Optimization-based hologram design for fine optical tweezer arrays and extension of super-resolution criteria

Aligning light spots into arbitrary shapes is a fundamental challenge in holography, leading to various applications across diverse fields in science and engineering. However, as the spot interval approaches the wavelength of light, interference effects among the spots become prominent, which complicates the generation of a distortion-free alignment. Herein, we introduce a hologram design method based on the optimisation of a nonlinear cost function using a holographic phase pattern as the optimisation parameter. We confirmed a spot interval of 0.952(1) $μ$m in a $5 \times 5$ multispot pattern on the focal plane of a high-numerical-aperture (0.75) objective by observing the near-infrared (wavelength: 820 nm) holographic output light from a spatial light modulator device, a result which overcomes the limitation of a few micrometres under similar conditions. Furthermore, the definition of the Rayleigh diffraction limit is refined by considering the separation of spots and the spot interval, thereby concluding the achievement of "super-resolution." The proposed method is expected to advance laser fabrication, scanning laser microscopy, and cold atom physics, among other fields.