About a century ago the corpuscular theory of light was falling into disfavor among scientific men in general and the wave theory was taking its place. Among the many contributions to the subject we find the writings of Fresnel. It was he especially who struck the decisive blow at the dying hypothesis. That part of his work which is of particular interest to us is his application of Huyghen\u27s principle to phenomena of diffraction

Boehm, W. M.

English

University of Northern Iowa

Proceedings of the Iowa Academy of Science Volume 9 Annual Issue Article 27 1901 A Ruling Engine for Making Zone Plates W. M. Boehm Copyright ©1901 Iowa Academy of Science, Inc. Follow this and additional works at: https://scholarworks.uni.edu/pias Recommended Citation Boehm, W. M. (1901) "A Ruling Engine for Making Zone Plates," Proceedings of the Iowa Academy of Science, 9(1), 181-188. Available at: https://scholarworks.uni.edu/pias/vol9/iss1/27 This Research is brought to you for free and open access by the Iowa Academy of Science at UNI ScholarWorks. It has been accepted for inclusion in Proceedings of the Iowa Academy of Science by an authorized editor of UNI ScholarWorks. For more information, please contact scholarworks@uni.edu. IOWA ACADEMY OP SCIENCES. 181A KULING ENGINE FOR MAKING ZONE PLATES.BY W. M. BOEHM.About a century ago the corpuscular theory of light wasfalling into disfavor among scientific men in general andthe wave theory was taking its place. Among the manycontributions to the subject we find the writings of Fresnel.It was he especially who struck the decisive blow at the.dying hypothesis. That part of his work which is of particular interest to us is his application of Huyghen's principle to phenomena of diffraction.According to this principle, every particle on the wave-front, I B, figure 19, may be regarded as the source and.center of a new wave. Suppose our figure were a sectionthrough a wave. A is the center of the disturbance; IBpart of the wave-front, and F some particle on the straightline passing through A B, and farther from A than the wave-front. We know that, in a homogeneous medium, IB, thesection through the wave-front, will be an arc of a circle. Ifthere is no opaque obstacle on the line between A and F, thewave will in time reach F, for light travels in straight linesin such a medium. But, suppose we had an obstaclebetween A and F. Why is it that we will not receive lightfrom the other particles on the wave-front if, as we have•said, each particle there acts as the center of a new wave?In other words, why will light not travel in a crooked orcurved path in a homogeneous medium? Fresnel's explanation is not the most satisfactory but is sufficient for thepresent purpose.He divides the wave-front into a number of zones. Inthe figure these are shown as arcs of a circle. The lineIF is equal to B F plus one half a wave-length. The next1Boehm: A Ruling Engine for Making Zone PlatesPublished by UNI ScholarWorks, 1901182 IOWA ACADEMY OF SCIENCES.line is half a wave-length longer than I F, etc., every line-is half a wave-length longer than the preceding. We willnot go farther into these details since they are now too-well known. Suffice it to say that, by simple mathematicalmeans we can show that the motions given to F by anyhalf zone are exactly balanced by the motions from thesucceeding half zone as a result of destructive interference.There is one exception to this, i. e., the motion transmittedby the particles in the immediate vicinity of B. Themotion from these particles is what causes the motionof F. It is evident that when we interpose some obstacle,,like the dark film of a photographic negative,, so that themotions from each alternate zone cannot arrive at F, wewill have the motions from the remaining alternate zonesarriving a F, practically, at the same time and in the same-phase. A negative of this kind will have a series of concentric^circles whose radii are proportional to the square roots ofthe respective numbers of the circles. Soret, in 1875, produced a plate of ninety-eight dark circles and obtainedsome very satisfactory results. In 1898 Prof. Wood, thenof the University of Wisconsin now of Johns Hopkins,,made a plate of 115 dark circles. He also produced phase-reversal plates, i. e., plates which were entirely transparentbut in which the alternate zones would retard the motionby one half a wave length. His results, in addition to aplate, were published in the Philosophical Magazine forthat year. His plates were made by first producing adrawing and photographing it afterwards. He used anordinary beam-compass. Now, anyone who has had thefortune to manipulate one of these instruments