A grating ruling engine

Brian Manning

Scientific American, 232 (4), April 1975

In 1954 my interest in diffraction gratings was aroused by the desire for a grating to use in a spectrohelioscope. I knew virtually nothing about diffraction gratings except that they were expensive and that a successful one had never been ruled by an amateur. The idea of making one with a ruling engine of my own construction was attractive. I had completed several reflecting telescopes in my home shop, which has a 3-inch lathe and a drill press in addition to the conventional tools and materials for telescope making.

I knew that ruling engines resemble the shaper, a common power tool in machine shops. The shaper has a reciprocating ram that carries a chisel-like tool in a straight line. The chisel makes straight cuts in the workpiece during outbound strokes. The workpiece is displaced sideways automatically by its screw-driven carriage during each return stroke of the ram in preparation for the next cut. A well-maintained precision shaper can work to a tolerance of about 0.0001 inch. A ruling engine must work within 0.000001 inch!

As the late Albert G. Ingalls of Scientific American, who popularised telescope making as a hobby, once wrote: ‘On the scale of ultra precision with which we must deal in a ruling engine we may regard the machine as made of rubber!’ Ingalls pointed out that the screw in shifting the carriage can be elastically compressed as much as 0.00001 inch – 10 times the error that can be tolerated by the grating it pushes. This is why pioneering developers of ruling engines spent much time eliminating friction of the stick–slip type. The framework and the other parts of the ruling engine are similarly flexible because no perfectly rigid material exists.

More than 80% of all gratings employed in research have been ruled with engines of purely mechanical design. The uniform spacing of the rulings, and hence the optical quality of the grating, can be no better than the quality of the screw and its mountings. Like many amateurs I tried without success to make and mount a screw of the required accuracy. Finally I hit on the idea of achieving the desired precision by using optical measurements of carriage displacement to control the rotation of a crude screw (see illustration below). A similar scheme had been undertaken seven years earlier by George R. Harrison and his colleagues at the Massachusetts Institute of Technology, but I did not learn of that work until my engine had been finished.

Interferometer control As the first of several experiments to measure carriage displacement I set up a Michelson interferometer on a cast-iron plate. The moveable mirror of the interferometer was temporarily mounted on the end of a screw-actuated carriage of the kind that serves as a milling attachment on engine lathes. The light source was a neon lamp. When the instrument was in proper adjustment, it displayed a pattern of alternately dark and light interference fringes in the form of concentric circles that expanded or contracted as the carriage moved forward or backward. One difficulty was that the interval between bright fringes varied with the position of the moving mirror. Moreover, the conversion of the movement of the circular fringes into electric pulses with a photomultiplier tube turned out to be difficult. In time I learned of the Twyman–Green modification of the interferometer. In this scheme Michelson’s extended light source is replaced by monochromatic rays that diverge from an illuminated pinhole placed at the focal point of a simple lens. The lens bends the diverging rays into a parallel bundle. By adjusting the mirrors to be virtually parallel the experimenter can produce a constant difference in the path of the interfering rays over the entire aperture of the interferometer. The pattern of concentric fringes is replaced by an illuminated field that varies sinusoidally from light to dark. The pulsating light falls on a photomultiplier tube. The electrical output of the tube is correspondingly sinusoidal, and the pulses vary in proportion to the displacement of the mirror.

A monochromatic light source

Generating the interference effect throughout a 3-inch excursion of the moveable mirror requires that the interferometer be illuminated with light of a single colour. The efficiency of the lamp must also be as high as possible to minimise heat that would expand the engine and ruin the grating. The only adequate sources of monochromatic light prior to the advent of the stabilised gas laser were gas-discharge lamps, particularly those filled with argon and mercury vapour. They were expensive. For some years a relatively inexpensive krypton lamp was available, but its brightness was barely adequate. In the end I built a cadmium lamp. To avoid the difficulty of sealing electrodes in glass I excited the lamp with radio-frequency energy. My first lamp operated for about 10 minutes before turning black. After much experimenting I hit on the right combination of temperature, filling pressure and glass. Most recently I have made the lamps with an electromagnetically enriched isotope of cadmium (Cd-114) that I get from the atomic energy establishment at Harwell in England. The light emission of this material is largely free of the fine spectral structure that broadens the blue emission line at 4799.9 Å when ordinary cadmium is used. This line matches the spectral response of my Type 931A photomultiplier. The improved lamps have a minimum operating life of 1,000 hours.

The engine evolves

Having developed the optical measuring system, I proceeded with the construction of the first version of the engine. The principle of its operation was simple and remained so as the engine evolved. The moveable mirror of the interferometer is fixed to one end of the carriage that supports the grating. All other parts of the interferometer (indeed, all other parts of the engine except the driving motor, the stabilising flywheel and the electronic components, including a regulated power supply) are mounted on a thick cast-iron base and are enclosed in an iron box with walls a quarter of an inch thick.

