The mirror is next rinsed with water and swabbed with concentrated nitric acid, a powerful oxidizing agent which removes organic matter adsorbed on the glass. The swab for applying the acid is made by wrapping absorbent cotton on a glass rod and fastening it with cotton twine as shown in Fig. 1. Care is exercised in using the swab to prevent the end of the rod from coming in contact with the mirror face. This nitric acid treatment should be carried out in the container in which the mirror is to be silvered to avoid possible contamination later with oil from the hands when the mirror is handled. If it is necessary to handle the mirror, it is advisable to use rubber gloves.

Cleaning solution (chromic and sulphuric acid mixture) may be used for cleaning glass, but it is not ordinarily necessary. This solvent is very effective. Even paraffin and carbonized organic material may be removed from glass in cases where the glass and the chromic acid solution can be heated together.

After being rinsed with tap water, the mirror is treated with a concentrated solution of stannous chloride. This is removed after a few minutes by a very thorough rinsing. All chloride ions must be washed away, first with tap water and finally with distilled water. The mirror can stand in the distilled water until the silvering begins.

It is important in silvering to clean carefully all the receptacles and graduates used. A long stick with an ink eraser fastened to the end will be found helpful to remove water stains and other contaminations.

Brashear's process.⁴ The Brashear process is described graphically in Fig. 2. The three formulas for the reducing solution given there afford different ways to effect the same end. In the first formula the nitric acid slowly digests the table sugar, to yield the sugars dextrose and levulose. This requires time and so the solution must be aged before use. In the second formula this aging is accelerated by boiling, and the solution can be used as soon as it is cool.

In the third formula dextrose is used directly. The alcohol is a preservative, and it is not required for the second and third solutions unless they are to be stored, in which case the same proportion of alcohol is used as called for in the first formula.

There is danger of an explosion after the fourth stage, indicated in Fig. 2. The formation of the explosive, fulminating silver, is not particularly favored by the low concentration of solutions and moderate temperatures that obtain here, but these relatively weak solutions will give fulminate on warm days if they are allowed to stand. This compound explodes on the slightest provocation when dry and sometimes when wet. Accordingly, all spent silver solutions should be rinsed down the sink at once. Goggles are recommended for safety.

As soon as the reducing reagent is added, the silvering solution is poured over the mirror. Filtering is optional. The distilled water in which the mirror has been standing may or may not be poured off first. Soon after the reducer is added, the solution becomes dark brown and then black. After this, it gradually develops a muddy brown appearance. At this stage the deposit of silver on the mirror is already continuous or should soon become so. The container for the mirror and solution may be tipped from time to time to stir the solution and allow inspection of the surface. When the silver film covers the whole surface and as soon as black specks begin to settle on it, a light swabbing with a cotton pad is recommended. This rubbing must be delicate at first, but it may be more vigorous as the silver becomes thicker, the surface being inspected from time to time for bloom. Usually when the solution begins to clear, it is nearly spent, and since the possibility of bloom becomes greater at this stage, it is best to pour off the solution and rinse the mirror with distilled water. For a full silver coat, Brashear's process requires, on the average, from 6 to 10 minutes.

If a bright light, such as the sun, is visible through the coat, it is too thin. In this case the mirror should be covered with distilled water, and the chemical solution for a second coat prepared. Do not let the mirror dry between coats.

After a satisfactory coat is obtained, the rinsed mirror is rubbed with a pad of cotton until it is dry. The silver is burnished with a burnishing pad (chamois skin tacked on a Shinola shoe-polishing pad) to "compact" the coat. It is then polished with a similar chamois pad charged with optical rouge. The rouge pad may also be used from time to time to burnish away tarnish which forms on the silver mirror,

Rochelle salt process.⁵ Two solutions are required for the Rochelle salt process. Solution A is made as follows: 5 g of silver nitrate are dissolved in 300 cc of water and ammoniated, as in the Brashear process, so that the silver oxide precipitate formed at first is almost but not completely clear. In case it inadvertently becomes clear, it must be back-titrated with a dilute solution of silver nitrate, so that the liquid finally presents a distinct straw color. This is filtered and diluted with water to 500 cc. Solution B is made as follows: 1 g of silver nitrate is dissolved in 500 cc of water. It is then brought to a boil, and 0.83 g of Rochelle salt, dissolved in a little water, is added. The boiling is continued until a gray precipitate is deposited. The solution is filtered hot and diluted to 500 cc. These solutions may be stored for a month or so if they are protected from light.

