaphragm something like the one shown in the drawing [at the upper right in the illustration on the next page] could be used. Instead of building up the thickness for figuring purposes, it would be reduced to allow light to pass through without being reflected.

"The aluminum coating would have the usual thickness over most of the mirror, but it would taper off to nothing at the edge and at a spot at the center. This tapering of the coating would have the same effect as a zone, so the mirror would have to be figured with a turned-up edge and a high zone around the center to compensate."

William Sinton, a graduate student in the department of physics at the Johns Hopkins University, read Webb's proposal and pointed it out to the experimental physicist John Strong, for whom he is a research assistant. Sinton has made a six-inch telescope mirror and has devised a new stellar interferometer for measuring double stars that gives achromatic fringes. Strong asked him to prepare an analysis of Webb's proposal which, Sinton believes, contains merit but needs modification. He writes:

"It seems to be an idea of Webb's and probably of many amateur astronomers that it is the sharp edges that cause diffraction or diffraction effects. This, however, is not the case. You correctly stated the situation when in introducing the proposal in the May issue you wrote that 'diffraction is a process that goes on continuously in all wave fronts.'

"There is a set mathematical procedure for finding the diffraction pattern formed by an object that blocks off part of a wave front. Simply stated it is this: The diffraction pattern in terms of amplitude of light is the Fourier integral transform of the object. Actually this is not strictly true in all cases, but it is quite applicable to telescopes. To get the diffraction pattern in terms of intensity we square the amplitude pattern. In most cases the integrals that are involved are too difficult to evaluate in simple terms. Problems dealing with circular apertures usually involve Bessel functions, which most people abhor. But I have worked out a couple which will throw light on Webb's suggestion.

"The diffraction pattern of a circular opening such as the lens in a refractor is proportional to (J₁ (t)/t)², where J₁(t) is the Bessel function of first order, and t is a coordinate in the image plane of the objective and is proportional to the radius from the center of the pattern. This function is plotted in the two graphs [at the lower left in the illustration on this page]. The normal diffraction pattern of a refractor is obtained by rotating the diagram about the ordinate axis. The height of the resulting figure at any point is the intensity of the diffraction ring or Airy disk at this point. (After their first minimum all the diagrams are blown up by a factor of 10 to emphasize the rings.)

"The diffraction pattern of a reflector with a secondary mirror one-third the diameter of the primary is also shown in the first graph, as is its mathematical expression where a is the ratio of the diameter of the secondary to that of the primary. One-third is admittedly rather large, but it was desired to find the effect in an extreme case. From the first graph we see that the first dark ring has moved in [full line] toward the center. In other words, the Airy disk is now smaller and the telescope will actually show higher resolving power than without the obstructions. This is because most of the light comes from near the edges of the mirror. The increase in resolving power is entirely similar to that obtained with the Michelson interferometer where the whole objective is replaced by two parallel slits at opposite edges of the objective. Notice also that in general the rings have become stronger, but the first ring is only about twice as strong.

"Now we take up Webb's suggestion. Instead of just tapering the edge for an eighth or a quarter of an inch as he suggested, I went whole hog and tapered as shown in the diagram [in the lower right-hand corner of the illustration]. The transmission of the lens or the reflectivity of the mirror decreases from the center out to the edge as shown. The reason is that this was easy to work out, whereas Webb's tapering would have been much more difficult. The diffraction pattern is shown in the graph [at the lower left in the illustration] in comparison to that of the normal objective. The first dark ring has moved farther from the center. The Airy disk is larger and the resolution is somewhat reduced. However, the rings are also reduced. The second ring now just barely shows on the graph, and the rest not at all. The reason is in the formula for the new pattern which is shown on the graph. The intensity in the rings of the normal pattern is approximately proportional to 1/t³. For the modified pattern the intensity is proportional to 1/t⁵. This gets smaller much faster than 1/t³ as t gets larger.

"A numerical example will help here. Suppose we want to see the companion of Sirius, which is only 1/10,000 as bright as Sirius, with a six-inch telescope. The companion is at present about five seconds from Sirius. With the normal telescope the intensity of the rings at the companion is 1/2,700 the intensity of Sirius; the companion is lost in the glare. But with a filter over the objective which is faded in the manner described and is non-scattering, the intensity of the rings at the companion is only 1/610,000 the intensity of Sirius. The companion should then be all by itself. A few things should be noted. The intensity in the center of the Airy disk is one-fourth that of the unmasked objective, and the total light in the Airy disk is approximately one-third. Thus the limiting magnitude of the telescope becomes one magnitude less.

"It is seen that a tapering over only one fourth or one eighth of an inch will probably not do much good, but a drastic tapering over the whole objective has interesting possibilities. However, the loss in resolving power is something to be considered. The tapering could be useful, though, for seeking dark companions or perhaps for the observation of certain types of planetary detail.

"The general picture is that decreasing the light in the center yields higher resolving power but also increased ring structure, and fading out at the edges lowers the resolution and decreases the ring structure. Indeed, it is quite possible by the method of Fourier transforms to work backward. We can decide what diffraction pattern we want and then calculate how the lens has to be modified to do it. The only trouble is that for the diffraction patterns we might like to have this usually results in infinite-sized lenses. Whether there is some distribution that would result in a better general-purpose compromise than the normal objective, I don't know. It would certainly reduce the available light. In any event, the possibility of modifying the diffraction pattern to suit the needs of a specific problem should be kept in mind.

"I suggest that these filters might be made by evaporation of aluminum to produce partial transmitting or reflecting coats which are graduated during the evaporation by means of a moving diaphragm. Dr. Strong has corrected mirrors in this way. However, since the transmission depends greatly on how much aluminum is deposited, this effect will be difficult to control."

In a second communication Sinton says he has learned that the idea of reducing the diffraction rings by tapering over the whole objective has been worked out by P. Jacquinot and described in French in the Proceedings of the Physical Society (London), Series B, Volume 63, page 969 (December, 1950) and in Comptes rendus, Institut de France, Volume 223, page 661 (1946). There the method is called "apodization." Sinton has provided, as an alternative to the Bessel function approach to this problem, an approach by the method of vectors. This is available for loan to interested readers.

After seeing Lipp's proposal, Sinton commented further: "Lipp's suggestion seems to me ideal; I wish I had thought of the umbra-penumbra method. Yet his idea is tied to Webb's original distribution. Although I worked out a distribution by a mathematical formula I do not think this has to be adhered to very strictly. The important thing is to have a rather even tapering from the edge to the center. At present I am primarily interested in the problem from the standpoint of refractors, since I have the nine-inch refractor here at my disposal. For such an instrument a filter transmitting 100 per cent, or nearly so, in the center and tapering to zero at the edges can be made by the adaptation of Lipp's method shown in the drawing [second from the upper left in the illustration in Figure 2]. For the reflectivity distribution for mirrors I suggest the method shown in the drawing [third from the upper left].

"I asked Dr. Strong about the crucible source," Sinton continues. "He suggests that a coil of tungsten bent into a toroid will do as a disk source. With this it might be necessary to rotate the mirror to get an even distribution. With the simplifications, for which I thank Mr. Lipp, I hope to make one of these filters for the nine-inch telescope this summer. I don't plan to make it the same size as the objective, but instead to place it is the cone of light about two feet from the focus where it will have to be only about two inches in diameter. This will avoid the necessity for a nine-inch plate.

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