Mask shape calculation method, program, and storage medium

A program for causing a computer to execute:

• sampling K representative points from a contour of a lithography target, wherein K is an integer equal to or greater than 1;
• selecting a first kernel provided in a first function representing a projection optical system related to a mask shape corresponding to the lithography target;
• determining a first optical image intensity at each of the K representative points corresponding to a first convolution integral of the first kernel and a second function representing the mask shape;
• discretizing the first convolution integral into N dimensions to generate (i) a first matrix of K rows and N columns related to the first kernel;
• and (ii) a first vector of K rows related to the first optical image intensity;
• and
• solving a linear equation Am=b using a matrix A including the first matrix, a vector b including the first vector, and a vector m corresponding to the second function, and calculating the second function.

A storage medium on which a program is stored, the program for causing a computer to execute:

• sampling K representative points from a contour of a lithography target, wherein K is an integer equal to or greater than 1;
• selecting a first kernel provided in a first function representing a projection optical system related to a mask shape corresponding to the lithography target;
• determining a first optical image intensity at each of the K representative points corresponding to a first convolution integral of the first kernel and a second function representing the mask shape;
• discretizing the first convolution integral into N dimensions to generate (i) a first matrix of K rows and N columns related to the first kernel;
• and (ii) a first vector of K rows related to the first optical image intensity;
• and
• solving a linear equation Am=b using a matrix A including the first matrix, a vector b including the first vector, and a vector m corresponding to the second function, and calculating the second function.