Efficient freeform lens optimization for computational caustic displays.

Gerwin Damberg,Wolfgang Heidrich

doi:10.1364/oe.23.010224

Abstract

Phase-only light modulation shows great promise for many imaging applications, including future projection displays. While images can be formed efficiently by avoiding per-pixel attenuation of light most projection efforts utilizing phase-only modulators are based on holographic principles which rely on interference of coherent laser light and a Fourier lens. Limitations of this type of an approach include scaling to higher power as well as visible artifacts such as speckle and image noise. We propose an alternative approach: operating the spatial phase modulator with broadband illumination by treating it as a programmable freeform lens. We describe a simple optimization approach for generating phase modulation patterns or freeform lenses that, when illuminated by a collimated, broadband light source, will project a pre-defined caustic image on a designated image plane. The optimization procedure is based on a simple geometric optics image formation model and can be implemented computationally efficient. We perform simulations and show early experimental results that suggest that the implementation on a phase-only modulator can create structured light fields suitable, for example, for efficient illumination of a spatial light modulator (SLM) within a traditional projector. In an alternative application, the algorithm provides a fast way to compute geometries for static, freeform lens manufacturing.

Highlights

In this work we propose to use phase only spatial light modulation combined with broadband illumination for image formation
We achieve this by treating the spatial phase modulator as a programmable freeform lens, and devising a simple and computationally efficient optimization procedure to derive a lens surface or modulation pattern that will form a caustic representing a predefined target image when illuminated by a collimated, broadband light source
Coherent light can result in high resolution artifacts, including screen speckle and diffraction on structures such as the discrete pixel grid of a spatial light modulator (SLM)

Summary

Introduction

In this work we propose to use phase only spatial light modulation combined with broadband illumination for image formation. There has been strong interest in freeform lens design, both for general lighting applications and to generate images from caustics [4] In the latter application, we can distinguish between discrete optimization methods that work on a pixelated version of the problem In our work we derive a simple and efficient formulation in which we optimize directly for the phase function (i.e. the shape of the wavefront in the lens plane) without the need for a subsequent integration step. This is made possible by a new parameterization of the problem that allows us to express the optimization directly in the lens plane rather than the image plane

Phase Modulation Image Formation

Optimization Problem

Simulation Results

Static Lenses

Implementation on Spatial Light Modulators