US3338730A

US3338730A - Method of treating reflective surfaces to make them multihued and resulting product

Info

Publication number: US3338730A
Application number: US345609A
Authority: US
Inventors: Albert E Slade; Carl R Smallman
Original assignee: Arthur D Little Inc
Current assignee: Arthur D Little Inc
Priority date: 1964-02-18
Filing date: 1964-02-18
Publication date: 1967-08-29
Anticipated expiration: 1984-08-29
Also published as: BE659407A; FR1431922A

Description

g-' 1967 E. SLADE ETAL 3,338,730

METHOD OF TREAT REFLECTIVE SURFACJ' TO MAKE THEM MULTIHUED AND RESULTING PR 'CT Filed Feb. 18, 1964 2 Sheets-Sheet 1 ll l2 ll Albert E. Slade Curl Russell Smollmun INVENTORS Aug. 29, 1967 A. E. SLADE ETAL 3,338,730

METHOD OF TREATING REFLECTIVE SURFACES TO MAKE THEM MULTIHUED AND RESULTING PRODUCT Filed Feb. 18, 1964 2 Sheets-Sheet E DIRECTION OF VAPOR USED TO DEPOSIT FILMS Al berf E. Slade Curl Russell Smul lmun INVENTORS BY 3% 4 A M Attorney United States Patent ABSTRACT OF THE DISCLOSURE Decorative surfaces are formed by depositing on a reflective surface a transparent film of a dielectric material and then covering it with a thin semi-reflective film. The reflective surface so treated is one which is formed of a multiplicity of sharply defined regions, the surface of each region having a plurality of parallel planes at an angle to the surface, the angles of the planes varying from region to region.

Attractive packaging materials find Wide use in the distribution of many items in commerce as well as the field of gift wrapping and the like. The ability to create attractive surfaces is also of great importance in the field of decorating and of advertising. The decorative materials of this invention provide a unique attractive foil or a decorative coating for a substrate which may or may not be flexible. The surface formed by this method is brilliant and multihued; it is moveover capable of changing color with orientation to give a very rich and unique finish.

It is the primary object of this invention to provide a method of forming a unique and very attractive surface coating on a substrate. It is another object of this invention to provide a method of the character described which is capable of imparting a brilliant, multihued effect to the surface of a variety of items. It is another object of this invention to provide decorative packaging and wrapping maetrials and decorative surfaces in general. Other objects of the invention will in part be obvious and will in part be apparent hereinafter.

The invention accordingly comprises the several steps and the relation of one or more of such steps with respect to each of the others, and the article possessing features, properties and the relationship of elements which are exemplified in the following detailed disclosure, and the scope of the invention will be indicated in the claims.

In brief, the method of this invention comprises the application of one or more films of specific optical properties to a reflecting surface. The reflecting surface is further characterized by the fact that it is made up of a multiplicity of sharply defined regions, the surface of each region having a plurality of parallel planes positioned at angles relative to the horizontal plane of the surface. The areas of the parallel planes and their positional angles in any one of the regions is different from that of the region or regions adjacent to it.

The final coated foil or other material having the sur face created by the method to be described exhibits a multihued brilliance which varies in color and design with the orientation of the surface with respect to the viewer. An almost infinite number of possibilities of color and design may be obtained, and the final characteristics of the surface can be determined and controlled as will be made apparent in the following description.

Optical reflection filters based upon the phenomena of light ray interference and light absorption as applied to a smooth reflecting substrate are known (see for example U.S.P. 2,590,906). Filters constructed on smooth substrates result in the production of bright monochromatic 3,338,730 Patented Aug. 29, 1967 effects. In contrast to the prior art, the decorative surfaces of this invention are formed on a specifically contoured surface which results in a multicolored surface of a controllable and widely variable design.

For a fuller understanding of the nature and objects of the invention, reference should be had to the following detailed description taken in connection with the accompanying drawings in which:

FIG. 1 is a perspective view illustrating in somewhat simplified form the type of basic or initial surface which is treated to give the decorative effect; 4

FIG. 2 is a cross-sectional, much-enlarged representation of a portion of the surface of FIG. 1 wherein the basic surface is itself reflecting;

FIG. 3 is a cross-sectional representation similar to FIG. 2 showing the application of a reflecting coating to a normally non-reflecting surface having the required basic structure;

FIG. 4 is a much-enlarged, cross-sectional representation of a fragment of the basic surface showing the application of a transparent spacer film;

FIG. 5 and 6 illustrate the use of different techniques for applying the spacer film;

FIG. 7 illustrates the application of a semi-reflecting film over the spacer film on the substrate illustrated in FIG. 4;

FIG. 8 represents a much-enlarged, fragmentary crosssection of the decorative coating showing the effect of using the basic contoured surface; and

FIGS. 9 and 10 illustrate modifications of the method and article of this invention.

