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The hologram density on a photopolymer could be improved with the recording using the fiber speckle reference beam. The spatial selectivity of the hologram is enhanced enormously, which is from the thinness of the polymer material. The long interaction length in the photorefractive crystal could also make good selectivity for the typical (i.e., not complicated) reference wave. The thin layer can not interact with the simple reference beam so effectively. Therefore the selectivity for the speckled random phased reference beam case is much enhanced. We find that the speckled reference beam is much more effective for the photopolymer material than for photorefractive crystals. Detailed experimental data are presented.