1. A method for obtaining a distribution of light at an illumination pupil of an illuminator, which illuminator is configured

to distribute light from a light source at the illumination pupil via a distributing optical element, and which illuminator

is configured to illuminate a target surface with the distributed light, the method comprising:

preparing a far field distribution of the distributing optical element; and

calculating the distribution of light at the illumination pupil with the use of a plurality of point spread functions of a

partial optical system, which point spread functions represent a plurality of positions at the illumination pupil,

wherein the partial optical system is positioned between the distributing optical element and the illumination pupil,

wherein the evaluating the distribution of light at the illumination pupil is effectuated according to

Areticle(xmn,ymn)??i?jAs(?ij,?ij)psf(xmn,ymn,?ij,?ij,IUsetting),

wherein the far field distribution of light, corresponding to the distributing element configured to scatter light, is represented

by As and is a function of coordinates ?ij and ?ij of an entrance pupil of the illumination system,

wherein subscripts i and j correspond to a discrete sum across a two dimensional array of pixels in the entrance pupil such

that each pixel (i,j) has a pair of pupil coordinates (?, ?),

wherein a distribution of light in an exit pupil of the illumination system, corresponding to an optical far field incident

at the reticle, is represented by Areticle which is a function of exit pupil coordinates (xm,n, ym,n),

wherein psf represents a point spread function, and

wherein IUsetting includes an array of values that determine adjustable parameters of the illumination system.