► Circular shape mirrors give as good results as parabolic for Fresnel applications. ► With specific reference for each mirror more constant radiation intensity is obtained. ► A focusing procedure is described. ► The maximum mirrors widths are obtained for limiting reflection lateral drifts. ► Linear Fresnel Reflectors have a great potential for cost reductions in CSP. This paper is aimed at characterizing the concentration process for LFRs, and to analyze the use of different optical designs, including circular-cylindrical and parabolic-cylindrical mirrors with different reference positions. A new approach to analyze and optimize the performance of Fresnel arrays is presented, which is based on a newly formulated optical property that can be used to evaluate the drift of the reflected sunbeams from the mirrors as they rotate to follow the sun. This new optical-geometric property sets upper bounds for the deviation of the reflected sunbeams, in relation to trajectories of the reference situation. It is observed that the maximum deviation depends on the width of the mirror, which must be limited for maximizing the optical efficiency. From this theory an optical design process is suggested to minimize such lateral drifts and to minimize the concentration factor variation along the day. A new mirror layout is defined for keeping a constant value of the radiation impinging onto the receiver from effective sunrise to effective sunset.