Limits of a digital micromirror device in topological charge measurement

Abstract

In this work, we discuss the limitations of a digital micromirror device (DMD) as a computer-controllable diffracting aperture for measuring light's topological charge (TC). Theoretically, we can relate the TC to the size and shape of the aperture and the resulting intensity patterns. However, when we compare the intensity patterns generated using the aperture's theoretical image (TI) with the displayed image (DI) created by numerically mimicking the DMD, we observe that the patterns are structurally similar only for a particular size. We calculate the Structural Similarity index between the patterns to define a criterion that quantitatively describes this limit. We find that apertures with radius r that enable at least n = 13312 pixels in DMD to be on an "ON"-state mode allow a wider TC range that we can measure. Below this threshold, we can only probe lower TC values. Our results aid as a caution when using the DMD as a diffracting element for measuring the TC of light.