EP1711311B1 - Device and method for polishing an optical surface and method for the production of a polishing tool - Google Patents

Abstract

An apparatus for polishing an optical surface, in particular an optical surface of a spectacle lens, is disclosed. The apparatus comprises a polishing head having a polishing tool, the polishing tool being provided along a common axis, one behind another, with a first preferably rigid member, a second elastic member, and a polishing lining, each extending essentially radially relative to the axis. The second elastic member is configured to be increasingly soft in a radial outward direction. Moreover, a method of polishing an optical surface, in particular a surface of a spectacle lens, an optical component manufactured according to that method, in particular a spectacle lens, as well as a method of manufacturing a polishing tool are disclosed.

Description

The invention relates to a device for polishing an optical surface, comprising a polishing head, the polishing tool along a common axis one behind the other, a first, preferably rigid body, a second, elastic body and a polishing pad, each extending substantially radially to the axis ,

The invention further relates to a method of polishing an optical surface.

Finally, the invention relates to a method for producing a polishing tool which has, along a common axis, one after the other a first, preferably rigid body, a second, elastic body and a polishing pad which extend in each case substantially radially to the axis.

In the context of the present invention, when referring to "optical surfaces", all such surfaces of optical components are meant as e.g. Surfaces, in particular aspheric surfaces or free-form surfaces, of spectacle lenses, mirrors, plastic optics, etc.

From DE 102 48 105 A1 a device and a method of the type mentioned are known.

Eyeglass lenses are usually made from a blank by machining the so-called prescription surface or surfaces. This is the optically relevant design of the lens fixed. Finally, the lens is still polished, which, however, no significant change in the optical properties may be more effected.

For polishing a surface of a spectacle lens, usually a polishing head is used, which is a polishing tool whose polishing surface is at least approximately adapted to the shape of the surface of the spectacle lens to be polished. The polishing tool and / or the spectacle lens are hinged, in particular with a ball joint, mounted and are guided relative to each other with a predetermined movement, usually with the help of multi-axis robots.

When polishing spherical or toric spectacle lenses, it is less problematic due to the relatively simple shape of the surface to be polished to find a suitable, complementary formed polishing tool that can be performed with simple movements over the surface and there causes no undue deformation. Due to the large number of possible spherical or toric spectacle lenses, it is only necessary to have a corresponding large number of polishing tools available.

In this context, different groups of polishing tools have become known.

In a first group of such polishing tools (DE 101 00 860 A1, EP 0 567 894 B1), an always rigid polishing body is used, which is immutable adapted to the shape of the surface to be polished and therefore can be used only for this surface.

In a second group of such polishing tools (DE 44 42 181, DE 102 42 422), a polishing body is used which, although rigid in use, is previously displaceable, for example by heating, into a plastic state, so that it initially settles in This plastic state can adapt to any surface before it solidifies.

These two groups of polishing tools have in common that they are rigid in use and therefore can only be used for polishing regularly shaped surfaces.

In a third group of polishing tools (EP 0 804 999 B1, EP 0 884 135 B1, DE 101 06 007 A1), a polishing body is provided which can also be deformable during use. This deformability is achieved by a bundle of parallel metallic rods, which are mounted at one end on an elastic membrane and individually displaceable. The total area formed by its end face at the other end adapts to the shape of the surface to be polished.

One disadvantage of these polishing tools is that the membrane, like every membrane has a course of elasticity in which the center is the softest point and the elasticity decreases radially outward, ie the membrane becomes stiffer or the spring characteristic becomes steeper. This is, as stated in the present invention, disadvantageous for polishing tools of the type of interest here, because this elasticity profile causes larger shape errors. Furthermore, it is disadvantageous in these polishing tools that the movement of the rods is associated with mechanical friction, so that hardly any dynamic polishing processes can be realized.

In a fourth group of polishing tools (EP 0 779 128 B1, Patent Abstracts of Japan to JP 08-206 952 A) are polishing bodies used, which have an immediately pneumatically deformable polishing body. Here too, the previously described disadvantage of an unfavorable elasticity curve arises.

In a fifth group of polishing tools (DE 101 06 659 A1, DE 102 48 105 A1, DE 102 48 104 A1, US 2003/0017783 A1, WO 03/059572 A1), in the polishing tool, a body of elastic material is disposed between a rigid body Carrier body and the polishing pad arranged.

In this case, however, the axial thickness of the elastic body in the known polishing tools is constant and the material of the elastic body is homogeneous. Thus, the elasticity in the radial direction is constant.

Overall, therefore, with regard to known polishing tools for the processing of optical surfaces, in particular spectacle lenses, it should be noted that in these the radial profile of the compressive rigidity either increases or is constant from the inside to the outside.

This is sufficient for relatively simple shaped surfaces (spherical and toric surfaces). By contrast, when polishing aspherical or punctiform asymmetric free-form surfaces, such polishing tools can not be used without problems.

Such free-form surfaces have also been polished by means of numerically controlled polishing machines or polishing robots. In these machines, usually the polishing tool is CNC-guided over the surface of the spectacle lens to be polished. The polishing head drives the polishing tool usually rotational and presses it simultaneously against the surface to be polished.

Aspherical or point-symmetric free-form surfaces have curvatures that change over the surface. The polishing tool moves during polishing at least over part of this irregularly curved surface. It must therefore be able to adapt with its elasticity to the respective local curvature, specifically in such a way that the polishing pressure is as constant as possible over the contact surface. Only then does a predeterminable, constant removal result, and the polished surface becomes optimally smooth. If this can not be ensured and the polishing pressure fluctuates across the contact surface, the desired aspheric surface topography is deformed and thus degraded in optical quality. Such deformations occur with known polishing tools in conventional production processes and therefore have to be compensated step by step, with iterative reworking methods. However, this is time consuming and expensive.

For the general state of the art in the field of polishing tools DE 296 08 954 U1 should be mentioned. This document describes an adaptable grinding head for clamping in rotating tools. The grinding head has a body coated with abrasive material, which consists of a soft, extremely yielding material, such as foam rubber. The grinding head is mushroom-shaped, cone-shaped or spherical in axial section, so that it is thinner in the edge region than in the middle. This makes it harder in the edge area.

