A Simple Proposal for a Solution to the Accommodation-Vergence Mismatch Problem in 3D Displays

Dal-Young Kim Department of Optometry, Seoul Tech, 232 Gongneung-ro, Nowon-gu, Seoul 139-743, Korea Tel.:82-2-970-6229, E-mail: dykim@seoultech.ac.kr

Keywords: 3D display, accommodation-vergence mismatch, visual fatigue

Abstract

Here is suggested a solution to the accommodation- vergence mismatch problem in 3D stereoscopic displays. It can be achieved by compensating the mismatched focal length with refractive power of adjustable-focus 3D glasses. The compensation would make vergence of human eyes match with position of virtual stereoscopic motion pictures, reducing visual fatigue.

1. Introduction

The accommodation-vergence mismatch (AVM) has been considered as a cause of the visual fatigue induced by watching three-dimensional (3D) stereoscopic displays,[1-3] though some recent researches suggested that it was not an essential cause.[4,5] Owing to rapid growth of the 3D TV and cinema industry, much attention is paid to it. Various ideas have been proposed to solve the AVM problem, and most of solutions are belonged to one of two categories, that is, the wave front reconstructing displays or the volumetric displays.[6] Differently from those previous solutions, we would propose a solution based on physiological optics and adjustable-focus 3D glasses.

2. The Accommodation-Vergence Mismatch

The AVM is a mismatch between focal length (adjusted by accommodation) of human eye and binocular vergence (convergence or divergence) angle when a viewer watches the 3D display or head-mounted display. Fig. 1 (a) depicts the viewer is watching a conventional two-dimensional (2D) display. Here N1 and N2 are the nodal points of left and right eyeballs. Visual axes of the viewer’s both eyes converge to a fixation point (FP) on the 2D display, and the vergence angle is defined as θ1. The focal lengths of both eyes are adjusted to N1-FP and N2-FP for left and right eye, respectively. On the other hand in Fig. 1 (b), the viewer is watching a (2-view type) 3D stereoscopic display. Every frame of displayed motion pictures is divided into two pictures for stereoscopic vision. One picture is incident from FP1 to left eye while the other picture is incident from FP2 to right eye, inducing binocular disparity. The human stereopsis produces a virtual 3D image at V point to which the visual axes of viewer’s two eyes converge. The convergence angle changes from θ1 to θ2. However, the focal lengths of left and right eyes are neither N1-V nor N2- V, but N1-FP1 and N2-FP2, respectively. It is because the 3D image at V point is not a real one but real pictures are still on the surface of 3D display.

Fig. 1. Relation between the fixation points, vergence angle and images when a viewer watches (a) a 2D display or (b) a 2-view type 3D display.

It is well known that the vergence and accommodation are not independent but highly correlated with each other.[7] The focal lengths have to shorten with wide vergence angle when the viewer watches a near point, while they have to lengthen with narrow vergence angle when the viewer watches a far point. This coupling of vergence and accommodation is so strong that the viewer can feel discomfort if it is broken. Long focal lengths with wide vergence angle or short focal lengths with narrow vergence angle are quite unusual. The situation of Fig. 1 (a) is natural and comfortable for the viewer, but that of Fig. 1 (b) is discomfort due to abnormal long focal lengths with wide vergence angle. This is the AVM.

3. Physiological-Optical Compensation

In the view point of the physiological optics, the most simple but efficient solution to the AVM problem is to compensate the mismatched accommodation (focal length) by refractive power of lenses.

D-Y. Kim IMID 2012 DIGEST

Fig. 2. Focal lengths of eye and a lens of 3D glasses.

Fig. 2 describes relations between the focal lengths of the left eye and a spectacles-lens. Here let me introduce the concept of refractive power D, which is defined as an inverse of focal length. It is well known that total refractive power DR of a certain ophthalmic-optical system is approximately a sum of refractive powers of the eye and the lens. Taking the refractive power of lens into account, DR in Fig. 2 is given as

C V R D D D  

(1).

Here, DV and DC are refractive powers of the viewer’s eye and the lens. In order to watch the real image (FP1) on the surface of 3D display, the focal length and refractive power of the total system must be N1-FP1 (fR) and 1/fR. As mentioned above, the viewer feels comfortable when the focal length and refractive power of eye are N1-V (fV) and 1/fV. From these constraints, focal length (fC) and refractive power (DC) of the lens required to satisfy Eq. (1) is calculated as;

C V R V R C f f f D D D 1 1 1  