The screw that drives the carriage is coupled to the motor through a magnetic clutch. During the return stroke of the ruling engine’s ram the clutch is temporarily engaged to rotate the screw until the electronic circuit counts seven interference pulsations. On the count of seven the clutch disengages, thus positioning the aluminium film to receive the next groove. The operation is repeated automatically until the grating is finished or something goes wrong. Seven pulsations correspond to a carriage displacement of 66.14 x 10^–6 inch, or 15,120 rulings per inch. The interferometer of the first version of the engine usually went out of adjustment after about half an inch of the aluminium had been ruled. The main reason was that the slideways were not rigid or straight enough.

The carriage slideway of the present machine consists of a straight steel bar 6 inches long and 1 inch square. This form was selected because it can easily be tested for straightness on an optical flat. I made three 6-inch optical flats of Pyrex glass expressly for this purpose, although in the end the bar had to be finished by observing the tilt of the fringes with the interferometer as the carriage traversed. Rotation of the carriage around the slide bar is restrained by outriggers carrying ball races that roll on straight cylindrical rails. A spring assembly on one of the outriggers can be adjusted to remove most of the weight from the slide bar. The lead screw has 26 threads per inch. It was cut on my 3-inch lathe and lapped for smoothness, but no attempt was made to correct errors of pitch.

At the end of the ruling stroke, a cam on the crankshaft that operates the ram closes the electronic circuit. A second cam on the crankshaft communicates rotation to the input of an electronic clutch. The clutch rotates the lead screw through a train of reduction gears. After the required fringe count has been made electronically the clutch disengages. The angular rotation of the lead screw averages about 0°.6 of arc per ruling.

The ram that carries the reciprocating diamond tool slides on a bar of steel eight inches long and ¾ inch in diameter. A friend ground the bar for me between centres of a precision lathe. The bar came off the lathe straight and cylindrical to within 0.0001 of an inch, and required only slight lapping. The ram consists of an aluminium ‘L’ section, and is supported on the horizontal slide bar by four bearing pads of Graflon. This remarkable substance appears to be the intimate mixture of polytetrafluoro-ethylene (Teflon) and graphite. Not only does it have the lowest coefficient of friction of any solid but also its static coefficient is lower than its dynamic coefficient. Therefore when Graflon slides, it does not exhibit stick–slip friction. The chattering movement that has been the bane of builders ruling engines for more than a century is thus eliminated. The bearing pads were cut from a sample of Graflon that was donated to me by the Morgan Crucible Company. The crank that drives the ram through a rocking-arm linkage that I devised to conserve space on the baseplate. The diamond tool The diamond tool or stylus does not cut the aluminium. It displaces metal sideways. The shape of

the tool resembles the keel of a boat. The diamond is supported by a dop made of copper wire. A

small hole to receive the stone was drilled axially in the square-cut end of the wire. Surrounding copper was then crimped over the diamond and fastened with silver solder. Excess metal was cut away from the mounted stone to expose areas that became the working facets.

The tool bears on the aluminium with a force of only about a gram, but in effect the minute working facet exert a displacing force of several tons on the metal. I first attempted to use the natural faces on a crystal of Carborundum, as the American physicist R. W. Wood had done when he pioneered the production of gratings for the infrared portion of the spectrum. When this effort failed, I polished flat facets on the Carborundum with a rotating copper lap charged with diamond paste. My first good grating was ruled with one of these tools. Its dimensions were 5/8 by 3/16 inch. Although the grating was small, it easily resolved the D lines of sodium.

Ultimately, however, I accepted the fact that a diamond tool is essential. I obtained a fragment of diamond from a shattered grinding wheel and fastened it to a mounting with cellulose cement. Through beginner’s luck the resulting tool worked splendidly until the cement gave way. I then attempted to cut facets on the diamond. The project almost drove me to distraction. The diamond consistently cut deep grooves in the laps, but no facets appeared on the stone. A visit to our local reference library produced the explanation. Diamonds can be polished in a reasonable length of time only if the direction of cutting is appropriately oriented for the crystal plane that is being abraded. The keel shape of the tool requires a minimum of three facets. The procedure for determining the cutting directions of each facet is complex and tedious. It is fully described in the technical literature.

During the final stage of polishing the facets are examined under a microscope with intense vertical illumination at a magnification of roughly 400 diameters. The intersecting edges of the facets should appear as perfect diffraction lines devoid of spots or thickening. The faceted diamond and its dop are assembled in the pivoted tool holder at an angle close to the desired blaze, which is the slope where the reflecting surface of the ruled grooves concentrates maximum light in the spectral order of interest.