A similar grinding head is also disclosed in US 3,043,065. This known grinding head is mushroom-shaped and therefore also harder in the edge region than in the middle.

Finally, the Patent Abstract of Japan to JP 61-103768 A still describes a grinding head also mushroom-shaped. This grinding head is divided into three concentric areas, which consist of the same material, but in which air bubbles are embedded in different concentrations. The central area contains the largest density of air bubbles, so that the effective surface is the smallest. It is the largest at the edge.

The invention is therefore the object of developing a device and a method of the type mentioned in such a way that these disadvantages are avoided. In particular, it should be possible to polish eyeglass lenses with irregularly curved freeform surfaces by means of simply constructed tools in a surface quality that makes post-processing dispensable.

In a device of the type mentioned above, this object is achieved in that the second body in the radial direction from the inside to the outside is increasingly softer.

In a method for polishing an optical surface of the initially mentioned type, this object is achieved in that a device of the aforementioned type is used. In a method for producing a polishing tool of the type mentioned at the outset, this object is achieved in accordance with the invention in that the second body is progressively softer in the radial direction from the inside to the outside.

The object underlying the invention is completely solved in this way.

Namely, the invention provides an amazingly simple polishing tool which is similar to polishing tools known in its structure, but, in contrast to conventional polishing tools, can also grind irregularly curved free-form surfaces on spectacle lenses without an irregular removal during polishing occurring. This is achieved by a targeted influencing the elasticity of the polishing pad-bearing elastic body in the radial direction by the elastic body is softer in the radial direction from the inside to the outside, thus having an increasingly flatter spring characteristic.

In a preferred embodiment of the device according to the invention, the second body is formed continuously softer in the radial direction to the outside.

This measure has the advantage that the contact pressure is transmitted particularly evenly to the surface to be polished.

Alternatively, the second body in the radial direction to the outside but also be formed discontinuous softer.

It is particularly preferred if the second body has an increasing axial thickness in the radial direction.

This measure has the advantage that the desired radial stiffness profile can be set almost arbitrarily if the radial profile of the axial thickness is set accordingly. In this way the tool can be very sensitively optimized.

In a particularly preferred variant of the last-mentioned embodiment, the second body is adjacent to the first body with an inner contour and to the polishing pad with an outer contour, wherein the course of the axial thickness over the radial direction is determined as a function of the radial course of the contours.

This measure has the advantage that an optimization with two contours is possible, so that the outer contour can be adapted particularly well to the surface to be polished, and essentially the inner contour can be used to set the desired radial profile.

Depending on the surface to be polished, there are various preferred options for the special shaping of the contours:

Thus, the inner contour may be convex and the outer contour convex, or the inner contour convex and the outer contour plan, or the inner contour concave and the outer contour concave, or the inner contour plan and the outer contour concave, or the inner contour convex and the outer contour concave.

Furthermore, it is preferred if the outer contour is spherical or aspherical or formed as a freeform surface.

In a practical embodiment, the second body is made of a material whose elastic modulus is greater than 0.02 N / mm ² .

This range of elasticity has proven to be optimal in practical experiments.

With regard to the choice of material for the second body is preferred if it is selected from the group of rubber, rubber, polyurethane, polyetherurethane, elastomer.

A particularly economical production is possible if the second body is a casting.

A further embodiment of the invention is characterized in that the second body is formed of a material whose elasticity in the radial direction increases from the inside to the outside, i. the compression spring characteristic becomes increasingly flatter from the inside to the outside.

This measure has the advantage that one is free in the shape of the second body within wide limits. It is therefore possible to form the second body with a constant thickness, that is to say in the form of a disk, but has the special, inhomogeneous one Texture of the material still the desired radial profile of elasticity, in which the second body is radially outwardly softer than inside.

Consequently, as already mentioned, the second body may advantageously have a constant axial thickness in the radial direction.

If in the context of the present application of a "polishing pad" is mentioned, so it is any entity that can represent a polishing surface.

Thus, advantageously, the polishing pad may merely be a polishing paste, or it may be physically formed as a polishing membrane, polishing pad or polishing layer material.

As already mentioned, the present invention preferably relates to the polishing of surfaces of spectacle lenses or mirrors or aspherical mirrors or aspheric optical surfaces.

The polishing tool may be according to embodiments of the invention either to the axis round or non-circular. It may also be articulated either in the axle or off-axis.

In a particularly preferred embodiment of the method according to the invention for producing a polishing tool, the second body is produced in the radial direction with increasing axial thickness, wherein the second body with an inner contour of the first body and an outer contour of the Polierbelag_angrenzend made and the course the axial thickness over the radial direction in dependence on the radial shape of the contours is determined.

These measures have the advantage already described above that the desired radial profile of the elasticity can be adjusted in a very accurate manner.

For this purpose, two variants are provided according to the invention for a practical implementation:

1. a) Festlegen eines gewünschten mittleren Polierdrucks pm des Polierwerkzeugs;
2. b) Bestimmen der notwendigen Anpresskraft Fk aus der Polierfläche des Polierwerkzeugs;
3. c) Auswählen eines Elastizitätsmoduls E für den Werkstoff des zweiten Körpers;
4. d) Auswählen einer Mittendicke Di des zweiten Körpers;
5. e) Auswählen einer anfänglichen äußeren Kontur;
6. f) Berechnen einer mittleren Einfederungstiefe di für einen zweiten Körper unter der Annahme, dass der zweite Körper eine konstante axiale Dicke D aufweist, die gleich der ausgewählten Mittendicke Di ist;
7. g) Bestimmen einer Polierbewegung des Polierwerkzeugs auf der zu polierenden Oberfläche;
8. h) Diskretisieren der Polierbewegung in eine vorbestimmte Anzahl n Bewegungsinkremente, wobei die Anzahl n hinreichend groß gewählt wird;
9. i) Berechnen einer Einfederungsfläche aus den Abweichungen der axialen Dicke z_Di in Richtung z der Achse zwischen der Oberfläche und der äußeren Kontur in einem vorgegebenen Punkt i bei relativer Polierbewegung zwischen dem Polierwerkzeug und der optischen Fläche;
10. j) Addieren der Abweichungen z_Di bei allen Punkten i;
11. k) Bestimmen einer maximalen Abweichung z_Dmax;
12. l) Bestimmen einer minimalen Abweichung z_Dmin;
13. m) Bestimmen eines Mittelwerts z_Dm aus allen Abweichungen z_Di;
14. n) Bilden einer Differenz z_Dmt zwischen dem Mittelwert z_Dm und der Summe einer Kippung und eines zentralen Offsets des Mittelwerts z_Dm;
15. o) Berechnen der axialen Dicke D in Abhängigkeit von der radialen Richtung h für runde bzw. x, y für unrunde Polierwerkzeuge mit den Unterschritten: $$\mathrm{K}\mathrm{2}\left(\mathrm{h}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{h}\right)\mathrm{+}\mathrm{z\_Dmt}\left(\mathrm{h}\right)\mathrm{;}$$
    