To silver a mirror, solutions A and B are mixed, volume for volume, and poured at once into the silvering vessel. The quantity of solutions given above is sufficient for a thick film on a glass surface of 200 cm² area. The temperature recommended for silvering is 20°C. (68°F.).

Silver is deposited slowly by the Rochelle salt process; an hour may be required for a thick deposit to form. Partial reflecting films are obtained as desired by withdrawing the glass from the solution at the appropriate time. The progress of the deposition may be judged from auxiliary glass plates, which are removed from time to time to determine the progress of the coating on the main plates. Fig. 3 illustrates a simple test for determining when the silver film is half-reflecting (for 45° incidence).

Partial reflecting plates are washed with distilled water and dried. Afterward they are polished by a light brushing with an eiderdown powder puff charged with optical rouge, as recommended by Pfund.

Silver films are protected from tarnishing by covers of filter paper that have been soaked with lead acetate solution and dried. These covers are applied whenever the films are not actually in use.

Lacquering. Another procedure for protecting the silver from tarnishing involves coating the film with a thin layer of colorless lacquer. The layer of lacquer destroys some of the reflectivity of the mirror, and in addition it exhibits interference colors. R. W. Wood has pointed out that a thin transparent film of lacquer on a good reflector should not show interference colors.⁶ The colors usually exhibited by a lacquer film are due to frilling. This frilling can be observed directly only with the highest-power microscopes. Wood states that no frilling occurs and that there are, accordingly, no interference colors if collodion dissolved in chemically pure redistilled ether is used to lacquer the mirror.

In order to obtain uniform lacquer films with the ether solution of collodion, it is necessary that the ether evaporate slowly. The can illustrated in Fig. 4 is suggested for use in lacquering with an ether solution.

Gold and copper. A chemical process for depositing gold from solution is described by von Angerer.⁷ A process for copper is described by French.⁸

Sputtering. Although the sputtering phenomenon at the cathode of a glow discharge has been known for a long time,⁹ the mechanism of the process is not fully understood even now.¹⁰ There are two current theories of sputtering. One of these holds that the emission of metal by the cathode is pure thermal evaporation due to high temperatures attained in areas of molecular dimensions. These temperatures are produced by the energy of impinging ions. The other theory invokes a mechanism for transferring the energy of the gas ion into energy of a metal molecule which is similar to the mechanism by which the energy of a light quantum is transformed to energy of an emitted electron. However, in spite of its being incompletely explained, sputtering is understood empirically, and its practical application for obtaining metal films on glass is simple.

Sputtering can be carried out successfully under a wide variety of conditions. For example, the pressure of the glow discharge may range from 1 down to 10 mm. The cathode is naturally made of the metal to be sputtered, although its shape may vary considerably. The anode is usually aluminum or iron. The glow discharge is preferably produced by a direct potential, although an alternating potential can be used. The potential usually ranges above 1000 volts and frequently is as high as 20,000 volts. The residual gas in the sputtering chamber may be air, hydrogen, argon, or other gases. (The sputtering rate with helium is extremely low, and this gas is used for glow discharges where sputtering is to be avoided.) The surface to be sputtered is usually placed tangent to the boundary of the cathode dark space, although it may lie within or beyond it. The low pressure required can be obtained with a mechanical pump of small capacity on a tight system or with a faster mechanical or diffusion pump on a system equipped with a regulating leak.

A typical setup for the sputtering process is shown in Fig. 5. The sputtering chamber is usually a glass bell jar with a hole in the top for the cathode connection. It may be made from an old bottle with the bottom cut out and the base ground flat. It is best to have a glass plate for the base, although a metal one (preferably iron) will suffice. An aluminum plate can be used to cover any exposed metal parts which may give trouble by sputtering. It is advisable to heat all aluminum before it is used in order to drive off the machine oils which may be contained in it. Glass cylinders and plates, as shown in Fig. 5, are useful for confining the discharge. If these plates and cylinders are not used, the outgassing induced by the discharge may give rise to foreign substances deleterious to the film produced.