Ploughing the aluminium grooves The grooves of blazed gratings are saw-toothed in form. A grating of 15,000 groves per inch, in which the reflecting surfaces are inclined at about 10° with respect to the surface of the aluminium and with which the second surfaces make a right angle, is blazed for the first spectral order. Initially I place the diamond tool as close as possible to the calculated angle. Then I rule and test a small grating, readjust the tool accordingly and repeat the procedure until the required slope is closely approached by successive approximations. Rulings blazed for the first order that are 66 millionths of an inch wide are about 12 millionths of an inch deep. As I have mentioned, the tool grooves by deforming the metal. For this reason the aluminium coating should be at least 30 millionths of an inch thick to allow unrestricted plastic flow. (At right is an electron micrograph of rulings.)

Figuring and aluminising the grating blanks

The equipment consisted of a 6-inch bell jar, a pair of piston backing pumps connected in series, a diffusion pump, and the kind of evaporating coils previously described in these columns (Scientific American, March 1960). Incidentally, I devised an inexpensive valve for operation between the backing pumps. Experiments demonstrated that an oil film across a small aperture prevents the flow of gas at pressures of up to about two torr. To make the valve I inserted a piece of gauze between the pumps. The gauze is wetted with oil during each stroke. During the evaporation of aluminium the optically flat glass blanks are rotated continuously by a synchronous motor that revolves at the rate of 30 revolutions per minute. In order to prevent outgassing, the motor was thoroughly cleaned, rewound with 20 turns of thick enamelled wire and lubricated with silicone vacuum oil. It runs on 1 volt and three amperes. I have no difficulty exhausting the system to a hard vacuum. Glass blanks were made originally by refiguring rectangular pieces of plate glass. Unfortunately the errors of flatness and parallelism of the new ‘Float’ glass are so large that the material must be ground, finished and figured with the aid on an optical flat.

Electronic control: temperature and barometric pressure

The electronic system consists of the photomultiplier, an amplifier, a neon-lamp circuit that transforms the sinusoidal output of the photomultiplier into a series of flat-topped pulses, a flip-flop pulse counter and a thyratron switch that controls the magnetic clutch. All these circuits use old-fashioned valves (vacuum tubes). Friends chide me for not switching to solid-state devices, but I am content to stick with my red-hot wires in glass bottles. They do not blow up if I make a wrong connection!

About two days are needed to rule 45,000 grooves in an aluminised blank three inches long. The ram makes 16 strokes per minute. Variations in the temperature of the engine must be minimised throughout the 48-hour interval to prevent dimensional changes that would ruin the grating. I keep the engine in a room on the north side of my house. A bimetal thermostat and an electronic relay control an electric room heater. The thermostat is close to but not inside the housing of the engine. I do not attempt to rule a grating during extreme variations of outside temperature. The controlled heater confines the temperature of the engine to excursions of less than 0°.1 C.

Variations of barometric pressure equivalent to one inch of mercury can cause an error in groove spacing of about 11 millionths of an inch per inch of grating length. The problem can be avoided by sealing the tank with a lid and a gasket and maintaining the pressure at 27.6 inches of mercury, plus or minus 0.003 inch. A small barometer in the tank is fitted with a photoelectric detector, which switches on a small pump to make up for leakage into the tank. The pressure is a little lower than the lowest barometer reading and ensures that the lid is always held on. The mass of the tank also averages out short-term temperature variation and damps vibration.

Ruling begins

To rule a grating I position a suitably prepared blank on the carriage. About 100 grooves are ruled to check the mechanism, including the action of the rocking-arm linkage that lowers the diamond into contact with the aluminium at the beginning of the ram’s traverse and lifts it for the return traverse. The electro-optical system is similarly observed to ensure that the carriage is indexing in appropriate increments. Ruling is then stopped. The electric heater continues to operate for roughly 10 hours until all parts of the machine reach a predetermined temperature. The engine is then started, but ruling is delayed for 30 minutes. During this interval final checks are made of the adjustment of the mirrors of the interferometer and the output of the photomultiplier. To start ruling, the diamond is lowered. During the ruling procedure the output of the photomultiplier slowly decreases owing to fatigue of the cathode surface. Full output is restored at intervals by increasing the brightness of the cadmium lamp. The adjustment causes small but acceptable errors in the spacing of the rulings.

