IN THE APRIL number, Dave Broadhead, Wellsville, N. Y., a leading member of the war-time Amateur Roof Prism Gang, described his "moist" technique of mirror figuring and in June told how he made a pair of matched 36" mirrors. July his modified Draper machine as described, and this month he gives compact working instructions for operating such machines with subdiameter tools. Except for fragments in Ritchey's classic book now out of print and rare, and a valuable paragraph by Ferson in "A.T.M.A.," page 84, (printings since June) nothing has been available to give the owner of a Draper machine his start in life. What follows will therefore be valuable. By Broadhead:

Nearly all machines used in precision optics are basically related to the Draper, with the following characteristic adjustments:

1) Rotating table, very slow-1/2 to 8 r.p.m. according to size of work, speed being governed by optimum balance of accomplishment against heat.

2) Reciprocating arm driving tools over work (stroke, S, Figure 1) at rate several times that of turntable-perhaps 5 to 1. Means to vary the length of stroke.

3) Means to vary the offset, O, or average path distance of the reciprocating arm from the center of the work.

4) Means to de-center, D, the driving pin so that more of the stroke takes place on one side of the center of the work than the other-usually only a fraction of an inch.

5) Variable ratio (cone pulley, for example) drive, so that speed of machine can be adjusted to size of work.

It is convenient to designate sizes of grinding and polishing tools, also stroke lengths and offsets, in abstract terms of decimal fractions of the size of the disk being worked. Thus, discussion becomes applicable to any size of work.

The discussion which follows will be confined to the tool on top method.

A good grinding tool should be channeled. It should be driven by a pin which bears deep down, close to the working surface, to reduce tilting thrust. Most important of all, it should be possible to choose a tool of such size that stroke can be balanced against overhang at will and thus gain fairly evenly distributed abrasion over the entire work, as will later be explained. Roughing tools of 0.66 (2/3) work diameter, and finishing or "truing" tools of 0.83 (5/6) work diameter, are strongly recommended. Their use is common practice. My tools are made by cementing blocks of glass on a steel backing but, instead of making the two tools described, I make only one, of 0.83 diameter, and make the outer ring of thinner blocks so as, by normal grinding down, to contact the work about when it would be desired to shift from the 0.66 to the 0.83 size. If this shift happens too soon it is easy to grind off the outer ring on a grinding disk or even on a wet grindstone.

The roughing tool is used with a stroke which passes near the center of the work and extends so that the edge of the 0.66-diameter working part of the tool just passes over the edge of the work. This tool is used with the coarsest abrasive until full depth of sagitta is reached. Sagitta should be measured with a spherometer having micrometer dial indicator-an inexpensive one is good enough for average needs-or one having a micrometer movement.

When full depth is reached the outer ring of glass blocks should start working, now an 0.83 tool. If it does, the stroke (S, Figure 1) is readjusted to about 0.35 diameter and the offset, O, to about 0.2. If, however, the outer ring of blocks does not yet hit it will be necessary to take a longer stroke- say 0.5 stroke and 0.3 offset-to hold the sagitta fixed till all the blocks are grinding.

We are still using coarse abrasive. Now assume we have run a wet or two with 0.35 stroke, 0.2 offset, and with the 0.83 circle of blocks all working. We read the spherometer and note whether we are deep or shallow. If too deep we run with 0.5 stroke and 0.3 offset to shallow the curve. If too shallow a very short 0.2 stroke with 0.1 offset will deepen it a bit. Still on same grade of abrasive.

When finally we have the right depth we change to next grade of abrasive. We must now discover the exact combination of strokes that will hold the desired depth of sagitta. This is very important. It is about the only "secret" I know. It is important because it is the combination of strokes which, after shaping has been accomplished, will yield and hold a sphere (Dévé's "condition of uniform wear." Dévé, "Optical Workshop Principles") without resort to guessing and other monkey work; while work whose radius is constantly being changed is having the center or else the edge ground faster than the other and therefore has differing zonal radii. True, an approach to uniform wear, an oscillation around a sphere, may be had by working half time erect, other half inverted. But an 0.83 tool is enough smaller than the mirror so that the stroke can be made concaving, convexing, or neutral, at will. Since machines and workers differ it is difficult to state an exact set of ratios that will yield a sphere. Start perhaps, with an 0.3 stroke and 0.2 offset and after each wet measure the sagitta.

Don't change to the third grade of abrasive until, by small changes in the adjustments, you have found the neutral position accurately. When you have it, grind and polish by it.

When polishing flats this "condition of uniform wear" works at its nicest refinement, a flat being a sphere having infinite, fixed radius. On a flat every slight change in stroke and offset is made evident-usually painfully so.

