Calculation of Beam Propagation through a Defected or a Misaligned   Two-Lens System
  An inadvertent or unwanted angular deviation to a passing beam can be introduced by any single optical component within an optical system. The problem arises due to an imperfect tilt alignment of the optical component or manufacturing defects which results in a slightly different response than expected from an ideally aligned/manufactured component. The resulting beam deviation can plague any well-designed optical system that assumes the use of ideal components. The problem is especially introduced by non-ideal lenses, transparent plates and optical windows. Here we present a simple method of manually introducing a deviation error angle which we assume to be constant for all beam incidence angles over the paraxial range. 
Tariq Shamim Khwaja and Syed Azer Reza
physics.gen-ph