Apparatus and method for deterministic control of surface figure during full aperture polishing

1. A computerized method for calculating an amount of material removed from a workpiece during a polishing process on a polishing system comprising:

receiving at a computer system a set of polishing properties;

calculating, by the computer system, a set of kinematic values for a lap and a workpiece of a polishing system based at least in part on the set of polishing properties;

calculating, by the computer system, a time of exposure for a set of lap points on the workpiece based at least in part on the set of polishing properties and the set of kinematic values;

calculating, by the computer system, a friction force between the lap and the workpiece from at least a portion of the set of polishing properties;

calculating, by the computer system, a slope between the lap and the workpiece based on a moment force between the lap and the workpiece, wherein the moment force is based on the friction force;

calculating, by the computer system, a pressure distribution between the lap and the workpiece based on information for a lap type included in the set of polishing properties;

calculating, by the computer system, a cumulative pressure distribution between the lap and the workpiece based on the slope, the pressure distribution for the lap type, and the time of exposure; and

calculating, by the computer system, an amount of material removed from the workpiece based on the cumulative pressure distribution, the friction force, and the set of kinematic values.

2. The computerized method of claim 1 , wherein each calculating step is executed for a plurality of points on a surface of the workpiece.

3. The computerized method of claim 1 , further comprising executing each calculating step for a plurality of successive time periods.

4. The computerized method of claim 1 , further comprising executing each calculating step for a plurality of successive time periods until a surface of the workpiece has a desired shape.

5. The computerized method of claim 1 , wherein the set of polishing properties includes a set of material properties, a set of polisher configuration properties, and a set of polisher kinematic properties.

6. The computerized method of claim 5 , wherein the set of material properties are properties of the polishing system and includes information for a lap type, a Stribeck friction curve for the lap, and a workpiece-lap mismatch response function.

7. The computerized method of claim 6 , wherein the set of material properties further includes the Preston's constant for Preston's equation.

8. The computerized method of claim 7 , wherein the information for the lap type includes information to identify the lap type as viscoelastic, viscoplastic, or elastic.

9. The computerized method of claim 5 , wherein the set of polisher kinematic properties includes a rotation rate of the workpiece, a rotation rate of the lap, a stroke length of the workpiece relative to the lap, and a stroke frequency.

10. The computerized method of claim 5 , wherein the set of polisher configuration properties includes a workpiece shape, a lap shape, a workpiece size, a lap size, a lap curvature, a load distribution of the lap on the workpiece, and a moment arm of the workpiece relative to the lap.

11. The computerized method of claim 10 , further comprising:

subtracting the amount of material removed from the workpiece shape for a first time period to determine a new workpiece shape for the first time period; and

executing each calculating step for a successive time period following the first time period using the new workpiece shape to determine a successive amount of material removed from the workpiece for the successive time period.

12. The computerized method of claim 10 , further comprising:

determining a set of control settings for the polishing system from the new workpiece shape and a final workpiece shape; and

setting on the polishing system a set of controls to the set of control settings to adjust the polishing system to polish the workpiece shape to the final workpiece shape.

13. A non-transitory computer readable storage medium containing program instructions that, when executed by a controller within a computer, cause the controller to execute a method for calculating an amount of material removed from a workpiece during a polishing process on a polishing system, the method comprising:

receiving at a computer system a set of polishing properties;

calculating, by the computer system, a set of kinematic values for a lap and a workpiece of a polishing system from at least a portion of the set of polishing properties;

calculating, by the computer system, a time of exposure for a set of lap points on the workpiece based on at least a portion of the set of polishing properties and the set of kinematic values;

calculating, by the computer system, a friction force between the lap and the workpiece from at least a portion of the set of polishing properties;

calculating, by the computer system, a slope between the lap and the workpiece based on a moment force between the lap and the workpiece, wherein the moment force is based on the friction force;

calculating, by the computer system, a pressure distribution between the lap and the workpiece based on information for a lap type included in the set of polishing properties;

calculating, by the computer system, a cumulative pressure distribution between the lap and the workpiece based on the slope, the pressure distribution for the lap type, and the time of exposure; and

calculating, by the computer system, an amount of material removed from the workpiece based on the cumulative pressure distribution, the friction force, and the set of kinematic values.

14. The non-transitory computer readable storage medium of claim 13 , wherein each calculating step is executed for a plurality of points on a surface of the workpiece.

15. The non-transitory computer readable storage medium of claim 13 , wherein the method further comprises executing each calculating step for a plurality of successive time periods.

16. The non-transitory computer readable storage medium of claim 13 , further comprising executing each calculating step for a plurality of successive time periods until a surface of the workpiece has a desired shape.

17. The non-transitory computer readable storage medium of claim 13 , wherein the set of polishing properties includes a set of material properties, a set of polisher configuration properties, and a set of polisher kinematic properties.