    
    bzw. $$\mathrm{K}\mathrm{2}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{+}\mathrm{z\_Dmt}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{;}$$
    
    $$\mathrm{D}\left(\mathrm{h}\right)\mathrm{=}\mathrm{Di}\mathrm{+}\mathrm{Di}\mathrm{*}\left(\mathrm{z\_Dmax}\left(\mathrm{h}\right)\mathrm{-}\mathrm{z\_Dmin}\left(\mathrm{h}\right)\right)\mathrm{/}\mathrm{di}\mathrm{/}\mathrm{f\_a}\mathrm{;}$$
    
    
    bzw $$\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{Di}\mathrm{+}\mathrm{Di}\mathrm{*}\left(\mathrm{z\_Dmax}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{-}\mathrm{z\_Dmin}\left(\mathrm{x},,\mathrm{y}\right)\right)\mathrm{/}\mathrm{di}\mathrm{/}\mathrm{f\_a}\mathrm{;}$$
    
    $$\mathrm{K}\mathrm{1}\left(\mathrm{h}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{h}\right)\mathrm{+}\mathrm{D}\left(\mathrm{h}\right)\mathrm{;}$$
    
    
    bzw. $$\mathrm{K}\mathrm{1}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{+}\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{.}$$
    

The first variant is characterized by the following steps:

1. a) setting a desired mean polishing pressure pm of the polishing tool;
2. b) determining the necessary contact force Fk from the polishing surface of the polishing tool;
3. c) selecting a modulus of elasticity E for the material of the second body;
4. d) selecting a center thickness Di of the second body;
5. e) selecting an initial outer contour;
6. f) calculating a mean deflection depth di for a second body assuming that the second body has a constant axial thickness D equal to the selected center thickness Di;
7. g) determining a polishing movement of the polishing tool on the surface to be polished;
8. h) discretizing the polishing movement into a predetermined number n movement increments, the number n being chosen to be sufficiently large;
9. i) calculating a jounce area from the deviations of the axial thickness z_Di in the direction z of the axis between the surface and the outer contour at a predetermined point i during relative polishing movement between the polishing tool and the optical surface;
10. j) adding the deviations z_Di at all points i;
11. k) determining a maximum deviation z_Dmax;
12. l) determining a minimum deviation z_Dmin;
13. m) determining a mean value z_Dm from all deviations z_Di;
14. n) forming a difference z_Dmt between the mean value z_Dm and the sum of a tilt and a central offset of the mean value z_Dm;
15. o) calculating the axial thickness D as a function of the radial direction h for round or x, y for non-round polishing tools with the substeps: $$\mathrm{K}\mathrm{2}\left(\mathrm{H}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{H}\right)\mathrm{+}\mathrm{z\_Dmt}\left(\mathrm{H}\right)\mathrm{;}$$
    
    
    respectively. $$\mathrm{K}\mathrm{2}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{+}\mathrm{z\_Dmt}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{;}$$
    
    $$\mathrm{D}\left(\mathrm{H}\right)\mathrm{=}\mathrm{di}\mathrm{+}\mathrm{di}\mathrm{*}\left(\mathrm{z\_Dmax}\left(\mathrm{H}\right)\mathrm{-}\mathrm{z\_Dmin}\left(\mathrm{H}\right)\right)\mathrm{/}\mathrm{di}\mathrm{/}\mathrm{fa}\mathrm{;}$$
    
    
    respectively $$\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{di}\mathrm{+}\mathrm{di}\mathrm{*}\left(\mathrm{z\_Dmax}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{-}\mathrm{z\_Dmin}\left(\mathrm{x},,\mathrm{y}\right)\right)\mathrm{/}\mathrm{di}\mathrm{/}\mathrm{fa}\mathrm{;}$$
    
    $$\mathrm{K}\mathrm{1}\left(\mathrm{H}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{H}\right)\mathrm{+}\mathrm{D}\left(\mathrm{H}\right)\mathrm{;}$$
    
    
    respectively. $$\mathrm{K}\mathrm{1}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{+}\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{,}$$
    

