Imaging characteristics of ball lens

In most digital imaging applications, high-resolution imaging or videos are usually desired for later processing and analysis. The desire for high-resolution stems from two principal application areas: improvement of pictorial information for human interpretation, and helping representation for automatic machine preception. While the image sensors limit the spatial resolution of the image, the image details are also limited by the optical system, due to diffraction, and aberration¹. Monocentric lens are an attractive option for gigapixel camera because the symmetrical design focuses light identically coming from any direction. Marks and Brady proposed a monocentric lens design imaging 40 gigapixels with an f-number of 2.5 and resolving 2 arcsec over a 120 degrees field of view². Recently, Cossairt, Miau, and Nayer proposed a proof-of-concept gigapixel computational camera consisting of a large ball lens shared by several small planar sensors coupled with a deblurring step³. The design consists of a ball element resulting in a lens that is both inexpensive to produce and easy to align. Because the resolution of spherical lens is fundamentally limited by geometric aberrations, the imaging characteristics of the ball lens is expressed by the geometrical aberrations, in which the general equations for the primary aberration of the ball lens are given. The effect of shifting the stop position on the aberrations of a ball lens is discussed. The variation of the axial chromatic aberration with the Abbe V-number when the refraction index takes different values is analyzed. The variation of the third-order spherical aberration ,the fifth-order spherical aberration and the spherical aberration obtained directly from ray tracing with the f-number is discussed. The other imaging evaluation merits, such as the spot diagram, the modulation transfer function(MTF) and the encircled energy are also described. Most of the analysis of the ball lens is carried out using OSLO optics software from Lambda Research Corporation⁴.