Weighting IFT algorithm for of f-axis quantized kinoforms of binary objects

Abstract

The results of experiments on the synthesis of the off-axis quantized kinoforms of binary objects with the use of the weighting iterative Fourier transform (WIFT) algorithm are presented. Kinoforms are registered with a liquid-crystal spatial light modulator (SLM). A simple procedure to introduce the carrier frequency into the structure of an axial kinoform is proposed. An image reconstructed by an off-axis kinoform is free from the noises with the zero and close frequencies caused by the imperfection of both the phase mode of operation of the SLM and the effects of quantization of the registered phase. Data on the diffraction efficiency are also given.OCIS codes: 090.1995, 100.5070, 230.6120. doi: 10.3788/COL201109.120007. Possessing a high diffraction efficiency, the kinoform optical elements are widely used for the beam splitting (fanout), beam shaping, and pattern or image generation [1,2] . The detailed description of the weighting iterative Fourier transform (WIFT) algorithm was given earlier [3] , where we also showed that it is most efficient for the synthesis of the kinoforms of binary objects. In brief, the essence of the WIFT-algorithm consists in the following. Firstly, one or several iterations (K gs ) with an input real object f o are realized by the classical Gerchberg-Saxton (GS) scheme. Then, in all iterations with k > K gs at the formation of the input, the amplitude f o will be replaced by a new amplitude defined as f k = α k f o , where the weight coefficients α k are determined by the recurrence| is the reconstructed amplitude at the (k − 1)th iteration, and ε is a small number ∼ 10 −10 . The processing of the phases of an object plane and the kinoform remains the same as that in the classic GS-algorithm. From the viewpoint of optics, the system of weight coefficients α k normalized to unity can be interpreted as some objectdependent amplitude filter which acts on the initial object f o and varies in the process of iterations. We note that all the coefficients α k in the iteration process tend to unity in the case when the iterative process converges.In this letter, we study the potentialities of the WIFT algorithm at the synthesis of the off-axis kinoforms of binary objects with regard for the quantization of a phase registered with a spatial light modulator (SLM). In the course of modeling and optical experiments, we compared the WIFT algorithm with the kinoform version of the Fienup input-output (IO) algorithm [4] . The latter is most convenient for the sake of comparison, because it is well known and, like the weighting algorithm, differs from the GS-algorithm only by means of processing of a field in the object plane. The programming of the IO algorithm is realized by Eqs. (8)−(10) from Ref. [4].A number of model experiments with various binary objects (with sizes of 64×64 and 128×128) were realized with the purpose to compare the potentialities of the WIFT and IO algorithms at the synthesis of quantized kinoforms. In all the cases, the same phase starting diffuser with a uniform di...