Freeform surface lens design for uniform illumination of a rectangular area

Optical design for an integrated light source is currently a hot topic, but it is also difficult due to the complexity of the calculations. In this paper, based on the edge-ray principle and the grid division method, two types of lenses for creating a 3:1 uniformly illuminated rectangular spot and 1:1 uniformly illuminated square spot are designed. Research results show that when the ratio of the size of the LED light source to the lens height is 1:10 and 1:5, i.e. it is equivalent to a point source, the uniformity of illuminance on the target surface is as high as 90%, and the system energy utilisation is 88%. When the ratio of the size of the LED source to the lens height is 1:3.3, 1:2.5 or 1:2.0, i.e. the equivalent of an extended source, the uniformity of illuminance on the target surface is more than 80% and the system energy utilisation is about 88%. This means the lenses can maintain the high energy efficiency and illuminance uniformity for an extended source. Tolerance analyses were also conducted. It seems that the illumination uniformity is sensitive to light source installation errors, but when the offset of the LED from the lens is less than 0.2 mm, illumination uniformity is maintained at a high level.