The cathode is fitted in the top of the bell jar as shown. It is pulled up against the square end of the depending glass tube by the connector wire. This wire is secured by wrapping it around the top end of the tube, where it is sealed with wax (Apiezon "W," shellac, or DeKhotinsky wax).

Batteries or motor-generator sets are ideal sources for the sputtering potential, but other sources of potential are often employed. An induction coil makes a convenient source of potential, giving partially rectified current. However, alternating current from a 10,000-volt neon-sign transformer can be used. It is advisable but not necessary to rectify the current from this transformer with a Kenetron rectifier.

The use of a milliammeter to measure the discharge current is advisable when making partially transmitting coats. When the sputtering equipment has been calibrated, this current serves as an index to determine proper exposure for obtaining a desired ratio of transmission and reflection. The sputtering rate can be controlled, for example, by adjusting the filament current of the Kenetron. The rate of sputtering increases a little more than linearly with the sputtering current, depending somewhat upon the conditions of temperature, pressure, and geometry which obtain. For work in which high reproducibility in the film thickness is required, it is advisable to use a fast pump and to wash the bell jar continuously with air or hydrogen. Inasmuch as the first part of the sputtering may be erratic and the discharge unsteady, it is well to cover the mirror with mica until sputtering has definitely started and become stable. This mica is mounted on pivots with an attached iron armature, so that it can be operated with the help of a magnet through the walls of the bell jar; or it may be operated by tipping the whole system.

The pressure for sputtering is usually adjusted so as to give a dark space of about the same length as the distance of the mirror from the cathode.

The cathode should be shaped so that the boundary of the dark space is roughly parallel to the mirror surface. For flat or nearly flat mirrors the cathode is made flat, while for strongly curved mirrors it should be correspondingly curved. A U-shaped sheet cathode can be used for coating the two sides of a plate at once, and a central wire cathode can be used to coat the inside of tubes, provided that their length is not much greater than their diameter. Conversely, a cylindrical cathode can be used for coating fibers on all sides at once and for coating the outside of tubes.

Hulburt states that the use of mercury vapor enormously increases the sputtering rate of chromium, aluminum, and silicon. Optical films of these metals were produced in less than 15 hours in this vapor. Good but not entirely opaque optical films of beryllium were obtained after sputtering for 60 hours in hydrogen and mercury vapor.

Clean dry surfaces and breath figures. To get a surface both clean and dry as required for sputtering and evaporation is a great deal more difficult than to clean it for chemical silvering as described above. Most surfaces cleaned and then dried with absorbent cotton or a towel are found to condense the breath in a gray film. The reason is that in the drying process the glass surface becomes coated with a layer of contamination, which is probably a monomolecular film of fatty acid gathered from the cotton. Water condenses on such a film in tiny droplets, while on a really clean surface it condenses in an invisible uniform film.

Surfaces can be chemically cleaned and dried in a desiccator. Such surfaces give a continuous deposit when breathed on. Also, surfaces may be dried with linen without 8 contaminating them, as Wm. B. Hardy has succeeded in doing. Hardy found it necessary, however, to use linen from which the oily compounds had been extracted with -pure benzene.

However, a method to remove the contamination picked up from the towel when the mirror is dried is more practical than to depend upon successfully avoiding such contamination. This dry cleaning can be effected by the action of ions.

The study of this action of ions on the surface of glass started with Aitken and Lord Rayleigh.¹² They found that when the tip of a blowpipe flame was passed quickly over the surface of the glass, it cleaned the surface and produced a so-called breath figure; that is, if one breathed on the glass, the moisture condensed in a gray film of fine droplets, except that where the flame had traversed the surface, the moisture condensed in the form of a continuous "black" film. T. J. Baker and others have carried the study of breath figures further.¹³ For example, Baker found that they were produced only by the hotter flames, which are rich in ions. Among the interesting, phenomena revealed by his investigation was that breath figures could also be produced by sparks, and that, curiously, they could be transferred from one glass plate to another if the two plates were held together but not quite in contact. He also discovered that the black area is a relatively good conductor of electricity and that the coefficient of friction between glass and glass was very high in the black area. Fig. 7 illustrates a simple experiment for demonstrating this difference in friction between glass which has been flamed and that which has not been flamed.

