Optical EngineeringIntensity distribution transformation for rotationally symmetric beam shaping
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Holography and optical processing often require coherent input beams with intensity distributions that are different from the usual Gaussian distribution of a laser. Aspherical lenses are used to perform general beam shaping in order to obtain the required intensity distributions. Computer-generated holograms (CGHs) can also be used for beam shaping. In this paper the computational procedure for CGHs, which implements a rotationally symmetric transformation, is supplied. The computational procedure consists of two steps. In the first step a transformation equation is computed from the two known intensity distributions by using an integral equation. This transformation equation will transform the available intensity distribution into the required intensity distribution. It is substituted into a differential equation from which a phase function is cornputed, and is then encoded as a CGH. Two CGHs are required to perform the transformation. The first one diffracts the light to form the desired intensity distribution at a given distance behind the CGH. At that position the second CGH is placed to cancel the diffraction in order to retain the desired intensity distribution. The resulting intensity distribution remains unchanged from then on except for the effect of the diffraction of the distribution itself. General intensity distributions have been implemented with CGHs produced with this technique, and the results are presented in this paper.