Dolly Zoom in Stereo 3D – technical description
The video below contains the first ever Dolly Zoom scene in stereoscopic 3D. This is true at least to my knowledge. Please post a comment in case you know of prior examples.
Two questions to be answered in this blog.
1. What is a Dolly Zoom (DZ) ?
2. How does a DZ shot in stereoscopic 3D differ from a conventional DZ?
Answers :
1. Conventional DZ, also known as Vertigo Zoom, Hitchcock Zoom, or Push-Pull effect.
While performing a DZ the camera approaches the main subject and at the same time ‘zooms out’, steadily decreasing the focal length. If done at the correct rate the main subject will be ‘fixed in the frame’, whereas the background somehow warps around the subject.
The resulting artistic effect can be used to heighten ‘surprises’ in a scene, or to convey a surreal emotion to the viewer.
The DZ-equation can be derived from elementary geometric optics :
(1) f1/f2=N1/N2
f signifies the focal length, while N signifies the distance to the nearest object in the scene, which I presume to be the subject of main interests.
This equation ensures that the main subject always occupies the same width in the video frame, regardless of the camera position. The equation tells us that the focal length varies in proportion to the distance.
Example : if the initial camera distance N1 = 5m at focal length f1= 50mm, we have to change the the focal length to f2 = 25mm at a distance of N2= 2.5m. The same calculation applies to all distances in between, so we have to decrease the focal length continously while appraching the subject.
2. There is an important complication shooting DZ in stereoscopic 3D : while performing the effect the parallax content of the scene will change. That might result in exceeding the parallax budget.
Even if still within the parallax budget there will be a change of relative parallax between the main subject and the background. The main subject seems to ‘grow’ gradually out of the frame. This effect might be artistically very interesting, however the the artist must be aware of it.
Fortunately the stereo artist has an additional control to balance-out the parallax content : we have to change the inter-axial settings while performing the DZ effect.
But how? It turns out that it is possible to fix the relative parallax between precisely two points at different depth. If we call the distance between the camera and the main subject N (which is our ‘near’ point) and the distance between the camera and a point in the background F ( our ‘far’ point), then there is a precise way we can fix the relative parallax between the two points while performing a DZ effect.
I derived the following equations, by demanding 1. the main subject at distance N to occupy a constant frame width and 2. a constant parallax between ‘near point’(camera distance N) and ‘far point’ (camera distance F) :
(1) f1/f2=N1/N2
(2) t1/t2=F1/F2
where t signifies the camera inter- axial.
What does this mean practically ? While approaching the main subject, the cameras not only have to zoom out (equation 1), but also have to decrease their inter-axial (equation 2) in proportion to the far-distance F.
The resulting image sequence will have a constant relative parallax between the the near-point and the far-point. However, the relative parallax between other point pairs will change.
I demonstrated this in the video below,’The Spiders 3D’, showing a spider sitting at the back end of a long tunnel, waiting for the prey to come.
I have chosen the midpoint of the spider (not the front leg!) as the near-point and the tunnel wall as the far-point. You can clearly see that the depth between these two points is constant and that the middle of the spider occupies a constant frame width. In contrast to this, the front leg seems to grow out of the screen, in accordance with my explanation above.
One more complication : the left-right video streams require dynamic HIT ( Horizontal Image Translation) shift.
In summary : the proper Dolly Zoom in stereoscopic 3D can best be described as a
Dolly/Zoom/Inter-Axial/HIT ———-Shift.
