Freeform lens design using a spreadsheet

In illumination optics an important design task is to create a light source with a certain intensity profile. One way to achieve this is to use LEDs and secondary optics that use freeform surfaces. Freeform lens design is a very powerful tool with many sophisticated design techniques. However, it is not always necessary to use difficult techniques or complicated software algorithms to design a freeform lens surface. This paper presents a method for designing a radially-symmetric freeform lens using a spreadsheet. The spreadsheet designs freeform lenses that transform a Lambertian (cosine[theta]) intensity profile from a light source to any output profile of the form (cosine<boolean AND>N[theta]) where N is a real number. The input and output are radially symmetric, and the lens controls the angular extent (cone half-angle) of the output beam. Several example lenses are presented and one lens is analyzed with a raytrace simulation.