Conclusions Although the interference-control system is capable of detecting the position of the carriage within a hundredth of a fringe (a tenth of a millionth of an inch), it is not easy to construct a mechanism that will advance the carriage with this accuracy. Precision is degraded by the effects of friction, the uncertain driving action of the screw and nut and the elasticity of the metal. The cam that drives the magnetic clutch is shaped so that for each advance of the carriage the rate of fringe counting is initially high and decreases almost to zero as the last count is approached. Even so there is some random overshoot. These small errors can be tolerated because they are random. On the other hand, diffraction gratings that contain periodic errors of groove spacing display false spectral lines known as ‘Rowland ghosts’ that flank the parent line. An example is depicted by the accompanying spectrograms (at left). The upper illustration displays the green spectral line of mercury at 5460 Å, together with flanking ghosts that are almost as intense as the parent line. This spectrogram was made with a diffraction grating that was ruled on an engine made by Henry A. Rowland at Johns Hopkins University. The photograph at right displays the sample spectral line of mercury as diffracted by a grating that was ruled on my machine.

Without interference control the gratings ruled on my machine would scarcely diffract recognisable spectral lines. Even with the control the engine is not without limitations. The carriage and the ram can rule aluminised blanks up to 2 x 3 inches in size, whereas the best professional machines accept blanks at least three times larger.

One of the most difficult problems with my machine was controlling the motion of the diamond to a single straight line as it reciprocates several tens of thousands of times. Putting a lubricant between the ram bearings and the slide bar introduces problems of variable film thickness. On the other hand, dry bearings operating at light loads acquire a high polish and start to wring, or adhere to the slide bar by molecular attraction. The Graflon bearing material shows a minimum of this effect along with low wear and freedom from stick–slip effects. Even so the ram is still subject to minute deviations.

Addendum : A piezoelectric crystal compensator

The original article for Scientific American mentions the problem of creep after the advance of the grating carriage has finished, and Maurice Gavin has asked me to write a note on the Piezo Corrector I made to compensate for this. I think I may have seen a reference at that time to the fact that this had been done on one of the large ruling engines, but this is so long ago that my memory is unclear on this.

If the creep were constant at all times, then the corrector would superfluous, unfortunately the carriage friction is not absolutely constant and results in very small errors of groove spacing, which can contribute to scattered light as well as a loss of resolution. Another effect is that it takes place during the diamond travel (during ruling of each groove). This has rather complicated effects. If the diamond travel was at uniform speed, and the creep also at uniform speed, then the result would just be straight grooves slightly inclined to the grating blank, quite unimportant. In fact the diamond motion is by a crank giving simple harmonic motion, combine this with non-linear creep and I will leave the reader to imagine the result. The effect on the grating would be small, but I enjoyed adding this refinement to the engine.

It so happened that at about that time I did some work at my place of work on the design of piezoelectric gas igniters and therefore had access to piezoelectric crystals. From data that I no doubt had, it was deduced that two of these crystals would produce sufficient displacement with an applied potential of up to 250 volts, and I could now use a high voltage transistor instead of a valve as 250v transistors were now readily available. The crystals were arranged with similar polarities on each side of a central electrode, both ends were then of the same polarity and had a common connection.

A subsidiary table had to be fitted on top of the main grating table. It had to be rather thin as there was little height to spare. It was supported on four leaf springs – a spring hinge structure with no motion lost due to joints and bearings. The piezo actuator with thinned down crystals being below it. The moving interferometer mirror had also to be transferred to this table.

The output from the interferometer is a sinusoidal wave form and the trigger point at which the carriage stops is at the half way point, which is set simply by observation of the output on a 5ma meter. The creep is of the order of no more than 1/10 of a fringe, and must not be too large in order to remain within the capacity of the corrector. The output that drives the meter is also fed to the high voltage transistor via some circuitry that delivers an error signal which causes the piezo crystals to contract and retract the subsidiary table by a distance equal to the main table creep; that is, the milli-ampere reading stays close to the midpoint reading of the interferometer fringes.

The corrector is switched off just prior to carriage advance and fringe counting, and is switched on immediately advance ceases and while the diamond is raised and lowered (out of contact with the grating) – the polarity having to be such that the subsidiary carriage is retracted and not adding to the creep! I would not swear to the exact accuracy, but from memory (I have not run the ruling engine for many years) it holds the position to a few milli-fringes.

This article was originally published in the ‘Amateur Scientist’ column of Scientific American, 232 (4), April 1975, and here appears in a modified form. Brian Manning was an engineering draughtsman when the basic work was completed, and a laboratory technician with the Department of Engineering, University of Birmingham (UK), when the article was originally published. He had the distinction of being the first amateur to make diffraction gratings of unsurpassed optical quality with an instrument of ultimate mechanical precision – a ruling engine. This project occupied him for two decades. He subsequently devised a refinement to his ruling engine (see Addendum, above) by utilising the piezoelectric effect on a crystal to minimise the ‘rubbery’ consistency of metal at the molecular level that his ruling engine probed. After his retirement he received an honorary PhD from the University of Birmingham and was awarded the Horace Dall Medal of the British Astronomical Association.