The substrate to which the film coatings of this invention are applied to obtain the final decorative coating is illustrated in somewhat simplified form in the FIG. 1. The surface of the substrate 10 to which the coating films are applied must be of a special nature, i.e., must be divided into sharply defined and visibly identifiable regions 1-1 which are divided from adjacent regions by a relatively sharp boundary 12. FIG. 2 illustrates in crosssection the nature of the contour of these regions, showing that the contour varies from region to region but is represented by a consistent periodic pattern within any one single region. The surface of a single region may be defined as being made up of a plurality of parallel planes such as 13, 13 and 14, 14 in region 15;

planes

16, 16 and 17, 17 in region 18; and

planes

19, 19 and 20, 20 in region 21. It will be seen from FIG. 2 that these planes are positioned With respect to the over-all horizontal plane of the surface (indicated by the heavy black line) at various angles. For example in the rather stylized illustration of FIG. 2, planes 13 are at essentially right angles (angle a) to the horizontal; while parallel planes 14 form an acute angle b with the horizontal. In like manner in region 18,

parallel planes

16 and 17 form angles 0 and d which may or may not be equal, and in region 21 parallel planes 19 are at right angles with the horizontal while planes 20 are parallel to the horizontal.

On any one decorative surface the regions 11 (FIG. 1) may be of irregular size and shape, they may be of a geometric pattern, or they may be an artistic attempt to create a pleasing design. The size of the regions 11 may vary over a wide range and and will be determined and controlled within the range by aesthetic considerations. On very large areas of decorative material such as wall coverings the regions may be as large as 10 or 12 inches in their maximum dimensions. The regions may also be parallel stripes of varying Widths, the stripes running the full length of the material. On smaller objerts such as cosmetic cases the areas may be more pleasing in smaller dimensions. Areas as small as a few thousandths of an inch will give a pleasing effect if there are many of these areas whose parallel plane surfaces (such as

planes

13 and 14 in region 15 in FIG. 2) are all facing in the same direction. A particularly pleasing effect may be obtained by intermixing large regions and small regions, that is, the large regions may have many small regions sprinkled inside of them.

The area of any one plane (e.g., plane 13 of FIG. 2) may vary over a wide range. Planes as small as a few millionths of a meter (microns) give very pleasing and colorful results. In any one region the allowed height of the peaks (l in FIG. 2) which defines the maximum height of the contoured surface above the grooves, will depend upon the thickness of the substrate. For thick substrates and large areas, each plane may be rather large and the height 1 may be as much as one-half inch. On the other hand, if the planes are small, the height I may be as little as a few microns.

The required basic surface may be formed by machining, by etching, or by replicating a master surface. Machining may be done by cutting grooves into a suitable surface such as metal or plastic, and etching is preferably done by the vprocess described in a copending application filed in the name of Paul E. Doherty, Ser. No. 268,283 now abandoned and assigned to the same assignee as this application. Ser. No. 268,283 teaches a process by which fine grained recrystallized thin aluminum foils may be annealed and etched to form crystals at different orientations on the surface and through the thickness of the foil. Aluminum foils prepared in this manner are particularly Well-suited for the basic surface required in the practice of this invention. However, many metal surfaces are amenable to a variety of etching techniques to create on their surfaces the required basic structure, and they need not, of course, be in foil form since the over-all thickness of the substrate is not critical.

The basic surface structure may also be formed in plastic materials which lend themselves to either being used to form replicas from solution coatings or to being properly contoured through the application of heat with or without pressure application. Such surfaces (for example those illustrated in FIG. 3) can readily be formed by contacting a hot thermoplastic film against a suitably contoured metallic surface, or by pressing a thermoplastic film against the surface of a hot metal master surface. It is also, of course, possible to make replicas by dissolving the film-forming material in a suitable volatile solvent, applying the solution to the master surface to be copied, removing the solvent, and stripping the film from the surface. Thermoplastic films of the order of 1 mil thick have been successfully used to replicate etched aluminum surfaces in the production of the decorative material of this invention. However, the thickness of the substrate with the replicated surface is not critical.

