Aspherical optical element and method for producing same

Abstract

The invention relates to an aspherical optical element and method for producing same based on numerical control data for controlling a surface processing machine such as a CNC wet-grinding machine for processing workpieces made of optical materials to produce aspherical forms, the data of the aspherical forms to be formed being overlaid with correction data.

1 . A method for producing an aspherical optical element from a workpiece using a: 
 computer numerically controlled (CNC) machine of the type having a surface processing tool movable relative to the workpiece under program control in accordance with numerical control data, said method comprising the steps of:    (a) inputting numerical control data which includes parameters representing the desired aspherical form of an aspherical optical element;    (b) calculating correction data based on a correction function;    (c) overlaying said numerical control data with said correction data over at least a central portion of said surface of said aspherical form to produce corrected numerical control data; and    (d) moving the tool under program control relative to the workpiece based on said corrected numerical control data to produce said aspherical optical element from the workpiece.    
   
   
       2 . The method of  claim 1  wherein said numerical control data is overlaid with said correction data over the entirety of said surface of said aspherical form, whereby sudden changes in the profile of said aspherical optical element are avoided.  
   
   
       3 . The method of  claim 1  wherein said correction function is a function, Zcorrection, of the form:  
     
       
         
           
             
               Z 
               correction 
             
             = 
             
               
                 ( 
                 
                   
                     Z 
                     min 
                   
                   * 
                   
                     Z 
                     max 
                   
                   * 
                   
                     D 
                     / 
                     2 
                   
                 
                 ) 
               
               
                 ( 
                 
                   
                     
                       D 
                       / 
                       2 
                     
                     * 
                     
                       Z 
                       min 
                     
                   
                   + 
                   
                     x 
                     * 
                     
                       ( 
                       
                         
                           Z 
                           max 
                         
                         - 
                         
                           Z 
                           min 
                         
                       
                       ) 
                     
                   
                 
                 ) 
               
             
           
         
       
     
     where: 
 D is the diameter of said aspherical optical element;  
 Z min  is a constant representing a minimum correction height at which the overlaying is still effective;  
 Z max  is a constant representing a maximum correction height in said surface of said aspherical form; and  
 x is a parameter representing radial distance from the center of said aspherical optical element.  
 
   
   
       4 . A method for producing an aspherical optical element from a workpiece using a computer numerically controlled (CNC) machine of the type having a surface processing tool movable relative to the workpiece under program control in accordance with numerical control data, said method comprising the steps of: 
 (a) inputting numerical control data which includes parameters representing the aspherical form of an aspherical optical element, said form having a surface which includes a useful region and a runout region located radially outside said useful region, said runout region having a gradient which increases with increasing radius, said useful region having an aspherical profile and a steeply rising peripheral portion;    (b) overlaying said numerical control data with correction data to produce corrected numerical control data, said correction data being calculated based on a correction function selected such that said runout region, as defined by said corrected numerical control data, includes an inflection point and is flattened, at least part of said runout region having a gradient which decreases with increasing radius; and    (c) moving the tool under program control relative to the workpiece based on said corrected numerical control data to form said aspherical optical element from the workpiece.    
   
   
       5 . An aspherical optical element produced from a workpiece using a computer numerically controlled (CNC) machine of the type having a surface processing tool movable relative to the workpiece under program control in accordance with numerical control data, said aspherical optical element being produced using a method comprising the steps of: 
 (a) inputting numerical control data which includes parameters representing the desired aspherical form of an aspherical optical element;    (b) calculating correction data based on a correction function;    (c) overlaying said numerical control data with said correction data over at least a central portion of said surface of said aspherical form to produce corrected numerical control data; and    (d) moving the tool under program control relative to the workpiece based on said corrected numerical control data to produce said aspherical optical element from the workpiece.    
   
   
       6 . The aspherical optical element of  claim 5  wherein said numerical control data is overlaid with said correction data over the entirety of said surface of said aspherical form, whereby sudden changes in the profile of said aspherical optical element are avoided.  
   
   
       7 . The aspherical optical element of  claim 5  wherein said correction function is a function, Zcorrection, of the form:  
     
       
         
           
             
               Z 
               correction 
             
             = 
             
               
                 ( 
                 
                   
                     Z 
                     min 
                   
                   * 
                   
                     Z 
                     max 
                   
                   * 
                   
                     D 
                     / 
                     2 
                   
                 
                 ) 
               
               
                 ( 
                 
                   
                     
                       D 
                       / 
                       2 
                     
                     * 
                     
                       Z 
                       min 
                     
                   
                   + 
                   
                     x 
                     * 
                     
                       ( 
                       
                         
                           Z 
                           max 
                         
                         - 
                         
                           Z 
                           min 
                         
                       
                       ) 
                     
                   
                 
                 ) 
               
             
           
         
       
     
     where: 
 D is the diameter of said aspherical optical element;  
 Z min  is a constant representing a minimum correction height at which the overlaying is still effective;  
 Z max  is a constant representing a maximum correction height in said surface of said aspherical form; and  
 x is a parameter representing radial distance from the center of said aspherical optical element.  
 
   
   
       8 . An aspherical optical element produced from a workpiece using a computer numerically controlled (CNC) machine of the type having a surface processing tool movable relative to the workpiece under program control in accordance with numerical control data, said aspherical optical element being produced using a method comprising the steps of: 
 (a) inputting numerical control data which includes parameters representing the aspherical form of an aspherical optical element, said form having a surface which includes a useful region and a runout region located radially outside said useful region, said runout region having a gradient which increases with increasing radius, said useful region having an aspherical profile and a steeply rising peripheral portion;    (b) overlaying said numerical control data with correction data to produce corrected numerical control data, said correction data being calculated based on a correction function selected such that said runout region, as defined by said corrected numerical control data, includes an inflection point and is flattened, at least part of said runout region having a gradient which decreases with increasing radius; and    (c) moving the tool under program control relative to the workpiece based on said corrected numerical control data to form said aspherical optical element from the workpiece.