A. C. F. Pollard¹⁴ found it easy to obtain good adherent films of chemical silver on glass by passing a blowpipe over the surface of the glass before immersion in the silvering solution. He also found that for a short time a freshly fractured glass surface condenses moisture in a continuous black film.

As a parallel to Pollard's discovery, it was found that aluminum coats prepared by evaporation in vacuum adhere so tenaciously to areas that have been flamed that they cannot be removed by stripping Scotch tape off the film, although the tape removes the aluminum from regions not traversed by the flame.¹⁵ Also, the black type of condensation, as well as good adhesion of an aluminum film, occurs after a glass surface is exposed to sparks at atmospheric pressure or to a glow discharge at reduced pressure. The explanation of all these phenomena is that the ions of the hotter flames, sparks, or glow discharges clean the surface of the glass.

The practices adopted to effect a final cleaning of a glass surface are either to expose it to the brush discharge from the electrode of a high-frequency transformer at atmospheric pressure or to expose the glass to a glow discharge in an evaporation chamber while it is being evacuated.

Cleaning mirrors for aluminizing. When aluminum is deposited on a glass surface which is not adequately cleaned, the adhesion will be inferior to that exhibited by a coat on a properly cleaned surface. In most cases the mirror will look good at first but will develop countless tiny blisters after standing a day or so.

The first phases of the cleaning procedure for aluminizing are like those for chemical silvering. The preliminary cleaning with the rubber eraser is carried out with particular thoroughness. Small bubble holes in the face of the mirror that contain rouge and pitch from the figuring should be ground out with emery as shown in Fig. 8. If the rouge and pitch in small bubble holes is not removed, the towel used for drying the mirror may pick up some of the pitch and spread it over the surface of the mirror face in layers too thick to be removed by electrical cleaning.

After the glass has been cleaned and rinsed as described above for silvering, it is dried with clean cotton towels. It is well to use old cotton towels, because after many launderings they become more absorbent and contain less fatty substances than absorbent cotton. Care is exercised to avoid contaminating the freshly laundered towel by touching it with the hands in the areas to be used to dry the mirror face.

Finally, the glass is exposed to a glow discharge during the evacuation.

Evaporation. The evaporation method for producing thin films on glass, quartz, and so forth, is simple both in its mechanism and in its practical application. A small piece of the metal (or nonmetal, for that matter) is simply heated in a high vacuum until its vapor pressure is about 10 mm of mercury or greater, whereupon it emits molecular rays in all directions. The degree of vacuum required for successfully carrying out the process is such that the mean free path of the molecules is larger than the diameter of the vacuum container. Therefore molecular rays propagate from their source without disturbance until they impinge on the walls of the vacuum or some object within them. The mirror surface to be coated is exposed to these molecular rays, which condense on it to form the desired film. An interesting feature of the condensed film is that it apparently exhibits the same degree of polish as the underlying glass and so requires no subsequent burnishing, as does chemical silvering. Also, this film forms without material heating of the mirror.

Although the evaporation method was known by 1912, it remained obscure, for some reason, long after it should have become a practical "tool" in the laboratory.¹⁶ Among the items which have influenced its recent rather extensive applications are the development of a bare tungsten heater technique,¹⁷ the adaptability of the process to nonmetals and for the application of aluminum,¹⁸ and the development of high-speed vacuum pumps. (See "Technique of High Vacuum".)

Whether or not a particular material is suited to giving films by the evaporation process is determined by the thermal stability and vapor pressure of the material and the practicality of bringing the material to the evaporation temperature in vacuum.

Tungsten heaters useful for bringing some of the metals to the evaporation temperature are shown in Figs. 12 and 15 to 20. The evaporation temperatures of the metals are given in Table III.

Most of the metals melt first before they evaporate, the molten metal being kept from falling out of the coil by surface tension.

