Web page and text by Marc Levoy
February 12, 2002

Overview

The Stanford Spherical Gantry is a room-sized goniometer, consisting of two computer-controlled arms that describe concentric shells around an object platform. A variety of illumination and sensing devices can be mounted on the arms. The clear working volume above the object platform is 40 cm in diameter. Originally conceived as a device for acquiring full-surround light fields of small objects, the Stanford Spherical Gantry has proven useful for a variety of measurement projects in our laboratory, ranging from capturing the reflected light field of a painted statuette to characterizing scattering from a single human hair fiber.

Geometric design

The object platform, on which the Stanford bunny has been placed in the image at right above, has one degree of rotational freedom, denoted by the orange arrow in the image. The inner arm, labeled "camera" in the image above, has two degrees of rotational freedom, permitting it to traverse any point on the surface of a sphere centered on the object platform (except for a 10-degree stayout at the bottom). The outer arm, labeled "light" in the image, has only one degree of rotational freedom. However, this last axis, combined with rotation of the object platform, effectively permits the outer arm to also traverse (almost) any point on the surface of a sphere relative to the object on the platform.

Illuminators and sensors

The inner arm currently has a high-quality 3-CCD digital still/video camera mounted on it. We designed this arm to also accommodate a triangulation range scanner. The outer arm currently has a focusable broadband point light source on it, conducted to the end of the arm using a fiber-optic cable. We designed this arm to also accommodate a video projector. In this configuration, the arms and platform provide 4 degrees of freedom (DOFs), the camera provides 2 DOFs (pixel u and v coordinates) and the projector provides another 2. This provides the ability to generate any 4D incident light field, and for an object placed on the platform measure the reflected 4D light field. The resulting function is 8-D! Note that some points in this 8D space cannot be measured using our gantry, in particular retroreflection, because the camera would block the light source. Also, the camera and its arm will cast shadows on the object under certain illumination conditions.

Accuracy

In addition to its flexibility, the gantry is stiff, and its motions are accurate and repeatable. As an example, the end of the inner arm, which lies about 1 meter from the center of the working volume, can be positioned to within 0.2mm. If a camera is mounted on this arm, its angular deflection, hence its aiming error, will be less than 0.02 degrees. This is sufficiently accurate to capture a light field in which which rays that are supposed to cross in a voxel measuring 0.4mm on a side (e.g. to implement Steve Seitz's voxel coloring algorithm over the 40cm working volume, assuming a 1000 x 1000 pixel camera) can be trusted to cross there.

Credits

The gantry geometry was conceived by Marc Levoy and Brian Curless. Its accuracy requirements were analyzed by Marc Levoy and Szymon Rusinkiewicz, with input from Pat Hanrahan. The structure and mechanics were designed by Duane Fulk of Cyberware Inc., who also oversaw fabrication and testing. Calibration of the gantry was performed by Szymon Rusinkiewicz. Steve Marschner improved the light source and performed further calibration. Our current gantry guru is Mike Cammarano. The gantry cost $130,000 to design and build. Financial support for building the gantry was provided by Interval Research.

Design alternatives

The problem of measuring the angular dependence of reflection and scattering is well studied in the applied physics community, where the devices are generally called scatterometers or gonioreflectometers. The working volume of our device is larger than most of these, and we were unwilling to require that the object be fixtured. This enables us to digitize casually placed collections of objects, or nonrigid objects like cloth or liquids, which would change shape if rotated. However, this requirement forced us to look at novel geometric designs. Here are a few of the many designs we considered:

July 11, 1996 July 12, 1996 July 18, 1996 September 8, 1996
First practical design, with translating arms on tall posts and a roller bearing Alternative design with no posts, but a large equitorial roller bearing A simpler design, with rotating arms instead of translating arms Essentially the same design, but with the collision eliminated

Click on a drawing to bring up larger version, some with explanatory notes. Click here for an incomplete draft set of specifications, including sizes and tolerances. These are not the specifications for the final (as built) gantry. And here is an informal discussion of these specifications by Szymon Rusinkiewicz

Published papers that used the gantry

We envisioned four uses for the gantry:

Not all of these uses have yet been realized. Here is a list of published papers (current to 2004) whose data was acquired on the gantry. These are listed in inverse chronological order.

Light Scattering from Human Hair Fibers,
Marschner, S., Jensen, H.W., Cammarano, M., Worley, S., Hanrahan, P.,
Proc. SIGGRAPH 2003.
Conveying Shape and Features with Image-Based Relighting,
Akers, D., Losasso, F., Klingner, J., Agrawala, M., Rick, J., Hanrahan, P.,
Proc. IEEE Visualization 2003.
Light Field Mapping: Efficient Representation and Hardware Rendering of Surface Light Fields,
Bouguet, J.-Y., Grzeszczuk, R., Chu, M.,
Proc. SIGGRAPH 2002.
See also their OpenLF project on Source Forge.
Image-Based Hair Capture by Inverse Lighting,
Grabli, S., Sillion, F., Marschner, S.R., Lengyel, J.E.,
Proc. Graphics Interface 2002.
A Practical Model for Subsurface Light Transport,
Jensen, H.W., Marschner, S., Levoy, M., Hanrahan, P.,
Proc. SIGGRAPH 2001.
Surface Light Fields for 3D Photography,
Wood, D.N., Azuma, D.I., Aldinger, K., Curless, B., Duchamp, T., Salesin, D.H., Stuetzle, W.,
Proc. SIGGRAPH 2000.
A New Change of Variables for Efficient BRDF Representation,
Rusinkiewicz, S.,
Proc. 1998 Eurographics Rendering Workshop.

Click here for our other papers on light fields, and here for our other major light field acquisition device, the Stanford Multi-Camera Array. Click here for a full list of our lab's technical publications, here for our other research projects, or here to return to our home page.

Next-generation gantries

The design drawings for the Stanford Spherical Gantry are available (for free, we think) from Cyberware, if anybody would like them. As of August 2005, we know of two descendents of our gantry:

  1. Steve Marschner, formerly a postdoc at Stanford, now at Cornell University, has built a version that improves the mounting arrangement at the ends of the two arms. This permits more flexibility in the illumination and imaging devices that can be attached to these arms.

  2. Henrik Wann Jensen, also formerly a postdoc at Stanford, now at UC San Diego, is building a version in which the outer arm has the same degrees of rotational freedom as the inner arm. This permits the object platform to be stationary, which facilitates measuring delicate objects or objects illuminated by complex lighting.

  3. Jason Lawrence, a former student of Szymon Rusinkiewicz, has built a version that is identical to Steve Marschner's, but with coaxial light/camera devices designed and mounted to each of the arms. This setup has some nice properties for jointly measuring an object's 3D geometry and surface reflectance, as described in this paper.

Copyright © 2004-2005 Marc Levoy
Last update: August 13, 2010 01:45:55 PM