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If you have any questions, please contact our experts. Using 3D fringe projection, the whole surface of the sample is acquired at once, projecting a stripe pattern to the surface that is recorded by a camera perpendicular to the surface. Stereoscopic vision uses the disparity of two camera images looking at the same scene to calculate depth information, just like the human eye. Cameras that measure the time for the reflection from a light pulse to return to the camera.

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This is because when changing the eye separation, the intersection of the two projections lines from left and right eyes to left and right onscreen points will always lie on the line passing through the origin middle of two eyes and the center of the onscreen points. The ratios of the x , y , and z components of any two points on a line passing through the origin are the same.

In these plots, the black dotted horizontal lines represent the orthoscopic condition i. The area below the black horizontal line represents compression and above the line represents expansion.

The red and yellow dotted vertical lines are the asymptotes of the red and yellow curves. Fig 6a represents relative size change i. A smaller camera separation e. Fig 6b represents relative depth change i.

The area below and above the horizontal line represents objects being closer and farther than where they are in the original world, respectively Fig 6b. In this case, viewers may not be able to fuse them even if they try to fixate on those objects and perceive double vision. Note that in real-world condition, when a viewer gaze on a near object, a farther object becomes double, but when the viewer gazes on the farther objects, the farther objects will be fused becomes single and the near object becomes double. However, in the reconstructed world, the objects beyond the asymptote distance cannot be fused even if the viewer gazes on it.

Here we assume that only screen width and camera frustum width at the convergence distance are mismatched i. Under this assumption, the ratio between screen FOV and camera FOV k f becomes the same as the ratio between screen width and camera frustum width, i. Fig 7 shows examples of the 3D simulations when screen and camera frustum widths are mismatched. Since we assume camera convergence distance and screen distance are matched, the reconstructed cube stays centered at the screen distance. The brown cube and gray plane are the same as in Fig 5.

Fig 8 shows that the relative size and depth change compared to the orthoscopic condition in xy -dimension and z -dimension. The relative size in xy -dimension and relative depth in z -dimension can be expressed as and , respectively. When screen width is smaller red solid lines or larger blue dashed lines than camera frustum width, the relative size becomes smaller or larger than 1, suggesting the reconstructed world appears compressed or expanded, respectively Fig 8a.

In terms of depth, when screen width is smaller red solid lines or larger blue dashed lines , than camera frustum width, the virtually constructed world behind the screen will suffer from progressive compression, while the world in front of the screen will suffer from expansion, respectively Fig 8b. Note that objects located at the screen distance are not largely affected in terms of depth distortion, but are still affected by size distortion.

The blue dotted lines are the asymptotes i.

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Again, the viewer may not be able to fuse objects farther than the asymptote and perceive double vision. The blue dotted vertical lines are the asymptotes of the blue curves. This analysis assumes that only camera convergence distance and screen distance are mismatched i. The transfer function 1 can be simplified as follows: 5 Eq 5 shows that changing screen distance affects the depth in z -dimension but does not affect the size in xy -dimensions.

Fig 9 shows the 3D simulations when convergence and screen distances are mismatched. The simulations confirm that changing the screen distance only affects the depth of the cube i. The gray plane represents the display screen. Fig 10 shows that the relative size and depth change as a function of the depth in the real world. When screen distance is closer than red solid lines or farther than convergence distance blue dashed lines , the relative size does not change, suggesting the linear size is independent of the screen distance Fig 10a.

In terms of depth, when screen distance is closer red solid lines or farther blue dashed lines than the convergence distance, the constructed world appears closer and compressed or farther and expanded, respectively Fig 10b. Since and , the transfer function 1 can be simplified as follows: 6. Fig 11 shows the 3D simulations when convergence and screen distances are mismatched. Fig 12 shows the relative size and depth change compared to the orthoscopic condition. When camera convergence distance is shorter or larger than screen distance, the size of the object appears expanded red solid line or compressed blue dashed line , respectively Fig 12a.

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In terms of depth, objects appear farther red solid line or closer blue dashed line to the viewer, respectively Fig 12b. The red dotted lines are the asymptotes of the red curves. When camera convergence distance is smaller than screen distance, the viewer may not be able to fuse objects farther than the asymptote and may see double vision.