Other metals, like magnesium, sublime. Of these, some sublime very slowly, because the metal will not fuse to the tungsten wire in vacuum. Chromium affords an example The evaporation of such a metal is managed as follows: It is first brought to fusion temperature in the tungsten coil in an atmosphere of hydrogen or helium. These gases facilitate heat transfer between tungsten and the chromium or other metal, and, in addition, they restrain evaporation of the metal. (See Fig. 9.) After intimate contact with the tungsten wire is established, the metal will then sublime faster in the vacuum, because the heat is transmitted to it more effectively. An alternate way of attaining the same end is to electroplate the chromium or other metal onto the tungsten coil.¹⁹ The metals best managed by the above I procedures include, besides chromium, the platinum metals and beryllium.

Frequently, it is desirable to prefuse a metal which otherwise sublimes, in order to free it from included impurities. Such metals as calcium, magnesium, and cadmium can be prefused in helium to outgas them and to prepare them for evaporation.

A great many metals react with the tungsten coil, as, for example, iron, nickel, beryllium, chromium, the platinum metals, and aluminum. In spite of this, it is possible to evaporate them for the preparation of small laboratory mirrors.

Fig. 10 shows a neat simple insulated support for wires in vacuum.

Evaporation technique for aluminum. The technique for evaporation of aluminum from tungsten coils is of special interest, since this metal is important for surfacing where high ultraviolet and high visible reflectivity are desired in combination with freedom from tarnishing.

Pringsheim and Pohl discovered that several metals (including aluminum) could be evaporated in vacuum and condensed on a glass surface to form a polished reflecting film. They used a magnesia crucible from which to distill the metal.²⁰ R. Ritschl, in 1928, in making an application of the evaporation method to the preparation of half-silvered interferometer mirrors, heated the silver in a bare tungsten coil.²¹ This change in technique has the advantage that the tungsten does not evaporate or outgas so much in a vacuum as does the magnesia crucible.

Following this, Cartwright and Strong developed a simple apparatus for carrying out the evaporation process in the laboratory and made a survey of its applicability to different metals.²² The usual technique, in which the metal to be evaporated was heated in a helix of tungsten wire, was found successful, except with the metals aluminum and beryllium, which dissolved the tungsten coil.

Other attempts were made to develop this technique of evaporating aluminum.²³ Experiments were carried out with crucibles of graphite, pure fused magnesia, and alumina (sapphire), as well as with sintered and fused crucibles of thorium oxide. These experiments showed that heating in a crucible was apparently impractical, since either the metal reacted chemically with the material of the crucible or the latter evaporated when the aluminum was heated.

The discovery that tungsten has a limited solubility in molten aluminum led to the bare tungsten method of evaporation-the most practiced of all the methods.²⁴

A chemical analysis of the tungsten alloy that is formed when aluminum is fused on a tungsten coil showed the solubility of tungsten in aluminum to be about 3 per cent by volume. Accordingly, the burning out of the tungsten wire may be avoided by the simple expedient of making it of relatively large diameter and arranging the charge so that the solubility of the molten aluminum for tungsten can be satisfied without dangerously reducing the diameter of the wire. It might be expected that some of the dissolved tungsten would boil away, especially since its spectrum has been observed during evaporation.²⁵ In order to test this point, a coil was weighed before and after evaporating several charges of aluminum. Instead of a loss in weight, an increase was observed, indicating that some aluminum had diffused into the tungsten. However, extended heating in vacuum at a very high temperature decreased the weight, until, within the experimental error, it became the same as in the beginning. A chemical analysis of the condensed metal film was made to test whether or not tungsten is evaporated. The analysis gave no definite indication of tungsten. A concentration of 0.03 per cent by weight was detectable. The tungsten which is dissolved thus appears to be almost completely precipitated back onto the coil as the evaporation proceeds. Although it may hot be deposited back in exactly the same place, it does compensate in a large measure for the decrease in diameter of the tungsten wire.

