The following picture beautifully tie everything together with set of mathmatical equation
1)The mask is represented by a mask transmittance function t(x1, y1)
When single frequency light shine go the the first len (condenser len), the mask diffracted the light into multiple frequencies and multiples order. This is equivalent of taking the mathmatical function Fourier Transform function on the mask function. And the result is Electric field E function E(fx, fy)
2)Then Pupil opening or Pupil function P(fx, fy) limit the entry of 0th, 1st and -1st order of diffracted light into the second len which is the projection len. The rest of the order 2nd, 3rd, -2nd, -3rd of the diffracted light got throw away.
3)The projection len perform an inverse Fourier Transform Function of the Electric field and pupil function.
or another word ,it gather back the diffracted (spread out) light , in this case 0st, 1st, -1st light and bring them all together and projected on to the wafer.
In summary, the optical system cause the single frequency light to diffracted or spread out by the mask, and then gather the needed light such as 0th, 1st, -1st and throw away the rest and projected the resultant light on the wafer. It uses Fourier transform and Inverse Fourier transform functions and tmask perform the Fourier transform and projection len perform inverse Fourier transform