The contoured basic surface which is to be treated must be reflective, and if it is not inherently so, it must be coated with a reflective coating to make it so. If the surface is a metal, such as for example the foil described in U. S. Ser. No. 268,283, then no treatment is necessary to make it reflective inasmuch as it has a reflective surface 22 (FIG. 2). If, however, the surface is a plastic replica, and has a non-reflecting surface 24 (FIG. 3), then a suitable coating 25 of a reflective material must be applied to give it the necessary reflective characteristics. This can conveniently be done by coating surface 24 with a very thin aluminum coating applied from the vapor phase in accordance with well-known vacuum deposition techniques. Preferably, if a reflective coating is to be applied, it will be as thin as possible to minimize cost and to retain the sharp peaks and grooves defining the parallel planes of the original basic surface. Other techniques, such as the chemical reduction of silver (Brashear process) or electroplating a metal, can be used to apply the reflective coating to a nonreflecting surface. However, vapor phase deposition is preferred.

The coating applied to the reflective contoured surface (FIG. 2 or FIG. 3) comprises a transparent film of a dielectric material, and if required, a semi-reflective metal coating on the dielectric film. The steps in the formation of the decorative coating are illustrated in FIGS. 4 and 5. The techniques available for application of the spacer film and their effect on film characteristics are shown in FIGS. 5 and 6. The optics of the decorative coating are then described with reference to FIG. 8. Finally, modifications of the basic method of forming the decorative coatingare discussed with reference to FIGS. 9 and 10.

Given the reflective contoured surface of FIG. 2 or FIG. 3, the first step in forming the decorative film is the deposition on the reflective surface of a thin transparent spacer film of a dielectric material. Such materials may include, but are not limited to silicon monoxide, cadmium telluride, titanium dioxide, aluminum oxide, zinc sulfide, magnesium fluoride, calcium fluoride and the like. The spacer film should be of a material and thickness so as to be transparent to visible light. Typically it will be between 100 and 5,000 A. thick, although it may be thicker depending upon the dielectric material used, and the colors desired in the decorative surface. The manner in which the thickness of the transparent spacer film determines colors will be discussed in detail with respect to FIG. 8. There is virtually no minimum thickness for the spacer film, so long as it is present and has an index of refraction different from the reflective surface on which it is deposited and from the material which forms a layer on top of it-either a semi-reflective metal or air.

The application of the transparent spacer film to the reflective contoured surface is shown in FIG. 4, and it may constitute the method of this invention without the further addition of any other film. Thus the much enlarged cross-sectional portion of FIG. 4 can be considered to illustrate one modification of the decorative surface. It will be seen to consist of a substrate 10 formed in this case of a plastic material having a non-reflective surface 24 to which a reflective film 25 has been added and over which the transparent spacer film 27 is deposited. The single transparent spacer film 27 may also be applied to an inherently reflective surface such as that in FIG. 2 in which case the reflective film 25 of FIG. 4 is omitted.

The multicolored effect of the decorative surface will be different for various methods of depositing the transparent spacer film. Applying the spacer film from the vapor phase is a technique which achieves a gradient in the thickness of the film. This is illustrated in FIG. 5 in which it will be seen that when a film 31 is applied to a surface 30 from the vapor phase with the vapor striking the surface at the angle indicated by the arrows, there will result a film of uneven thickness with the greatest thicknesses being built up on those planes directly in the path of the vapor. Those areas which are blocked or partially blocked from the vapor path will receive thinner layers of the spacer film. Variations in spacer film thickness result in a greater variation in colors reflected as will be obvious in the discussion of the optics involved.

The spacer film may also be applied by the process of anodization, and if this process is used, the film will be of uniform thickness throughout as shown in FIG. 4. The transparent spacer film may also be applied from solution, a process which produces a thickness gradient as illustrated in FIG. 6. In this case the solution tends to build up in the grooves and remain thin on the lands or peaks, giving rise to a final spacer film 33 of the type shown in FIG. 6.