The arrangement used at first for aluminizing mirrors at the California Institute of Technology is shown in Figs. 11 and 12. It is in the form of a helix, consisting of 10 turns of 30~ru1 tungsten wire, 5/16 of an inch in diameter and pitched 4 turns to the inch. A U-shaped piece of aluminum wire 1 mm in diameter and about 10mm in total length is clamped to each turn as is shown in Fig. 11. A potential of 20 volts applied to the coil in vacuum for 4 seconds prefuses these pieces as shown in Fig. 12. At this stage, surface tension keeps the molten aluminum from dropping. This prefusion also serves to free the metal from oxide and other impurities. It is customary to make a separate run in order to effect this fusing of the aluminum to the tungsten wires. In the 40-inch tank (see Fig. 13), however, the coils are covered by a baffle during the preliminary firing. The aluminum is finally distilled from the coils by applying the same voltage to each coil for about 15 seconds.

Actually, the aluminum does not evaporate from the fused metal but from the adjacent tungsten wire. This is clearly shown by the "self-photograph" of the filament reproduced in Fig. 14. This "self-photograph" was recorded on glass with the molecular rays of aluminum passing through a pinhole.

A recently developed evaporation source allows a much higher rate of evaporation of aluminum with less tendency to burn out or drop molten aluminum. The new source uses three or four 20-mil tungsten wires twisted together as shown in Fig. 15. The metal charge applied as illustrated in Fig. 11, flows out to fill the space between the wires when heat is applied. The aluminum covers the tungsten completely, so that a minimum "ratio" of heat radiation to molecular radiation of aluminum is achieved.

Fig. 16 shows the form by which the new source is applied to the evaporation of gold. When the gold melts in the "cup," it is drawn out to coat the tungsten and it fills up the spaces between wires from one end to the other.

For evaporation of silver and copper the source should be made from tantalum or molybdenum rather than tungsten, as the latter metal is not easily wet with silver and copper.

For evaporation of the platinum metals, a unit similar to the one shown in Fig. 15 is made up of three 20-mil tungsten wires and one platinum metal wire of the same diameter. The "ratio" of heat to metal | radiated is a minimum. Furthermore, the awkward process of electroplating the platinum on the filament is avoided. The evaporation should proceed slowly,. Even from this source, because if too much current is applied, the evaporation is no longer smooth, and globules of metal are discharged from the source.

Chromium is easily evaporated from a source like the one I shown in Fig. 16. A piece of the metal is put in the "cup" and is preheated in an atmosphere of hydrogen or helium to fuse it and distribute it over the tungsten. Various other evaporation sources are illustrated in Figs. 17 to 20.

Vacuum equipment. The evaporation process is carried out in a vacuum of 10 mm of mercury or better. For small mirrors the necessary vacuum may be obtained with a kinetic pumping system such as the one shown in the previous chapter The 40-inch tank, Fig. 13, shows the type of equipment used at the California Institute of Technology for larger mirrors. Still larger systems have been used.²⁶

The cleaning electrode shown in Fig. 13 allows the vacuum vessel, containing the mirror, to be filled with a glow discharge during the preliminary evacuation with the roughing pumps; and this discharge effects the final cleaning of the mirror face.

It is recommended that the aluminum be evaporated soon after a nonconducting vacuum has been reached, in order to obtain maximum tenacity between the aluminum film and the glass. Also, this procedure yields harder films.

Uniform films. In order to obtain a uniform coat on large mirrors, aluminum is evaporated from several tungsten sources suitably arranged, rather than from one movable source. The evaporation of polonium in a high vacuum from a point source has been investigated by Bonét-Maury.²⁷ This metal was chosen on account of its radioactivity. He found that the condensation on a plane surface is proportional to the inverse square of the distance from the source, and to the cosine of the angle between the normal to the surface and the line connecting the surface with the source. We may assume that the same is true of other metals which have a low vapor pressure at room temperature.

Starting with this assumption, we may consider the distribution of the film thickness produced by various experimental arrangements. In the case of evaporation to the inside surface of a sphere of radius from a point source of vapor at its center, the situation is very simple. We get a uniform film of which the thickness is

. (1)

Here m is the mass of metal evaporated and is its density. The film thickness at P on a plane surface at the normal distance from a point source of evaporation is

(2)

Here is the thickness at P, r is the distance from the source to P, and is the inclination of the surface P to the molecular rays emitted by the source which impinge on it there.

