Pixelated light modulators, including LCoS Spatial Light Modulators inevitably suffer from the formation of spurious orders of diffraction in far field. This problem is essential in holographic image projection, where copies of the central useful image are created, distracting the viewer and taking away a solid portion of the illumination energy. Although there is not any straightforward way to break the regularity of the cartesian SLM array, its individual pixels can be engineered in order to change the shape of the far field intensity envelope, which being the Fourier transform of a single pixel shape, can be altered by physically applying an apodization mask directly to the SLM surface. The mask effectively changes the transmittance of any given SLM pixel, opening the ways of suppressing selected image duplicates in the far field. In this work we present the numerical simulations showing the possibilities of localization of the light energy into two lower orders, while heavily suppressing the upper order duplicates. Moreover, we present the experimental validation preformed with a binary dithered electron-beam written filter, which proved the significant decrease of the number of visible spurious image duplicates for a human eye. The positioning of the mask has been found to be non-critical, as opposed to the rotational precision, nevertheless such a solution could potentially be implemented as an add-on element providing the improved functionality of pixelated light modulators of any kind. As the Fourier transform of amplitude-only masks is inevitably symmetrical, the possibility of the attenuation of only a single diffraction order are limited. For this reason we investigate the phase-only and mixed filters providing more degrees of freedom in the design and in the tailoring of the far field envelope, leading to the demonstration of projection of a single image with all other orders highly suppressed.

In this research, we propose the application of a deep-learning method for recognizing fractional orbital angular momentum (OAM) beams distorted by atmospheric turbulence (AT). In order to acquire data sets for model training and testing, we first simulate the propagation of fractional OAM beams through a 1000-m optical channel. Here, AT effects in the channel are modeled with five random phase screens equally spaced. Then, the effects of turbulence strength and OAM mode spacing on the recognition accuracy are analyzed. In particular, we compare the recognition accuracy for three types of OAM-encoding schemes, two single-mode sets (integer and fractional OAM) and one multiplexed fractional mode set. Despite the strong distortion, our designed model shows the ability to recognize transmitted OAM modes with high accuracy and high resolution. In addition to this, we investigate the generalization ability of deep learning to accommodate unknown turbulence environments.