THEORY OF SPECKLES IN DIFFRACTIVE OPTICS AND ITS APPLICATION TO BEAM SHAPING

The design of diffractive phase elements (DPEs) for solving the genera l beam shaping problem where the signal wave is specified by an intens ity distribution on a continuous support in a finite signal window is considered. In this case serious design problems due to speckles may a rise. After introducing a mathematical definition and description of s peckles, the influence of the phase of the signal wave on the design p rocess is examined. It turns out that depending on the application a p seudo-random or a spherical phase should be used as an initial phase o f the signal wave for an iterative design procedure. Due to its smooth ness the spherical phase prevents the occurrence of speckles during th e iteration process whereas the pseudo-random phase is accompanied by speckle effects. For applications where the imaging properties of the spherical phase are undesirable, a soft coding method is presented whi ch significantly reduces the number of speckles of the pseudo-random p hase. For cases where speckles still remain we finally present an appr oach for removing these in pairs.