The film thickness produced on a plane surface by a circular array of vapor sources can be determined by applying the above formula to each of the sources. (See Fig. 21.) If there are N coils spaced uniformly around a circle at a distance from the surface to be coated, the film thickness on the surface at P, which is at a distance a from the intersection of the axis of the circle with the face of the mirror, is given by the expression

(3)

Here M is the total mass of metal evaporated, and r is the distance from P to the coil represented by the summation index i.

Dr. Edward M. Thorndike made the same calculation, assuming a continuous circular source. The thickness is given in this case by

(4)

Here the point source at distance r from the point P is replaced by a line source represented by the angle element at distance r, as before. This calculation involves the integration

, (5)

in which E represents the elliptic function.²⁸ Values of this integral calculated by Thorndike are given in Table IV.

In a larger 108-inch tank it was not convenient to use a similar array of coils spaced 50 inches from the face of the mirror. Instead, three arrays were used, each about 20 inches from the mirror. The arrangement is shown in Fig. 22. From the expressions developed above, as well as from actual tests, it was found that four coils in the center, twelve on a circle of 50 inches in diameter, and twenty-four on a circle of 100 inches in diameter gave the proper loading. This arrangement produced a uniform film of proper thickness on a 100-inch mirror, the film being just a little thicker than that required to be opaque to sunlight. It is desirable to have this thickness (about 1000 angstroms), since much thicker films are more easily scratched, while thinner ones may in time become transparent as a result of the gradual growth of thickness of the oxide layer which forms on the aluminum coat.

Parabolizing a spherical mirror with aluminum. As soon as the technique for the attainment of uniform films was perfected, it became possible to prepare nonuniform films, with the thickness of the film varying in just the manner required to parabolize a spherical mirror. The difference between the circle and parabola illustrated in Fig. 23 is given to close approximation by the expression

, (6)

where y is the ordinate and R is the radius of curvature of the circle. represents the ordinate where the two curves intersect. The difference is zero at y = 0 and at and has a maximum at .

If a spherical mirror of diameter (represented by the surface generated by rotation of the circle in Fig. 23 about the X axis) is to be transformed to a paraboloidal surface (the surface generated by rotation of the parabola), it is evident from Eq. 6 that it is necessary to add to the sphere a zone of aluminum which has its maximum thickness at, tapering off on either side of this as required by the equation.

The maximum thickness of aluminum, , required depends naturally upon the radius of curvature of the sphere, R. The connection between , R, and is given by the expression

(8)

Inasmuch as it is possible to put down films of aluminum to thickness and greater, it is possible to parabolize a 12-inch mirror f/6, which requires a maximum thickness of only of aluminum. This is not an uncommon example encountered in astronomical mirrors.

The correct procedure for applying such a parabolizing film is first to compute the thickness and distribution of the aluminum film produced by a point source positioned opposite the center of the mirror as shown in Fig. 24. This can be done by the use of the formula given below for the thickness of aluminum produced at a distance y from the center of the mirror.

. (9)

Here m is the total mass of aluminum evaporated, in grams, and d is the distance between the source and the point in question on the mirror face.

A baffle of the shape illustrated by Fig. 25 is then cut from thin sheet brass and placed directly in front of the mirror as shown in Fig. 24. This baffle can be rotated, or, what is more convenient, it may be fixed and the mirror rotated as shown in Fig. 24. The baffle is so designed as to modify the thickness which would otherwise be obtained (given by Eq. 9), so that it will conform with that required by Eq. 6. The baffle will have zero angular opening at the center and edge and a maximum opening very near to . It is to be remembered that the effect of the baffle in a given zone is to decrease the thickness by a factor which is the ratio of the quantities, 360 minus the angular opening of the baffle opposite the particular zone in question, to 360. In order to avoid astigmatism, the mirror is rotated a great many times during the deposition.

It is necessary, for some reason not yet clearly demonstrated, to evaporate slightly more aluminum than the simple theory outlined above predicts. The procedure in this case is to deposit some metal (about the theoretical amount) and then test the mirror. On the basis of the Foucault test, an additional amount is evaporated, and so on until the required figure is obtained. If too much metal is added, the coat can be washed off with caustic soda. Usually the mirror can be finished on the second attempt. When several mirrors, all alike, are to be parabolized, this preliminary testing may be done once for all.