1. a) Festlegen eines gewünschten mittleren Polierdrucks pm des Polierwerkzeugs;
2. b) Bestimmen der notwendigen Anpresskraft Fk aus der Polierfläche des Polierwerkzeugs;
3. c) Auswählen eines Elastizitätsmoduls E für den Werkstoff des zweiten Körpers;
4. d) Auswählen einer Mittendicke Di des zweiten Körpers;
5. e) Auswählen einer anfänglichen äußeren Kontur;
6. f) Berechnen einer mittleren Einfederungstiefe di für einen zweiten Körper unter der Annahme, dass der zweite Körper eine konstante axiale Dicke D aufweist, die gleich der ausgewählten Mittendicke Di ist;
7. g) Bestimmen einer Polierbewegung des Polierwerkzeugs auf der zu polierenden Oberfläche;
8. h) Diskretisieren der Polierbewegung in eine vorbestimmte Anzahl n Bewegungsinkremente, wobei die Anzahl n hinreichend groß gewählt wird;
9. i) Berechnen einer Einfederungsfläche aus den Abweichungen der axialen Dicke z_Di in Richtung z der Achse zwischen der Oberfläche und der äußeren Kontur in einem vorgegebenen Punkt i bei relativer Polierbewegung zwischen dem Polierwerkzeug und der optischen Oberfläche;
10. j) Addieren der Abweichungen z_Di bei allen Punkten i;
11. k) Bestimmen einer maximalen Abweichung z_Dmax;
12. l) Bestimmen einer minimalen Abweichung z_Dmin;
13. m) Bestimmen eines Mittelwerts z_Dm aus allen Abweichungen z_Di;
14. n) Bilden einer Differenz z_Dmt zwischen dem Mittelwert z_Dm und der Summe einer Kippung und eines zentralen Offsets des Mittelwerts z_Dm;
15. o) Berechnen der axialen Dicke D in Abhängigkeit von der radialen Richtung h für runde bzw. x, y für unrunde Polierwerkzeuge mit den Unterschritten: $$\mathrm{D}\left(\mathrm{h}\right)\mathrm{=}\mathrm{Di}\mathrm{+}\mathrm{Di}\mathrm{*}\mathrm{z\_Dmt}\left(\mathrm{h}\right)\mathrm{/}\mathrm{di}\mathrm{/}\mathrm{f\_a}\mathrm{;}$$
    
    
    bzw. $$\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{Di}\mathrm{+}\mathrm{Di}\mathrm{*}\mathrm{z\_Dmt}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{/}\mathrm{di}\mathrm{/}\mathrm{f\_a}\mathrm{;}$$
    
    $$\mathrm{K}\mathrm{1}\left(\mathrm{h}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{h}\right)\mathrm{+}\mathrm{D}\left(\mathrm{h}\right)\mathrm{;}$$
    
    
    bzw. $$\mathrm{K}\mathrm{1}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{+}\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{.}$$
    

The second variant is characterized by the following steps:

1. a) setting a desired mean polishing pressure pm of the polishing tool;
2. b) determining the necessary contact force Fk from the polishing surface of the polishing tool;
3. c) selecting a modulus of elasticity E for the material of the second body;
4. d) selecting a center thickness Di of the second body;
5. e) selecting an initial outer contour;
6. f) calculating a mean deflection depth di for a second body assuming that the second body has a constant axial thickness D equal to the selected center thickness Di;
7. g) determining a polishing movement of the polishing tool on the surface to be polished;
8. h) discretizing the polishing movement into a predetermined number n movement increments, the number n being chosen to be sufficiently large;
9. i) calculating a jounce area from the deviations of the axial thickness z_Di in the direction z of the axis between the surface and the outer contour at a predetermined point i during relative polishing movement between the polishing tool and the optical surface;
10. j) adding the deviations z_Di at all points i;
11. k) determining a maximum deviation z_Dmax;
12. l) determining a minimum deviation z_Dmin;
13. m) determining a mean value z_Dm from all deviations z_Di;
14. n) forming a difference z_Dmt between the mean value z_Dm and the sum of a tilt and a central offset of the mean value z_Dm;
15. o) calculating the axial thickness D as a function of the radial direction h for round or x, y for non-round polishing tools with the substeps: $$\mathrm{D}\left(\mathrm{H}\right)\mathrm{=}\mathrm{di}\mathrm{+}\mathrm{di}\mathrm{*}\mathrm{z\_Dmt}\left(\mathrm{H}\right)\mathrm{/}\mathrm{di}\mathrm{/}\mathrm{fa}\mathrm{;}$$
    
    
    respectively. $$\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{di}\mathrm{+}\mathrm{di}\mathrm{*}\mathrm{z\_Dmt}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{/}\mathrm{di}\mathrm{/}\mathrm{fa}\mathrm{;}$$
    
    $$\mathrm{K}\mathrm{1}\left(\mathrm{H}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{H}\right)\mathrm{+}\mathrm{D}\left(\mathrm{H}\right)\mathrm{;}$$
    
    
    respectively. $$\mathrm{K}\mathrm{1}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{+}\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{,}$$
    

Further advantages of the invention will become apparent from the drawing and the accompanying drawings.

Fig. 1

eine schematische Seitenansicht, teilweise aufgebrochen, eines Ausführungsbeispiels eines erfindungsgemäßen Polierkopfs zum Polieren einer Oberfläche eines Brillenglases;

Fig. 2

eine noch weiter schematisierte Darstellung eines Polierwerkzeugs, wie es in dem Polierkopf gemäß Fig. 1 verwendet wird;

Fig. 3

eine Darstellung, ähnlich Fig. 2, einer ersten Variante des Polierwerkzeugs;

Fig. 4

eine Darstellung, ähnlich Fig. 2, einer zweiten Variante des Polierwerkzeugs;

Fig. 5

eine Darstellung, ähnlich Fig. 2, einer dritten Variante des Polierwerkzeugs;

Fig. 6

eine Darstellung, ähnlich Fig. 2, einer vierten Variante des Polierwerkzeugs;

Fig. 7

ein Blockschaltbild zur Erläuterung einer Ausführungsform eines erfindungsgemäßen Verfahrens zum Herstellen eines Polierwerkzeugs.

Embodiments of the invention are illustrated in the drawings and are explained in more detail in the following description. Show it:

Fig. 1

a schematic side view, partially broken away, of an embodiment of a polishing head according to the invention for polishing a surface of a spectacle lens;

Fig. 2

a still further schematic representation of a polishing tool, as used in the polishing head of FIG. 1;

Fig. 3

a representation, similar to Figure 2, a first variant of the polishing tool.

Fig. 4

a representation, similar to Figure 2, a second variant of the polishing tool.

Fig. 5

a representation, similar to Figure 2, a third variant of the polishing tool.

Fig. 6

a representation, similar to Figure 2, a fourth variant of the polishing tool.

Fig. 7

a block diagram for explaining an embodiment of a method according to the invention for producing a polishing tool.

