Holographic data storage applications often use liquid crystal displays as spatial light-amplitude modulators for writing data images. The hologram created in the Fourier plane is usually applied to store the information, since this plane supplies optimal data density. A well known technique for homogenizing the light distribution in the Fourier plane is the application of external random phase modulating masks. The requirement for pixel by pixel matched positioning of the phase modulating mask and the pixels of the spatial light-amplitude modulator is hard to solve in the optical systems and any positioning error leads to significant signal degradations. The article analyses the possibilities of realizing the required simultaneous amplitude and phase modulation of light with the application of a single LCD. Twisted nematic LCDs with different maximal birefringence are numerically investigated using the Jones matrix method. Elliptical incident and exit polarizations are proposed, by which ternary phase-amplitude modulation (+1,–1,0) can be realized. Test measurements are also presented that demonstrate the validity of the calculated results.