Digital holography is popular tool for research and practical applications in various fields of science and technology. Most widespread method of optical reconstruction implements digital hologram display on spatial light modulators (SLM). Optical reconstruction of digital holograms is used for remote display of static and dynamic 2D and 3D scenes, in optical information processing, metrology, interferometry, microscopy, etc. Holograms recorded with digital cameras are amplitude type. Therefore quality of its optical reconstruction with phase SLM is worse compared to amplitude SLM. However application of phase SLM can provide higher diffraction efficiency. To improve quality of optical reconstruction with phase SLM, method of SLM phase modulation depth reduction at digital hologram display is proposed. To our knowledge, this method was applied only in analog holography. Also two other methods of quality improvement are considered: hologram to kinoform conversion and holograms multiplexing. Numerical experiments on modelling of digital Fourier holograms recording and their optical reconstruction by phase SLM were performed. Method of SLM phase modulation depth reduction at digital holograms display was proposed and tested. SLM phase modulation depth ranged from 0 to 2π. Quantity of hologram phase levels equal to 256 corresponds to 2π phase modulation depth. To keep SLM settings while changing phase modulation depth hologram phase distribution was renormalized instead. Dependencies of reconstruction quality on hologram phase modulation depth were obtained. Best quality is achieved at 0.27π÷0.31π phase modulation depth. To reduce speckle noise, hologram multiplexing can be applied. Modeling of multiplex holograms optical reconstruction was conducted. Speckle noise reduction was achieved. For improvement of digital hologram optical reconstruction quality and diffraction efficiency hologram to kinoform conversion can be used. Firstly numerically reconstructed image of object was obtained. Then this image was used for kinoform synthesis. Diffraction efficiency was increased by 6.4 times in comparison with hologram reconstruction.