If the transparent spacer film 27 is to serve as the only film applied, it may also contain some metallic contaminant material such as vaporized metal. Thus if the dielectric material forming the transparent spacer film is deposited from the vapor phase (by well-known vacuum deposition technology), metallic vapors may be mixed in to form a film of dielectric material and metal. An example of such a combination film is a mixture of silicon monoxide and aluminum. A coating such as this produces brighter colors.

The transparent spacer film, whether or not it is to serve as the only film coating on the contoured surface, may also be formed in more than two layers of dielectric materials having different indices of refraction. Spacer films formed of multilayers possess enhanced brilliance and color intensity.

If more than one film is to be put onto the reflective surface to form the decorative coating, then the film which is deposited on the transparent spacer-film is one which may be referred to as a semi-reflecting film. This film is preferably of a thickness ranging between about 50-500 A., and it should be capable of transmitting between about 25% and 65% of the incident light. The optimum thickness of the semi-reflecting film will depend upon the desired characteristics of the final decorative surface. Finally, the reflectivity of the semi-reflective film 28 in FIG. 7 should essentially balance or be equivalent to the reflectivity of the reflective surface 25 of FIG. 7 on which the transparent spacer film is deposited.

The semi-reflective fil-m may be formed of any easily deposited metal such as aluminum, silver, gold and the like, and it is also preferably applied from the vapor phase, since this technique is known to produce smooth thin films. However, it is also possible to apply it by other techniques such as chemical reduction of silver (Brashear process).

' The decorative surface formed of two film layers is shown in a much-enlarged cross-sectional representation in FIG. 7. In the decorative material illustrated in FIG. 7, the plastic replica shown in FIG. 4 having a reflective surface 25 and transparent spacer film 27 has deposited on it a semi-reflective film 28. The combination of

films

25 and 28 with spacer film 27 in between gives the surface a brilliant multihued effect.

The multicolored or multihued effect exhibited by the decorative surface of this invention may be explained in a somewhat simplified form with reference to FIG. 8 which is a much-enlarged, not-to-scale, cross-sectional representation of a fragment of such a surface. It will be appreciated that light is striking the surface of the semirefl ective film 28 from all directions; however, in this simplified presentation it may be assumed to be reaching the eye 40 of the observer from only two directions represented by incident'rays 41, 41 and 51, 51. It will be assumed further that the films were deposited from the vapor phase and that the direction of the vapor (shown by arrows) was responsible for forming the transparent spacer film 27 with the thickness difference shown.

Incident rays 41 strike the semi-reflective film surface 28 and a portion is reflected as rays 42. The remaining portion is transmitted as ray 43 through the transparent spacer film 27 to be reflected as ray 44, a portion of which is transmitted through the semi-reflective film to reinforce or cancel part of reflected ray 42. The remaining portion of ray 44 may be reflected back into the transparent spacer film. If the distance represented by the total of the length of

rays

43 and 44 is equal to n/ 2 times the wavelength X of a reflectedray 42 (where n is an odd whole number) then that wavelength of light reflected from the reflective surface 25 will be 180 out of phase with that portion of the incident light which is reflected by the semi-reflective film 28. The result will be to cancel out that color the wavelength of which is A. r In a similar manner a portion of the incident rays 51, reflected, as rays 52, will becancelled out, in this case the wavelength so cancelled being a function of the sum of the lengths ,of

rays

53 and 54. Because 43+44 is not equal to 53-1-54, different wavelengths will be cancelled out in reflected

rays

42 and 52, and the observer will see two planes of different colors. By orienting the surface, the observer will see different reflected light and hence a plane surface which was red at one orientation may become green at another orientation.

It can be seen that deposition of the spacer film from the vapor phase tends to enhance the variations in color by reason of the variations in thickness on the various reflective planes.

It is also possible to build up decorative surfaces having even more brilliant and unique characteristics by repeating the coating steps of FIGS. 4 and 7. This is illustrated in FIG. 9 which shows a substrate 10 (such for example as a foil prepared in accordance with US. patent application 268,283) having an inherently reflective surface 22 on which are deposited alternate layers of a transparent spacer film 27 and semi-reflective film 28. It is, of course, within the scope of this invention to build up a number of layers as illustrated in FIG. 9, making the topmost layer either a transparent spacer layer or a semireflective layer.

