Analyzing phase masks for wide étendue holographic displays

Spatial light modulator (SLM) technology forms the centerpiece of digital holographic displays. However, an inherent limitation of these devices is that their etendue, defined as the product of the display's eye box and field of view, is bounded by the number of pixel units. As a consequence, current SLMs are far from meeting the required field-of-view and eye box for the human visual system, which would require scaling the number of display units by a few orders of magnitude. Existing strategies for etendue-expansion rely on introducing a diffractive optical element (DOE), a fixed random phase mask whose pitch is much smaller than that of the original display, thereby spreading light over a wider angle. Displayed content is then optimized under perceptual constraints on the generated image. However, since the phase mask is fixed, the number of degrees of freedom does not increase and hence, the expansion in etendue necessarily comes with a loss of image quality. The tradeofts involved with such phase masks are not well understood. This paper studies the space of phase masks that can be attached to an SLM to increase its angular range. It attempts to characterize what trade-offs are involved in etendue-expansion, and whatever specific phase mask designs would support better holograms. Our theoretical results show that etendue expansion comes with a commensurate loss of contrast or resolution, depending on the specifics of the mask that we use. We show that while pseudo random masks support wide-etendue, they involve an inherent loss of contrast. Perhaps surprisingly, simple commonly-available phase masks like lenslet arrays provide near-optimal results that can largely outperform random masks.