Eero Willman

Finite-element modeling of liquid-crystal hydrodynamics with a variable degree of order

A finite-element model of liquid-crystal hydrodynamics based on the Qian and Sheng formulation has been developed. This formulation is a generalization of the Ericksen-Leslie theory to include variations in the order parameter, allowing for a proper description of disclinations. The present implementation is well suited to treat properly the various length scales necessary to model large regions yet resolve the rapid variations in the order parameter in proximity to disclinations

Laser-Based Head-Tracked 3D Display Research

The construction and operation of two laser-based glasses-free 3D (autostereoscopic) displays that have been carried out within the European Union-funded projects MUTED and HELIUM3D is described in this paper. Both use a multi-user head tracker to direct regions viewers referred to as exit pupils to viewers eyes. MUTED employs a direct-view LCD whose backlight comprises novel steering optics and in HELIUM3D image information is supplied by a horizontally-scanned fast light valve whose output is controlled by a spatial light modulator (SLM). The principle of operation, construction and results obtained are described.

Contact-Free Scanning and Imaging with the Scanning Ion Conductance Microscope

Scanning ion conductance microscopy (SICM) offers the ability to obtain very high-resolution topographical images of living cells. One of the great advantages of SICM lies in its ability to perform contact-free scanning. However, it is not yet clear when the requirements for this scan mode are met. We have used finite element modeling (FEM) to examine the conditions for contact-free scanning. Our findings provide a framework for understanding the contact-free mode of SICM and also extend previous findings with regard to SICM resolution. Finally, we demonstrate the importance of our findings for accurate biological imaging.

Modeling of Weak Anisotropic Anchoring of Nematic Liquid Crystals in the Landau–de Gennes Theory

The anisotropic anchoring effect of a treated solid surface on a nematic liquid crystal is described in the Landau-de Gennes theory using a power expansion on the tensor-order parameter and two mutually orthogonal unit vectors. The expression has three degrees of freedom, allowing for independent assignment of polar and azimuthal anchoring strengths and a preferred value of the surface-order parameter. It is shown that in the limit for a uniaxial constant-order parameter, the expression simplifies to the anisotropic generalization of the Rapini-Papoular anchoring energy density proposed by Zhao et al. Experimentally measurable values with a physical meaning in the Oseen-Frank theory can be scaled and assigned to the scalar coefficients of the tensor-order- parameter expansion. Results of numerical experiments comparing the anchoring according to the study of Zhao et al. in the Oseen-Frank theory and the power expansion in the Landau-de Gennes theory are presented and shown to agree well.

Laser scanning based autostereoscopic 3D display with pupil tracking

An autostereoscopic 3D display based on direct-view RGB laser projection via a transparent display screen is presented. Dynamic exit pupils are formed at the target eye locations with the help of a pupil tracker.

Computer Modeling of Liquid Crystal Hydrodynamics

Liquid crystals are highly anisotropic materials that can be described by a tensor which contains information on their average local orientation and the degree of ordering. The accurate modeling of liquid crystal devices, involves the consideration of the elastic interactions within the material, and between the liquid crystal and the walls of the containing cells, the influence of the electric fields governed by the Poisson equation, flexoelectric properties which link the electric fields and the elastic distortion, and flow, governed by the Navier-Stokes equations. All this constitutes a highly nonlinear system, involving the order tensor, the potential, pressure and velocity fields. We present here a finite element solution of this problem, adequate for the study of devices in three dimensions.

Diffraction and fringing field effects in small pixel liquid crystal devices with homeotropic alignment

Reducing the pixel dimensions of liquid crystal microdisplays in search of high resolution has a fundamental impact on their electro-optic behavior. The liquid crystal director orientation becomes distorted due to fringing fields and diffraction effects influence the optical characteristics of the device once the structure features approach the wavelength of the incident light. Three-dimensional finite element simulation of the liquid crystal dynamics with a variable order approach is combined with a full-vector beam propagation analysis to investigate how elasticity and diffraction limit the resolution as a function of the pixel size for transmissive and reflective architectures with vertical liquid crystal alignment. The key liquid crystal properties are considered and the importance of materials with high birefringence is confirmed for small pixel devices as these improve the contrast for a fixed pixel size.

Switching Dynamics of a Post-Aligned Bistable Nematic Liquid Crystal Device

The operation of a post-aligned bistable nematic (PABN) liquid crystal device is simulated using a dynamic finite-element implementation of the Landau-de Gennes theory in 3D. Two topologically distinct stable director profiles of higher and lower tilt angles are identified. The switching process between these two states is simulated while monitoring the variation in total free energy of the liquid crystal material. Maxima in the free energy, acting as energy barriers separating the two stable states, are shown to coincide with the formation of -1/2 defect lines in the director field.

Light engine and optics for HELIUM3D auto-stereoscopic laser scanning display

This paper presents a laser-based auto-stereoscopic 3D display technique and a prototype utilizing a dual projector light engine. The solution described is able to form dynamic exit pupils under the control of a multi-user head-tracker. A prototype completed recently is able to provide a glasses-free solution for a single user at a fixed position. At the end of the prototyping phase it is expected to enable a multiple user interface with an integration of the pupil tracker and the spatial light modulator.

Dynamic exit pupil trackers for autostereoscopic displays

This paper describes the first demonstrations of two dynamic exit pupil (DEP) tracker techniques for autostereoscopic displays. The first DEP tracker forms an exit pupil pair for a single viewer in a defined space with low intraocular crosstalk using a pair of moving shutter glasses located within the optical system. A display prototype using the first DEP tracker is constructed from a pair of laser projectors, pupil-forming optics, moving shutter glasses at an intermediate pupil plane, an image relay lens, and a Gabor superlens based viewing screen. The left and right eye images are presented time-sequentially to a single viewer and seen as a 3D image without wearing glasses and allows the viewer to move within a region of 40 cm × 20 cm in the lateral plane, and 30 cm along the axial axis. The second DEP optics can move the exit pupil location dynamically in a much larger 3D space by using a custom spatial light modulator (SLM) forming an array of shutters. Simultaneous control of multiple exit pupils in both lateral and axial axes is demonstrated for the first time and provides a viewing volume with an axial extent of 0.6-3 m from the screen and within a lateral viewing angle of ± 20° for multiple viewers. This system has acceptable crosstalk (< 5%) between the stereo image pairs. In this novel version of the display the optical system is used as an advanced dynamic backlight for a liquid crystal display (LCD). This has advantages in terms of overall display size as there is no requirement for an intermediate image, and in image quality. This system has acceptable crosstalk (< 5%) between the stereo image pairs.