In Fig. 1, 10 as a whole denotes a device for polishing a spectacle lens 12. It is understood that the application "spectacle lens" is to be understood only as an example, because the invention is generally applicable to optical surfaces. By this is meant areas of optical components such as e.g. Surfaces, in particular aspherical surfaces or free-form surfaces of spectacle lenses, mirrors, plastic optics, etc.

In Figure 1, the spectacle lens 12 is held by a conventional holder 14, in the example shown spatially fixed. A first axis is designated 15. This is at the same time the geometric axis of the body of the spectacle lens 12 and the vertical axis of the holder 14.

The spectacle lens has an inner rear surface 16 and an outer front surface 18. The inner surface 16 in the example shown is the so-called recipe surface, which is optically processed in a predetermined manner and in particular designed as a free-form surface.

A polishing head 20 carries at its free end a polishing tool 22. The polishing tool 22 has a first, preferably rigid body 24 in the form of a shell. This is followed flush with a second, elastic body 26, which is also referred to as a buffer. On its opposite side, in turn, there is a polishing pad 28. The polishing pad 28 may consist only of an applied polishing paste or may be its own physical entity, e.g. a polishing membrane, a polishing pad or a polishing layer material.

The first body 24 is provided on its rear side with a ball socket 30 or other suitable hinge part into which engages a ball head 32 of a symbolized actuator 34 of a polishing robot (not shown) which extends along a second axis 36. The thus indicated joint allows pivoting movements of the polishing tool 22 relative to the spectacle lens, but at the same time makes it possible to rotate the polishing tool 22 about the second axis 36. This makes it possible to drive the polishing tool 22 and to guide it with the polishing pad 28 over the surface 16 of the spectacle lens 12 to be polished, as is known to the person skilled in the art.

The second elastic body 26 is preferably made of rubber or rubber. It can also consist of a polyurethane material, eg polyurethane, polyether urethane or an elastomer. Such materials are known and, for example, under the trade names Sylomer, Sylodyn and Sylodamp of the Getzner available. The elastic modulus E of this material should be greater than 0.02 N / mm ² .

The elements 24, 26 and 28 sit in the direction of the second axis 36 close to each other and extend substantially in the radial direction. As will be explained, in the context of the present invention a distinction is made between round and non-round polishing tools 22.

It should also be noted that the second axis 36 need not necessarily be located in the center of the polishing tool 22. The present invention also includes other embodiments in eccentric or tumbling construction.

In Fig. 2, the polishing tool 22 is again shown schematically with the three elements 24, 26 and 28. It is important in this embodiment that the second body 26 has an axial thickness D which varies with the distance from the axis 36. This is therefore provided because the elasticity of the second body 26 in the radial direction from the inside to the outside in a predetermined manner, ie with a predetermined profile to increase. This means that the second, elastic body is softened towards the outside, thus has an increasingly flatter spring characteristic. It makes use of the fact that an elastic plate material has a spring characteristic, ie a dependence of the pressure (N / mm ² ) of the deflection (mm), which runs the flatter, the thicker the plate material. When polishing an optical surface, the applied polishing pressure corresponds to the pressure.

The already mentioned axial thickness D is measured between the contours 40 and 42.

For the sake of completeness, it should be mentioned at this point that the desired increasing elasticity towards the edge of the polishing tool can alternatively also be achieved by the use of a material for the second body whose elasticity is not homogeneous but increases towards the outside. One is then largely free in the course of the axial thickness as a function of the radial distance from the axis.

It should also be noted that the radial increase in elasticity towards the edge of the polishing tool can be adjusted continuously or in steps.

For a more detailed explanation of the embodiment shown in the drawing, the direction of the second axis 36 is denoted by z. The radial distance from the second axis is one-dimensional in round polishing tools 22, ie h. In the case of non-round polishing tools 22, it is two-dimensional, ie it is expressed in coordinates x, y.

FIG. 2 further shows that the second body 26 is bounded on its upper side by an inner contour 40 and on its underside by an outer contour 42. The outer contour 42 is substantially equal to the envelope of the contour of the surface 16 to be polished. In FIG. 2, the inner contour 40 is concave and the outer contour 42 is convex.

Figures 3 to 6 show variants of Fig. 2, wherein like elements are provided with the same reference numerals and differentiated only by adding a letter.

In Fig. 3, the inner contour 40a is convex and the outer contour 42a is planar.

In Fig. 4, the inner contour 40b and the outer contour 42b are concave.

In Fig. 5, the inner contour 40c is flat and the outer contour 42c is concave.

In Fig. 6, the inner contour 40d is convex and the outer contour 42d is concave.

The polishing tool 22 is pressed with a pressing force Fk to the surface 16 of the spectacle lens 12 to be polished. In order to achieve the desired uniform contact pressure over the contact surface between polishing pad 28 and surface 16, an optimization process is performed, which is illustrated in the block diagram of FIG. 7.

bzw. $$\mathrm{p}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{E}\mathrm{*}\mathrm{d}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{/}\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right)$$

For this purpose, a simplified model of Hooke's law is used for the polishing pressure calculation. This model represents a one-dimensional relationship between the polishing pressure p (h) and the surface pressure for round and p (x, y) for non-circular polishing tools 22 and the thickness D (h) and D (x, y) of the second body 26, respectively represents: $$\mathrm{p}\left(\mathrm{H}\right)\mathrm{=}\mathrm{e}\mathrm{*}\mathrm{d}\left(\mathrm{H}\right)\mathrm{/}\mathrm{D}\left(\mathrm{H}\right)\mathrm{.}$$

respectively. $$\mathrm{p}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{e}\mathrm{*}\mathrm{d}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{/}\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right)$$

In a first step (block 50), the desired mean polishing pressure pm or the surface pressure in N / mm ^{2 is} set.

In a second step (block 52), the necessary contact force Fk in N is determined from the dimensions of the polishing tool 22, that is to say from the size of the contact surface.

In a third step (block 54), the elasticity modulus E of the material for the second body 26 is selected in N / mm ² and its center thickness Di determined.

In a fourth step (block 56), the outer contour 42 of the second body 26 is determined on the surface 16, starting from a basic position of the polishing tool 22.

