Irradiance formations of on-axis Lambertian pointlike sources in polygonal total-internal-reflection straight light pipes

Different geometric shapes of light pipes cause different irradiance distributions. We analytically explore the irradiance distributions of on-axis Lambertian pointlike sources in polygonal total-internal-reflection (TIR) straight light pipes. It is analytically shown that the irradiance of pentagonal light pipes concentrates on the center of the exit plane. Numerical verifications are also provided, and experimental explorations with different shapes of acrylic light pipes are carried out for comparison. We also analyze the influence of light-pipe length on distribution uniformity and deduce the smallest uniform-mixing length/circumradius ratios for polygonal light pipes.