Design of computer generated beam shaping holograms

For the design of computer generated holograms reconstructing certain intensity patterns with phase freedom we use an object-oriented approach. The given pattern is decomposed into elementary objects for which appropriate phase-only hologram functions can be found. The total hologram function is received by subsequent superposition of its constituents with a relative amplitude and phase weighting, respectively. Thus, the degrees of freedom are dramatically reduced compared to sampling approaches. The design algorithm allows to compensate for the intensity and phase distribution of the impinging laser beam and for the shape of the hologram aperture. The phase-only hologram function for an elementary focal object is found by a raytracing approach for the light beams propagating from point x at the hologram plane to point u ¯ at the focal plane. To get the correspondence x ¯ ( u → ) the equation for light flux transformation, I ( x ¯ ( u ¯ ) ) det ∂ x ¯ ∂ u ¯   = I 0 ( u ¯ ) , is integrated with respect to the intensity distribution I ( x → ) of the laser beam within the hologram aperture and the intensity distribution I 0 ( u ¯ ) of the desired focal pattern at the distance z. Moreover, conservation of total energy is assumed. The equation for the slope of the light ray in paraxial approximation, ∇ ψ ( u → )   =   x → ( u → ) − u → z , is integrated to get the phase k ψ ( u → ) immediately behind the hologram. This phase function has to be encoded in the hologram together with a phase compensation for the input beam. The phase-only hologram functions for the elementary objects which are implemented so far are eiven in table 1.