Fundamental concepts (2 стр)

Figure 4

So it's important that we give ourselves means to evaluate in which measure the artificial generation of stereoscopic images is viable. The objective here will be to minimize the conflict strength previously mentioned. Since the accommodation is controlled by the ocular convergence, we have to determine an operational zone where the accommodation correction needed is less than a certain limit.
We have the following situation:

Figure 5

Given the following graph which gives the angle of convergence for a given gaze distance:

Figure 6

The graph of figure 6 contain a lot of information. It enables us to visualize the convergence effort as a function of the gaze distance. The convergence angle is given for an eye in regard with a parallel axis going at an infinite distance.
Since there seems to be a direct relation between the convergence angle and the crystalline accommodation, we can, practically speaking, say that there is a direct proportionality relation between these two factors.
The convergence angle is considered proportional to the accommodation
The maximal accommodation for an average 20 years old human adult is approximately 12 cm
So, we can say that the maximal stress of the muscles controlling the crystalline accommodation is reached when the gazing distance is approximately 10 cm. Moreover, the muscular effort will be zero for an infinite gazing distance.
From the first hypothesis, we can replace the accommodation variable with the convergence one. So, from figure 6, a convergence of 20 degrees is equivalent to an accommodation of 10cm. This point represent the 100% muscular effort. This gives us figure 7.

Figure 7

It shows from figure 7 that, for a usable range starting at 1 meter up to infinity, the muscular effort of the human visual system stays under 10%. In this range, there won't be any major problems from extended exposition time. On the other side, the muscular effort will raise quite rapidly beyond this critical point of 1 meter. We now begin to foresee what will be the usable operational range as long as stereoscopic scene generation goes.
Let's go a bit further in our analysis. In reality, the objects surrounding us are always located at the real focal distance where they are perceived as for the convergence. On the opposite, in the case of an artificial stereoscopic visualization system, all the objects appears at the same distance, the image plane one. So, as opposed to the real case, artificial stereoscopy will cause a conflict between convergence and the needed accommodation to see a given object, and this, in the case where the distance of the virtual object is different from the one of the image plane.
The first graph represent the difference between the real accommodation effort and the one dictated by the convergence created by the stereo pair images in the case where the image plane is located at infinite.

Figure 8

Here, we note that the obtained graph is identical to the one found in figure 7. This result is quite normal in fact. We can conclude that, for artificial stereoscopy, the accommodation effort is in fact a conflict of accommodation in this present case. More precisely, the difference between the accommodation effort needed in the real case and the one required by the convergence information transmitted to the brain.
The second graph represent the difference between the real accommodation effort and the one dictated by the convergence of the stereo image pair in the case where the image plane is located at 1 meter.

Figure 9

Here, we see that the accommodative conflict doesn't correspond to the accommodation effort as such. Here is how we can interpret this graph. One point of interest of the graph is the 1 meter distance. At this point, the accommodative effort is 10% like we could have suspect it. Still, the accommodation conflict is nonexistent since the convergence information correspond to the image plane distance.
If we consider the accommodative conflict and the accommodation itself like being of the same nature (the physiological effects on the human are the same in the two cases), we can take 10% as the limit that we must never exceed. From the last graph, this enable us to show virtual objects from 0.5 meters to infinite respecting the human physiological constraints.
So, this operation point permits an important gain on the dynamic range of the permitted distances for virtual objects. On the other side, the conflict is present on a wider range (from 10m to infinite) but much less important from 0.5 to 1 meter.
We can conclude that the image plane at 1 meter is ideal in the case where the virtual objects are to be showed between 0.5 and 5 meters most of the time. One the other side, an image plane at infinity does constitute a good operation point in applications where the virtual objects will be more frequently showed in the 1 meter to infinity range.
To complicate matters even more, it's important to note that the human eye, being an optical system, as a fundamental characteristic of these last one. Indeed, an experimented photographer knows how to exploit what we call the focal range. The focal range is related to the size of the iris numerical opening figure and the focal distance of the optical system. The perceivable effect of this is to be able to clearly see parts of a scene which are not at a distance that represent the focal point of the optical system (the crystalline lens and all the fluids contained inside the eye by example). For a given focal distance, the pupil opening diameter of the eye dictates what will be the accommodative tolerance in regard with the central gazing point. The focal range correspond in some way to an error range on a given value. By example, for an accommodation of 1 meter, the focal range is such that the retinal image will be clear from 0.8m to 1.4m when the luminosity is such that the pupil diameter is 4 mm [2].
This notion of focal range is quite important. It will effectively enable us the minimize the blur effect perceived when there is a conflict between the image plane distance and the virtual object distance. This imply that it is possible to display objects in front or behind the physical image plane in such a way that they will remain clear if the image is bright enough so that the pupil closes to a certain diameter. We will come back on this point when we will talk about the virtual reality applications with HMD helmets.

23 ноября 2006

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