Method for producing an aspherical optical element

A method for producing an aspherical optical element from a workpiece using a computer numerically controlled (CNC) machine of the type having a grinding 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;
• (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, is flattened;
• and
• (c) moving the grinding tool relative to the workpiece under program control based on said corrected numerical control data to form said aspherical optical element from the workpiece, whereby said aspherical optical element is formed having a flattened runout region.

A method for producing an aspherical optical element from a workpiece using a computer numerically controlled (CNC) machine of the type having a grinding 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;
• (d) rotationally driving the workpiece at a rotational speed in accordance with a hyperbolic spindle speed function such that said rotational speed increases with the distance to the center of said workpiece decreasing;
• and
• (e) moving the grinding tool under program control relative to the workpiece based on said corrected numerical control data to produce said aspherical optical element from the workpiece.

A method for producing an aspherical optical element from a workpiece using a computer numerically controlled (CNC) machine of the type having a grinding 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;
• (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, is flattened;
• (c) rotationally driving said grinding tool at a substantially constant rotational speed and rotationally driving the workpiece at a rotational speed in accordance with a hyperbolic spindle speed function such that said rotational speed increases with the distance to the center of said workpiece decreasing;
• and
• (d) moving the grinding tool relative to the workpiece under program control based on said numerical control data to form said aspherical optical element from the workpiece, whereby said aspherical optical element is formed having a flattened runout region.

A method for producing an aspherical optical element from a workpiece using a computer numerically controlled (CNC) machine of the type having a grinding 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;
• (b) calculating first correction data based on a first correction function;
• (c) calculating second correction data based on a second correction function;
• (d) overlaying said numerical control data with said first correction data and said second correction data to produce corrected numerical control data, said second correction function being a function selected such that said runout region, as defined by said corrected numerical control data, is flattened;
• and
• (e) moving the grinding tool relative to the workpiece under program control based on said corrected numerical control data to form said aspherical optical element from the workpiece.

A method for producing an aspherical optical element from a workpiece using a computer numerically controlled (CNC) machine of the type having a grinding 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;
• (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, is flattened, at least part of said runout region having a gradient which decreases with increasing radius, wherein an inflection point is located within said runout region;
• and
• (c) moving the grinding tool under program control relative to the workpiece based on said corrected numerical control data to form said aspherical optical element from the workpiece.