Geometrical optics analysis for reduction of trapezoidal image distortion in a single prism-based optical fingerprint scanner

A single prism-based optical fingerprint scanner structure is mathematically analyzed by using geometrical optics approach. Important parameters including a tilting angle of the fingerprint accepting plane, a geometrical-optic distant difference, a trapezoidal image distortion, an object compression ratio, and an orientation of a two-dimensional image sensor are formulated for the first time in terms of all three angles of the prism and the prism material. In addition, based on our mathematical model, we propose to design all three angles of the prism in such a way that the plane accepting the fingertip observed from one side of the prism is normal to the optical axis of the system. In this way, the imaging plane is perpendicular to the optical axis, eliminating the trapezoidal image distortion and leading to ease of implementation. Experimental verification using three commercially available dispersion prisms made from three different glass materials and one prism based on our design concept shows that a prism with higher refractive index provides lower trapezoidal image distortion. The experimental data generally obeys our theoretical analysis.