Abstract: Disclosed are an optical system for conditioning a beam of radiation, and an illumination system and metrology apparatus comprising such an optical system. The optical system comprises one or more optical mixing elements in an optical system. The optical system defines at least a first optical mixing stage, at least a second optical mixing stage, and at least one transformation stage, configured such that radiation entering the second optical mixing stage includes a transformed version of radiation exiting the first optical mixing stage. The first and second optical mixing stages can be provided using separate optical mixing elements, or by multiple passes through the same optical mixing element. The transformation stage can be a Fourier transformation stage. Both spatial distribution and angular distribution of illumination can be homogenized as desired.

Abstract: A method, an optical system and a lighting arrangement for homogenizing a bundle of light rays (110) by means of an elongated optical element (100) arranged for homogenizing light. The bundle of light rays is directed into a transversal entry face (101) of the optical element, and into at least one of the following geometrical regions: (a) a neighbourhood of the perimeter of the entry face; (b) a neighbourhood of at least a portion of a first line segment (R1) extending from the centre of the entry face to a mid-point of a vertex (123); (c) a neighbourhood of at least a portion of a second line segment (R2a) extending from the centre of the entry face to a midpoint of an edge (122).