In a fifth step (block 58), the mean deflection depth di for a second body 26 of assumed constant thickness Di is calculated according to the specification of the third step (block 54) according to the following formula: $$\mathrm{di}\mathrm{=}\mathrm{pm}\mathrm{*}\mathrm{di}\mathrm{/}\mathrm{e}$$

In a sixth step (block 60), the polishing movement of the polishing tool 22 on the surface 16 to be polished is determined.

In a seventh step (block 62), this polishing movement is discretized in a sufficiently large number n of small movement increments.

In an eighth step (block 64), the deviations in the z-direction z_D (h) and z_D (x, y), respectively, between the outer contour 42 of the second body 26 which is displaced and / or twisted with respect to the surface 16 to be polished are positioned at one position i calculated. This is the local jounce surface.

In a ninth step (block 66), these deviations z_D (h) and z D (x, y) are added at all motion incremental intermediate positions. This happens component by component in the respective polar or Cartesian system.

In a tenth step (block 68), the minimum deflection depth z_Dmin is recorded and, accordingly, in an eleventh step (block 69), the maximum deflection depth z_Dmax.

Finally, in a twelfth step (block 76), the tilt and the central offset of the averaged aspheric deformation surface are subtracted, and a value z_Dmt is obtained.

The required iterations take place via the loops 74, 78 and 80.

With the value z_Dmt it is then possible to continue working according to two different variants A and B, which are identified in blocks 84 and 86 with the corresponding equations IV to IX or X to XIII.

bzw. für unrunde Polierwerkzeuge 22: $$\mathrm{K}\mathrm{2}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{+}\mathrm{z\_Dmt}\left(\mathrm{x},,\mathrm{y}\right)$$

In variant A, first the outer contour 42 is corrected by the value z_Dmt in order to compensate the averaged deflection deviations, namely for round polishing tools 22: $$\mathrm{K}\mathrm{2}\left(\mathrm{H}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{H}\right)\mathrm{+}\mathrm{z\_Dmt}\left(\mathrm{H}\right)$$

or for non-circular polishing tools 22: $$\mathrm{K}\mathrm{2}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{+}\mathrm{z\_Dmt}\left(\mathrm{x},,\mathrm{y}\right)$$

bzw. für unrunde Polierwerkzeuge 22: $$\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{Di}\mathrm{+}\mathrm{Di}\mathrm{*}\left(\mathrm{z\_Dmax}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{-}\mathrm{z\_Dmin}\left(\mathrm{x},,\mathrm{y}\right)\right)\mathrm{/}\mathrm{di}\mathrm{/}\mathrm{f\_a}$$

The not yet compensated dynamic deviations are reduced by the function of the thickness D of the second body 26, namely for round polishing tools 22: $$\mathrm{D}\left(\mathrm{H}\right)\mathrm{=}\mathrm{di}\mathrm{+}\mathrm{di}\mathrm{*}\left(\mathrm{z\_Dmax}\left(\mathrm{H}\right)\mathrm{-}\mathrm{z\_Dmin}\left(\mathrm{H}\right)\right)\mathrm{/}\mathrm{di}\mathrm{/}\mathrm{fa}\mathrm{;}\mathrm{respectively}$$

or for non-circular polishing tools 22: $$\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{di}\mathrm{+}\mathrm{di}\mathrm{*}\left(\mathrm{z\_Dmax}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{-}\mathrm{z\_Dmin}\left(\mathrm{x},,\mathrm{y}\right)\right)\mathrm{/}\mathrm{di}\mathrm{/}\mathrm{fa}$$

bzw. für unrunde Polierwerkzeuge 22: $$\mathrm{K}\mathrm{1}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{+}\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{.}$$

Variant A thus completely compensates the mean dynamic spring deviation and reduces the dynamic spring pressure deviation by the function of the thickness D of the second body 26. The inner contour 41 (here called K1) then results for round polishing tools 22: $$\mathrm{K}\mathrm{1}\left(\mathrm{H}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{H}\right)\mathrm{+}\mathrm{D}\left(\mathrm{H}\right)$$

or for non-circular polishing tools 22: $$\mathrm{K}\mathrm{1}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{+}\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{,}$$

bzw. für unrunde Polierwerkzeuge 22: $$\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{Di}\mathrm{+}\mathrm{Di}\mathrm{*}\mathrm{z\_Dmt}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{/}\mathrm{di}\mathrm{/}\mathrm{f\_a}$$

In variant B, the correction of the outer contour 42 is dispensed with. Then the average spring deviations z_Dmt can be reduced via the functions of the thickness D of the second body 26, for round polishing tools 22: $$\mathrm{D}\left(\mathrm{H}\right)\mathrm{=}\mathrm{di}\mathrm{+}\mathrm{di}\mathrm{*}\mathrm{z\_Dmt}\left(\mathrm{H}\right)\mathrm{/}\mathrm{di}\mathrm{/}\mathrm{fa}$$

or for non-circular polishing tools 22: $$\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{di}\mathrm{+}\mathrm{di}\mathrm{*}\mathrm{z\_Dmt}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{/}\mathrm{di}\mathrm{/}\mathrm{fa}$$

bzw. für unrunde Polierwerkzeuge 22: $$\mathrm{K}\mathrm{1}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{+}\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{.}$$

The inner contour 40 or K1 then results for round polishing tools 22: $$\mathrm{K}\mathrm{1}\left(\mathrm{H}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{H}\right)\mathrm{+}\mathrm{D}\left(\mathrm{H}\right)$$

or for non-circular polishing tools 22: $$\mathrm{K}\mathrm{1}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{+}\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{,}$$

The factor f_a is used as a special factor assigned to the aspheric type. The factor can ideally be between 1/2 and 2. The dynamic spring pressure variations are not compensated in this variant.