The red dotted vertical lines are the asymptotes of the red curves. The amount of geometric distortions both size and depth ratio between the reconstructed object to original world object monotonically increases as the distance from the viewer increases. When the amount of compression progressively increases along the depth direction, objects become thinner in depth direction.

Generally, the effect is more severe for distant objects. A distant object appears to be flat demonstrating the cardboard effect [ 10 , 12 ] Fig 12b.

Since objects in the foreground and background i. The mismatch between screen and camera convergence-distance results in a perceptual distortion called the Alice in Wonderland syndrome [ 17 ]. Observers with such syndrome experience various size and depth distortions such as micropsia objects are perceived to be smaller than they actually are , macropsia objects are perceived to be bigger than they actually are , peliopsia objects are perceived to be closer than they actually are , and teliopsia objects are perceived to be farther than they actually are. An extreme case is worth further discussion where the convergence distance is infinity, i.

In this case, the reconstructed world fits the following transfer function: 7. In both cases, the apparent objects are in front of the screen all in crossed disparity and become smaller and closer.

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The compression of the depth is severer in farther cube condition Fig 13b because the depth at all distances including infinite distance is compressed in between the screen and viewer distance. As a result, the cardboard effect becomes amplified for distant objects. In this case, xyz dimensions are scaled in the same ratio in different depths so that the reconstructed world is an undistorted but scaled version of the original world.

When the ratio is smaller than 1, the cube appears smaller and closer, as shown in Fig 14a. When the ratio is larger than 1, the cube appears larger and farther, as shown in Fig 14b. However, the reproduced objects shape appears to be remained as a cube as it is presented in the original world. Fig 15 shows that the relative size and depth change as a function of the depth in the real world. The relative size in xy -dimension can be expressed as and the relative depth in z -dimension can be expressed as.

When the ratio is smaller red solid lines or larger blue dashed lines than 1, both the relative size and depth are scaled in the same ratio Fig 15a and 15b , respectively. Note that since the reconstructed world is only scaled but not distorted in this condition, it provides a way to remove geometric distortions in S3D by adjusting the variables to equate the ratio of pairs. In this condition, the transfer function 1 is simplified as follows: 9. The cubes are expanded away from the screen Fig 9b or compressed towards the screen Fig 9a , respectively.

Overall, the part of the displayed cube in front of the screen moves in the same direction as the head translation, and the part behind the screen moves to the opposite direction of the head translations. Onscreen points stay on the screen without any change. Thus, the cube always appears to follow the head movements while maintain the fronto-parallel characteristics of the front and back surfaces.

The distortion is apparent especially while the viewer is in motion. The results of our analyses suggest guidelines that may eliminate or minimize geometric distortion for content developers and users. These are explicitly developed below. In these conditions, the cardboard effect may affect distant objects.


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In these conditions, the effect is opposite to the cardboard effect, we call it the expansion effect. More critically, the depth in the real world has asymptotic limits i. Objects at depths farther than these limits are presented with large uncrossed screen disparities that the viewer may not be able to fuse, even if they are fixated.

Therefore, for S3D producers, a smaller camera separation, a larger camera convergence distance, or a larger camera FOV is recommended, so that to avoid large uncrossed screen disparities.

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The solid curves represent relative depth distortions in the z -dimension as a function of the depth in original world. The dotted vertical lines are the asymptotes of the curves. Fig 18 shows the relative depth of the four viewing conditions when eye separation is smaller than camera separation e. The four dotted vertical lines in Fig 18 are the asymptotic limits corresponding to the four convergence distance conditions. The solid curves, dotted lines, and black dashed line refer to Fig When the depth composition in the original world have an asymptotic limit i.

For the S3D graphic rendering of the virtual world, the far plane of virtual camera frustum can be defined at or slightly beyond the asymptotic limit. Any objects farther than the far plane e. Limiting the original virtual world to the asymptotic depth not only reduces the render time but also avoids the problem of large uncrossed screen disparity. We define the far plane of camera frustum at Under these conditions, the reconstructed world is only scaled from the original world but without distortions Fig To equate the three ratios, we need to match screen FOV with camera FOV by adjusting screen distance, and match the distance ratio with the separation ratio by adjusting converge distance i.

Users can adjust the screen distance by moving closer or farther from the screen, and adjust camera convergence distance by shifting the left and right view horizontally e.