Because it may be desirable to view :the decorative surface through a transparent substrate, such as a thin plastic film, it is also within the scope of this invention to form the decorative surface in a reverse order. Thus for example, in FIG. 10 if substrate 10 is a relatively thin transparent plastic film, the semi-reflective surface 28- may be applied first to the contoured surface 24 and then the transparent spacer layer 27 applied to it, with the reflective layer 25 being deposited last to serve as the final layer of the assembly. The decorative surface in this case will then be viewed from the top as oriented in FIG. 10 down through the plastic substrate 10. The substrate 10 is then in a position to offer protection to the decorative surface.

The following examples are given to further illustrate the method and article of this invention and they are not meant to be limiting.

Example 1 Aluminum foil prepared in accordance with the method described in copending application Ser. No. 268,283 was used as the basic substrate to form a decorative foil. A film of SiO was deposited on this basic substrate by vapor phase techniques in an evacuated bell jar in accordance with known procedure. The SiO film which served as the transparent spacer film was about 2,000 A. thick. Various semi-reflective materials were then deposited by vacuum deposition from the vapor phase. These included aluminum, silver, gold, and copper. The thickness of the SiO film determined the final colors or hues and the thickness of the semi-reflective film (which normally ranges between 50 and 500 A.) determined the intensity and brilliance of the final decorative film. By observing the color and intensity as it was developed during the deposition of the semi-reflective film, it was possible to stop the film formation at the point where the desired color and brilliance were achieved.

Example 2 The aluminum foil of Example 1 was anodized in a bath of 1% citric acid and 1% ammonium citrate in distilled water in accordance with standard electrochemical techniques to form a film of about 2000 A. thickness of A1 0 on the foil as the transparent spacer film. One of the vario-us semi-reflective coatings such as those used in Example 1 was then deposited from the vapor phase onto the A1 0 film to form a decorative foil, the color and brilliance of which was controlled by the thickness of the A1 0 and the semi-reflective films respectively.

Example 3 The aluminum foil of Example 1 was coated with a film of cadmium telluride as the transparent spacer film. No additional semi-reflective film was required inasmuch at this transparent spacer film developed deep colors on the aluminum foil. In like manner titanium dioxide and zinc sulfide were used as spacer films without the further deposition of a semi-reflective film.

7 Example 4 A master basic substrate Was formed by heating and cooling an aluminum bar about one-eighth of an inch thick so that the bar formed into a large number of aluminum crystallites. The surface of this bar Was then etched to create on its surface the required regions having different contours such as described with respect to FIGS. 1 and 2. Films and sheets of thermoplastic materials including polyvinyl chloride and polystyrene were then used to replicate the surface of this master aluminum bar. The film or sheet of thermoplastic material was placed in contact with the aluminum bar surface and the assembly put into a heated press wherein the temperature was sufficient .to soften the thermoplastic material. The application of slight pressure accompanied by the heating was suflicient to form in the thermoplastic surface a surface which was a precise replica of the aluminum surface. These replicated surfaces were then made reflective by depositing on them from the vapor phase a very thin, e.g., of the order of 500 to 1000 A. coating of aluminum. The resulting reflective surfaces were then treated as in Examples 1 and 3 to give comparable decorative surfaces.

It is possible to prepare a wide variety of decorative surfaces, and the character of the decorative surface is controlled by controlling the thickness of the transparent spacer film which exercises control over the wavelengths of visible light which are reflected as described in FIG. 8; and by controlling the character and thickness of the semireflective film, if used, which acts as a mirror and contributes to the over-all intensity and brilliance.

It will thus be seen that the objects set forth above among those made apparent from the preceding description are efficiently attained, and since certain changes may be made in carrying out the above method and in the article set forth without departing from the scope of the invention, it is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense.

We claim: 1. A method of forming a decorative coating on a substrate, comprising the steps of (a) applying a transparent spacer film of a dielectric material to a reflecting surface which comprises a multiplicity of sharply defined regions, the surface of each region characterized by having a plurality of parallel planes positioned at an angle relative to the horizontal plane of said surface, the areas of said planes and their positional angles in any one region being different from that of the regions adjacent to it; and (b) applying over said transparent spacer film a semirefiective film; whereby said reflecting surface is transformed into a brilliant, multihued decorative surface. 2. A method in accordance with claim 1 wherein said dielectric material is silicon monoxide.

