Theoretical Considerations on Compensation of the Accommodation- Vergence Mismatch by Refractive Power of Focus-Adjustable 3D Glasses

Transcription

1 Theoretical Consierations on Compensation of the Accommoation- Vergence Mismatch by Refractive Power of Focus-Ajustable 3D Glasses Dal-Young Kim* Department of Optometry, Seoul National University of Science an Technology (Seoul Tech), Seoul , Korea * Corresponing author: ykim@seoultech.ac.kr ABSTRACT The accommoation-vergence mismatch has been consiere as a cause of the visual fatigue inuce in watching 3D isplay. We woul propose the mismatch can be compensate by refractive power of ajustable-focus 3D glasses. From lens optics an geometrical consierations, we also evelope equations that calculate require refractive power of the 3D glasses. The compensation we propose is suppose to reuce the visual fatigue of 3D isplay. 1

2 Introuction Owing to rapi growth of three-imensional (3D) TV an cinema inustry, the visual fatigue problem of 3D isplay is rawing much attention. Although some researchers recently claime that the accommoation-vergence mismatch (AVM) was not an essential cause [1,2], the AVM has been regare as a main cause of the 3D visual fatigue [3-5]. A lot of ieas have been propose to solve it [6], most of which are still uner evelopment. Here we woul propose another solution base on optometry, giving some theoretical consierations on it. Theoretical Backgroun A simple iagram of Fig. 1(a) epicts that the viewer is watching a two-imensional (2D) isplay. N 1 an N 2 are the noal points of left an right eyeballs. Visual axes of the viewer s both eyes converge to a fixation point (FP) on the 2D isplay with vergence angle of θ 1. Object lengths are N 1 -FP an N 2 -FP for left an right eye, respectively. (For simplicity, hereafter we will consier the left eye only. It is because the same consierations can be applie to the right eye.) The eye accommoation is efine as an inverse of the object length, so that accommoation of the left eye becomes 1/(N 1 -FP). On the other han in Fig. 1(b), the viewer is watching a 2-view type 3D isplay, in which every frame of isplaye motion pictures is ivie into two pictures (FP 1 an FP 2 ) for stereoscopic vision. One picture is incient from FP 1 to the left eye while the other is incient from FP 2 to the right eye. As a result, artificial binocular isparity is inuce, locating a virtual 3D image at V point with change vergence angle of θ 2. Although istance from the left eye to the virtual image is N 1 -V ( V ), real object istance is N 1 -FP 1 ( O ). It is because isplaye real picture is not at V but at FP 1. Likewise, accommoation of the left eye is not 1/ V but 1/ O. 2

3 It is well known that the accommoation an vergence angle are not inepenent but couple with each other [7]. Strong accommoation an wie vergence angle must come together when object is at near point, while weak accommoation an narrow vergence angle o when object is at far point. The viewer feels visual iscomfort if this coupling is broken. Long object istance O (that is, weak accommoation 1/ O ) with wie vergence angle θ 2 as epicte in Fig. 1(b) is quite unusual, an cause visual iscomfort. This is the AVM that means a mismatch between viewer s accommoation an binocular vergence angle when he/she watches 3D isplay or hea-mounte isplay. Compensation by Refractive Power of 3D Glasses Fig. 2(a) escribes the AVM simplifie in a viewpoint of the object istances. If we can change the eye accommoation from 1/ O ( D O ) to 1/ V ( D V ) keeping focus on FP 1, the accommoation-vergence coupling (A-V coupling) woul be kept unbroken, so that the visual iscomfort coul be remove. It can be achieve by aing extra refractive power of an eye-glasses lens. For watching the 2-view type 3D isplay in real, the viewer has to wear 3D glasses as shown in Fig. 2(b). Up-to-ate conventional 3D glasses o not have refractive power. Let us assume the lens of 3D glasses has refractive power of D C. In orer to keep the focus on FP 1, total refractive power of the left eye an 3D glasses lens must remain as D O. From Gullstran equation for summation of refractive powers of two lenses, we can buil a relation between D O, D V, an D C. D O D D D D (1) V C V C I 3