Examples:

The design of the second body 26 is carried out for the processing of a toric aspherical surface of a spectacle lens according to variant B. The starting point is a toric surface with the radii R1 = 100 mm and R2 = 150 mm. For a toric lens surface, a base radius RB of 150 mm with a refractive index of 1.6 means a refractive index of 4 diopters. A cylinder radius RZ of 100 mm means a refractive index of 6 diopters for the same refractive index. Such an aspheric toric surface thus represents a cylindrical refractive power of 2 diopters. Over 90% of all spectacle lenses have a cylinder effect of less than 2 diopters. The asphericity of the described torus is in the diameter range of 45 mm at about 900 microns.

The contact pressure is assumed to be Fk = 90.478 N. With a diameter of the contact surface of Dm = 45 mm, an average polishing pressure pm = 0.057 N / mm ^{2 is then} exerted.

The elastic modulus is chosen to be E = 0.25 N / mm ² . The center thickness Di of the second body 26 is 4 mm.

It is first assumed that the contours 40 and 42 are identical and correspond to the radius of the spherical surface of RB = RZ = 150 mm. This gives the ideal case with constant polishing pressure.

Example 1 (prior art):

The polishing tool 22 is pressed in a conventional manner, assuming a constant thickness D of the second body 26 of 4 mm against the aforementioned surface with the radii 100/150 mm. The radii of contours 40 and 42 are identical and chosen to be between the two radii of the torus. It then shows that the polishing pressure fluctuations in the outer area amount to at least 96% of the averaged polishing pressure. This causes a strong discontinuous polishing erosion and is counterproductive for a uniform polishing and smoothing effect. It is to be expected a strongly fluctuating polishing process.

Example 2 (invention):

Therefore, according to the invention, a second body 26 optimized in the radial course of the thickness Di is used, in which the thickness Di widens from 4 mm in the center to DR = 10 mm at the outer edge. The factor f_a is chosen here with f_a = 2/3. The radii of the contours 40 and 42 are calculated so that the outer contour 42 presses somewhat shallower than the base radius RB and the radius of the inner contour 40 correspondingly compensates for the difference in thickness from the inside to the outside. The now calculated polishing pressure then returns in its dynamics to less than 40% of the average polishing pressure pm.

Example 3 (invention):

If a second body 26 thickening outwards from Di = 4 mm to DR = 8 mm is selected and the radii of the contours 40 and 42 are designed analogously to the previous calculation, then the polishing pressure fluctuation is less than 47% when the factor fa = 1 is assumed.

Claims (30)

1. An apparatus for polishing an optical surface, comprising a polishing head (20) having a polishing tool (22), the polishing tool (22) being provided along a common axis (36) and one behind another with a first, preferably rigid member (24), a second, elastic member (26), and a polishing lining (28), each extending essentially radially relative to the axis (36), characterized in that the second member (26) is configured to be increasingly soft in a radial outward direction (h; x, y).
2. The apparatus of claim 1, characterized in that the second member (26) is configured to be continuously increasingly soft in a radial outward direction (h; x, y).
3. The apparatus of claim 1, characterized in that the second member (26) is configured to be discontinuously increasingly soft in a radial outward direction (h; x, y).
4. The apparatus of one of claims 1 to 3, characterized in that the second member (26) is configured to have an increasing axial thickness (D) in a radial direction (h; x, y).
5. The apparatus of claim 4, characterized in that the second member (26) adjoins the first member (24) with an inner contour (40) and adjoins the polishing lining (28) with an outer contour (42), and that function of the axial thickness (d) vs. the radial direction (h; x, y) is determined depending on the radial function of the contours (40, 42).
6. The apparatus of claim 5, characterized in that the inner contour (40) is configured convex and the outer contour (42) is configured convex.
7. The apparatus of claim 5, characterized in that the inner contour (40a) is configured convex and the outer contour (42a) is configured plane.
8. The apparatus of claim 5, characterized in that the inner contour (40b) is configured concave and the outer contour (42b) is configured concave.
9. The apparatus of claim 5, characterized in that the inner contour (40c) is configured plane and the outer contour (42c) is configured concave.
10. The apparatus of claim 5, characterized in that the inner contour (40d) is configured convex and the outer contour (42d) is configured concave.
11. The apparatus of one of claims 5 to 10, characterized in that the outer contour (42) is configured spherical.
12. The apparatus of one of claims 5 to 11, characterized in that the outer contour (42) is configured aspherical.
13. The apparatus of one of claims 5 to 10, characterized in that the outer contour (42) is configured as a free-form surface.
14. The apparatus of one of claims 1 to 13, characterized in that the second member (26) consists of a material having a modulus of elasticity of more than 0.02 N/mm².
15. The apparatus of one of claims 1 to 14, characterized in that the second member (26) consists of a material selected from the group: rubber, caoutchouc, polyurethane, polyetherurethane, elastomer.
16. The apparatus of one of claims 1 to 15, characterized in that the second member (26) is a moulded piece.
17. The apparatus of one of claims 1 to 16, characterized in that the second member (26) is configured from a material having an elasticity increasing outwardly in a radial direction.
18. The apparatus of claim 17, characterized in that the second member has a constant axial thickness in a radial direction.
19. The apparatus of one of claims 1 to 18, characterized in that the polishing lining (28) is a polishing paste.
20. The apparatus of one of claims 1 to 16, characterized in that the polishing lining (28) is configured as a polishing membrane.
21. The apparatus of one of claims 1 to 20, characterized in that the polishing tool (22) is configured round relative to the axis (36).
22. The apparatus of one of claims 1 to 20, characterized in that the polishing tool (22) is configured out of round relative to the axis (36).
23. The apparatus of one of claims 1 to 22, characterized in that the polishing tool (22) is gimballed within the axis (36).
24. The apparatus of one of claims 1 to 22, characterized in that the polishing tool (22) is gimballed outside the axis (36).
25. A method of polishing a surface (16) of an optical component, in particular of a spectacle lens (12), characterized in that an apparatus according to one of claims 1 to 24 is used.
26. A method of manufacturing a polishing tool (20), the polishing tool (20) being provided along a common axis (36) and one behind another with a first, preferably rigid member (24), a second, elastic member (26), and a polishing lining (28), each extending essentially radially relative to the axis (36), characterized in that the second member (26) is configured to be increasingly soft in a radial outward direction (h; x, y).
27. The method of claim 26, characterized in that the second member (26) is manufactured to have an increasing axial thickness (D) in a radial direction (h; x, y).
28. The method of claim 27, characterized in that the second member (26) is manufactured to adjoin the first member (24) with an inner contour (40) and to adjoin the polishing lining (28) with an outer contour (42), and that the function of the axial thickness (d) vs. the radial direction (h; x, y) is determined depending on the radial function of the contours (40, 42).
29. The method of claim 28, comprising the steps of:

    a) Determining a desired medium polishing pressure (pm) of the polishing tool (20);

    b) Determining the necessary application force (Fk) from the polishing area of the polishing tool (20);

    c) Selecting a modulus of elasticity (E) for the material of the second member (26);

    d) Selecting a central thickness (Di) of the second member (26);

    e) Selecting an initial outer contour (42);

    f) Calculating a central elastic deflection (di) for a second member (26) under the assumption that the second member (26) has a constant axial thickness (D) being equal to the central thickness (Di);

    g) Determining a polishing movement of the polishing tool (20) on the surface (16) to be polished;

    h) Subdividing the polishing movement into a predetermined number (n) of motion increments, the number (n) being elected sufficiently high;

    i) Calculating an elastic deflection area from the deviations of the axial thickness (z_Di) in the direction (z) of the axis (36) between the surface (16) and the outer contour (42) in a predetermined point (i) during a relative polishing movement between the polishing tool (20) and the optical surface;

    j) Adding the deviations (z_Di) at all points (i);

    k) Determining a maximum deviation (z_Dmax);

    l) Determining a minimum deviation (z_Dmin);

    m) Determining a mean value (z_Dm) from all deviations (z_Di);

    n) Establishing a difference (z_Dmt) between the mean value (z_Dm) and the sum of a tilting and a central offset of the mean value (z_Dm);

    o) Calculating the axial thickness (D) as a function of the radial direction (h) for round and out of round polishing tools (22), resp., with the substeps of: $$\mathrm{K}\mathrm{2}\left(\mathrm{h}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{h}\right)\mathrm{+}\mathrm{z\_Dmt}\left(\mathrm{h}\right);$$

    

    and $$\mathrm{K}\mathrm{2}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{+}\mathrm{z\_Dmt}\left(\mathrm{x},,\mathrm{y}\right),\mathrm{resp}\mathrm{.};$$

    

    $$\mathrm{D}\left(\mathrm{h}\right)\mathrm{=}\mathrm{Di}\mathrm{+}\mathrm{Di}\mathrm{*}\left(\mathrm{z\_Dmax}\left(\mathrm{h}\right)\mathrm{-}\mathrm{z\_Dmin}\left(\mathrm{h}\right)\right)\mathrm{/}\mathrm{di}\mathrm{/}\mathrm{f\_a};$$

    

    and $$\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{Di}\mathrm{+}\mathrm{Di}\mathrm{*}\left(\mathrm{z\_Dmax}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{-}\mathrm{z\_Dmin}\left(\mathrm{x},,\mathrm{y}\right)\right)\mathrm{/}\mathrm{di}\mathrm{/}\mathrm{f\_a},\mathrm{resp}\mathrm{.};$$

    

    $$\mathrm{K}\mathrm{1}\left(\mathrm{h}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{h}\right)\mathrm{+}\mathrm{D}\left(\mathrm{h}\right);$$

    

    and $$\mathrm{K}\mathrm{1}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{+}\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right),\mathrm{resp}\mathrm{.}$$

    
30. The method of claim 28, comprising the steps of:

    a) Determining a desired mean polishing pressure (pm) of the polishing tool (20);

    b) Determining the necessary application force (Fk) from the polishing area of the polishing tool (20),

    c) Selecting a modulus of elasticity (E) for the material of the second member (26);

    d) Selecting a central thickness (Di) of the second member (26);

    e) Selecting an initial outer contour (42);

    f) Calculating a mean elastic deflection (di) for a second member (26) under the assumption that the second member (26) has a constant axial thickness (D) being equal to the central thickness (Di);

    g) Determining a polishing movement of the polishing tool (20) on the surface (16) to be polished;

    h) Subdividing the polishing movement into a predetermined number (n) of motion increments, the number (n) being elected sufficiently high;

    i) Calculating an elastic deflection area from the deviations of the axial thickness (z_Di) in the direction (z) of the axis (36) between the surface (16) and the outer contour (42) in a predetermined point (i) during a relative polishing movement between the polishing tool (20) and the optical surface;

    j) Adding the deviations (z_Di) at all points (i);

    k) Determining a maximum deviation (z_Dmax);

    l) Determining a minimum deviation (z_Dmin);

    m) Determining a mean value (z_Dm) from all deviations (z_Di);

    n) Establishing a difference (z_Dmt) between the mean value (z_Dm) and the sum of a tilting and a central offset of the mean value (z_Dm);

    o) Calculating the axial thickness (D) as a function of the radial direction (h) for round and out of round polishing tools (22), resp., with the substeps of: $$\mathrm{D}\left(\mathrm{h}\right)\mathrm{=}\mathrm{Di}\mathrm{+}\mathrm{Di}\mathrm{*}\mathrm{z\_Dmt}\left(\mathrm{h}\right)\mathrm{/}\mathrm{di}\mathrm{/}\mathrm{f\_a};$$

    

    and $$\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{Di}\mathrm{+}\mathrm{Di}\mathrm{*}\mathrm{z\_Dmt}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{/}\mathrm{di}\mathrm{/}\mathrm{f\_a},\mathrm{resp}\mathrm{.};$$

    

    $$\mathrm{K}\mathrm{1}\left(\mathrm{h}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{h}\right)\mathrm{+}\mathrm{D}\left(\mathrm{h}\right);$$

    

    and $$\mathrm{K}\mathrm{1}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{=}\mathrm{K}\mathrm{2}\left(\mathrm{x},,\mathrm{y}\right)\mathrm{+}\mathrm{D}\left(\mathrm{x},,\mathrm{y}\right),\mathrm{resp}\mathrm{.}$$

    

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