3. A method in accordance with claim 1 wherein said semi-reflective film is aluminum.

4. A method of forming a decorative coating on a sub. strate, comprising the steps of (a) applying a reflective coating to a surface which comprises a multiplicity of sharply defined regions, the surface of each region characterized by having a plurality of parallel planes positioned at an angle relative to the horizontal plane of said surface, the areas of said planes and their positional angles in any one region being different from that of the regions adjacent to it; (b) applying to said reflective surface thus formed a transparent spacer film of a dielectric material; and (c) applying over said transparent spacer film a semireflective film, whereby said surface is transformed into a brilliant, multihued decorative surface.

5. A method according to claim 4 wherein steps (b) and (c) are repeated.

6. A method in accordance with claim 4 wherein said surface is characterized as being a plastic replica.

7. A method of forming a decorative coating on a transparent substrate, comprising the steps of (a) applying a semi-reflective film to one surface of said substrate, the surface being characterized as one which comprises a multiplicity of sharply defined regions, the surface of each region characterized by having a plurality of parallel planes positioned at an angle relative to the horizontal plane of said surface, the areas of said planes and their positional angles in any one region being different from that of the regions adjacent to it;

(b) applying to said semi-reflective film a transparent spacer film; and

(c) applying to said transparent spacer film a reflective film, whereby said substrate when viewed from the uncoated surface presents a highly brilliant, multihued effect.

8. A brilliant, multihued decorative material, comprising in combination (a) a basic substrate having a reflective surface which comprises a multiplicity of sharply defined regions, the surface of each region characterized by having a plurality of parallel planes positioned at an angle relative to the horizontal plane of said surface, the areas of said planes and their positional angles in any one region being different from that of the regions adjacent to it;

(b) a transparent spacer film of dielectric material affixed to and covering said surface; and

(c) a semi-reflective film affixed to and covering said transparent spacer film.

9. A decorative material in accordance with claim 8 wherein said transparent film of dielectric material contains a metal contaminant.

10. A decorative material in accordance with claim 8 wherein the thickness of said transparent spacer film is between and 5000 A. and the thickness of said semireflective film is between 50 and 500 A.

11. A decorative material in accordance With claim 8 wherein said basic substrate is an etched aluminum foil. 12. A decorative material in accordance with claim 8 wherein said basic substrate is a plastic film coated with a reflective material.

13. A decorative material in accordance with claim 8 wherein said transparent spacer film is silicon monoxide.

14. A decorative material in accordance with claim 8 wherein said semi-reflective film is aluminum.

15. A brilliant, multihued decorative material, comprising in combination (a) a basic substrate having a reflective surface which comprises a multiplicity of sharply defined regions, the surface of each region characterized by having a plurality of parallel planes positioned at an angle relative to the horizontal plane of said surface, the areas of said planes and their positional angles in any one region being different from that of the regions adjacent to it;

(b) a plurality of transparent spacer films of dielectric materials, the first of which is afiixed to and covers said surface; and

(c) a plurality of semi-reflective films, said transparent spacer films and said semi-reflective films being in alternating relationship.

16. A brilliant, multihued decorative material, comprising (a) a thin transparent material as a basic substrate, said substrate having a surface which comprises a multiplicity of sharply defined regions, the surface of each region characterized by having a plurality of parallel planes positioned at an angle relative to the horizontal plane of said' surface, the areas of References Cited UNITED STATES PATENTS Bauer 16133 McKinney.

Turner 161-4 Magnuson et al. 161-4 Menconi et a1. 161-34 Ruderman 161--1 coated side, is seen as a brilliant, multihued decora- 10 ALFRED LEAVITT, Primary Examiner- A. ROSENSTEIN, Examiner.

tive material.

Claims

1. A METHOD OF FORMING A DECORATIVE COATING ON A SUBSTRATE, COMPRISING THE STEPS OF (A) APPLYING A TRANSPARENT SPACER FILM OF A DIELECTRIC MATERIAL TO A REFELCTING SURFACE WHICH COMPRISES A MULTIPLICITY OF SHARPLY DEFINED REGIONS, THE SURFACE OF EACH REGION CHARACTERIZED BY HAVING A PLURALITY OF PARALLEL PLANES POSITIONED AT AN ANGLE RELATIVE TO THE HORIZONTAL PLANE OF SAID SURFACE, THE AREAS OF SAID PLANES AND THEIR POSITIONAL ANGLES IN ANY ONE REGION BEING DIFFERENT FROM THAT OF THE REGIONS ADJACENT TO IT; AND