Method for controlling dwell time during processing to optical component

Abstract

A method for smoothing a dwell time during a processing to an optical component belongs to the field of processing optical components, and solves a problem of an adverse effect of dwell time jumps on a stability of the machine tool during processing. The method achieves a smoothing treatment to the dwell time by a diffusion transformation to the distribution of the conventionally calculated dwell time using a time diffusion model. After the smoothing treatment to the dwell time, the difference between times at adjacent discrete points is relatively small, thereby achieving a smooth transition between adjacent discrete points, and limiting the effect of the polishing tool on machine stability due to its frequent acceleration and deceleration during processing.

What is claimed is: 
     
         1 . A method for smoothing a dwell time during a processing to an optical component, wherein the dwell time of the polishing tool at each discrete point on a surface of the optical component is controlled such that a distribution of the dwell time on the surface is smoothened, and a smoothing control to the dwell time is achieved by a diffusion transformation to the distribution of the dwell time using a time diffusion model, in which the method comprises:
 (a) establishing a time diffusion model D(x, y) with a center position D(x 0 , y 0 ), and D(x, y) satisfies a requirement for normalization to the total amount:
   Σ i,j   D ( x   i   ,y   j )=1  (1)
 
   (b) a surface shape error of the component to be processed is M(x, y), and a removal function of the polishing tool in a unit time is I(x, y), and in an iterative calculation process, a dwell time obtained by a single iteration solution is T 1 (x, y); in the dwell time T 1 (x, y), a difference between a theoretical removal amount and the surface shape error M(x, y) of the component to be processed is a calculated residual E 1 (x, y), which can be expressed as:
     E   1 ( x,y )= M ( x,y )− T   1 ( x,y )** I ( x,y )  (2)
 
   
       where ** denotes a convolution, T 1 (x, y)**I(x, y) denotes a removal amount of the component to be processed by the polishing tool during the dwell time T 1 (x, y);
 (c) for each discrete coordinate point (x i , y j ) in T 1 (x, y), the time diffusion model D(x, y) is translated in both X and Y directions so that its center position (x 0 , y 0 ) is moved to (x i , y j ) and is expressed as D ij (x, y):
     D   ij ( x,y )= D ( x−x   i   ,y−y   j )  (3)
 
 
 subsequently, performing a point-to-surface diffusion process to the point T 1 (x i , y j ) with the diffusion function D ij (x, y), thereby obtaining a post-diffusion time distribution K ij (x, y):
     K   ij ( x,y )= D   ij ( x,y )· T   1 ( x   i   ,y   j )  (4)
 
 
 since D ij (x, y) also satisfies the requirement for normalization to the total amount as in equation (1), so there are:
   Σ i,j   K   ij ( x,y )= T   1 ( x   i   ,y   j )  (5)
 
     k   ij ( x,y )** I ( x,y )≈ T   1 ( x   i   ,y   j )· I ( x,y )  (6)
 
 
 (d) according to those described in said (c), obtaining a post-diffusion time distribution K ij (x, y) for each discrete point (x i , y j ), and the dwell time distribution T 1 ′(x, y) after smoothing can be expressed as:
     T   1 ′( x,y )=Σ i,j   K   ij ( x,y )  (7)
 
 
 
       and the removal amount corresponding to the dwell time distribution T 1 ′(x, y) after smoothing should be approximately equal to the removal amount corresponding to the dwell time distribution T 1 (x, y) before smoothing:
     T   1 ′( x,y )** I ( x,y )≈ T   1 ( x,y )** I ( x,y )  (8)
 
 (e) a difference between the surface shape error M(x, y) of the component to be processed and the removal amount corresponding to the dwell time T 1 ′(x, y) after smoothing is a calculation residual E 1 ′(x, y) of the dwell time by a single iteration solution after smoothing:
     E   1 ′( x,y )= M ( x,y )− T   1 ′( x,y )** I ( x,y )  (9)
 
 
 (f) selecting the calculation residual E 1 ′ as the surface shape error M of the component to be processed, and repeating said (b) to (e), and performing iterative calculations, until the calculation of the n th  iteration is completed, and the corresponding calculated residual E n ′ satisfies the requirement, thereby obtaining a total dwell time distribution T′(x, y) after smoothing:
     T ′( x,y )=Σ k=1   n   T   k ′( x,y )  (10)
 
 
 
       where n denotes a total number of iteration cycles; thereby achieving a smoothing processing to the dwell time during a processing to the optical component. 
     
     
         2 . The method according to  claim 1 , wherein the performing of a smoothing control to the dwell time using a time diffusion model, includes adjusting the time diffusion model to improve the smoothing effect of the dwell time, wherein a shape of the removal function I(x, y) being normalized after rotating the removal function I(x, y) by 180 degrees is normalized to be the time diffusion model D(x, y).