Device for collimating a light radiation field emanating from at least one light emitter and having a beam characteristic with respect to the beam angle relative to the beam direction which is different in a first plane from a second plane, the first plane being spanned by the fast-axis direction of the light emitter and the beam direction and the second plane being spanned by the slow-axis direction of the light emitter and the beam direction, so that the planes are orthogonal to one another, comprising at least one first collimating lens for collimating the light radiation field in the first plane, namely for fast-axis collimation, and at least one second collimating lens for collimating the light radiation field in the second plane, namely for slow-axis collimation, wherein the device has an additional optical element which is configured such that portions of the light radiation field which have not yet been aligned parallel with the first and the second collimating lens are aligned parallel to the beam direction, namely the light radiation field is collimated in at least one plane which is different from the first plane and from the second plane and which also extends along the beam direction, wherein the first collimating lens and the second collimating lens as well as the additional optical element are formed in one piece, wherein the additional optical element is formed by a region on the second collimating lens (10, 20) and as an integral part of the second collimating lens, characterized in that the region is arranged in the direction of radiation of the second collimating lens on the exit side in the direction of radiation and a surface for collimating the light radiation field in the second plane is arranged on the second collimating lens on the exit side in the radiation direction, and the collimating lens, which comprises the additional optical element, has a surface topography with the form of a two-dimensional polynomial of even order, the polynomial having the form h x y = a 20 x 2 + a 40 x 4 + a 22 x 2 y 2 + a 60 x 6 + a 42 x 4 y 2 + a 24 x 2 y 4, where h indicates the height of the surface in the direction of radiation and where x and y are the orthogonal coordinate axes in the plane perpendicular to the direction of radiation and the parameters a are not equal to zero. the device has an additional optical element which is configured such that portions of the light radiation field which have not yet been aligned parallel with the first and the second collimating lens are aligned parallel to the beam direction, namely the light radiation field is collimated in at least one plane which is different from the first plane and from the second plane and which also extends along the beam direction, wherein the first collimating lens and the second collimating lens as well as the additional optical element are formed in one piece, wherein the additional optical element is formed by a region on the second collimating lens (10, 20) and as an integral part of the second collimating lens, characterized in that the region is arranged in the direction of radiation of the second collimating lens on the exit side in the direction of radiation and a surface for collimating the light radiation field in the second plane is arranged on the second collimating lens on the exit side in the radiation direction, and the collimating lens, which comprises the additional optical element, has a surface topography with the form of a two-dimensional polynomial of even order, the polynomial having the form h x y = a 20 x 2 + a 40 x 4 + a 22 x 2 y 2 + a 60 x 6 + a 42 x 4 y 2 + a 24 x 2 y 4, where h indicates the height of the surface in the direction of radiation and where x and y are the orthogonal coordinate axes in the plane perpendicular to the direction of radiation and the parameters a are not equal to zero.