4 In Eq. (1), I is the inter-vertex istance between the eye an 3D glasses lens. When Eq. (1) is satisfie, the viewer can obviously watch the picture at FP 1 because the total refractive power is D O. On the other han, he/she oes not feel visual iscomfort because accommoation of the left eye becomes D V keeping the A-V coupling unbroken. The refractive power D C of 3D glasses compensates the mismatch between D O an D V. This is compensation of the AVM by refractive power of eye-glasses lens. The require refractive power D C can easily be calculate from Eq. (1) as a function of the istances O, V, an I. D C 1 1 DO DV O V V O (2) 1 D 1 V I 1 O( V I ) I V Although we consiere a case that the virtual 3D image locates at V point in front of the 3D isplay, Eqs. (1) an (2) are also vali when the V point locates behin the isplay. Focus-Ajustable Eye-Glasses The compensation metho iscusse above is not a new one, but sometimes has been use for watching 3D pictures even from 1800s [8]. It seems impractical for motion pictures because location of the virtual 3D image an V continuously change. To apply the compensation metho to 3D TV an cinema, eye-glasses lens that can changes its refractive power has been require but imppossible. Fortunately, focus-ajustable eye-glasses that can be utilize for this compensation metho are invente just few years ago [9]. They are compose of liqui crystal panels that electrooptically iffract incient lights pixel by pixel, behaving like optical lenses as a result. By controlling external electric fiel applie to the pixels, its refractive power an focal length 4

5 are continuously changeable. We woul like to propose that, combining the compensation metho an focus-ajustable eye-glasses, we coul solve the AVM problem an reuce the visual fatigue. Accoring to Ref. 9, the focus-ajustable eye-glasses were originally evelope for presbyopia, but their ability of changing refractive power is yet restricte to a range between -1 an +1 D. It is insufficient for utilization in 3D isplay system, so that further investigation is neee to enhance the range. Estimation of Virtual Image Location To make the focus-ajustable 3D glasses work in practice, we have to calculate continuously the refractive power D C from Eq. (2). Among I, O, an V, we think I an O are easy to know because they are irectly measurable. In optometry, I is fixe to 12 mm uring the fitting process, though 3D glasses are not yet fitte by optometrist or optician. Therefore, I can be approximately regare as a constant. If exits, the error of I is within few millimeters, while that of V is tens of centimeters. Effect of the error of I on Eq. (2) may be very small. Existence of the refractive power D C slightly changes the position of noal point N 1, which must be consiere in calculation. However, since O an V are much longer than the change of N 1, their errors are not so effective on Eq. (2) that is suppose to hol goo approximately. As to O, it can be irectly measure by signal communication between the 3D glasses an isplay. In the shutter-glasses type 3D glasses, 3D isplay has to continuously communicate with the 3D glasses for synchronization. Electronic measurement of O may be possible if using this communication. We also nee V to calculate D C. It is very har to etermine the epth perceive by human binocular vision, but geometric etermination of the location of V point is relatively easy. Assuming that the 3D isplay, the 3D glasses, an the viewer s both eyes are aligne parallel 5

6 to one another as shown in Fig. 3, a proportional relationship given below is vali because triangles V-FP 1 -FP 2 an V-N 1 -N 2 are similar to each other. FP PD O V (3) V In Eq. (3), FP is istance between two motion pictures ivie for inucing the binocular isparity, an PD is the inter-pupillary istance between the viewer s both eyes. Now we can calculate V from Eq. (4) given below. V O 1 FP PD (4) Eq. (4) is not just a substitution of V for PD an FP. Direct measurement of V is almost impossible, but PD an FP are measurable quantities. The inter-pupillary istance PD is an iniviually fixe parameter, which is about 60 mm on average. Like I, it can be measure an input by optometrist for private 3D glasses, or approximately regare as an optometric constant. The istance FP can be rawn from electronic ata processing of 3D isplay. For example, a 3D isplay monitor that ajusts the epth by input parameter is commercially available [10], therefore FP must be a programming parameter that can easily be obtaine from isplay. Discussion It is suppose that rapi change of the refractive power of eye-glasses can make the viewer feel izzy. To avoi such izziness, change of the refractive power of 3D glasses must not be 6