18. The non-transitory computer readable storage medium of claim 17 , wherein the set of material properties are properties of the polishing system and includes information for a lap type, a Stribeck friction curve for the lap, and an workpiece-lap mismatch response function.

19. The non-transitory computer readable storage medium of claim 18 , wherein the set of material properties further includes the Preston's constant for Preston's equation.

20. The non-transitory computer readable storage medium of claim 19 , wherein the information for the lap type includes information to identify the lap type as viscoelastic, viscoplastic, or elastic.

21. The non-transitory computer readable storage medium of claim 17 , wherein the set of polisher kinematic properties includes a rotation rate of the workpiece, a rotation rate of the lap, a stroke length of the workpiece relative to the lap, and a stroke frequency.

22. The non-transitory computer readable storage medium of claim 17 , wherein the set of polisher configuration properties includes a workpiece shape, a lap shape, a workpiece size, a lap size, a lap curvature, a load distribution of the lap on the workpiece, and a moment arm of the workpiece relative to the lap.

23. The non-transitory computer readable storage medium of claim 22 , wherein the method further comprises:

subtracting the amount of material removed from the workpiece shape for a first time period to determine a new workpiece shape for the first time period; and

executing each calculating step for a successive time period following the first time period using the new workpiece shape to determine a successive amount of material removed from the workpiece for the successive time period.

24. The non-transitory computer readable storage medium of claim 22 , wherein the method further comprises:

calculating a set of control settings for the polishing system from the new workpiece shape and a final workpiece shape; and

setting on the polishing system a set of controls to the set of control settings to adjust the polishing system to polish the workpiece shape to the final workpiece shape.

25. A computer program product on a non-transitory computer readable medium for calculating an amount of material removed from a workpiece during a polishing process on a polishing system comprising:

code for receiving at a computer system a set of polishing properties;

code for calculating, by the computer system, a set of kinematic values for a lap and a workpiece of a polishing system from at least a portion of the set of polishing properties;

code for calculating, by the computer system, a time of exposure for a set of lap points on the workpiece based on at least a portion of the set of polishing properties and the set of kinematic values;

code for calculating, by the computer system, a friction force between the lap and the workpiece from at least a portion of the set of polishing properties;

code for calculating, by the computer system, a slope between the lap and the workpiece based on a moment force between the lap and the workpiece, wherein the moment force is based on the friction force;

code for calculating, by the computer system, a pressure distribution between the lap and the workpiece based on information for a lap type included in the set of polishing properties;

code for calculating, by the computer system, a cumulative pressure distribution between the lap and the workpiece based on the slope, the pressure distribution for the lap type, and the time of exposure; and

code for calculating, by the computer system, an amount of material removed from the workpiece based on the cumulative pressure distribution, the friction force, and the set of kinematic values.

26. The computer program product of claim 25 , wherein the code for each calculating step is executed for a plurality of points on a surface of the workpiece.

27. The computer program product of claim 25 , further comprises code for executing each calculating step for a plurality of successive time periods.

28. The computer program product of claim 25 , further comprising code for executing each calculating step for a plurality of successive time periods until a surface of the workpiece has a desired shape.

29. The computer program product of claim 25 , wherein the set of polishing properties includes a set of material properties, a set of polisher configuration properties, and a set of polisher kinematic properties.

30. The computer program product of claim 29 , wherein the set of material properties are properties of the polishing system and includes information for a lap type, a Stribeck friction curve for the lap, and a workpiece-lap mismatch response function.

31. The computer program product of claim 30 , wherein the set of material properties further includes the Preston's constant for Preston's equation.

32. The computer program product of claim 31 , wherein the information for the lap type includes information to identify the lap type as viscoelastic, viscoplastic, or elastic.

33. The computer program product of claim 29 , wherein the set of polisher kinematic properties includes a rotation rate of the workpiece, a rotation rate of the lap, a stroke length of the workpiece relative to the lap, and a stroke frequency.

34. The computer program product of claim 29 , wherein the set of polisher configuration properties includes a workpiece shape, a lap shape, a workpiece size, a lap size, a lap curvature, a load distribution of the lap on the workpiece, and a moment arm of the workpiece relative to the lap.

35. The computer program product of claim 34 , further comprising:

code for subtracting the amount of material removed from the workpiece shape for a first time period to determine a new workpiece shape for the first time period; and

code for executing each calculating step for a successive time period following the first time period using the new workpiece shape to determine a successive amount of material removed from the workpiece for the successive time period.

36. The computer program product of claim 34 , further comprising:

code for calculating a set of control settings for the polishing system from the new workpiece shape and a final workpiece shape; and

code for setting on the polishing system a set of controls to the set of control settings to adjust the polishing system to polish the workpiece shape to the final workpiece shape.