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This work provides the design of a multifocal display that can create a dense stack of focal planes in a single shot. We achieve this using a novel computational lens that provides spatial selectivity in its focal length, i.e, the lens appears to have different focal lengths across points on a display behind it. This enables a multifocal display via an appropriate selection of the spatially-varying focal length, thereby avoiding time multiplexing techniques that are associated with traditional focus tunable lenses. The idea central to this design is a modification of a Lohmann lens, a focus tunable lens created with two cubic phase plates that translate relative to each other. Using optical relays and a phase spatial light modulator, we replace the physical translation of the cubic plates with an optical one, while simultaneously allowing for different pixels on the display to undergo different amounts of translations and, consequently, different focal lengths. We refer to this design as a Split-Lohmann multifocal display. Split-Lohmann displays provide a large étendue as well as high spatial and depth resolutions; the absence of time multiplexing and the extremely light computational footprint for content processing makes it suitable for video and interactive experiences. Using a lab prototype, we show results over a wide range of static, dynamic, and interactive 3D scenes, showcasing high visual quality over a large working range.

The wave equation of electromagnetism, the Helmholtz equation, has the same form as the Schrödinger equation, and so optical waves can be used to study quantum mechanical problems. The electromagnetic wave solutions for non-diffracting beams lead to the two-dimensional Helmholtz equation. When expressed in elliptical coordinates the solution of the angular part is the same as the Schrödinger equation for the simple pendulum. The resulting optical eigenmodes, Mathieu modes, have an optical Fourier transform with a spatial intensity distribution that is proportional to the quantum mechanical probability for the pendulum. Comparison of Fourier intensities of eigenmodes are in excellent agreement with calculated quantum mechanical probabilities of pendulum stationary states. We further investigate wave-packet superpositions of a few modes and show that they mimic the libration and the nonlinear rotation of the classical pendulum, including revivals due to the quantized nature of superpositions. The ability to ‘dial a wavefunction’ with the optical modes allows the exploration of important aspects of quantum wave-mechanics and the pendulum that may not be possible with other physical systems.

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