7 so sharp but smoothene. It is well known in optometry that the A-V coupling is not so strong that small mismatch oes not cause visual iscomfort. The smoothene change of refractive power an slightly broken A-V coupling woul not inuce 3D visual fatigue. Such flexibility of the A-V coupling can also be useful for approximations in our operation scheme. In the above calculations, we aopte approximations of I an PD, an assume that the 3D isplay, the 3D glasses, an the viewer s both eyes are aligne parallel to one another. These approximations an assumption can cause small error in estimation of D C, but flexibility of the A-V coupling is expecte to buffer the error. One of possible arguments against our proposal is that there exist multiple objects of ifferent epths within a 3D scene. Even the V point of one object locates in front of the 3D isplay while that of another object locates behin the 3D isplay. Which object o we have to focus on? It is relate to the visual attention problem in vision science, which is very complicate. Consiering the problem just in an instrumental point of view, we think a possible solution is regaring normal irection of the 3D glasses as viewer s gaze. The irection can electronically be etecte, an the refractive power is ajuste to the epth of object on the gaze. For more systematic solution, well-evelope eye movement tracking technic can be aopte to etect viewer s gaze. Don t the multiple objects with various epths in a fiel of view cause any confusion? Maybe not. The situation is the same with natural vision, in which many objects exist with various istance in a fiel of view. The human eyes focus on an object with narrow view angle, so that the multiple objects with various epths in a 3D scene are not suppose to cause any confusion. Various solutions have been propose for the AVM problem, an most of them can be classifie into two categories, wave front reconstructing or volumetric isplays [6]. For the wave front reconstruction, the 3D isplay is the multi-view type or the holography type. Any solution to the AVM problem has not been consiere for recently commercialize 2-view 7

8 type 3D isplays. We think the compensation metho using focus-ajustable lens is an expectable solution for the 2-view type 3D isplays. Concluing Remarks We propose that the AVM in 3D motion pictures can be compensate by refractive power of focus-ajustable 3D glasses. Mathematical equations are evelope for calculation of require refractive power of 3D glasses. The compensation metho is suppose to remove visual iscomfort cause by the AVM. To realize this scheme, further theoretical, instrumental, an clinical stuies are neee. 8

9 References 1. Patterson R (2009) Human factors of stereo isplays: An upate. J Soc Inf Disp 17: Hoffman DM, Girshick AR, Akeley K, Banks MS (2008) Vergence-accommoation conflicts hiner visual performance an cause visual fatigue. J Vision 8: Lambooij M, Ijsselsteijn W (2009) Visual iscomfort an visual fatigue of stereoscopic isplays: a review. J Imag Sci Technol 53: Lambooij M, Ijsselsteijn W, Heynerickx I (2011) Visual iscomfort of 3D TV: Assessment methos an moeling. Displays 32: Ukai K, Howarth PA (2008) Visual fatigue cause by viewing stereoscopic motion images: Backgroun, theories, an observations. Displays 29: Love GD, Hoffman DM, Hans PJW, Gao J, Kirby AK, Banks MS (2009) High-spee switchable lens enables the evelopment of a volumetric stereoscopic isplay. Opt Express 17: Toates FM (1972) Accommoation function of the human eye. Physiol Rev 52: Howar IP (2002) Historical backgroun. In: Howar IP, eitor. Seeing in epth (v olume 1: Basic Mechanisms). Toronto: I. Porteous. pp Li G, Mathine DL, Valley P, Ä yräs P, Haock JN, Girihar MS, Williby G, Schwiegerling J, Mereith GR, Kippelen B, Honkanen S, Feyghambarian N (2006) Switchable electrooptic iffractive lens with high efficiency for ophthalmic applications. Proc Natl Aca Sci USA 103: ViewSonic VX2268wm. Available: Accesse 6 September

10 Figures Figure 1. Relations between fixation points, vergence angles, an 3D virtual image when a viewer watches (a) a 2D isplay or (b) a 2-view type 3D isplay. 10

11 Figure 2. Simplifie length relations between O, V, an I when the viewer watches (a) by the nake eye or (b) through a lens of the 3D glasses. 11

12 Figure 3. Geometric relations between PD, FP, V-N 1 (= V ), an V-FP 1 (= O - V ). Triangles V-FP 1 -FP 2 an V-N 1 -N 2 are similar to each other. 12