A lighting system, comprising: an array of LEDs; a collimators arrangement (40,50) mounted over the array of LEDs for collimating the light output from the LEDs; a lightguide mounted over the collimators arrangement, the lightguide comprising: an elongate structure having a length direction with one light input end mounted over the collimator arrangement, light extraction features extending widthwise parallel to the light input end for out-coupling light from an outer arcuate surface of the lightguide, wherein in each light extraction feature an angle β is the angle between the normal n of the light extraction feature and a normal to the length direction, characterized in that the general shape in cross section perpendicular to the length direction comprises a non-circular arc, and the array of LEDs follows a corresponding non-circular arc, wherein said angle β at least once is gradually or abruptly changed over the cross section of the outer arcuate surface of the light guide, and wherein in a direction parallel to the light input end the lightguide comprises a plurality of sections (140a, 140b, 140c) positioned side to side, and wherein β is the same within a respective section, but for at least two sections β is mutually different. an array of LEDs; a collimators arrangement (40,50) mounted over the array of LEDs for collimating the light output from the LEDs; a lightguide mounted over the collimators arrangement, the lightguide comprising: an elongate structure having a length direction with one light input end mounted over the collimator arrangement, light extraction features extending widthwise parallel to the light input end for out-coupling light from an outer arcuate surface of the lightguide, wherein in each light extraction feature an angle β is the angle between the normal n of the light extraction feature and a normal to the length direction, characterized in that the general shape in cross section perpendicular to the length direction comprises a non-circular arc, and the array of LEDs follows a corresponding non-circular arc, wherein said angle β at least once is gradually or abruptly changed over the cross section of the outer arcuate surface of the light guide, and wherein in a direction parallel to the light input end the lightguide comprises a plurality of sections (140a, 140b, 140c) positioned side to side, and wherein β is the same within a respective section, but for at least two sections β is mutually different. an elongate structure having a length direction with one light input end mounted over the collimator arrangement, light extraction features extending widthwise parallel to the light input end for out-coupling light from an outer arcuate surface of the lightguide, wherein in each light extraction feature an angle β is the angle between the normal n of the light extraction feature and a normal to the length direction, characterized in that the general shape in cross section perpendicular to the length direction comprises a non-circular arc, and the array of LEDs follows a corresponding non-circular arc, wherein said angle β at least once is gradually or abruptly changed over the cross section of the outer arcuate surface of the light guide, and wherein in a direction parallel to the light input end the lightguide comprises a plurality of sections (140a, 140b, 140c) positioned side to side, and wherein β is the same within a respective section, but for at least two sections β is mutually different.