An LED print head has a gradient index array. In order to improve resolving power of the array, resolution of the arrays were analyzed by using the illumination analysis. The array has plural gradient index rods, which have a refractive index distribution in the radial direction of the rods. An erected image is exposed at same magnification of an object by the array. In the illumination analysis, a large amount of random rays was radiated from light sources to images in a simulation models. The current results showed the resolution of the array depend on a coefficient of refractive index distribution (gradient coefficient) and a rod radius. A small gradient coefficient improved the resolution of the array. A reduction in the radius improved the resolution of the array. The small gradient coefficient and the reduction in the radius causes small aperture angle of the rod. The rod has a small aperture angle don't pass through rays which have a large comatic aberration and causes a large field curvature. If the rod has a stable refractive index distribution in manufacturing but poor resolution, it seems to be effective that after forming the refractive index distribution, the rod is trimmed and the radius is reduced to improve the resolution.