can appreciate the value of a steady hand, when he obtains goodresults. It was with the intention of producing theseplates with greater ease and accuracy that an engine, orrather machine, was built at the University of Iowa this,year.Mechanical details are always tiresome but, if you willdraw on your liberal supply of patience, we will considerthe engine which has enabled us to make plates of, not 2302Proceedings of the Iowa Academy of Science, Vol. 9 [1901], No. 1, Art. 27https://scholarworks.uni.edu/pias/vol9/iss1/27Huw Q3Boehm: A Ruling Engine for Making Zone PlatesPublished by UNI ScholarWorks, 1901Figure 214Proceedings of the Iowa Academy of Science, Vol. 9 [1901], No. 1, Art. 27https://scholarworks.uni.edu/pias/vol9/iss1/27IOWA ACADEMY OF SCIENCES. 183circles, but of 900 circles, in the short time of eighteenhours.First of all, the pen was not made to move about a centerand describe a circle as in the ordinary process, but thedrawing-board was made to revolve and the pen held stationary. In its general outline the machine may be seenin figure 20. A C is a long gas-pipe, selected on account ofits smooth surface and cylindrical form. At B the drawing pen is attached. The operator governs it by means ofa long brass rod between A and B. This enables him tolift the pen from the paper and lower it at will. Parallelto this rod there runs a long capillary tube through whichink is forced into the pen. The gas-pipe is fastened tothe bed of the dividing-engine DE. The drawing-boaVdis supported by a heavy steel shaft which rests in a conicalbearing at H.Figure 21 shows the method of attaching the pen to thegas-pipe, A. Two brass bars, D B and B F, form a hinge.The pen is fastened at B by an arrangement which permitsits removal. Here may also be seen the glass capillarytube through which the ink is forced into the pen. Thistube is fastened to the hinge in such a manner that thepen can be filled at any position of the hinge. A rubbertube, not shown in the drawing, connects this glass tubewith the capillary tube running to the operator's table.At F there is a spring which tends to keep the pen pressedmildly against the surface of the paper. When the operator desires to lower the pen he turns the eccentric at Dso as to draw F against the pipe and the pen at B descends.In order to lift the pen he reverses the process and thespring, which is attached to a screw at D, is drawn in theopposite direction. Thus one spring is made to do thework of two. At one time there was a second springemployed to raise the pen but it was found obnoxious andwas soon discarded. The screw which you see above thepipe at A is not used when a drawing is made. Its purpose is to hold the point of the pen in a constant positionso that depressions in the drawing table may be detected.5Boehm: A Ruling Engine for Making Zone PlatesPublished by UNI ScholarWorks, 1901184 IOWA ACADEMY OF SCIENCES.While the work is proceeding the pen becomes empty.The operator must have some means of watching the penand the paper just below it. For this purpose a mirror,E, is attached at an angle of about forty-five degrees tothe plane of the drawing-board. This reflects the imageof the pen toward the operator's telescope. Occasionally,the pen must be cleaned. This can be done without disturbing its position. The width of the line can also beregulated. The hinge is made to fit closely in order toprevent a motion of the pen from side to side. To providean additional safeguard against this possibility, a strongwire spring, not shown in the drawing, is attached to F soas to keep the end of the hinge drawn always to one side.'The pen can be moved up or down by gentle pressure butnot from side to side. It follows any slight elevation or.depression in the surface of the drawing-board.One of the most perplexing of the problems that had tobe solved was that concerning the drawing-board. Suppose we had a board seven feet square. In a damp atmosphere it would swell more in one direction than in theother, which is a very undesirable property in this case.Suppose you made your board in two sections, an upperand a lower, having the long fiber at right angles. Youwould be adopting the method of the man who made thewooden saddle. The surface of the board would not bea plane. After some deliberation the following methodwas adopted: several pieces of broad pine flooring weretaken and a line drawn down the middle of the broadside. Fifteen of these pieces were laid side by side so asto leave about three millimeters between each board andthe adjoining one. Over these was placed a second layerof boards with their medial lines also marked. Wherevertwo of these medial lines intersected a screw was driven.In all about 230 screws. This gives a board which willhold its shape sufficiently for the present purpose. Theexpansion in the direction of the long fiber is very small.At right angles to this direction let the wood shrink orswell for we have 'given it sufficient room to do' so in the6Proceedings of the Iowa Academy of Science, Vol. 9 [1901], No. 1, Art. 27https://scholarworks.uni.edu/pias/vol9/iss1/277Boehm: A Ruling Engine for Making Zone PlatesPublished by UNI ScholarWorks, 1901IOWA ACADEMY OP SCIENCES. 