Specifications for the Stanford Spherical Gantry

compiled by Marc Levoy
(covering the July 11 and July 12 designs)

General specifications

Sizes

The working volume should be about an 8-inch radius sphere.
For this working volume, the camera arm should have a radius of about 30 inches. This allows 22 inches so that a 40-degree FOV camera lens can see the entire working volume, plus 8 inches for camera assemblies.
Given this radius, the light arm should have a radius of about 40 inches to allow for camera and light source assemblies.
Given this outer radius, and leaving a few inches for the light, the diameter of the light arm orbit is about 7 feet. To fit in the 8-foot high room, the optical bench surface must be within 1 foot of the floor! By removing the lighting and the hung ceiling, we can, at least in some parts of the room, go up to 9 feet.

Other specifications

Object platform should be capable of supporting 50 pounds.
Ability of light and camera arms to cover the full 360 degrees should be limited only by collisions with the post supporting the object platform.
We may wish to mount a roughly 12-inch secondary arm at the end of the camera arm and perpendicular to it, permitting us to use two cameras and hence eliminate shadows from light fields. Sufficient clearance between the camera and light arms is necessary for this to work. Range cameras with long baselines may impose similar constraints.
If possible, we'd like one of the horizontal translations (X or Y) to be long enough to sweep the object past a range scanner. For an 8-inch radius working volume, this would require 16 inches of motion.

Design issues and alternatives

Advantages of allowing the camera arm to cover both hemispheres

For range scanning, allows a backdrop opposite the camera
Allows the camera arm to be opposite the light arm, permitting measurement of BTDFs (transmittance).
For light fields and range scanning, allows views from beneath the object without tilt axes for the object platform (and the need to affix possibly heavy objects to the platform).

Digitizing light fields

A backdrop is probably unnecessary. A dark room and a black gantry will suffice.
Lights should be collimated or at least barn-doored to avoid lens flare in the camera.
The user interface can gently "flow" the observer around dead spots in the light field by applying a force field analogy.

BRDF and BTDF measurement of flat samples

In the July 12 design, it might be more convenient if the mounting order of axes 3 and 4 were reversed. In astronomical terms, as it stands, axis 3 chooses declination and axis 4 chooses right ascension. If reversed, axis 3 would control altitude, and axis 4 would control azimuth. In simpler words, as it stands, axis 3 chooses the angle from the horizon to the highest point on an arc stretching from horizon to horizon, and axis 4 controls position along this arc. If reversed, axis 3 would control angle above the horizon and axis 4 would control compass bearing.
To minimize changes in focal distance to the sample, the center of rotation of the tilt table (axis 3) should be at the plane of the object platform or slightly above to allow for the thickness of the sample.

Backdrops for range scanning

For carving from range-scanned backdrops, the backdrop must be placed in the range camera's working volume. For carving from video-scanned backdrops, the backdrop could alternatively be placed beyond the range camera's working volume.
For a nodding range camera, a large backdrop is required due to the large angle of view. For a translating range camera, a backdrop equal in width to the working volume suffices.
For video-scanned backdrops, the entire volume swept out by the camera arm could be enclosed in a stationary "eggshell" backdrop. The advantage of an eggshell over an arm-mounted backdrop is that the eggshell would never collide with the object support, e.g. when the camera is overhead. The disadvantage of an eggshell is that it would have a gap at the equator where the support for the camera arm enters the shell. By combining a partial eggshell to cover the lower hemisphere with a removable arm-mounted backdrop to cover the upper hemisphere, both collisions and gaps could be avoided. However, this solution requires manual intervention to remove the arm. If an eggshell backdrop is used, a curved surface is probably best, in which case the camera arm should then be curved to fit within it.

Tolerances

For Light fields

Let us assume a camera with a 40-degree FOV lens looking at a 16-inch object (8-inch radius spherical working volume). The corresponding standoff distance, from the point of projection (typically at the camera aperture) to the focal plane, is 22 inches. Let us also assume that the camera arm is 30 inches long.

Object positioning. The governing factor is sensor resolution. Let us assume a 1024 x 1024 pixel sensor, the highest resolution we envision using in the near future. Each pixel then covers 0.04 degrees of visual arc, which is 0.4mm at the focal plane. Because light fields have a limited depth of field, accuracy at the focal plane presents the strongest constraints. To maintain scan repeatability to +- 1/2 pixel, object positioning (in X, Y, and Z) must be repeatable to +- 0.2mm.
Camera positioning. Since video cameras have small apertures, we want to move the gantry by single aperture widths and then average together multiple views to generate a synthetic aperture. Thus, the governing factor in camera positioning accuracy is not the spacing between views in the final light field, but rather the aperture size of the camera. Let us assume a 6mm aperture. To maintain scan repeatability to +- 1/2 aperture width, camera positioning (in altitude and azimuth) must be repeatable to +- 0.3 degrees, which is +- 3mm at the aperture or +- 4mm at the end of the camera arm. For a 32 x 32 view light field over a 90 x 90 degree sweep, this implies 4 x 4 apertures averaged together to construct the synthetic aperture for one view.
Camera aiming. For shape-from-light fields methods, viewing rays that are supposed to cross at a single point in 3-space must cross there. The governing factor is camera arm rigidity, including the axis joint, arm, and camera mount. To insure that rays cross within +- 1/2 pixel at the focal plane, this assembly must flex no more than 0.015 degrees, or 0.21 mm at the end of the camera arm. This is a difficult requirement. It was the limiting factor on the Apple ObjectMaker. If it cannot be satisfied, a calibration procedure will be necessary, and this procedure must be repeated whenever the weight on the arm (typically the camera) is changed.

For flat sample BRDF and BTDF measurement

For BRDF and BTDF measurement of 3D objects

For range scanning

[Document not finished.]

levoy@cs.stanford.edu