Final polishing for a sphere should be done at much slower speed, about 8' per minute polisher travel, than in grinding: heat. Close, tight contact should be held at all times.

Parabolize with small star tools, using great caution since a machine cuts fast. Overcorrect a little, then run the 0.83 lap a few moments (after careful pressing) on the neutral stroke to reduce the correction and smooth the figure. O Hell, it's late and I've got to go to bed.

End of Broadhead's notes.

Of course, after you get your hand in you will begin formulating your own rules which will probably differ, just as you differ. These then will be the correct rules-for you. The idea, often encountered, that there must somewhere be a single correct method in everything optical is hogwash.

THE SCHUPMANN telescope seeks a parent. Joseph Dwight, Hyannis, Mass., writes:

In 1899 Ludwig Schupmann, a German, was granted U. S. Patent 620,978 for the telescope that bears his name. It has the closed tube and long focus of the refractor, and the convenient view and short tube of the reflector. Imagine a conventional Newtonian, with a concave lens of crown glass resting on the mirror, and a convex lens of the same crown glass at the top of the tube, and you have the Schupmann, as in 7 of the patent illustration, Figure 2. The concave lens corrects the color error of the convex lens, and the mirror keeps the rays convergent in spite of the concave lens. The concave lens and the mirror may be combined in a concavo-convex lens, whose convex lower surface forms the mirror, as in 1. The separate mirror and corrector are shown in 2.

It seems that no one has taken the trouble to design a completely satisfactory Schupmann and that, perhaps for this reason, no completely satisfactory Schupmann has yet been made. It is therefore worth while to give the dimensions of a Schupmann which gives a good degree of magnification, though the field is small.

The lenses are of rolled optical plate made by the Pittsburgh Plate Glass Co. N=1.52, V=58.8. The objective and corrector have the lower face plane and the radii of their curved faces are 58.4" and 26" respectively, and that of the mirror is 56.8". The distance from objective to corrector is 58.75", and that from corrector to mirror is 0.55". These distances are measured between the edges. The diagonal is very close to the objective, and therefore not as in 7. The advantage of a separate mirror is that the mirror, if it has too shallow a curve, can be placed farther back of the corrector. If the corrector and mirror are combined in one lens, the curves must be exactly right. All previous makers seem to have submitted t this handicap.

I used 8" disks, which exactly fitted a strong paper tube. This facilitated accurate alinement, which is essential The objective was stopped down to 6", and the focal length was probably about 150". A 1" monocentric eyepiece gave an actual field of about 12'. As the tube was not mounted, an unsilvered diagonal was used, and only the moon was observed. The color correction seemed satisfactory, and the definition very good.

I believe that this telescope is superior to the Newtonian for magnification, owing to the great focal length and the closed tube. And the protected position of the silvered or aluminized mirror should be noted. The field probably has considerable curvature, but with a small field this is not very objectionable. It is, however, perhaps the chief fault that a designer should try to eliminate. I should add that my lenses were repolished by Mr. G. E. Gordon, a skilled amateur, of 6 Franconia Avenue, Natick, Mass.

Perhaps the easiest way to make a Schupmann would be to grind a plane mirror on the plane face of the objective, and an equi-concave corrector on the convex face. If the silvered plane mirror is placed at the bottom of the tube, the lower face of the corrector will act as the concave mirror. This combination can be tested on the moon and, even if not satisfactory, it will probably help one to estimate the best curvature for a concave mirror to replace the plane. It may then be necessary or desirable to give the corrector non-reflective coatings. Should the focal length of the objective be found inconveniently short in relation to that of the corrector, which I think unlikely, it can be lengthened till the proportion is the same as in the actual Schupmann described above. And the mirror can be made to correspond.

When the lenses of a Schupmann are correctly spaced, the image of Venus, both inside and outside focus, will be pure gold. The objective should be permanently fixed, and the corrector and mirror should be adjustable as a unit. If this unit is tilted, one edge of the moon's image will be reddish, and the opposite edge bluish. The moon's brightest crater, Aristarchus, should be colorless.

My telescope shows that the Schupmann should not be condemned because the first attempts were failures and that high-priced optical glass is not absolutely necessary. But ordinary plate glass or Crystallex are not recommended. And it will be safest to begin with an f/25 telescope.

Figure 3 shows the tube in a very crude mounting, used when I first experimented with this telescope, and is from Scientific American, 1943 April. The present tube has the lenses repolished and relocated, and they now give a much better image. The tube is, however, unmounted, as I prefer to give my limited skill and energy to the making of an 11-1/2" Schupmann having an equi-concave corrector, which I have begun. I hope that someone with more skill will make and mount a good Schupmann, and that some designer will show us how to get as good achromatism and as flat a field as possible. But I think the design given needs no apologies, provided alinement and adjustment are good.

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