Figs. 26, 27, and 28 show focograms of a mirror parabolized by this method. It was originally a sphere true to 1/20 of a wave length of green light, as the first focogram (Fig. 26), taken at its center of curvature, shows. This sphere was 152-1/4 inches in radius of curvature. was 12- inches. The next focogram, Fig. 27, shows it at its mean focus when tested with parallel light with the aid of a testing flat, obviously in need of parabolizing to give a good knife-edge cutoff. After it was parabolized with a coat of aluminum, it appeared as shown in the third focogram, Fig. 28. Here, again, it exhibits a true figure of revolution, this time a parabola true to less than 1/20 of a wave length of green light.

Mirrors imperfectly figured by conventional methods can be improved by this procedure. In this case the baffle design is determined by a preliminary quantitative survey of the mirror with a knife-edge testing outfit. (See "Laboratory Optical Work".)

It is possible to apply a thin film of aluminum to a convex sphere and transform it to a hyperbolic figure of revolution for use as the secondary mirror in a Cassegrain telescope. The formula for the difference between the hyperbola, or any conic of eccentricity , and the sphere tangent to it at the center and touching it at the radius distance is

(10)

Eq. 6 for the parabola is Eq. 10 when = 1. To obtain a hyperbola, it is necessary to have the aluminum thick at center and edge with a minimum at. The baffle to effect this is just the inverse of the one shown in Fig. 25, being open where the other is opaque and vice versa. The further details of the process are described in a paper by Strong and Gaviola and in the paper of Gaviola on the quantitative use of the knife-edge test.²⁹

Partially reflecting films. Partially reflecting films of silver and aluminum are useful for dividing a beam of light in many optical instruments such as color cameras and interferometers.

Figs. 29 and 30 show the reflection and transmission characteristics of silver and aluminum films obtained by the evaporation of various amounts of metal. The curves illustrate the color characteristics of the films and their efficiencies. They also indicate approximately the amount of metal to be evaporated to obtain any desired ratio of reflection to transmission. The curves for silver refer to fresh deposits, whereas the curves for aluminum apply to films about 6 months old, which have more or less attained their equilibrium optical characteristics.

The reproducibility with which any given film can be prepared from the information given in Figs. 29 and 30 is unfortunately not very great. The variations to be expected are greater in the ease of aluminum.

The films from which the curves in Figs. 29 and 30 were obtained were evaporated with a vacuum of 1 to mm, the mirror distance being 33 cm in the case of aluminum and 27 cm in the case of silver A source like the one shown in Fig. 17 was used for silver. The metal was in the form of a 40-mil wire. A straight, horizontal 30-mil tungsten wire served as the evaporation source for aluminum as shown in Fig. 31. The metal was a weighed U-shaped piece of wire pinched onto the center of the tungsten wire.

Silver films have a greater efficiency than aluminum films, and they are, accordingly, best for coating Farby and Perot interferometer plates. They may be protected from the tarnishing gases in the atmosphere by a thin layer of calcium fluoride or quartz.

The calcium fluoride (or quartz) films should be about 1/4 of a fringe in thickness. If a copper sheet is placed close to the evaporation source, it is possible to count the fringes as they are formed on this sheet by the evaporated calcium fluoride (or quartz). The square of the ratio of the distance of the copper to that of the silver gives the ratio of film thickness of calcium fluoride (or quartz) evaporated onto these two surfaces. The evaporation of calcium fluoride (or quartz) is stopped after an appropriate number of fringes have appeared on the copper.

A thin film of aluminum on the silver will oxidize to a protecting layer of aluminum oxide on exposure to the air. The proper amount of aluminum to be evaporated is about one-sixteenth the amount required to give a hali-transmitting coat. Accordingly, the proper amount of aluminum may be gauged by means of an auxiliary glass plate positioned at one-fourth the silver film distance from the evaporation source. The proper amount of aluminum is evaporated when the film on the auxiliary glass plate appears to be about half-transmitting.

When a half-silvered mirror on glass is cemented with balsam to a second glass surface, the ratio of transmission to reflection is increased by about 5 per cent.

¹ McKelvy, E. C., and Taylor, C. S., "Glass to Metal Joints," Amer. Chem. Soc., J., 42, 1364 (1920).