3D METROLOGY BASICS

What is 3D Metrology?

3D Metrology is the art and science of creating extremely accurate three dimensional data models of complex surfaces and objects. 3D metrology has become more and more important with the rapid growth of the extensive computer modeling that is at the heart of today's technological advances. 3D Metrology takes us from existing objects to the theoretical model, and from the theoretical model to new accurately manufactured objects. 3D Metrology is the key connection between the physical and virtual worlds.

What is a Computer Aided Theodolite?

A theodolite is an optical instrument that can be manually aimed at a target and a horizontal and vertical angle recorded. A computer aided theodolite system is one where up to 8 theodolites can be connected to a computer to record angular readings from each of the theodolites and compute x, y, z coordinates for points of interest. The angular readings are accurate to +/- 1/2 of an arcsecond. An arcsecond is 1/3600 of a degree.

What is a Laser Tracker?

A laser tracker is similar to a theodolite, in that it records horizontal and vertical angles, but has the added feature of being able to record a distance using an interferometer at the same time. This permits the calculation of x, y, z values for any point from one tracker position (theodolites require a minimum of 2 positions). The angular readings are in the +/- 1/2 arc second range, and the distance is recorded by an interferometer to +/- 2 ppm.

What is a Portable CMM/Arm?

A portable CMM Arm is used to inspect, reverse engineer, or perform CAD-to-Part Analysis on parts, fixtures and assemblies with remarkable accuracy.Measures within +/- .0010 inches (+/- .25 mm). Available in spherical ranges of 4 ft - 12 ft (1.2m to 3.7m).

Basic Computations

With theodolites, the basic calculation is to use two horizontal and vertical angles and a baseline distance established between the theodolites to "triangulate" the position of the intersection of the two lines of sight to the point.

More complex computations are used for defining the location of the theodolites relative to a defined reference system through "a least-squares coordinate transformation". This process essentially allows moving a set of points and overlaying them on a similar set of points in a desired reference system by minimizing the sum of the squared deviations.

Laser trackers, since they don't require multiple instruments to read a single point to generate its coordinate values, primarily use the coordinate transformation to relate different sets of point measurements to a common reference frame. This would include relating points measured from different tracker set-ups.

Benefits of using CAT or Laser Tracker, or Portable CMM/Arm

• Fast Data Collection - reduces downtime of objects being measured.
• Highly Accurate - greater accuracy than conventional methods of using jig transits, levels, scales.
• Highly Portable - equipment can be easily shipped by air to a customer site or rolled across the factory.
• Surface Scanning - Laser trackers can collect data at a veryrate of 1000 points/second.