Method and system for improving aerial image simulation speeds

A simulator system for generating an aerial image, comprising:

• a processor;
• and
• a simulator application executed on the processor for approximating values by,
• receiving a mask;
• generating a matrix of node values based on the mask, wherein each node value corresponds to a node of a plurality of nodes in a lattice;
• performing a one-dimensional (1-D) approximation of a plurality of first approximation values at corresponding first approximation points between pairs of nodes of the plurality of nodes;
• and
• performing a two-dimensional (2-d) approximation of second approximation values at corresponding second approximation points between pairs of first approximation points, wherein chebyshev polynomials are used to approximate the first approximation values and the second approximation values,
• wherein the node values, the first approximation values, and the second approximation values are intensity values of a function f(x,y), and
• wherein each value is approximated according to the following expression:
• φ*=c0*T0(0)+c1*T1(0)+ . . . +cN−1*TN−1(0), wherein φ* represents the approximated value of the function, wherein c0, c1, . . . cN−1 denote coefficients, wherein T0(0), T1(0), . . . TN−1(0) are Chebyshev polynomials, and N is a number of the first approximation points.

A computer-readable medium containing program instructions for generating an aerial image, the program instructions which when executed by a computer system cause the computer system to execute a method comprising:

• receiving a mask;
• generating a matrix of node values based on the mask, wherein each node value corresponds to a node of a plurality of nodes in a lattice;
• performing a one-dimensional (1-D) approximation of a plurality of first approximation values at corresponding first approximation points between pairs of nodes of the plurality of nodes;
• performing a two-dimensional (2-d) approximation of second approximation values at corresponding second approximation points between pairs of first approximation points, wherein chebyshev polynomials are used to approximate the first approximation values and the second approximation values;
• and
• wherein a Chebyshev polynomial is defined as Tn(cos((2i+1)*/(2n)))=0, wherein n is a degree of the polynomial and i=0 . . . n−1 is applied to the approximation process.