185interspaces. The board is revolved at the rate of aboutone revolution in twenty seconds, by means of a smallelectric motor and a system of pulleys. Both motor andthe pulleys have separate structures. The motor is placedon a pier which is free from mechanical contact with thebuilding. The vibrations produced otherwise do not reachthe pen or board so that the machine is practically freefrom all ordinary vibrations.The diameter of this drawing-board is about 2.10 meters.The sheet of paper used was seventy-two inches wide.[Since drawing-paper is a commercial article, the ancientsystem is,of course, used.] The dividing-engine DE, figure22, is only 45 cm. long. Now we should have a screw of morethan 100 cm. in length. In order to get around this obstaclethe following method was adopted: the gas-pipe, A B,was passed through two supports, KB, one at each end ofthe drawing-table. They were provided with screws, K,so that the pipe could be firmly fastened and not movedbackward or forward. To HGr, the movable bed of theengine, a solid iron bar, Gr, having the same width as thegas-pipe, is fastened. To this, in turn, are fastened threeflat brass bars seen at F. A visitor once remarked thatthey reminded him of the inclined stacks of an oceansteamer, but you may rest assured that the artistic effectwas not thought of during the construction of the apparatus. When mechanical perfection is impossible it iswell to provide for the imperfections that are detrimental.No attempt was made to drill a hole through which thebolts would exactly fit. When the operator desires tofasten the pipe to the engine he first forces the bars backas far as possible and fastens the two lower bolts. Thenthe upper bolt is fastened and thus the pipe is firmlyclamped to the bed of the engine. In order that theoperator maj< make measurements and watch the actionsof the pen there is mounted, at I, a Frauenhofer telescope,CF. It is shown a little higher than the gas-pipe butwhen in operation it is much nearer the same elevation.From A to K are shown in part, the lever which raises thepen and parallel to it the capillary tube for conveying the13 I A 88Proceedings of the Iowa Academy of Science, Vol. 9 [1901], No. 1, Art. 27https://scholarworks.uni.edu/pias/vol9/iss1/27186 IOWA ACADEMY OF SCIENCES.ink. An injector or, what is more to the point, a force-pump forces ink through the tube and into the pen. It isoperated by hand. Along the side of the dividing-engineyou may see a scale. A pointer from H shows the numberof complete turns of the screw.Figure 23 shows the engine as seen from the operator'send; the mounting of the telescope between F and I; theattachment of the gas-pipe between A and F; and at Dthe pointer to the side of the engine. There are twoother pointers to be seen here. They are flexible pointersfor the divided head which is of a peculiar construction.Instead of having one divided circle it has three. Thiswas invented after half of the first zone plate was completed and its value is quite apparent from the strikingdifference in the results obtained. In order to set theengine the figures were taken from a table of square roots,but these could not be used directly since the factor usedin this case was thirty. It was simple enough to multiplyby ten but to multiply by three involved the manipulationof some thirty thousand figures. It was an immense taskbut was cheerfully begun. The use of the new scale atthe side of the engine, combined with the new form of thedivided head, now makes it possible to set the engine directlyfrom the tables without the use of another figure. It maybe well to state here that the method of this divided headmay be applied in a general manner. The head may bedivided into any number of circles, not necessarily three,but the complementary scale, H, figure 24, should bedivided into the same number of parts for direct reading.If you will look at this scale, H, you will see .that eachdivisions represents a complete turn of the screw aridevery third division is numbered in succession. Suppose,for instance, you werd to set the engine at 11. 85. Youwould turn until the pointer on the scale, H, stood at 11. 00.Now you would look at the divided head and use the outercircle, but you would not find .85 on this. It reads from0 to .83.J. Turn the screw one complete revolution andyour pointer on H would be on the next division which isnot marked. Look at the divided head once more and use9Boehm: A Ruling Engine for Making Zone PlatesPublished by UNI ScholarWorks, 1901Figure 23.10Proceedings of the Iowa Academy of Science, Vol. 9 [1901], No. 1, Art. 27https://scholarworks.uni.edu/pias/vol9/iss1/27Figure J411Boehm: A Ruling Engine for Making Zone PlatesPublished by UNI ScholarWorks, 1901IOWA ACADEMY OF SCIENCES 187the middle circle. It reads from .33| to .66§, not so far as.85. Turn the screw another complete revolution andlook at the divided head; use the inner circle this timeIt reads from .66§ to 1. 00. The pointer on H is at thesecond unmarked scale, but if you turn till the dividedhead is set at 1. 00 you will find the pointer on H at 12. 00.Every third division on H is marked in succession. Thereare three spaces between 11. 00 and 12. 00. They correspond to three turns of the screw. The two unmarkeddivisions show which circle, on the divided head, to use.The two pointers are used to allow for the width of thepen. The one at the right was used for the odd-numberedcircles. Suppose the position of one of these circles werethe lower margin of E, figure 24. If we had only this onepointer your next line would be at I, say. But, this is toofar in a light zone by just the width of the line drawn bythe pen. The pointer at the left is set so that, turning thehead from the one on the right in the direction indicated,will move the pen forward just the width of the line itdraws. The operator then works by the following method:he draws the line E by setting the head on the rightpointer. For the next line he again turns until the properfigure appears at this pointer but instead of drawing I heturn and sets by the left pointer. He then draws F. Theprocess is quite simple and the operator becomes mechanical in his actions as the work proceeds.There is one more point to consider before closing:When the work is done with the beam compass, a smallconical hole in a tack serves as the center for all thecircles. We cannot do that with the present machine. Inorder to have the pen pass through the axis of the Drawing-table, or through the center of the circle it draws, thetable is firmly clamped and the pen moved over the paper.It traces a long straight line. Now the board is revolvedthrough 180 degrees, firmly clamped, and the pen movedover the surface as before. If the two lines coincide, thepen passes through the center; if not, it can ba adjusteduntil it does.12Proceedings of the Iowa Academy of Science, Vol. 9 [1901], No. 1, Art. 27https://scholarworks.uni.edu/pias/vol9/iss1/27188 IOWA ACADEMY OP SCIENCES.There are other details of more or less importance butthey must be omitted. In its present condition the engineleaves room for improvement and improvements are continually being made. If it were to be reconstructed now,it would probably be slightly different from its presentform. Many suggestions have been made; some are good,others worthless. In the face of these it is well to remember the words of Mueller:" Wer jeden Rath berathen will der kommt zu Reiner that."Just what the final results of the investigations with theplates will be only a prophet can tell. This will form thesubject-matter for other papers. It has not been theobject to consider the plates themselves, but the enginewith which we make them. We have been enabled toconstruct plates of 930 circles, more than four times thenumber drawn by Prof. Wood, but we can admire thepatience with which he applied a beam compass to 230.The investigations with the plates will probably take twoyears of time at least and then the results may be negative. But what is the spirit of the scientist if not tothrow aside years of labor and the most favored opinions,that the truth may be seen more clearly.The engine was first planned after January 1, 1901. Inits present imperfect condition it stands as the interruptedwork of the past year. Had it not been for Professor A.A. Veblen, president of this learned body, the work wouldhave come to an abrupt close before this. For his encouragement and many valuable suggestions I desire to expressmy gratitude.13Boehm: A Ruling Engine for Making Zone PlatesPublished by UNI ScholarWorks, 1901

A Ruling Engine for Making Zone Plates

https://scholarworks.uni.edu/cgi/viewcontent.cgi?article=7101&amp;context=pias

A Ruling Engine for Making Zone Plates

Abstract

Similar works

Full text

Available Versions

University of Northern Iowa